Wesleyan ♦ University
Chemical Mechanisms of pH-Dependent Relaxivities for a Series of Structurally
Related Mn(II) Cyclen Derivatives
by
Breanna G. Craft
Faculty Advisor: T.D. Westmoreland
A Dissertation submitted to the Faculty of Wesleyan University in partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
Middletown, Connecticut
January 2015
Acknowledgements
I have without a doubt, the best graduate school advisor one could ever have.
Professor Westmoreland has always supported me both in research and in advancing
my teaching abilities and passions. I am a much better scientific writer because of
him. I know for a fact, that my experience in graduate school would have been
completely different had it not been for him. I enjoyed our weekly meetings and
discussions of our research and looked forward to the next. We worked well together
and I truly hope we can continue to do so.
I also had the very BEST graduate committee. Professor Novick is a
wonderful person and a fabulous physical chemist. His questions at my committee
meetings always helped me to grow in my research and taught me how to think like a
scientist.
Professor Taylor is one super-woman. I learned so many things from her,
confided in her, and looked up to her as a fellow woman in science. From her I
learned the power of an effective and powerful power-point for seminars. She has
ii
also been supportive and had my best interests at heart. Thank you for always having
an open door for Jessica and me.
There are two people in this world however, that I could absolutely not have
gotten through this journey without, my supportive husband Jay and my dear friend
Jessica. Jay you are my best friend and I can’t wait to see what the future brings for
us. “We are really doing this!”
At one point I thought this was going to be it for me, I thought enough was
enough and only crazy people put themselves through this to get a degree. It is not
any degree however. It is the highest earned, most honorable, and most respected
degree one can get in their field. Making it through the program would not have been
possible if I didn’t start the same year of graduate school as Jessica. Both our love for
God and our faith in each other is the sole reason I can say, that I finished, and that I
didn’t quit. There are simply no words to explain this bond and what we have been
through together. Well accept for the fact that I was promoted from “Grad Buddy” to
“Forever Friend” in our fourth year! I love you girl.
To my friends Danielle Caroccia, Laura Horniak, Marissa Vumback, my
softball girls and Courtney Gertz; thank you so much for the support and positive
encouragement. I loved to see the faith you had in me that I could finish this.
To my dear friend Brittany Long. You are one of the most up-lifting and
encouraging people I know. Continue to be fabulous.
To my brother Ryan for his love and support.
iii
To my lovely and supportive grandparents, Sheila and Larry Germain. I am
pretty sure every person in the state knows that I am going to Wesleyan for my Ph.D.
in chemistry, but don’t ask them which discipline or what I study! (So cute.)
To my father for his love and support.
To my mother. Thank you for always believing in me and encouraging me to
finish.
To my amazing and supportive in-laws, Sherry and Richard Craft, for always
believing in me and encouraging me.
To Roslyn, Sarah and Cait who worked in the office these seven years (but
who is counting!). You all are way under-paid as far as I am concerned. You are not
only administrative assistants, but you were/are my friends, and confidants. I love you
all!
To Doug and Don for all their help with instrumentation. Particulary Don, for
his help with the pressure project that never made it into this thesis.
To Professor Bolton for his unending patience and help to switch over the
probe so I could run the oxygen-17 relaxivity experiments. To Professor Fry,
Professor Roberts, Professor Bruno, Professor Calter, Professor Knee, Professor
Pratt, Professor Northrop, and Professor Pringle for all they have done to support me.
Wesleyan University is also acknowledged for financial support.
iv
Abstract
Complexes of Mn(II) have received attention recently as potential new
contrast agents for magnetic resonance imaging. Specifically, contrast agents that
respond to local pH changes are among those of current interest. The synthesis and
characterization of three Mn(II) complexes of structurally related cyclen-based
ligands with amide, carboxylate, or phosphonate side arms, which may coordinate to
the metal ion are reported. The pH dependencies of the 1H relaxivities of the
complexes are significantly different for each complex. On the basis of these data,
potentiometric titrations, pH-dependent solution IR spectroscopy and
17
O transverse
relaxation measurements, a model of the solution structures of the complexes is
proposed. The model also rationalizes the pH-dependent 1H relaxivities in terms of
the chemical exchange mechanisms contributing to relaxation and provides effective
values for the relaxivities of each protonation state of each species.
The chemical mechanisms of 1H relaxivities were investigated extensively for
each complex. The phosphonates appear to enhance the overall stability and may
provide sites for enhanced hydrogen bonding to the bulk water and prototropic
exchange.
v
Table of Contents
Chapter 1: Introduction……………………………………………………………..1
1.1 Background to Magnetic Resonance Imaging (MRI)……………………………..3
1.2 Relaxation times T1 and T2......................................................................................6
1.3 Introduction to MRI Contrast Agents……………………………………………10
1.4 Solution Structure Determination and Challenges……………………………….14
1.5 How MRI Contrast Agents Work…………………………….………………….15
1.6 Contrast Agent Requirements…………………………………………………....16
1.7 Chemical Mechanisms of Proton Relaxivity………………………………….…17
1.8 Distinguishing Between Water Exchange and Prototropic Exchange………...…23
1.9 What ELSE Makes Contrast Agents Have a (Theoretically) High Relaxivity…..23
1.10 “Smart” Contrast Agents………………………………………………………..27
1.11 Complexes Used in This Study…………………………………………………30
1.12 Stability Constants: What is log β?......................................................................31
1.13 This Study……………………………………………………………………....36
References………………...…………………………………………………………39
vi
Chapter 2: Materials and Methods………………………………………………..42
2.1 Synthesis of Mn(H6DOTP)·3H2O………………………………………………..43
2.2 Synthesis of 0.1 mM Cr(H2O)63+ and Mn(H2O)62+ Aqueous Solutions………….44
2.3 Synthesis of Zn(H2DOTA)………………………………………………………46
2.4 Temperature-Dependent NMR of Zn(H2DOTA)………………………………..47
2.5 Potentiometric Titrations………………………………………………………...47
2.6 pH-Dependent Solution Infrared Spectroscopy………………………………….49
2.7 pH-Dependent 1H and 17O Relaxivities………………………………………….50
References……….………………………………………………………………….55
Chapter 3: Results and Discussion…………………………………………...……56
3.1 Solid-State Structures of the Complexes…………………………………...……58
3.2 Solution Structures of the Complexes……………………………………..……..65
3.3 Stability and Speciation …………………………………………………..……..74
3.4 Infrared Spectrscopy……………………………………………………………..87
3.5.1 1H and 17O Relaxivity Profiles………………………………………………..101
3.5.2 Solomon-Bloembergen-Morgan Theory and the pH-Dependence of T1M…...105
3.6 Conclusion……………………………………………………………………...120
vii
References …………………………………………………………………………122
Chapter 4: Future Work………………………………………………………….125
4.1 R2 and R1 pH-Dependence Comparison……………………………………….126
4.1.2 Relaxation Time as a Function of Concentration for Mn(H6DOTP)………...130
4.2 Kinetic Isotope Effect…………………………………………………..………134
4.3 Temperature-Dependent 17O Transverse Relaxivities…………………………138
4.4 Conclusion……………………………………………………………………...138
References……………...…………………………………………………………..140
Appendix A- Models that Fit to the Titration Data for [Mn(HxDOTA)]x-2………..141
Appendix B- Models Used to Fit Pre-Formed [Mn(HxDOTP)]x-6 Titration Data…147
Appendix C- Measured 1H Longitudinal and 17O Transverse Relaxation Times.…151
Appendix D- Solution IR of Zn(DOTA)2-………………………………..………..153
Appendix E- Full NMR spectrum of Figure 3.7………………………………...…154
Appendix F- Figure of Second-Sphere Proton Transfer…………………………...155
viii
Chapter 1
Introduction
1
There are over 50 million MRI (Magnetic Resonance Imaging) scans done
around the world each year. MRI is a valuable diagnostic tool that allows doctors to
see inside our bodies without requiring surgery and is minimally invasive. Although
valuable images can be acquired, some procedures may require additional contrast in
order to differentiate or visualize certain diseased tissues like tumors, as demonstrated
in Figure 1.1.
Figure 1.1. Image showing an MRI without contrast on left and with contrast on
right.1
Contrast agents (CA) consist of a chemical that is usually a paramagnetic
Gd(III) complex. Gd(III) is a lanthanide and can be toxic. Therefore, it is bound to a
macrocyclic chelating ligand, which binds Gd(III) strongly and stabilizes it. However,
this chemical can dissociate in the kidney and cause NSF (Nephrogenic Systemic
Fibrosis) which is a serious disease that causes hardening of the skin and organs.
There is no known cure for NSF so there is a great need for a CA that does not
2
contain Gd(III) or has a high enough relaxivity where it will not need to be injected in
such large concentrations.
This study focuses on complexes similar to the current, clinically used,
contrast agents except they do not contain Gd(III): specifically those of
Manganese(II). Mn(II) is a paramagnetic transition metal with a high spin and fast
water exchange rates, which makes it an attractive candidate.
Contrast agents that respond to changes in the local pH can be used to
quantify pH or target specific biological sites that have low or high pH. Tumor cells
for example have a lower than normal extracellular pH. Therefore, this study aims
towards Mn(II) complexes that have a ligand with protons that can dissociate or come
on and off at a particular pH, which is dependent on the pKa’s of the ligand protons.
In this study the pH-dependent proton relaxivities are studied as a function of
pH to determine if there are any significant changes and at what pH. Data from pHdependent solution IR, potentiometric titration and speciation determination and
oxygen-17 relaxivities show why these changes are occurring and what is likely
responsible from a chemical mechanism perspective.
1.1 Background to Magnetic Resonance Imaging (MRI)
Magnetic Resonance Imaging (MRI) is a diagnostic imaging technology
derived from the phenomenon of Nuclear Magnetic Resonance (NMR). This
noninvasive technique specifically utilizes the nuclear spin of protons in the body
from water (in the presence of a magnetic field gradient) to create an anatomical
3
image of the inside of our bodies. This 41 year old technology is a relatively new yet
rapidly growing field with incredibly valuable diagnostic capabilities and applications
with no radiation risk to the patient.
As in NMR, MRI involves the study of the interaction between matter and
radiated energy. The energy levels studied are those associated with the different
orientations of the nuclear magnetic moment of an atom in an applied magnetic field.
The energy difference between the two states (ΔE) is directly proportional to
the strength of the applied magnetic field (Equation 1.1):
E  B0
(1.1)
where γ is the gyromagnetic ratio (SI units of rad∙s-1∙T-1) of the nucleus (a constant for
each NMR-active nucleus), B0 is the external magnetic field strength (in Tesla) and 
is the reduced Planck’s constant (in J∙s∙rad-1). The energy is then given in units of
Joules. While nuclei with a spin quantum number of I=1/2 such as 1H,
13
C,
19
F and
31
P are used, the majority of current MRI is based on 1H nuclei. Each 1H nucleus has
an angular momentum and its own personal magnetic field. The higher the
gyromagnetic ratio, the larger its local magnetic field.
For a 1H with a nuclear spin of I = ½ the allowed spin states in the presence of
the magnetic field are shown in Figure 1.2. The lowest energy spin state is when the
nuclear spins are aligned with the applied magnetic field and the higher energy spin
state is when they are against the magnetic field2. Since the energy difference is so
small, the protons continuously flip back and forth between the two states. However,
a thermal equilibrium is established between the two states. Even though this energy
4
difference is small, there will always be more protons in the lower energy state
(aligned with the magnetic field), from the Boltzmann distribution. Calculating the
(ratio of two states) number of proton spins against the magnetic field (flipped) over
the number of protom spins aligned with the magnetic field gives a ratio of
0.9999902. This number is only slightly less than 1 yet still represents a larger
number of proton spins aligned with the magnetic field.
ΔE=  γB0
Figure 1.2. Low and higher energy spin orientation states of a proton in a strong
external magnetic field.
The energy transitions are caused through the absorption of a photon of the
right energy. A photon that can cause a proton to flip over in a field of strength B0
must have a frequency of 2.68 x 108 rad∙s-1∙T-1 x B0. This is known as the proton
Larmor frequency (ω). The Larmor frequency for protons in a 1 Tesla field, for
example, is 2.68 x 108 rad∙s-1. The radio-frequency pulse applied (for a short time)
must be the proper frequency to be absorbed by the protons; when the frequency of
radiation is exactly equal to the energy difference between the two alignment states.
In NMR, the frequency of a NMR peak indicates the local magnetic field
strength of the proton and its chemical environment. Measuring NMR signal
5
amplitude as a function of RF frequency allows determination of proton densities as a
function of position.
Unlike NMR, which uses a constant magnetic field, MRI uses a gradient
magnetic field, so that each part of the body is in a slightly different magnetic
environment. The protons can now be distinguished based on their location in the
magnetic field. Intrinsic contrast between organs can be observed due to the varying
water proton density and local environments.3,4
It turns out, that the nuclear spin relaxation times of the water protons of
tissues are of much greater clinical importance than are the proton densities.
Relaxation times T1 and T2 are strongly influenced by the precise manner in which
the water molecules are moving around. They are real measurable times characteristic
of certain physical and chemical processes that occur on the atomic level.
1.2 Relaxation Times T1 and T2
When protons are placed in a magnetic field, a slight excess of those protons
will align with that field, due to the thermal equilibrium or Boltzmann distribution.
This equilibrium magnetization along the applied magnetic field (B0) is referred to as
longitudinal magnetization (Mz). Magnetization perpendicular to this direction is
referred to as transverse magnetization (Mxy). Before any RF pulses are introduced,
the net transverse magnetization of the sample will be zero.
When a 90° RF pulse is applied, the net magnetization aligned with Mz will be
rotated into the Mxy plane and the spins will precess about the applied magnetic field
6
B0 at the Larmor frequency. This rotating magnetization is what generates the MR
signal. Once, the 90° pulse is turned off, equilibrium is regained: the transverse
magnetization decays to zero and the longitudinal magnetization recovers to its initial
value (before 90° RF pulse).
Recovery of the longitudinal magnetization is referred to as T1 relaxation
(longitudinal relaxation time). This can be described mathematically using Equation
1.2, which turns out to be an exponential recovery5:
M 0  M z (t )  [M 0  M z (0)]expt / T1 (1.2)
where M0 is the equilibrium magnetization, Mz(t) is the longitudinal magnetization at
time t and t=0 is the time immediately following application of the 90° pulse. Mz(∞)
is the value of the longitudinal magnetization just prior to the 90° pulse. A graph of
Mz(t) versus time for water is shown in Figure 1.3 as an example.
7
70
65
%
60
55
50
45
40
35
0
20
40
60
80
100
120
140
160
Time (ms)
Figure 1.3. Exponential recovery of the longitudinal relaxation time (T1) of water at
37 ºC and 20 MHz.
The decay of transverse magnetization is referred to as T2 relaxation
(transverse relaxation time). This decay can be described mathematically using
Equation 1.3:
M xy (t )  M x, y (0)[exp t / T2 ]
(1.3)
where Mxy(t) is the transverse magnetization at time t and t=0 is the time immediately
following the 90° RF pulse. At this time the initial longitudinal magnetization is
8
completely converted into transverse magnetization. A graph of Mxy(t) versus time for
water is shown in Figure 1.4 as an example.
70
60
50
%
40
30
20
10
0
0
100
200
300
400
500
Time (ms)
Figure 1.4. Exponential decay of the transverse relaxation time (T2) of water at 37 ºC
and 20 MHz.
MRI images can be T1 or T2 weighted depending on whether image
brightening or darkening is desired. T1 weighted images cause an image brightening.
T2 weighted images cause an image darkening.
9
1.3 Introduction to MRI Contrast Agents
MRI images can be obtained without the use of contrast. However, sometimes
the contrast between normal and diseased tissue, is insufficient without the use of
paramagnetic contrast agents.
MRI contrast agents and their chemistry has sparked interest of many
chemists due to their ability to branch MR-imaging into new applications, including
but not limited to real-time modeling of molecular events.
From the beginning, in 1973, Paul Lauterbur6 pioneered imaging with NMR
which was extended to human imaging of a wrist on July 3, 19777- it took 5 hours to
produce one image; it now takes less than an hour to produce an image of much
higher resolution. At the end of the seventies, Lauterbur and his co-workers were the
first to demonstrate the great importance of paramagnetic contrast agents in MRI.
They administered manganese(II) chloride to dogs and were able to distinguish
normal from diseased tissues.
The first human MRI image study involving a contrast agent was performed in
1981 (only 33 years ago).8 Ferric chloride, orally administered, was used to enhance
the image of the gastrointestinal tract. There are currently 10 FDA (Food and Drug
Administration) approved contrast agents according to the MICAD (Molecular
Imaging and Contrast Agent Database). The first one was gadolinium(III) diethylentriaminepentaacetate (Gd-DTPA; Magnevist)9, and was approved in 1988. All but one
of the FDA approved contrast agents (see Scheme 1.1, showing 7 of them) contain
gadolinium(III). One of them (not shown in Scheme 1.1) contains Fe(II).
10
It was later determined that Magnevist, the most commonly used contrast
agent, was thermodynamically unstable and kinetically labile with respect to metal
dissociation, ligand exchange and transmetallation in vivo. For patients with poor
renal function, Gd(III) would dissociate and cause nephrogenic systemic fibrosis
(NSF)10. NSF causes a hardening of the skin, followed by the organs and tissues, and
ultimately can lead to death as there is no known cure.
11
Scheme 1.1. Magnevist and seven other FDA approved contrast agents.11
Thermodynamic, kinetic and transmetallation studies could have predicted the
potential for side effects and toxicity of these complexes. As part of developing 2nd
generation contrast agents, studying and developing new MRI contrast agents that are
12
less toxic, have a higher relaxivity and respond to metabolic changes. Additionally,
development of smarter second generation of contrast agents is underway to enable
monitoring of metabolism in vivo, visualization of gene expression38, metal ion
sensors37, targeting receptors39 and those that respond to changes in pH41,42,43.
Understanding how MRI contrast agents work and their underlying chemical
mechanisms of proton relaxivity will aid in the design and engineering of
paramagnetic complexes suitable for a particular application and purpose. In addition,
knowledge of their stability, solution structure, and hydration is key to understanding
function. The study of stable coordination complexes for use as MRI contrast agents
is growing in interest due to the identification of NSF, a rare but serious disorder
associated with the dissociated Gd(III) described above.
Manganese(II) is an attractive alternative because of its relatively high spin (S
= 5/2) and generally fast water exchange rates (109 s-1). As the number of reports on
Mn(II) complexes increases12, it is of interest to more fully understand the physical
and chemical properties that influence their relaxivities under a range of
environments. Coordination numbers of five through eight have been observed
crystallographically for high-spin Mn(II). Moreover, the solution structures of these
complexes are not always the same as its solid state structure. The coordination
number of Mn(II) complexes varies even when held within ligand frameworks of
identical denticity, which is why knowledge of their solution structure and hydration
is particularly important. The knowledge of their behavior in solution, particularly
13
their coordination number, is what will help determine the underlying chemical
mechanisms of relaxivity for the complexes being studied.
1.4 Solution Structure Determination and Challenges
Typically structure and coordination number for contrast agents are determined by
X-ray crystal structure analysis. Solid-state structure is not always maintained in
solution largely because of solvation effects and hydrogen bonding. Determining the
solution structure of Mn(II) complexes can be quite challenging. The complexes are
colorless, so UV-VIS is not informative. The complexes are paramagnetic, so NMR
spectra will only show a broad water peak; however, NMR of the diamagnetic
analogs can be studied. Solution IR spectroscopy can be used as long as the ligand
has a strong vibrational frequency and the solvent system does not have peaks that are
equivalent or overlapping. Additionally, many researchers look at the luminescence
lifetimes of the Tb(III) analog in H2O and D2O to obtain an accurate value for the
number of bound waters (q).13 This approach however, is only useful for lanthanides
and is most likely an estimation for the number of bound water molecules rather than
an accurate value.
Solution structure is important for determining how the complexes relax bulk
water protons. The disadvantages to many of these analog approaches, however is
that the solution structure and coordination of the metal in question (Mn(II) in this
study) is not being studied directly. This study will aim towards a more direct probe
of solution structure.
14
1.5 How MRI Contrast Agents Work
MR-images can be obtained without the use of a contrast agent due to the
relaxation of protons in the intrinsic magnetic field from the local environment.
Relaxation is the process by which equilibrium is regained, through interaction of the
spin system with the thermal molecular environment. For spins with I=1/2, relaxation
is caused by fluctuating magnetic fields at the sites of the nuclear spins, caused by
thermal motion of the molecules. For nuclear spins with I > 1/2, electric quadrupole
couplings are also involved.
After the Boltzmann distribution of spin states has been perturbed with an RF
pulse, equilibrium is regained and the net magnetization over time can be measured to
give the relaxation times discussed. Paramagnetic ions (contrast agents) affect the
time of this process.
MRI contrast agents work by relaxing bulk water protons through the
interaction of the unpaired electron spin of the paramagnetic ion with the nuclear spin
of the proton. By interacting with the spins of local protons, the contrast agents give
an additional pathway for relaxation, giving rise to a local change in relaxation time;
contrast with other tissues.
Bloch first described the use of a paramagnetic salt, ferric nitrate, to enhance
the relaxation rates of water protons in 194814. The standard theory relating solvent
nuclear relaxation rates in the presence of dissolved paramagnets was developed from
1948 to 1961 by Bloembergen, Solomon, and others15,16,17,18.
15
The paramagnet induces an increase in the longitudinal (1/T1) and transverse
(1/T2) relaxation rates of the solvent nuclei; in this case water protons. These protons
have a nuclear spin (I=1/2) which aligns with the applied magnetic field in its lowest
energy state (MI=+1/2). They then precess around the net magnetization vector
(applied magnetic field), around the z-axis, and the frequency of precession is
proportional to the magnetic field strength and is known as the Larmor frequency (ω):
similar to when a contrast agent is not present. Now rather than physical mechanisms
of relaxivity solely contributing, MRI contrast agents introduce possible chemical
mechanisms of relaxivity.
1.6 Contrast Agent Requirements
All of the FDA approved contrast agents have a bound water attached (q=1) to
their solid-state structure, see Scheme 1.1. Because of this and their efficiency, it is
thought to be a requirement for all contrast agents to have a bound water in the solid
state in addition to the requirements of having unpaired electron spins, a high
magnetic moment and fast water exchange rates. Until we know the role of this water
molecule in solution, how can one make this assumption?
There are general requirements for clinical contrast agents using paramagnetic
metal complexes. This includes the complexes ability to significantly increase the
relaxation rate of the protons in the bulk water and surrounding tissue (relaxivity
requirements).
16
In addition the metal-ligand complex thermodynamic stability (ability to be
excreted before metal dissociation) and kinetic inertness (lack of competition with
other metals in the body) are now very important in light of the NSF complications.
The stability and toxicity problems are often addressed by binding a chelate ligand
such as 1,4,710-tetraazacyclododecane N,N’,N’’,N’’’-tetraacetic acid (H4DOTA
structure shown in Scheme 1.4) which increases the stability constant and allows for
proper excretion of the paramagnetic metal.
While the thermodynamic stability19 and kinetic inertness20 can be measured
experimentally, the relaxivity requirements are better understood with knowledge of
relaxivity contributions and chemical mechanisms of proton relaxivity. Rather than
accepting that a high relaxivity is the goal, knowledge of what is contributing to the
overall relaxivity will help to design the most efficient MRI contrast agents.
1.7 Chemical Mechanisms of Proton Relaxivity
Relaxivity is defined as the increase in water proton relaxation rate per unit
concentration of contrast agent (CA). Equation 1.3 defines relaxivity and shows the
relationship between relaxation rate (1/T) and relaxivity (r). Relaxivity can be
experimentally21 determined by plotting 1/T versus concentration of CA in mM ([M])
with the slope being relaxivity in units of mM-1s-1:
1
𝑇1,2
−
1
°
𝑇1,2
= 𝑟1,2 [𝑀]
17
(1.3)
The higher the relaxivity of the paramagnetic complex per mM concentration,
the less has to be injected and therefore, better for the patient. In Equation 1.3, 1/T1
and 1/T2 are the longitudinal relaxation time and the transverse relaxation time
respectively (both defined in section 1.2). 1/T°1,2 is the relaxation time of the pure
solvent. Since relaxivity arises from the sum of the paramagnetic and diamagnetic
contributions, the relaxation time of the pure solvent (water) is subtracted to
determine the paramagnetic contribution. The paramagnetic contributions arise from
both inner-sphere and outer-sphere chemical mechanisms described below.
Inner-sphere relaxivity contributions arise from the exchange of water
molecules (or protons) bound to the metal ion, with water molecules from bulk
solution. This is known to be enhanced by the presence of bound inner-sphere water
molecules. The faster the water exchange is, the more efficient the paramagnet until it
reaches its optimum value, if the exchange is too fast then the paramagnet cannot
relax the water protons efficiently.
18
Scheme 1.2 Mechanisms of proton relaxivity. L = macrocyclic ligand or water. Red protons
are those with an inverted spin and blue or black atoms are those with equilibrium
magnetization. T1M-1 is the relaxation rate of protons in the inner coordination sphere of the
metal. 1) Outer sphere relaxation: kOS represents the rate of outer sphere relaxation. 2) Inner
sphere water exchange: τ-1water exch. is the rate of water exchange with the bulk. 3) Inner sphere
proton exchange: τ-1proton exch. is the rate of protropic exchange with bulk water protons. 4)
Transient water binding: τ-1assoc. represents the rate of associative water binding to form an
intermediate of higher coordinaton number and τ-1dissoc. is the corresponding rate for water
dissociation.
In cases where the metal is substitutionally inert, exchangeable protons on the
ligand itself or on the bound water may exchange with protons on bulk water
molecules. Outer-sphere relaxivity contributions do not include exchange effects.
Both will be described in more detail below.
Several generally accepted mechanisms for proton relaxivity have been
identified and are outlined in Scheme 1.2. 1) Outer sphere relaxation is a throughspace dipole-dipole interaction between the nuclear spins of the protons in bulk
solvent and the unpaired electrons of the metal ion. The efficiency of this mechanism
is critically dependent on the distance between the interacting spins and is usually
19
only important in the absence of other mechanisms. This mechanism is also
dependent on translational diffusion rates.21
2) Exchange of coordinated water
molecules with bulk water is often the most significant pathway for efficient
relaxivity. Inner sphere proton relaxivity is linearly proportional to the number of
water molecules directly coordinated to the paramagnetic ion22 as shown in Equation
1.4 and demonstrated in Table 1.1. In Equation 1.423 the concentration of water in a
pure water sample is 55.5 M. This equation was derived24 from the Bloch equations
using a steady-state approximation of a nuclei that exchanges between two
environments.
1
cq
1
  
 T1  (55.5M ) T1m   m
(1.4)
In Equation 1.4, c is the molal concentration, q is the number of bound water
molecules,  m is the lifetime of a water molecule in the inner sphere of the complex
(equal to the reciprocal water exchange rate, 1/kex) and 1/T1m is the longitudinal
proton relaxation rate of the bound water (different from the observed T1 of the
sample). Table 1.1 shows that the larger the value of q, the larger the relaxivity.
Changing the number of binding sites on the ligand, and therefore the coordination of
the complex, is the main way to change the number of bound waters. Table 1.3 shows
the structures for the ligands. For this reason, the design of contrast agents has usually
focused on labile
20
Table 1.1 Correlation between the number of bound water
Molecules (q) and relaxivity.
Complex
Temp °C q
r1(mM-1s-1)
Gd(H2O)q3+
35
8,9a
9.125 and 11.326
b
Gd(EDTA)
37
3
6.926
Gd(DOTA)
37
3.421
1b
All values acquired at 20 MHz aDetermined by X-Ray crystallography and
luminescence studies of Tb(III) analogs. There appear to be between 8 and 9
water molecules in solution. bFrom the solid-state crystal structure.
metal ions with coordinated water molecules. 3) Prototropic exchange is the exchange
of protons from coordinated ligands (often water) with protons of bulk water. If
water exchange is fast, this mechanism cannot be easily distinguished from water
exchange. However, if water exchange is slow then prototropic exchange is the
dominant pathway for proton relaxivity. For substitutionally inert complexes, e.g.
[Cr(H2O)6]3+, it is the dominant pathway for relaxation.27 4) Water exchange through
transient water binding has recently been suggested28 as a possibility for relaxivity in
complexes that have no apparent bound water molecules. In this pathway a metal
complex adds a water molecule by an associative mechanism to expand its
coordination sphere and form an aqua intermediate of higher coordination number.
The intermediate has a finite lifetime possibly on the order of nanoseconds. The
protons of the water molecule are relaxed and the water molecule dissociates,
regenerating the original complex.
The major evidence for this pathway is the
observation of relaxivities higher than expected from outer sphere pathways alone in
complexes that appear to have no coordinated water. Experimental29,30 and
21
computational31 studies have established that the mechanism of water exchange for
[Mn(H2O)6]2+ and many complexes of Mn(II) are associative in character.
Differentiating between dissociative (Mechanism 2) and associative
(Mechanism 4) mechanisms of water exchange can be difficult and describe reactions
in which an intermediate with a decreased or increased hydration shell, respectively is
formed. If the intermediate has a decreased hydration shell in the transition state then
the volume of activation will be experimentally determined to be -  V‡ and the
mechanism will be associative. If the intermediate shows an increased hydration shell
in the transition state then the volume of activation will be +  V‡ and the mechanism
of water exchange will be dissociative. The activation volume  V‡ can be measured
by high pressure NMR experiments which is the most common way to probe the
mechanism of water binding in the literature32. The work herein does not report this,
but is common in the literature and should be noted.
When a coordinatively saturated complex has a relaxivity greater than an
outer-sphere contribution, then water access is likely and possible either
dissociatively or associatively. Bound water is not necessary for a mechanism with
water binding directly to the metal center. This concept, introduced by Wang and
Westmoreland in 2009, is such an interesting addition to the field, because it means
that a bound H2O is not needed in all cases and many complexes are being
overlooked because of it.
22
1.8 Distinguishing Between Water Exchange and Prototropic Exchange
Distinguishing between water exchange and prototropic exchange, or
separating out their contributions to relaxivity, can be difficult. 1H relaxivities do not
separate the contribution from the water exchange protons (1H2O) to that of the
exchange of just the protons (1H without water exchange).
17
O relaxivities can be used to distinguish between the two. The 17O transverse
relaxation data will only reflect those that result from water (H217O) exchange. These
values can be compared to that of [Mn(H2O)6]2+ for which water exchange is the
dominant relaxation mechanism and to [Cr(H2O)6]3+ which is substitution inert and
can only relax bulk water by prototropic exchange and should have a much lower 17O
relaxivity.
17
O is a quadrupole nucleus with a nuclear spin of I = 5/2. Longitudinal
relaxation times (T1) do not change as a function of pH and only T2 values respond to
changes in the chemical environment.
Kinetic isotope effects using deuterium (2H) can be done to confirm the results
obtained in 17O data and details are discussed extensively in Chapter 4.
1.9 What ELSE Makes Contrast Agents Have a (Theoretically) High Relaxivity
In addition to dipolar outer-sphere mechanisms, prototropic exchange and
water exchange rates, there are other things that can be optimized in order to achieve
a high relaxivity.
An approach to increase proton relaxivity for MRI contrast agents is to slow
down rotation or optimization of the rotational correlation time. The relaxivity of
23
small molecular weight chelates is limited by rapid tumbling, or a fast rotational
correlation time, τR. The relaxivity maximum is achieved when the inverse of the
correlation time, 1/τC, equals the proton Larmor frequency ω (Equation 1.4) and τM
should be decreased but not so much that it starts to limit T1m. Equation 1.4 shows
that the correlation time, τC, may have contributions from molecular rotation (τR),
electron spin relaxation (T1e) and water exchange rates (τM).
For most small paramagnetic complexes, water exchange and electron spin
relaxation are slow when compared to rotational motion τR. This term is therefore, the
easiest to change.
 1
1
1
1 





  C  R  M T1e 
(1.4)
In order to slow down the rotational correlation time, many researchers are
adding large dendrimers or proteins to the molecule. As shown in Table 1.2 when
Gd(EDTA) is covalently attached to the amino groups on bovine serum albumin
(BSA), the relaxivity increases 7 fold.33
Table 1.2 Effect of increasing rotational correlation time
by binding to a protein.
Complex
Temp R1(mM-1s-1)
Gd(EDTA)
37
6.921
Gd(EDTA-BSA) 37
3621
With appropriate ligand design the second sphere relaxivity contribution can
also be important. The second sphere involves water molecules or protons that are
24
not directly bound to the metal, but can be hydrogen bonded to the inner-sphere water
molecules. Slow rotation of the molecule is beneficial for the second-sphere
contribution as well.
The interaction the CA has with H2O protons depends on the coupling
between the energy (from the spin flip) and the chemical mechanisms of proton
relaxivity. This energy coupling can occur through direct exchange or through space.
Because this energy is proportional to the magnetic field, some relaxation
mechanisms are not observed unless the strength of the magnetic field is changed.
The molecules can be forced to slow down their rotational motion in solution (by
binding them to a large protein) in order to match up with this energy and an
enhancement in relaxivity is seen and demonstrated in Table 1.2.
In fact, the relaxivity is now thought to be the sum of the inner-sphere, outersphere and second-sphere contributions. Dipolar interaction between the metal ion
and proximate water molecules represent an efficient mechanism for solvent
relaxation.34,35 This interaction can be promoted with hydrogen-bond-acceptor groups
on the ligand or by hydrogen bonding to the bound water.
This hydrogen bond network that forms increases the number of water
molecules in the second-sphere and brings them closer together. In the second-sphere
the protons of the water molecules can be closer than the oxygen atoms. These
second-sphere protons can even be closer than those of the inner-sphere water
molecule protons at times (demonstrated in Figure 1.5). If R = (C=O) then those
groups can form second-sphere hydrogen bonds as well. A bound water is not needed
25
for this effect to occur, as long as there are hydrogen-bond-acceptor groups on the
ligand itself.
Figure 1.5. Figure demonstrates the close distance to the metal center of the second
sphere protons in blue which are hydrogen bonded to an inner-sphere water molecule
proton in red. Where (ORN) represents a pendant arm (OR) attached to the (N) of the
cyclen ring and (R) is any functional group that contains an oxygen (O) that can be a
hydrogen bond acceptor.
One second-sphere water molecule has been proposed to contribute about
12% of the overall relaxivity shown in Figure 1.6.36 It should be noted that this is not
always the case and is strongly dependent on the nature of the solution structure and
the chemical mechanism of relaxivity. This figure also demonstrates that at clinical
field values (20-100 MHz) this effect is much smaller.
26
Figure 1.6. 1H NMRD profile of the [Gd(DO3APOEt)(H2O)]- complexes recorded at
37 °C. Lebduskova, P.; Helm, L.: Toth, E.; Kotek, J.; Binnemans, K.; Rudovsky, J.;
Lukes, I.; Merback, A.E. Dalton Trans. 2007, 493-2501.
[Gd(DO3APOEt)(H2O)]- is a mono-phosphonic ester substituted DOTA with
three carboxylate pendant arms and one mono-phosphonic ester pendant arm.
Interestingly the functional groups of the side arms are similar to those studied herein.
1.10 Smart Contrast Agents
MRI contrast agents expand the applications of MR-imaging. Many recent
studies have been directed towards the design of contrast agents that respond to
changes in the chemical environment. Complexes that serve as reporters for specific
metal ions37, visualization of gene expression38, biological targets39, the local
pH41,42,43, or the redox potential40 have been characterized. For a number of pHresponsive systems, a wide variety of pH profiles have been described as discussed
27
below. Rationalizations of these dependencies have been proposed, but many remain
to be firmly established. This particular study relates to those complexes that respond
to changes in local pH and have pH-dependent relaxivities.
The ligands on complexes that respond to pH typically contain functionalities
whose pKa values fall within the pH range of interest. One approach is to change the
hydration state or number of bound water molecules (q) in response to pH. This was
obtained by appending a sulfonamide nitrogen in the β position to a nitrogen donor of
DO3A (DO3A-SA)41 and forming a Gd(III) complex. DO3A is a tri-substituted
DOTA and the other pendant arm is a sulfonamide (SA). As a function of pH there is
a reversible on/off of the sulfonamide nitrogen donor, causing the relaxivity to go
from 2.0 mM-1s-1 (q=0) at high pH to 8.0 mM-1s-1 (q=2) at low pH, where the nitrogen
goes from being de-protonated and bound to protonated and un-bound.
Another interesting approach is changing the τR as a function of pH. The
Gd(III) complex with (DO3ASQ)30-Orn114)42 goes from a flexible long polymer chain
at low pH (r1 = 23 mM-1s-1) to a more rigid structure at high pH (r1 = 32 mM-1s-1).
This ligand is a DOTA derivative with a polyornithine chain as one arm. The
deprotonation of the –NH3+ groups on the chain favors the formation of
intramolecular hydrogen bonds and a more rigid structure. The specific nature of this
pH-dependence is not presented. This is however, an example of a change in the
rotational correlation time as a function of pH.
A particularly interesting compound (GdDOTA-4AmP) was one of the first
introduced to have an interesting pH-dependent longitudinal relaxivity in 1999.43 This
28
Gd(III) complex of a DOTA tetraamide derivative, shown in Scheme 1.3, has unusual
water relaxation characteristics. Although water exchange in this complex is quite
slow compared to more typical contrast agents, the relaxivity of GdDOTA-4AmP5was found to increase from 3.8 mM-1s-1 to 9.8 mM-1s-1 as the pH was decreased from
8 to 6, the same pH range over which the phosphonate groups are protonated in four
successive steps. Eight years later it was proposed that the increased relaxivity is due
to the formation of a hydrogen bonding network between the bulk solvent, the
phosphonates and the slowly exchanging, Gd3+-bound water molecule44. Derivatives
of this molecule were made and it was concluded that it may be necessary to have a
minimum of two hydrogen bonding groups on an amide side-chain group to catalyze
prototropic exchange.45 It was also shown that these second hydration sphere effects
on the relaxivity changed as a function of pH.
Scheme 1.3 Structure of (Gd(DOTA-4AmP))
29
The complex has both phosphonate and amide functionalities. The role of the
phosphonates is discussed, but not the role of the amides. For this reason we include
an extensive study of three ligands which have carboxylate, amide and phosphonate
functionalities. Studying them separately will help to determine what role they play in
the pH-dependent relaxivity profiles independently, which can ultimately lead to
complex studies of ligands with mixed functionality like this one and those discussed
in Sections 1.6 and 1.7.
1.11 Complexes used in this study
In order to address the issue of stability discussed in section 1.3, chelating
ligands with a high binding constant can be used. The ligands used in this study are
shown in Scheme 1.4. The 1,4,7,10 tetra-substituted derivatives of cyclen (1,4,7,10tetraazacyclododecane),
in
particular
1,4,7,10-tetraazacyclododecane-1,4,7,10-
tetraacetamide (DOTAM), 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid
(H4DOTA),
and
1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraphosphonic
acid
(H8DOTP), are an interesting class of ligands to study. Schematic structures for the
three ligands in their neutral forms21-23 are given in Scheme 1.4. The ligands are
structurally very similar, differing
30
Scheme 1.4. Chemical structures of the neutral forms of the ligands.
only in the identity of the functional groups on the pendant arms and their pKa’s. It
would not be unreasonable to assume that the structures of their complexes with
Mn(II) and their pH-dependent relaxivities might exhibit some similarities. This is
because of the similar size and structure (each possess four pendant arms) of the
ligands.
Despite these similarities, the pH-dependencies of the relaxivities of the three
Mn(II) complexes are considerably different, however. In order to understand the
chemical origins of these very different pH dependencies, the speciation of the
complexes at each pH must be defined and correlated to the observed relaxivities. By
a combination of potentiometric titration and solution IR spectroscopy, a model of the
solution structure of each complex over a wide range of pH values that is consistent
with all the observed data, has been developed.
1.12 Stability Constants: What is a logβ?
The most popular contrast agent [Gd(DTPA)]2- (Magnevist) is made up of a
linear chelate with carboxylate arms (Scheme 1.1). Due to the toxicity concerns it
31
caused with NSF, others in the field are studying macrocyclic DOTA-derivative
ligands46 which in fact bind more strongly to the metal ion and have the same
carboxylate functional groups as potential binding sites. Binding constants can be
compared to ligand structure for Gd(III) in Table 1.3. The macrocyclic ligand DOTA
has the highest binding constant, of 24.7, to Gd(III) when compared with the linear
chelates. For this reason, much research is geared toward studying macrocyclic
ligands rather than linear chelates.
Table 1.3 Binding constants compared to ligand structure.
Ligand
EDTA
Binding Constant (log K)
17.35
DTPA
22.39
H4DOTA
24.7
32
A stability constant (KML) is an equilibrium constant for the formation of a
complex in solution. The value is often expressed as its logarithm (log K) because it
makes the values easier to handle. It is a measure of the strength of the interaction
between the metal and the most basic form of the ligand:
𝑀 + 𝐿 ↔ 𝑀𝐿
The stability constant is defined as:
K ML 
[ ML]
[ M ][ L]
where [ML], [M], and [L] are the equilibrium concentrations of the complex, the
metal ion and deprotonated ligand, respectively. Due to the nature of the ligands used
in this study, there are a number of protonation constants of the ligand that vary as a
function of pH.
Therefore, the formation is then a kind of acid-base equilibrium where there is
competition for the ligand between the metal ion and the hydrogen ion. Consider the
equilibrium for the first protonation of the ligand separately first:
𝐻 + 𝐿 ↔ 𝐻𝐿
where the protonation constant is defined as:
K HL 
[ HL]
[ H  ][ L]
33
where [HL], [H+], and [L] are the equilibrium concentrations of the mono-protonated
ligand, the hydrogen ion and deprotonated ligand, respectively.
The stability constants that reflect the competition between the metal ion and
protons for ligand, used to describe the apparent stability of a complex at a given pH
is then:
K MHL 
[ MHL]
[ H  ][ L][ M ]
One can follow the hydrogen ion concentration during a potentiometric titration of a
mixture of M and HxL with acid or base to determine the stability constant of ML (as
long as the protonation constants HL, H2L, and up to the total number of protons
(HxL) in the ligand are determined first).
The potentiometric titration is then fit using HYPERQUAD, or another
similar program, to generate log β values for the stability and protonation constants.
These are the cumulative formation constants, rather than the step-wise constant (K).
Therefore, the first K is also the first β value and the above equation is also the
definition of the first β.
The following demonstrates the difference between the logK and logβ
constants using only protons (H+) and a ligand (L) with four basic group to protonate.
The first protonation is then:
𝐿4− + 𝐻+ ↔ 𝐻𝐿3−
[𝐻𝐿3− ]
𝐾1 = [𝐻 +][𝐿4−] = 𝛽1
34
The second protonation will be:
[𝐻 𝐿2− ]
𝐻𝐿3− + 𝐻+ ↔ 𝐻2 𝐿2−
2
𝐾2 = [𝐻 +][𝐻𝐿
3− ]
[𝐻 𝐿2− ]
𝛽2 = [𝐻 +2]2[𝐿4−]
where β2 is the cumulation of both the protonation steps as shown. And can be
mathematically shown to be the product of the two K values:
𝛽2 = 𝐾1 𝐾2
substituting K1 and K2:
[𝐿3− ]
[𝐻 𝐿2− ]
= [𝐻 + ][𝐿4− ] ∙ [𝐻 +2][𝐿3− ]
and simplifying:
[𝐻 𝐿2− ]
= [𝐻 +2]2[𝐿4−]
Proves β2 = K1K2.
Taking the log of both sides gives:
𝑙𝑜𝑔𝛽2 = 𝑙𝑜𝑔𝐾1 + 𝑙𝑜𝑔𝐾2
logK is therefore a step-wise constant where logβ is a cumulative or overall constant.
Since logβ values are the sum of logK values; subtracting them gives the pKa for the
protonation step (only if the β values are those for species that differ only by a
proton).
35
From these values a species distribution diagram can be constructed. A
speciation diagram is a powerful tool for the assessment of the concentration of the
species present as a function of pH. It provides the % species distribution (or
concentration) as a function of pH. Examples of these will be shown in Chapter 3. In
combination with solution IR these data can provide information on the solution
structure and protonation state at a particular pH.
1.13 This Study
MRI contrast agents typically either contain a coordinated water molecule in
their solid-state crystal structure or a metal site that is accessible to water in solution.
Is this bound water really necessary to achieve high relaxivities? Or can a high
relaxivity be accomplished by optimizing their dominating chemical mechanism of
relaxivity?
Optimizing the relaxivity of a given paramagnetic complex requires
knowledge of the relationship between the structure, the rate, and the mechanism of
the water/proton exchange. Specifically for the complexes herein it is important to
understand these relationships as a function of pH.
By studying these relationships in detail, we can determine whether solid state
structure is maintained in solution, the possible protonation state attributing to the
relaxivity and the pKa’s of the complex, the chemical mechanism of proton relaxivity
and whether or not a bound water is necessary.
36
The solution structure will be determined, or at least probed, by analyzing the
detail of the structure for a diamagnetic analog. Only the results of Zn(DOTA)2- will
be presented. Temperature-dependent spectra will also be acquired to probe solution
dynamics.
The stability constants and pKa’s will be determined with potentiometric
titration for each and correlated with the solution IR data. Speciation diagrams for
each complex will be derived.
The solution IR as a function of pH of these complexes will be used to
directly probe the changes in solution structure and protonation state.
The 1H relaxivity profiles as a function of pH can then be correlated with the
% species contribution as a function of pH for each complex. Each species
contribution to the relaxivity can then be calculated.
The
17
O relaxivity profiles as a function of pH can be compared to the 1H
relaxivities to determine whether or not there is a prototropic exchange contribution
for the complexes and at what pH. Prototropic exchange and second-sphere
contributions to relaxivity are smaller in comparison to direct inner-sphere water
binding, in complexes shown to date. Understanding this contribution and optimizing
it can in fact increase its contribution. It is better to understand the nature of this
contribution rather than make CA’s and determine their relaxivity.
Is the q or τR changing as a function of pH like the molecules described in
section 1.10? Will comparing the r2 and r1 proton relaxivities help to determine this?
37
In addition a kinetic isotope effect study will be done to further distinguish relaxivity
contributions of water exchange and prototropic exchange.
38
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41
Lowe, M.P.; Parker, D.; Reany, O.; Aime, S.; Botta, M.; Castellano, G.; Gianolio,
E.; Pagliarin, R. pH-Dependent Modulation of Relaxivity and Luminescence in
Macrocyclic Gadonlinium and Europium Complexes Based on Reversible
Intramolecular Sulfonamide Ligation. J. Am. Chem. Soc., 2001, 123, 7601-7609.
42
Aime, S.; Botta, M.; Geninatii Crich, S.; Giovenana, G.; Palmisario, G.; Sisti, M. A
Macromolecular Gd(III) Complex as a pH-Responsive Probe for MRI Applications.
Chem. Commun. 1999, 16, 1577-1578.
43
Zhang S.; Wu K.; Sherry A.D.; A Novel pH-Sensitive MRI Contrast Agent. Angew.
Chem. Int. Ed., 1999, 38(21), 3192-3194.
44
Kalman, F.K.; Woods, M.; Caravan, P.; Jurek, P.; Spiller, M.; Tirsco, G.; Kiraly,
R.; Brucher, E. Sherry, A.D. Potentiometric and Relaxometric Properties of a
Gadolinium-based MRI Contrast Agent for Sensing Tissue pH. Inorg. Chem. 2001,
46, 5260-5270.
45
Woods M.; Zhang S.; Ebron V.H.; Sherry A.D. pH-Sensitive Modulation of the
Second Hydration Sphere in Lanthanide(III) Tetramide-DOTA Complexes: A Novel
Approach to Smart MR Contrast Media. Chem. Eur. J., 2003, 9, 4634-4640.
46
Merbach, A.; Toth, E. The Chemistry of Contrast Agents in Medical magnetic
Resonance Imaging, John Wiley & Sons, Ltd: New York, 2001 p. 179-183.
41
Chapter 2
Materials and Methods
42
Chapter 2: Materials and Methods
The compounds H4DOTA and H8DOTP were purchased from Macrocyclics.
MnCl2·4H2O and MnCO3 were purchased from Sigma-Aldrich. All other reagents
were purchased commercially and used without further purification. DOTAM1,
[Mn(DOTAM]Cl22, and Mn(H2DOTA)·2H2O2 were synthesized as previously
described. Elemental Analysis was performed by Robertson Microlit Laboratories
(Ledgewood, NJ). D2O was purchased from Cambridge Isotopes. IR spectra were
obtained using a Spectrum BX FT-IR System (Perkin ELMER). Solution IR spectra
were obtained using a cell with CaF2 windows with a path length of 0.1 mm. Solidstate IR spectra were acquired using either Attenuated Total Reflectance (Pike
Technologies MIRacle ATR) or as KBr pellets. ESI-MS data were obtained using a
Finnigan LCQ Advantage Max spectrometer. 1H relaxation times were measured at 20
MHz and 37°C using a Bruker Minispec mq20 spectrometer. Transverse
17
O
relaxation measurements were obtained at in D2O at 54 MHz on a Varian Unity Plus
spectrometer.
2.1 Synthesis of Mn(H6DOTP)·3H2O
0.0499g (0.434 mmol) of MnCO3 was added to 0.2381g (0.434 mmol) of
H8DOTP dissolved in 50mL of de-ionized water. The mixture was stirred at room
temperature for 12 hours until all the MnCO3 had dissolved. The solvent was
removed by rotary evaporation and the resulting solid was washed with ether. (Yield
1.1630 g, 62% based on H8DOTP) Anal. Calcd for C12H36N4O15P4Mn: C 22.00%, H
43
5.54%, N 8.55%. Found: C 21.88%, H 5.39%, N 8.49%. Mass spectrum (ESI-MS:
m/z) 602.08, [Mn(H6DOTP)+H+]. IR (diffuse reflectance) 1148 cm-1, 1052 cm-1 and
916 cm-1 ν(P-O). Solid IR shown and explained in detail in Chapter 3.
Figure 2.1. ESI-MS of Mn(H6DOTP)•3H2O. 602.08 Da: [MnH6DOTP + H+] 549.09
Da: [H8DOTP + H+].
2.2 Synthesis of 0.1 mM Cr(H2O)63+ and Mn(H2O)62+ Aqueous Solutions
(Towards Probing Water Versus Prototropic Exchange)
For Kinetic Isotope Effect
0.1387 grams (0.5204 mmol) of [Cr(Cl2)(H2O)4]Cl∙2H2O was added to a 50
mL volumetric flask and diluted with doubly deionized water to make a 10.4 mM
44
aqueous solution. The solutions went from a green to purplish/gray solution over the
course of three days (Figure 2.2).
The UV-Vis spectrum (Figure 2.2) of [Cr(H2O)6]3+ shows two peaks at 576
nm and 407 nm, which is in good agreement with expected3 (588 nm and 416 nm).
Figure 2.2. UV-Vis spectrum of [Cr(H2O)6]3+
0.1018 grams (0.5143 mmol) of MnCl2·4H2O was added to a 50 mL
volumetric flask and diluted with double deionized water to make a 10.3 mM
colorless aqueous solution.
Two different solutions for each complex were made (Cr(H2O)63+ and
Mn(H2O)62+) for the kinetic isotope effect. The proton measurements were acquired in
45
1% by volume H2O in D2O solutions so that the detector is not saturated with proton
signal. A 0.1 mM solution of each compound was made by adding 0.25 mL of the 10
mM solution to a 25 mL volumetric flask and filling to the mark with D2O. The
deuterium measurements were acquired in 1% by volume D2O in H2O solutions. A
0.1 mM solution of each compound was made by adding 0.25 mL of the 10mM
solution to a 25 mL volumetric flask, 2.5 mL of D2O and then filling to the mark with
H2O.
For Other Experiments
For all the other experiments requiring a particular concentration of
(Cr(H2O)63+ and Mn(H2O)62+ fresh solutions were always made with the appropriate
concentration.
2.3 Synthesis of Zn(H2DOTA)
(Diamagnetic Analog)
0.1001 grams (0.2472 mmol) of H4DOTA·2.5H2O was dissolved in a minimal
amount of water. To this was added 0.0337 grams (0.2472 mmol) of ZnCl2. Using
KOH or NaOH the solution was brought to pH 5 and allowed to sit uncovered, with a
Kimwipe over it, overnight. Clear crystals formed and the solution was decanted off.
46
2.4 Temperature-Dependent NMR
(Towards Determining Solution Structure and Dynamics)
Temperature-dependent NMR of Zn(H2DOTA) was carried out on the 300
MHz Varian NMR in deuterium oxide. For this reason temperatures below 5 °C (278
K) and above 90 °C (363 K) were not attainable using this solvent. Increasing the
temperature was done in 5 degree increments using the software program and the
spectrometer is equipped with a temperature regulator. Lowering the temperature
required the direct cooling of the external coil using a mixture of dry ice and acetone.
Temperatures below 0 °C were possible using a 50/50 ratio of MeOD/D2O as
the solvent. However below -12 °C the moisture in the coil started to freeze and
airflow ceased.
2.5 Potentiometric Titrations
(Towards Determining Binding Constants and pKa’s)
Potentiometric titrations were carried out in a jacketed titration cell
maintained at 37 ± 0.1°C (physiological temperature). Constant ionic strength was
maintained with 0.1 M recrystallized KNO3 as electrolyte. Solutions of the complexes
at 1-10 mM concentrations were prepared from the isolated solids (pre-formed)
dissolved in the electrolyte solution. The in situ [Mn(HxDOTP)]x-6 titration was
carried out similarly except the reactants (MnCl2∙4H2O and H8DOTP) were added
separately and mixed together during the course of the titration in a 1:1 molar ratio.
During the titrations, the solutions were constantly stirred magnetically and water-
47
saturated N2 gas was flowed over the solutions. A nitrogen atmosphere was
maintained above the titration cell to minimize the amount of CO2 in solution, which
can act as a buffer in the basic region and may affect the titration. The nitrogen was
first bubbled through a solution of 0.1 M KNO3, the electrolyte used in the titrations.
The KNO3 electrolyte solution was prepared by dissolving recrystallized KNO3 in
freshly distilled water to make a 1.0 M solution. An electrolyte is used to maintain a
constant ionic strength, allowing the use of concentration in the determination of
stability constants.
After addition of each aliquot of standardized KOH solution, the pH was
measured with a Beckman combination electrode.
Titration data were fit using
Hyperquad 20084 and speciation diagrams were generated using HySS.5 Each
titration was carried out and fit at least twice and in each case, the results were
identical within the experimental error limits. In the fits of the data for the complexes,
the protonation constants of the free ligand species were obtained from independent
titrations of the free ligands. In each case, the pK values obtained were comparable to
the published values.6,7,8
10.115 g (0.100 mol) of recrystallized KNO3 was dissolved in 100 mL
distilled water to make the 1.00 M electrolyte solution. This was then diluted to make
a 0.100 M solution to bubble with nitrogen before the nitrogen reaches the titration
cell. This is done to prevent evaporation of water during the titration experiement.
Each titration used 2.5 mL of 1.0 M KNO3 and 22.5 mL of doubly de-ionized water to
make the total ionic strength 0.1 M.
48
2.6 pH-Dependent Solution Infrared Spectroscopy
(Towards Determining Solution Structure and Protonation State as a Function of pH
to Compare to Titration Data)
Solutions of [Mn(HxDOTA)]x-2 were made in D2O to avoid interference from
absorptions of H2O in the carbonyl region. The pD values of the solutions were
controlled by using phosphate buffers at 100 mM concentration. Phosphate buffer
was employed in this case since it provided a better reference spectrum for
background subtraction. Buffer solutions at high and low pD values were mixed to
obtain solutions across a pD range of 2.0-8.0. Samples were prepared by diluting an
aliquot of each buffer solution with an equal volume of a saturated solution of
[Mn(HxDOTA)]x-2 in D2O (about 10 mM). Background spectra were obtained using
buffer solutions diluted with D2O only. The effective pH values of the solutions were
measured using a pH meter and were converted to pD by adding 0.44 to the apparent
measured value.9 [Mn(DOTAM)]2+ solutions were made similarly in D2O.10
Solutions of [Mn(HxDOTP)]x-6 were made in H2O. Since phosphate buffers
interfere with the phosphonate stretching region of the IR, an alternative method of
adjusting the pH was used. A 10 mM solution of [Mn(HxDOTP)] x-6 at pH 1 (adjusted
using HCl) was prepared. A second 10 mM solution at pH 10 (adjusted using NaOH)
was also prepared. These solutions were then combined in varying ratios and the pH
values of the resulting mixtures were measured, thus obtaining a range of pH values
spanning about 1-10.
49
2.7 pH-Dependent 1H and 17O Relaxivities
Water for 1H relaxivity measurements was distilled from basic KMnO4. The
pH-dependent relaxivities of the three complexes were obtained using concentrations
of ~1-10 mM. The T1 and T2 relaxation times were measured with saturation recovery
and standard CPMG spin-echo pulse sequences respectively.
The saturation recovery method is based on the following pulse sequence:
90   90  AQ  D


n
the first 90° saturation pulse equalizes the populations of the two spin states. During
the variable delay τ the magnetization recovers. Then the 90° observation pulse is
applied and the FID is acquired (AQ). Lastly there is a delay (D) long enough for the
complete relaxation of the system (typically five times as long as the T1 relaxation
time), before another pulse is applied.
The Carr-Purcell-Meiboom-Gill (CPMG) spin-echo method is based on the
following pulse sequence:
90   (180   

0
echo
The pulse sequence begins with a 90° excitation pulse, followed by an
evolution time, τ. A 180° pulse that is phase shifted in the x,y plane by 90° relative to
the 90° excitation pulse, reverses the direction of the precessing spins and after
another interval τ, causes an echo to form.
50
The relaxation times were measured at each pH value and the relaxivity was
determined using Eqn 2.1 where T1,2 is the longitudinal or transverse relaxation time
of the sample, T1,2° is the relaxation time of water in the absence of complex, r1,2 is
the corresponding relaxivity, and [M] is the concentration of the paramagnetic
complex.
r1 , 2

 1

[ M ]  T1, 2
1



T1, 2 
1
o
(2.1)
For each compound, two solutions containing the same concentration of metal
complex, but with one adjusted to pH 1 using HCl and the other adjusted to pH 10
with KOH were made. For intermediate pH values, the high and low pH solutions
were mixed in appropriate ratios and the final pH of each resulting solution was
measured.
For 1H relaxation times, each sample was equilibrated at 37 ± 0.1°C for a
minimum of twenty minutes and this temperature was maintained in the spectrometer.
Magnetization decay curves of at least 25 data points were generated using a standard
saturation-recovery pulse sequence. Each point represented the average of 4-16 scans
using a recycle delay approximately five times the T1 value of the sample. The data
were fit to a mono-exponential recovery using routines supplied by Bruker.
Effective 1H relaxivities, defined in Equation 2.2,11 were derived for each
species present in the speciation diagrams for the [Mn(HxDOTA)]x-2 and
[Mn(HxDOTP)]x-6 complexes.
51
r1 (pH)   r1i fi (pH)
(2.2)
i
In the equation, r1(pH) is the observed relaxivity value as a function of pH, the
sum is over all metal-containing species present, r1i is the effective relaxivity of
species i, and fi(pH) is the mole fraction of species i at the specified pH value. For
each species, its concentration at each pH was extrapolated from the speciation
diagram generated by HySS. In the fits, the relaxivity of Mn2+(aq) was fixed at the
independently measured value of 6.71 mM-1s-1. Least-squares fits to Equation 2.2
using Origin V9.0.0 converged when a χ2 tolerance value of 1 x 10-9 was reached.
Transverse
17
O relaxation measurements were obtained at 23.7 ± 0.2 °C in
D2O. A standard CPMG spin-echo pulse sequence was used to generate the
magnetization decay curve for the T2 measurements. In a typical experiment, data for
13 delay times up to 0.6 s, each consisting of the average of 144-512 transients, were
collected. The decay data (Figure 2.4) was analyzed using routines supplied by
Varian to obtain T2 values. The peak was selected to determine the half-width. An
example spectrum is demonstrated in Figure 2.3, which shows only one peak present.
17
O T2 values for a D2O sample were obtained before the collection of each data set to
determine the T2o value under the prevailing environmental conditions. The
paramagnetic oxygen in the air can shorten the
17
O relaxation times. If the samples
have different atmospheric pressures above them, then you are not just comparing
sample to sample anymore.
52
Figure 2.3 Sample 17O spectrum to show the presence of one peak at 54 MHz.
53
Figure 2.4. Sample 17O transverse relaxivity array acquisition and example decay
data at 54 MHz.
54
References
1
Maumela, H.; Hancock, R.D.; Carlton, L.; Reibenspies, J.H.; Wainwright, K.P. The
Amide Oxygen as a Donor Group. Metal Ion Complexing Properties of Tetra-Nacetamide Substitued Cyclen: A Crystallographic, NMR, Molecule Mechanics, and
Thermodynamic Study. J. Am. Chem. Soc. 1995, 117, 6698-6707.
2
Wang, S.; Westmoreland, T.D. Correlation of Relaxivity with Coordination in Six-,
Seven-, and Eight-Coordinate Mn(II) Complexes of Pendant-Arm Cyclen
Derivatives. Inorg. Chem. 2009, 48, 719-727.
3
Bertini, I.; Fragai, M.; Luchinat, C.; Parigi, G. Solvent 1H NMRD Study of
Hexaazquachromium(III): Inferences on Hydration and Electronic Relaxation Inorg.
Chem. 2001, 40, 4030-4035.
4
Gans, P.; Sabatini, A.; Vacca, A. Investigation of Equilibrium Constants with
HYPERQUAD Suite of Programs, Talanta, 1996, 43, 1739-1753.
5
Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. Hyperquad
Simulation and Speciation (HySS): A Utility Program for the Investigation of
Euilibria Involving Soluble and Partially Soluble Species. Coord. Chem. Rev. 1999,
184, 311-318.
6
Clarke, E.T.; Martel, A.E. Stabilites of the Alkaline Earth and Divalent Transition
Metal Complexes of the Tetraazamacrocyclic Tetraacetic Acid Ligands. Inorg. Chim.
Acta, 1991, 190, 27-36.
7
Chaves, S.; Delgado, R.; Da Silva, J.J.R.F. The Stability of the Metal Complexes of
Cyclic Tetraazatetreacetic Acids. Talanta, 1992, 39, 249-254.
8
Geraldes, C.F.G.C; Sherry, A.D.; Cacheris, W.P. Synthesis, Protonation Sequence,
and NMR Studies of POlyazamarcrocyclic Methylenephosphonates. Inorg. Chem.
1989, 28, 3336-3341.
9
Mikkelsen, K.; Nielsen, S.O. Acidity Measurements with the Glass Electrode in
H2O-D2O Mixtures. J. Phys. Chem. 1960, 64, 632-637.
10
Nagata, M.K.C.T., B.A. Thesis, Wesleyan University 2013.
11
Kalman, F.K.; Woods, M.; Caravan, P.; Jurek, P.; Spiller, M.; Tircso, G.; Kiraly,
R.; Brucher, E.; Sherry, A.D. Inorg. Chem. 2007, 46, 5260-5270.
55
Chapter 3
Results and Discussion
56
In order to better design MRI contrast agents, chemical mechanisms of proton
relaxivity must first be investigated. As the number of reports on Mn(II) complexes
increases, it is important to more fully understand the physical and chemical
properties that influence their relaxivities under a range of environments. This works
studies three structurally related Mn(II) cyclen derivatives and their chemical
mechanisms of relaxivity as a function of pH (Figure 3.26 and Section 3.5.1).
MRI contrast agents typically either contain a coordinated water molecule in
their solid-state crystal structure or a metal site that is accessible to water in solution.
Is this bound water really necessary to achieve high relaxivities? Or can a high
relaxivity be accomplished by optimizing their dominating chemical mechanism of
relaxivity?
The three complexes studied are Mn(II) cyclen-derivatives containing
carboxylate, amide or phosphonate side arms, which may coordinate to the metal ion.
The three complexes studied have very different pH-dependent relaxivities although
they are similar in structure. The general functional groups do differ in their pKa
values: carboxylates generally have a pKa of 5, amides have a pKa of 15 and
phosphonates (R-CH2PO3H2) have pKa’s around 2.35 and 71. Within the pH range
studied (between 2 and 10) the amide derivate will likely not show an inflection in the
relaxivity due to a change in protonation state. It turns out that the protonation states
of the complexes are much more complicated when there are four side arms attached
to a cyclen ring and when in the presence of Mn(II). Each complex is presented in
detail.
57
Apparently a small change in the functionality (even though they each contain
at least one “hard” oxygen atom which will preferentially bind the “hard” Mn(II)) of
the complexes yield a large change in the pH-dependent relaxivities. What is causing
these particular changes? What is so different about the amides, carboxylates and
phosphonate pendant arms in each complex?
To best understand the chemical origins of these very different pH
dependencies reported herein, the speciation of the complexes at each pH must be
defined and correlated to the observed relaxivities. By a combination of
potentiometric titrations and solution IR spectroscopy, we have developed a model of
the solution structure of each complex over a wide range of pH values that is
consistent with all the observed data. This model was then used to rationalize the pH
dependence of the 1H relaxivity of each complex and to propose specific chemical
mechanisms for the relaxivity that dominate for each complex across the range of pH
values. This analysis provides new insights in the design of contrast agents based on
Mn(II) complexes of cyclen derivatives.
3.1 Solid-State Structures of the Complexes
The X-ray crystal structures of Mn(DOTAM)Cl2•2H2O and Mn(H2DOTA)
have been previously reported2 and solid-state coordination is shown in Figure 3.1. In
the solid-state, the [Mn(DOTAM)]2+ cation is an eight-coordinate distorted square
antiprismic geometry with coordination by the four nitrogen ring atoms and the four
58
amide oxygen atoms. The “hard” Mn2+ ion prefers negatively charged oxygen and
nitrogen donor atoms.
Unlike the amide cyclen derivative [Mn(DOTAM)]2+, Mn(H2DOTA) has a
six-coordinate distorted octahedral geometry with coordination by two deprotonated
acetates as well as the ring nitrogens. The other two acetate groups are protonated and
do not coordinate the metal. Also shown in Figure 3.1 is the presence of a
hydrophobic and hydrophilic region of the molecules. The bottom two representations
in the figure show the hydrophilic region on the top, where the carboxylates (left) and
amides (right) are located. The bottom region of the complex is where the
hydrophobic methylene (N-CH2-CH2-N) groups in the cyclen ring are oriented.
59
Figure 3.1 Solid state structure comparison of [Mn(DOTAM)]2+ (left column) and
Mn(H2DOTA) (right column). Hydrogens on carbons omitted for clarity. Carbon
(grey), oxygen (red), nitrogen (blue) and hydrogen (white). Figures adapted from
reference 28.
The X-ray crystal structure of a discrete molecular [Mn(HxDOTP)]x-6 species
has not yet been reported in the literature. Attempts to obtain a single crystal have
been largely unsuccessful presumably due to the presence of multiple protonation
states in solution as a function of pH.
60
A compound similar to it is that of [Mn(C3NH7(PO3H0.5)]4, where Mn(II) ions
bridge the oxygen atoms of the phosphonates from four different (H6DOTP)2- anions
which are coordinated to the metal
Scheme 3.1. Crystallographic structure of [Mn(C3NH7(PO3H0.5)]4 from Kong, D.;
Medvedeve, D.G.; Clearfield, A.; DOTP-Manganese and –Nickel Complexes:
from a Tetrahedral Network with 12-Membered Rings to an Ionic Phosphonate.
Inorg. Chem. 2004, 43, 7308-7314.
in a distorted tetrahedral geometry.3 This compounds’ known structure can be used to
compare properties and IR spectra to that of the Mn(H6DOTP) complex reported
herein (Scheme 3.1). It appears the two structures in comparison are very different.
The synthesis of the complex is different from the one reported herein and the
properties of the complex are different as well. According to the published
formulation, all four ring nitrogens are protonated. This does not seem likely
according to the solid-state X-ray crystal structure of H8DOTP4 shown in Figure 3.2.
Each of the nitrogens would be positively charged, and the electrostatic repulsion that
results, would likely be disfavored in that relatively small ring.
61
Figure 3.2. Structure of the H8DOTP molecule from the crystal structure; showing
only two of the nitrogens are protonated.4
Unlike in H4DOTA where all four carboxylates are positioned above the plane
of the ring nitrogens, two of the phosphonate groups (P1 and P3 in the figure) in the
H8DOTP ligand are positioned above the plane of the ring while the other pair (P2
and P4) are oriented away from the ring (in the solid-state). Figure 3.2 shows how the
protonated nitrogens that are positively charged pull the two monoprotonated
phosphonates in closer. Examination of the P-O bond lengths reveals that two of the
phosphonates are fully protonated while the other two are monoprotonated. Two of
the nitrogens N2 and N4, are also protonated, resulting in an overall neutral molecule
(as shown in Scheme 1.4). This was confirmed by locating the hydrogens on the six
oxygen atoms by difference Fourier electron density maps.4 The structure of
[Mn(C3NH7PO3H0.5)]4 shows all four nitrogens are protonated (Scheme 3.1). The
complex reported by Kong et. al. was made using a hydrothermal reaction at 150 °C
for 24 hours and a 1:1 molar ratio of ligand with MnCl2 bishydrate. It is unclear what
the structure of the H8DOTP ligand looks like under these high temperature and high
62
pressure conditions, and these conditions could be the reason for the difference in
nitrogen protonation.
Figure 3.3. IR spectra of Mn(II), red, and Ni(II), blue, complexes of DOTP
reported by Kong et. al.3
The complex we report, Mn(H6DOTP)•3H2O has significantly different
properties that reflect a different coordination environment. In particular, the
synthetic routes are different and the empirical formulas of the products differ in three
waters of hydration. In addition, the solid-state IR spectra of the products (shown in
Figures 3.3 and 3.4) are significantly different. Mn(H6DOTP)•3H2O exhibits no peak
near 3135 cm-1 which has been assigned to the N-H stretch of the protonated
nitrogens since these nitrogens are the most basic site of the ligand3, the nitrogen
63
atoms must be coordinated to the manganese instead. It should also be noted that
Mn(H6DOTP)•3H2O is soluble in water, which is not reported for the extended lattice
of [Mn(C3NH7(PO3H0.5)]4. Finally, ESI-MS results (shown in Figure 2.1) clearly
demonstrate the presence of a discrete 1:1 complex, showing the molecular weight for
[MnH6DOTP + H+] at 602.08 D.
Transmittance
Mn(H6DOTP)-3H2O
4000
3500
3000
2500
2000
1500
1000
Wavelength (cm-1)
Figure 3.4. Solid state IR of the complex Mn(H6DOTP)·3H2O studied herein.
64
`In fact, the IR spectrum for the Mn(H6DOTP)·3H2O complex reported herein
has a very similar spectrum to that of the [Ni(H4DOTP)][Ni(H2O)6]3+ complex Kong
et. al. synthesized. The most likely solid-state structure for Mn(H6DOTP) is thus
analogous to both Mn(H2DOTA) and [Ni(H4DOTP)][Ni(H2O)6]3+ with manganese
coordinated to the four nitrogen atoms and two mono-protonated phosphonate
pendant arms, shown in Scheme 3.2.
Scheme 3.2. Proposed solid state structure of Mn(H6DOTP)
3.2 Solution Structures of the Complexes
Studying the diamagnetic analogs of the Mn(II) complexes using Zn(II) will
help to determine if the solid-state structure is maintained in solution. It is in fact the
solution structure and coordination that is important when aiming toward determining
the chemical mechanism of relaxivity in water. This section aims to address whether
or not the solid state structure is maintained in solution.
One of the other questions we seek to answer is whether or not bound water is
necessary for small molecule contrast agents to efficiently relax water protons. If not
are there dynamic processes that are helping to facilitate a transient water binding?5
65
Solution structure and coordination determination of diamagnetic analogs can help to
answer this.
Mn(H2DOTA) is six-coordinate in the X-ray crystal structure. Zn(H2DOTA) is
also six-coordinate in the solid-state X-ray crystal structure6. Therefore the NMR for
the diamagnetic analog should show a series of splittings for the different ring
methylene protons (structural isomers as a result of ring movement)7 and two sharp
peaks for the side arm methylene protons.
Figure 3.5 1H NMR of (H4DOTA) at 22 °C (300 MHz, D2O) δ ppm 3.74 (s, 8 H) 3.26 (s, 16
H).
66
The NMR spectrum of the H4DOTA ligand shown in Figure 3.5 shows one
singlet at 3.74 ppm for the 8 side-arm methylene protons and another singlet at 3.26
ppm for the 16 ring methylene protons.
Figure 3.6. 1H NMR of Zn(H2DOTA) at 20 ºC (300 MHz, D2O)  ppm 3.32 (s, 8 H)
3.10 (m, 8 H) 2.85 (m, 8 H)
The NMR spectrum for Zn(H2DOTA) shown in Figure 3.6, shows two broad
multiplets for the rings methylene protons locked in a more rigid structure than the
free ligand, due to the metal center, at 3.10 and 2.85 ppm (compared to the sharp peak
in the free ligand in Figure 3.5). Unexpectedly, there is only one peak for the side arm
methylene protons at 3.32 ppm.
67
This suggests two things: First, either Zn(H2DOTA) is eight-coordinate in
solution or the side arms are “popping on and off” (demonstrated in Scheme 3.3)
faster than the timescale of the NMR Larmor frequency. This could be an explanation
as to why there is a signal averaging where the two forms are rapidly interconverting.
If this process is slowed down with cooling, the side arm methylene protons should
start to split, if the second explanation is true. The temperature at which the peaks
coalesce (become one peak) depends on the rate of exchange between the two states
and the spectrometer (carrier) frequency.8
Scheme 3.3. Six-coordinate side arm dynamics of Zn(DOTA)2-.
Therefore, studying the NMR spectra as a function of temperature for the
Zn(H2DOTA) complex will determine if there are dynamics in solution and what the
solution structure might be. Looking at these data in combination with solution IR
might help determine solution coordination for Zn(H2DOTA), which then suggests
something about the solution structure of Mn(H2DOTA).
This study is done with the Zn(H2DOTA) complex at pH = 7.5 (Zn(DOTA)2-).
This is where all the carboxylate arms are deprotonated according to the published
protonation constants.9
68
Figure 3.7. 1H NMR of Zn(H2DOTA) at 90 °C and pD 7.5 (300 MHz, D2O) δ ppm
3.30 (s, 8 H) 3.09 (m, 8 H) 2.86 (m, 8 H).
Increasing the temperature up to 90 ºC results in sharpening of the normal
coupling features, shown in Figure 3.7, in the two ring methylene multiplets.
Temperatures higher than this could not be achieved based on the limitations of the
solvent (D2O) and potentially over heating the probe. The side arm methylene protons
remain a singlet at 3.30 ppm.
69
Cooling down to -12.5 ºC (Figure 3.9) using a 50:50 mixture of methanol-d4
and D2O reveals a broadening of the side arm and ring methylene peaks.
Unfortunately cooling below this was impossible due to the condensation inside the
coil freezing resulting in a loss of air flow.
Figure 3.8. 1H NMR of Zn(DOTA)2- at 21.7 °C and pD 7.5 (300 MHz, D2O and
methanol-d4 (50:50))  ppm 3.28 (s, 8 H) 3.03 (m, 8 H) 2.79 (m, 8 H)
Figure 3.8 shows Zn(DOTA)2- in this solvent system at room temperature,
with a singlet at 3.28 and two broad unresolved multiplets at 3.03 and 2.79 ppm.
70
Figure 3.9. 1H NMR of Zn(H2DOTA) at -12.5 ºC and pD 7.5 (300 MHz, D2O and
methanol-d4 (50:50)) δ ppm 3.28 (br. s., 8 H) 3.02 (d, 8 H) 2.76 (d, 8 H)
Upon cooling of the complex down to -12.5 ºC the singlet at 3.28 begins to
broaden into the d4-methanol solvent quintet. The multiplets become less resolved
and broaden as well.
The 2D COSY spectrum in Figure 3.10 also reveals/confirms that the only
coupling (off-diagonal peaks) are the ring multiplets. These are coupled to one
another in an AA’BB’ pattern that can be seen at higher temperatures as the spectrum
and splitting become more resolved (Figure 3.7).
71
Figure 3.10. 2D COSY spectrum of Zn(DOTA)2- at room temperature and 300 MHz.
It would not be uncommon for a complex to have a different solution structure
than its solid-state structure. The crystal structure of Zn(DOTAM)2+ has been
reported10 and shows a 6-coordinate geometry with two sets of metal-to-oxygen bond
lengths. Two of them are too long to be considered even van der Waals contacts at
3.33 and 3.13 Å.
72
Molecular mechanics simulations were carried out to determine the nature of
these longer bonds, which was determined to be controlled by van der Waals
repulsions with the oxygen atoms coordinated to the metal ion at short M-O bond
lengths. The forces drawing the oxygens toward the metal center could be purely
electrostatic with some attractive van der Waals forces.
Temperature-dependent
13
C NMR for Zn(DOTAM)2+ shows that the four
pendant arms are equivalent from -55 ºC to 22 ºC. However, the macrocyclic ring
carbons are inequivalent. Inequivalence of the ring carbon atoms in molecules of this
type has been associated with eight-coordinate geometries and interchange of the
helicity of the pendant arms arrangement. The Zn(H2DOTA) 2D COSY spectrum
shows two inequivalent ring methylene protons that are in fact coupled together (next
to one another) and Zn(DOTAM)2+ has two different ring carbons.
In order to help confirm the solution structure it will be helpful to look at the
solution IR at a pD similar to that of the NMR experiment in D2O for Zn(H2DOTA).
The solution IR of Zn(H2DOTA) at pD = 7.54 shows one peak at 1592 cm-1. And can
be found in Appendix D. This suggests that the side arms are all the same and in fact
Zn(H2DOTA), is 8-coordinate in solution. In addition, there is only one peak from 12.5 °C to 90 °C at 300 MHz for the side arm methylene protons, suggesting an 8coordinate solution structure.
The point of this study was to determine if the solution structure of
Mn(H2DOTA) at high pH can be confirmed using the diamagnetic analog. It will be
73
helpful to then compare this conclusion and the solution IR of Mn(H2DOTA) around
pH 7. Figure 3.21 shows the solution IR of Mn(H2DOTA), where around a pD of 7
there are two peaks: one at 1584 cm-1 (assigned to unbound –COO-) and the other at
1616 cm-1 (assigned to bound –COO-). This data is consistent with a 6-coordinate
complex.
In addition, the side-arm peak linewidth of Zn(DOTA)2- at -12.5 ºC is 0.10
ppm. Multiply this by the carrier frequency (300 MHz) and you get 30 Hz. If it is
assumed that this is the coalescing temperature of the exchange dynamics, it can be
divided by two11 to give the rate of exchange as k = 15 s-1. This seems too slow to be
the dynamics shown in Scheme 3.3
In conclusion, the two metals have similar binding in the solid-state and
different binding to DOTA in solution. In solution Zn(H2DOTA) is 8-coordinate and
Mn(H2DOTA) is 6-coordinate. The ionic radius of Zn2+ is 88 pm where that of Mn2+
is larger at 97 pm. So one would expect that Mn(II) would in fact hold a higher
coordination. They do however; differ in their valence electron count and
electronegativities. Zn2+ is slightly more electronegative and has 10 valence delectrons, while Mn2+ has only 5. This could account for the differences.
3.3 Stability and Speciation
In order to understand the pH-dependent relaxivities of the complexes, it is
important to define the speciation of the complexes over the relevant pH range. The
74
most common approach is by using fits of potentiometric titration data to obtain
speciation models that incorporate all relevant species to determine binding constants
and pKa values for the system. A stability constant is provided by the fit of the
titration data to the model in the form of a log β which was defined in Section 1.12.
From these values a species distribution diagram can be constructed. A
speciation diagram is a powerful tool for the assessment of the concentration of the
species present as a function of pH. Examples of such diagrams will be shown and
discussed in detail.
The potentiometric titration of [Mn(DOTAM)]2+ in the pH range 1.92 to 5.85
shows no inflections characteristic of a protonation equilibrium. Figure 3.11 shows
the titration data as a function of mL HNO3 added and Figure 3.12 shows the data as a
function of log[HNO3]. The fact that Figure 3.12 is linear (pH = -log [H+]) supports
that there are no pKa values (the pH is monitoring the [H+] changes of the solution
only) for the complex in this range. Above pH 8 a brown precipitate forms, indicative
of decomplexation of Mn(II) and formation of insoluble manganese hydroxides. Thus
in the pH range of the relaxivity measurements, the only relevant species present is
[Mn(DOTAM)]2+.
75
2+
3mM [MnDOTAM] Titration
6
5
pH
4
3
2
1
0
5
10
15
20
25
30
35
40
mL HNO added
3
Figure 3.11. Mn(DOTAM)2+ titration at 3mM starting concentration at 37 ºC and
using 0.1 M HNO3.
76
2+
3mM [MnDOTAM] Titration
5
4.5
4
pH
3.5
3
2.5
2
1.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
log[HNO ]
3
Figure 3.12. Mn(DOTAM)2+ titration data from Figure 3.11 as a function of
log[H+].
The Mn(DOTAM)2+ complex is kinetically slow to dissociate. The time
dependence of the relaxivity as a function of pH (Table 3.1), for this complex, shows
only 5% dissociation over a period of 5 days in solution at pH 2.5. Above pH 4.25,
the relaxivity remains unchanged after 6 weeks.
77
Table 3.1. Analysis of dissociation kinetics of Mn(DOTAM)2+ at 37 ºC
pH
2.51
4.26
5.40
6.79
8.57
r1 (mM-1s-1)
Initial Value
1.07 ± 0.04
0.92 ± 0.01
0.99 ± 0.02
1.06 ± 0.03
1.14 ± 0.03
r1 (mM-1s-1)
6 Weeks Later
1.87 ± 0.04
0.99 ± 0.03
1.12 ± 0.03
1.11 ± 0.02
1.09 ± 0.02
For Mn(H2DOTA), a more complex behavior was observed. Four chemically
reasonable models were found that provide acceptable fits to the experimental
titration data (see Appendix A)12. On the basis of the pH-dependent IR spectra
(described later) and in light of the crystallographic evidence for Mn(H2DOTA) only
one of the models was consistent with all the data. The formation and protonation
constants for the [Mn(HxDOTA)]x-2 species in this model are reported in Table 3.2.
The model contains Mn2+(aq), Mn(H2DOTA), [Mn(HDOTA)]- and [Mn(DOTA)]2-,
as well as all protonation states of the ligand and a manganese hydroxyl species.
Table 3.2 Stability and protonation constants of [Mn(HxDOTA)]x-2 at 37 C and 0.1 µ
Species
[Mn(DOTA)]2[Mn(HDOTA)]Mn(H2DOTA)
(HDOTA)3(H2DOTA)2(H3DOTA)H4DOTA
log β
20.42 ± 0.07
24.31 ± 0.04
27.54 ± 0.11
12.04 ± 0.14
22.57 ±0.07
26.94 ± 0.11
30.44 ± 0.13
78
pKa
3.89 ± 0.08
3.23 ± 0.11
12.04 ± 0.14
10.53 ± 0.16
4.37 ± 0.13
3.50 ± 0.17
The model in Table 3.2 differs from that previously presented in the literature
by the inclusion of Mn(H2DOTA), the existence of which has now been confirmed by
X-ray crystallography. The values of the complex formation constants and pKa values
for the model in Table 3.2 are similar to those previously published13. The results are
summarized in Figure 3.13, which gives the speciation diagram determined from the
model in Table 3.12.
Mn2+
[Mn(DOTA)]2-
Mn(H2DOTA)
[Mn(HDOTA)]-
Figure 3.13. Speciation diagram of Mn-containing species for [Mn(HxDOTA)]x-2 at 1
mM according to the model in Table 3.2.
79
From the diagram it is apparent that as the pH is lowered below 4, the Mn(II)
ion decomplexes from the ligand and below pH 2 the only significant Mn(II) species
is the aqua ion. Above pH 6, the fully deprotonated [Mn(DOTA)]2- ion dominates.
The crystallographically characterized Mn(H2DOTA) complex appears just as the
complexation of the Mn(II) ion from the ligand starts to occur.
The potentiometric titration data for the complex of Mn(II) with H8DOTP for
the in situ and pre-formed complexes are presented individually and compared below.
For the in situ complex only one chemically reasonable model was consistent with the
known pKa values for the ligand. The results, given in Table 3.3 and Figure 3.14
include all possible protonation states of the complex
Table 3.3 Stability constant and protonation constants of [Mn(HxDOTP)]x-6 in situ.
Effective
pKa
log β
[Mn(DOTP)]610.35 ±0.31
5[Mn(HDOTP)]
19.39 ± 0.08 9.04 ± 0.32
4[Mn(H2DOTP)]
28.12 ± 0.05 8.79 ± 0.09
3[Mn(H3DOTP)]
35.84 ± 0.03 7.72 ± 0.05
2[Mn(H4DOTP)]
41.21 ± 0.03 5.37 ± 0.04
[Mn(H5DOTP)]45.32 ± 0.03 4.11 ± 0.04
Mn(H6DOTP)
45.38 ± 2.80a 0.18 ± 2.80 a
(HDOTP)710.9b
10.9
6b
(H2DOTP)
20.1
9.2
(H3DOTP)528.2b
8.1
4b
(H4DOTP)
34.2
6.0
3b
(H5DOTP)
39.9
5.7
2b
(H6DOTP)
41.7
1.8
b
(H7DOTP)
43
1.3
a
This species was not present at high enough concentrations to give a smaller
error. blog β values from the pKa values reported at 25 °C and 0.1M NaCl.14
Species
80
100
% formation relative to Mn
[Mn(H5DOTP)]-
[Mn(H3DOTP)]3-
80
[Mn(H4DOTP)]2-
[Mn(H2DOTP)]4-
60
40
Mn2+
20
0
0
2
4
6
8
10
pH
Figure 3.14. Speciation diagram of Mn-containing species for [Mn(HxDOTP)]x-6 in
situ at 7 mM according to the model in Table 3.3. A version with all curves labeled is
provided in Appendix B.
and the free ligand. The speciation diagram in Figure 3.14 shows that at each pH
value the speciation is dominated by [Mn(HxDOTP)]x-6 complexes and not free
Mn2+(aq). It is important to note that at each pH there are a number of species present
but for all pH values in the range 1 to 4, [Mn(H5DOTP)]- is dominant and between
pH 6 and 8 [Mn(H3DOTP)]3- is dominate.
81
The formation constants for the fully deprotonated ligands and Mn(II) in
Table 3.4 show that amides are more thermodynamically stable than the carboxylates
and the carboxylates are more thermodynamically stable than the phosphonates.
Table 3.4. Stability constants of three ligands with Mn(II)
Complex
[Mn(DOTAM)]2+
[Mn(DOTA)]2[Mn(DOTP)]6- (in situ)
log(K)
> 22
20.42
10.35
This is however, not always the case for every metal/lanthanide. These
macrocyclic ligands have high selectivity for metal ions based on the size of the metal
in comparison to the size of their nitrogen ring cavity, and their side arm functional
groups identity and charge. For instance, the stability constant for the complex of
DOTP (fully deprotonated) and Gd(III) is 28.8 compared to the complex of DOTA
which is 24.7. Unlike Mn(II), gadolinium(III) binds more strongly to the phosphonate
derivate than that of the carboxylates. These however, are the results for the in situ
complex. The lower stability constant could reflect this, although it is a
thermodynamic value and it should not matter how it arrives at equilibrium.
As shown in Figure 3.15, metals with a higher charge have a generally higher
formation constant with DOTA. This is likely so that the negative charge from the
carboxylates
side
arms
can
82
be
accommodated.
0
Metal Charge
1
2
3
4
0
5
10
15
20
25
30
logK
Figure 3.15. Charge effects of metal binding constants to DOTA15.
For the case of DOTA it makes sense that Gd(III) would have a higher
formation constant than with that of Mn(II) because of its higher charge and the trend
shown in Figure 3.15. Similarly DOTP has a higher binding constant to Gd(III) than it
does to Mn(II).
When comparing the same metal Gd(DOTP)5- > Gd(DOTA)- and
Mn(DOTA)2- > Mn(DOTP)6-. Table 3.5 shows the comparison of the two as well as
other 2+ metal ions to show that Mn(II) is not the only divalent metal that binds more
strongly to DOTA than to DOTP.
83
Table 3.5. Stability constant comparison for DOTA and DOTP.
Metal
Gd3+
Mn2+
Mg2+
Ca2+
Sr2+
Ba2+
Zn2+
Cu2+
logK with DOTA
24.7
20.42
11.1
16.37
14.4
11.8
21.1
22.2
logK with DOTP
28.8
10.35 (pre-formed)
7.3
10.3
9.8
8.8
24.8
25.4
The potentiometric titration for the pre-formed Mn(H6DOTP) complex was
performed twice using an isolated complex and the data show a much more stable
complex with very little free Mn2+ (aq) present at low pH (Figure 3.16).
84
Table 3.6. Formation constantsa for pre-formed [Mn(HxDOTA)]x-2, apparent
formation constants for [Mn(HxDOTP)]x-6, and pKa valuesb for Mn(II) containing
species (0.1 M KNO3, 37°C).
Species
Effective log β
pKa
a
(25.22 ±0.08)
[Mn(DOTP)]6[Mn(HDOTP)]5-
(33.85 ± 0.02)a
8.63 ± 0.08
[Mn(H2DOTP)]4-
(41.87 ± 0.01)a
8.02 ± 0.02
[Mn(H3DOTP)]3-
(48.95 ± 0.02)a
7.08 ± 0.02
[Mn(H4DOTP)]2-
(54.25 ± 0.02)a
5.30 ± 0.02
[Mn(H5DOTP)]-
(58.56 ± 0.03)a
4.31 ± 0.04
Mn(H6DOTP)
a
(62.58 ± 0.03)
a
4.02 ± 0.03
[Mn(H7DOTP)]+
(65.41 ± 0.08)
2.83 ± 0.09
(H2DOTP)6-
23.65
b
(H3DOTP)5-
32.59
8.94c (9.18)d
(H4DOTP)4-
40.1
7.51c (7.95)d
(H5DOTP)3-
45.85
5.75c (6.08)d
50.90
(H6DOTP)25.05c (5.20)d
a
Since there was a negligible amount of free Mn2+(aq) in the fit, the log β values for
[Mn(HxDOTP)]x-6 cannot be reliably determined from the titration (see text). bThis
pKa value is not known in this case because the log β value for (HDOTP)7- is not
included in the fit and are presented as “effective” log β values. cThis work. dFrom
titration results at 25 °C and 0.1M NMe4NO3.14
85
Figure 3.16. Speciation diagram of Mn-containing species for pre-formed
[Mn(HxDOTP)]x-6 at 7 mM according to the model in Table 3.6. A version with all
curves labeled is provided in Appendix B.
Table 3.7. Stability constants of three ligands with Mn(II)
Complex
[Mn(DOTAM)]2+
[Mn(DOTP)]6- pre-formed
[Mn(DOTA)]2-
86
log(K)
>22
25.22
20.42
The stability constant for [Mn(DOTP)]6- pre-formed (shown in Table 3.7) is
now greater than that of [Mn(DOTA)]2- which is consistent with results from the
Gd(III) comparison. This value is 15 orders of magnitude larger than the in-situ
complex and is best explained by the large differences in the log β values for the free
ligand (H8DOTP) which are likely a result of the different electrolytes used (NaCl
versus NMe4NO3). Since there was a negligible amount of free Mn2+ in the fit, the log
β values of [Mn(HxDOTP)]x-6 cannot be reliably determined from the titration. In
addition multiple chemical models were used to fit the data and are shown in
Appendix B. Only the model (Figure 3.16) that that is most consistent with all the
data (described below) is shown. Figure 3.16 is the diagram that should be used
because the conditions for the ligand and complex used in the titrations were the same
and the pre-formed complex is fully characterized. This diagram will be discussed in
detail along with the solution IR and relaxivity data in the following sections.
3.4 Infrared Spectroscopy
While potentiometric titration represents a powerful technique for determining
binding and protonation constants, it provides little direct insight into solution
structure. Standard NMR spectroscopic techniques give no structural information for
these complexes since they are strongly paramagnetic.
Solid and solution state IR spectroscopy, particularly of the C=O or P=O
stretching regions, provides a very short timescale probe of the protonation state of
87
the pendant arm functional group and thus, in combination with the potentiometric
data, constrains the solution structure to one or a very few possibilities.
Solid state IR spectra for the three complexes were obtained. The prominent
frequencies in the C=O or P=O stretching regions for the neutral ligands and their
Mn(II) complexes are given in Table 3.8.
Table 3.8. Solution and solid-state IR frequencies and assignments.
Solid-State
Frequency
(cm-1)
1678
1632 (sh)
1667
1618
1702
1636
1734
1573
1170
1080
Solution
Frequency
Species
Assignments
(cm-1)b
DOTAM
v(C=O)
1696
δ(NH2)
a
Mn(DOTAM)Cl2
v(C=O)
1642
δ(NH2)
a
H4DOTA
v(-COOH)
1727
v(-COO )
1584
Mn(H2DOTA)
v(-COOH)
1717
v(-COO )
1584
H8DOTP
v(-PO(OH)2)
1180
v(-PO2(OH) ) 1147
v(-PO3)21078
Mn(H6DOTP)
1150
v(-PO(OH)2)
1180
1032
v(-PO2(OH) ) 1150
v(-PO3)21080
a
Shifted out of the accessible range (see text). bD2O was used as the
solvent for DOTAM and DOTA and their Mn(II) complexes. H2O was used
for DOTP and its Mn(II) complex.
DOTAM shows a prominent peak at 1678 cm-1 with a shoulder at 1632 cm-1.
The peak corresponds to the C=O stretch of the amide group (amide I band), while
the shoulder may be assigned to an –NH2 bend (amide II band).16
88
Transmittance
DOTAM
4000
3500
3000
2500
2000
1500
1000
Wavelength (cm-1)
Transmittance
[Mn(DOTAM)]Cl2
4000
3500
3000
2500
2000
1500
1000
-1
Wavelength (cm )
Figure 3.17. Solid-state IR for DOTAM (top) and [Mn(DOTAM)]Cl2 (bottom).
89
For the [Mn(DOTAM)]Cl2 complex, the v(C=O) peak shifts to 1667 cm-1 and
the shoulder becomes a more distinct peak at 1618 cm -1. This result is consistent with
predominately ionic bonding between the manganese and the oxygen atoms and a
modest shift of electron density from nitrogen to the oxygen. Only one strong C=O
peak is observed, consistent with the equivalence of the four amide arms. The
shoulder is assigned to the amide NH2 bend (Table 3.8).
In D2O solution the [Mn(DOTAM)]2+ cation (Figure 3.18) exhibits a single
peak at 1642 cm-1 assigned as the C=O stretch. The NH2 bending modes observed in
the solid state are no longer observed, presumably shifted to lower frequency by
exchange of deuterium for hydrogen in the amide groups. The observation of a single
C=O stretching vibration in the IR suggests that the 8-coordinate solid state structure
is maintained in solution.
90
Relative Absorbance
[Mn(DOTAM)]2+
1800
1750
1700
1650
1600
1550
1500
cm-1
Figure 3.18. Solution IR of Mn(DOTAM)2+ in D2O.
In the neutral H4DOTA ligand, NMR studies17,18 have confirmed that two of
the acidic protons are located on two of the carboxylate oxygens and two are located
on ring nitrogens to which deprotonated pendant arms are attached (see Scheme 1.4).
This structure is reflected in the solid state IR spectrum of the free ligand (Figure
3.19), which exhibits two strong C=O stretching peaks of roughly equal intensity at
1702 cm-1 (-COOH) and 1636 cm-1 (-COO-). In addition, a strong N-H stretching
band is apparent at 3096 cm-1.
On coordination to the metal to form the Mn(H2DOTA) complex, the two
protons displaced by Mn2+(aq) are those on the ring nitrogens.19 The solid state IR
spectrum (Figure 3.20) exhibits two carbonyl peaks, one at 1734 cm-1 (-COOH) and
91
one at 1573 cm-1 (-COO-). No strong N-H stretching vibrations are apparent between
2400 and 3200 cm-1. The shifts of the peak frequencies relative to the free ligand can
be attributed to lattice effects, including hydrogen bonding to lattice water.4
Transmittance
H4DOTA-6H2O
4000
3500
3000
2500
2000
-1
Wavelength (cm )
Figure 3.19 Solid IR of DOTA
92
1500
1000
Transmittance
Mn(H2DOTA)-2H2O
4000
3500
3000
2500
2000
1500
1000
-1
Wavelength (cm )
Figure 3.20. Solid IR of Mn(H2DOTA)·2H2O
In the solution IR spectrum of Mn(H2DOTA) in D2O, peaks at 1717 and 1584 cm-1
vary in intensity depending on the pD of the solution as summarized in Figure 3.21.
An additional peak at 1630 cm-1 is present at low pD, but is replaced by a peak at
1616 cm-1 above pD 3.5. On the basis of previous assignments for similar species,20
the 1630 cm-1 peak is assigned to the free –COO- groups and the 1616 cm-1 peak to –
COO-
groups
coordinated
93
to
Mn(II)
[Mn(HxDOTA)]x-2
Relative Absorbance
pH=6.67
pH=1.69
1800
1750
1700
1650
1600
1550
1500
-1
cm
Figure 3.21. Top: Solution IR for Mn(HxDOTA)x-2 at high and low pH. Bottom:
Solution IR absorbance for the carboxylate C=O stretching bands as a function of pD
for Mn(HxDOTA)x-2 (= 1584 cm-1, = 1717 cm-1).
94
At pD values between 2 and 4, the peak at 1717 cm-1 is prominent in the spectra, but
disappears completely as the pD is raised above 4. The peak at 1584 cm-1 first appears
around pD 3 and rises in intensity reaching a limiting value above pD 6. These
solution IR bands correlate with the changes in the protonation state of the complex
from the speciation diagram (Figure 3.13). The peak at 1717 cm-1 is assigned to the
protonated carboxylates of the neutral free ligand and is consistent with the observed
pD dependence shown in Figure 3.21. This frequency is identical to that observed for
the free H4DOTA ligand in an acidic D2O solution. Similar arguments lead to the
assignment of the 1584 cm-1 peak to the C=O stretch of deprotonated COO- pendant
arms NOT bound to the metal ion. On the basis of previous assignments for similar
species,5 the 1630 cm-1 peak is assigned to the deprotonated –COO- groups of the free
ligand and the 1616 cm-1 peak to –COO- groups coordinated to Mn(II). The modest
shifts in frequencies relative to the solid state IR spectra can be attributed to the
changes due to the solvent, particularly hydrogen bonding, and may also involve
small H/D isotope effects on the frequencies. These assignments are fully consistent
with the speciation diagram derived from the model in Table 3.2. The low pH
spectrum corresponds to the neutral free ligand, H4DOTA, while above pD 6 the
spectrum corresponds to [Mn(DOTA)]2-.
The solid state IR spectrum of H8DOTP (Figure 3.22) exhibits peaks
corresponding to –PO(OH)2 groups (1170 cm-1) and -PO2(OH)- groups (1080 cm-1) as
expected from the X-ray crystal structure.21 pH-Dependent solution IR spectroscopy
of (HxDOTP)x-8
is similar to that previously reported.22 Under the conditions
95
employed in this work three peaks (at 1180, 1150 and 1080 cm-1) are present in
solution at pH values below 6 and have been assigned to P=O stretching modes of –
PO(OH)2, -PO2(OH)- and –PO32-, respectively.7,23,24
Transmittance
H8DOTP
4000
3500
3000
2500
2000
Wavelength (cm-1)
Figure 3.22 Solid IR of H8DOTP
96
1500
1000
Transmittance
Mn(H6DOTP)-3H2O
4000
3500
3000
2500
2000
1500
1000
-1
Wavelength (cm )
Figure 3.23. Solid IR of Mn(H6DOTP)·3H2O
On coordination to Mn2+, the general features of the P=O stretching region are
maintained and plots of absorbance vs pH shown in Figure 3.25 correlate the
protonation states to the speciation diagram in Figure 3.16. At low pH, peaks at 1180
cm-1, 1150 cm-1, and 1080 cm-1 are observed which are assigned to -PO(OH)2, –
PO2(OH)-, and -PO32- groups, respectively. As the pH is raised, the 1180 cm-1 band
decreases in intensity, and disappears completely above pH 6. Above pH 6 a peak at
1080 cm-1 (-PO32-) begins to increase in intensity as [Mn(H2DOTP)]3- begins to
dominate the speciation. Between pH 6 and 10, the 1150 cm-1 peak decreases in
97
intensity as the 1080 cm-1 peak grows. By comparison with Figure 3.16, changes in
this region correspond to the [Mn(H2/1/0DOTP)]4-/5-/6- equilibrium.
Relative Absorbance
[Mn(HxDOTP)]x-6
1500
1400
1300
-1
1200
1100
1000
cm
Figure 3.24. Solution IR absorbance for the phosphonate P=O stretching bands as a
function of pH for Mn(HxDOTP)x-6. Black = pH 1.23, red = pH 6.20, blue = pH 8.17
and pink = pH 10.15.
98
Figure 3.25. Solution IR absorbance for the phosphonate P=O stretching bands as a
function of pH for Mn(HxDOTP)x-6 (= 1080 cm-1, = 1150 cm-1, = 1180 cm-1).
These results, and the results of pH-dependent relaxivity measurements
(described in the next section and shown in Figure 3.26) suggest specific structural
assignments for some of the protonation states. The most chemically reasonable
structure for [Mn(DOTP)]6- is a six-coordinate metal ion with two bound
phosphonates. The first two protonations will most likely occur at the uncoordinated
phosphonates. Assuming that the six-coordinate geometry for Mn2+ is maintained,
there are two reasonable possibilities for the distribution of protons in
[Mn(H3DOTP)]3-. The complex could be formulated with one –PO32- group bound to
99
Scheme 3.4 Possibilities for the distribution of protons in [Mn(H3DOTP)]3-.
the metal and three –PO2(OH)- groups, one bound and two unbound to the metal.
Alternatively, there could be two bound –PO32- groups, one unbound –PO2(OH)-, and
one unbound –PO(OH)2 group. Electrostatic considerations suggest that –PO(OH)2
groups are unlikely to bind with significant strength to the Mn2+ ion and the IR
evidence described above indicates that there are no peaks for -PO(OH)2 until below
pH 5. Therefore, [Mn(H3DOTP)]3- which is present between pH 4 and 8 will likely
not have the structural assignment on the right of Scheme 3.4 with the –PO(OH)2
group. At pH 3.42, the complex exhibits its highest relaxivity. Upon protonation of
[Mn(H5DOTP)]- to [Mn(H6DOTP)], the relaxivities for both 1H and
17
O increase
significantly, which suggests a change in the number of bound waters, the water
exchange rate, and/or the coordination geometry (see below). There is, however, little
direct evidence regarding the geometry of the complex at low pH. One possibility
consistent with the large increase in both 1H and 17O relaxivity is the decomplexation
of a fully protonated phosphonate pendant arm and binding of a water molecule.
Alternatively, the fifth and sixth protonations could be occurring at the ring nitrogens
(similar to Scheme 3.1), displacing the Mn2+ from the ring, while remaining bound to
100
several of the phosphonate pendant arms. A similar protonation scheme and structural
change has been previously invoked to rationalize the pH dependent relaxivity of
GdDOTA-4AmP, a derivative containing acetamido methylenephosphonate pendant
groups.25 In the context of this structural possibility, several coordination sites for
water are made available, thus increasing the number of bound waters while
maintaining the overall [Mn(H5/6DOTP)]-/0 formulation.
3.5.1 1H and 17O Relaxivity Profiles
The combination of potentiometric titration and pH-dependent solution IR
spectroscopy provides a self-consistent description of the speciation in solution for all
three Mn(II) complexes. These models can be used to rationalize the very different
pH-dependent relaxivities in Figure 3.26 on the basis of changes in protonation state
and speciation. In each case an inflection in the relaxivity versus pH curve
corresponds to a change in proton content of the complex, although not every change
in protonation state is reflected by a change in relaxivity.
The following discussion aims to explain why the
1
H relaxivity for
[Mn(DOTAM)]2+ is pH-independent, for [Mn(HxDOTA)]x-2 there is a single large
change between pH 2 and 4, and for [Mn(HxDOTP)]x-6 there are multiple inflections
where in the pH range 2 to 3 the 1H relaxivity is greater than [Mn(H2O)6]2+.
The inner-sphere longitudinal 1H relaxivity of the complexes can be interpreted in
terms of Equation 3.1,26,27,28 where q
101


q
r1  1.814105 mM -1 

 T1M   M 


(3.1)
is generally taken as the number of coordinated water molecules, T1M is the
longitudinal relaxation time for the proton in the coordination sphere of the metal ion,
and M is the residence time of the water molecule in the inner sphere of the metal
ion. There may, however, be more than one pool of exchangeable protons that
contributes to the relaxivity or more than one mechanism for their chemical
exchange. This more general case can be described by Eqn 3.1. In Eqn 3.2, the sum
is over each pool of
r1  1.814  10  5 mM -1 
i
qi
i
i
T1M
M
(3.2)
102
Figure 3.26. pH-dependent 1H longitudinal relaxivities for [Mn(DOTAM)]2+ (top),
[Mn(HxDOTA)]x-2 (middle) and [Mn(HxDOTP)]x-6 (bottom) at 20 MHz and 37 ⁰C.
(N.B.: Error bars on some points are too small to display.)
exchanging nuclei and each independent exchange mechanism, qi is the effective
number of exchangeable protons of type i, and Ti1M and iM are the corresponding
relaxation and residence times.
103
A pH-dependent 1H relaxivity may reflect changes in any of the parameters in
Equation 3.2.
Changes in the proton residence time, iM, appear to be minor
contributors to the observed pH-dependent relaxivities at 20 MHz and 37°C since for
a variety of Mn(II) complexes similar to those under consideration, the denominator
of Equation 3.2 is dominated by the Ti1M term (described in the next section). The
value of Ti1M depends, in turn, on number of molecular parameters, including the
correlation times for electronic relaxation and rotational reorientation, as well as the
proton residence time,iM. The parameter most likely to dominate changes in Ti1M as
a function of pH, however, is rMn-H, the dynamically averaged distance between the
Mn(II) ion and the relaxing proton29 (see Section 3.5.2). The relaxivity of the
complexes as a function of pH should, therefore, reflect primarily changes in either
the effective hydration number, q, or the dynamically averaged Mn-H distance, rMn-H,
as given in Equation 3.3.
r1  
i
q i
6
rMn
Hi
(3.3)
3.5.2 Solomon-Bloembergen-Morgan Theory and the pH dependence of T1M
The most commonly invoked physical model for T1M of nuclei that are
exchanging with a paramagnetic center was developed by Solomon, Bloembergen,
and Morgan30 and is summarized in equations 3.4-3.7 below:
104
1
1M
T
1
 c1, 2
2
 3 c1
7 c 2 
2  o   I2 g 2  B2
 
S(S  1)


6
2 2
2 2 
15  4 
r
 1  I  c 1 1  s  c 2 

1
M

1
R

1
(3.4)
(3.5)
T1, 2 e
T1e1 


1 2
1
4

  V 4S(S  1)  3

2 2
2 2 
25
1



1

4


s V
s V 

(3.6)
T2e1 


1 2
5
2

  V 4S(S  1)  3 3 

2 2
2 2 
50
1



1

4


s V
s V 

(3.7)
Equation 3.4 includes only the dipolar contribution to T1M, since it dominates other
contributions.31 In Equation 3.4, o is the permeability of vacuum, I is the
gyromagnetic ratio for the nucleus of interest, g is the isotropic g value for the
paramagnet, B is the Bohr magneton, r is the distance between the paramagnet and
the relaxing nucleus, S is the spin of the paramagnet, c1,2 are correlation times
defined in Equation 3.5, and I and S are the Larmor frequencies of the relaxing
nucleus and the paramagnet, respectively, at the applied field strength. In Equation
3.5 M is the residence lifetime of the relaxing nucleus in the coordination sphere of
the paramagnet, R is the effective correlation time for molecular rotation, and T1,2e is
an electronic relaxation time defined in Equations 3.6 and 3.7. In Equations 3.6 and
3.7 2 is the mean-square zero field splitting energy and V is the corresponding
correlation time for modulation of the zero field splitting.
105
In terms of the origin of a pH-dependent T1M, the parameters that describe the
electronic structure (i.e., g, 2 , and V) are not expected to vary significantly with a
change in protonation state. While M is likely to be somewhat pH-dependent, for
small molecules at relatively low applied field values (such as those under
consideration here) the correlation times c1 and c2 are dominated by R (see Table
3.30). The rotational correlation time,R, in turn, is often modeled in terms of the
Stokes-Einstein-Debye relation32 in which the key molecular parameter is the
molecular volume, which is not expected to change significantly with the proton
content of the complex. Thus the parameter of T1M predicted to be most sensitive to
the protonation state is r, the distance between the paramagnetic nucleus and the
relaxing nucleus. Protonation generally induces structural changes, some of which
may be large, that lead to changes in r. Due to the sixth power dependence on r, T1M
is expected to be quite sensitive to these pH dependent structural changes.
For Mn2+ relaxing 1H (and assuming g ≈ ge) eqns 3.4, 3.6, and 3.7 become
7 c 2 
1  3 c1


6 
2 2
r  1  I  c1 1  s2 c22 

32 2 
1
4

T1e1 
  V 

2 2
2 2 
25
 1  s  V 1  4s  V 
T1M1  7.2925 10 45 ( m 6 s - 2 )
T2e1 
16 2 
5
2
  V  3 

2 2
25
1  s  V 1  4s2 V2




with S = 1.316 1010 s-1 and I = 2.00 107 s-1 at 20.0 MHz.
106
(3.8)
(3.9)
(3.10)
The parameters in Equations 3.4-3.7 have been determined for a number of relatively
small Mn(II) complexes through fitting of NMRD data at relatively low field
strengths and are compiled in Table 3.29. Table 3.30 gives calculated values for the
electronic relaxation times and correlation times of the complexes. Since the Mn-H
distances are not known for most of these cases, it was taken as 2.75 Å, the distance
in Mn2(ENOTA)(H2O)2.33 It is apparent from the data in Table 3.30 that at 20 MHz,
R dominates the correlation time for each of the complexes and only varies over a
relatively narrow range of values. R is thus likely to continue to dominate C as the
protonation state of a Mn(II) complex changes. It is further apparent that T1M is
several orders of magnitude larger than M under these conditions and dominates the
denominator of Equation 3.2 in the main text for all the complexes. With a change in
proton content for a typical Mn(II) complex, the parameters in Equations 3.4-3.10
should generally change less than the changes observed between different complexes
in Tables 3.29 and 3.30. Thus over the pH ranges reported in the main text, T1M
should remain much greater than M for [Mn(DOTAM)]2+, [Mn(HxDOTA)]x-2, and
[Mn(HxDOTP)]x-6. Likewise, T1M should be most sensitive to rMn-H as the protonation
state changes.
107
Table 3.29. Measured relaxation parameters for selecteda Mn(II) complexes.
kex
τM310K
τR
∆2
τv298
(x 107 s-1)
(x 10-10 s)
(x 10-11 s)
(x 1018 s-2)
(x 10-12 s)
Ref.a
[Mn(H2O)6]2+
2.10
273
3.00
5.6
3.3
34
[Mn(9-ane-N2O-2P)(H2O)]2-
1.20
437
10.30
60
30.7
35
[Mn(9-ane-N2O-2A)(H2O)2]2-
119
7.00
2.20
3.9
12.4
35
[Mn2(ENOTA)(H2O)2)]
5.50
127
2.60
4.7
7.7
33
[Mn[NODAHep)(H2O)]
2.70
247
8.40
70
60
36
[Mn(NODAHA)(H2O)]-
2.70
247
8.00
70
69
36
[Mn(NODABA)(H2O)]-
1.30
624
12.10
70
60
36
[Mn(12-pyN4A)(H2O)]-
303
3.00
2.30
40
8.7
37
Mn(12-pyN4P)(H2O)]-
177
4.00
3.86
302
14.3
37
[Mn(15-pyN3O2)(H2O)2]
0.38
1460
4.03
6.6
3.3
38
[Mn(15-pyN5)(H2O)2]
6.90
77.0
2.83
4.6
3.9
38
[Mn(EDTA)(H2O)]2-
47.1
17.0
5.70
69
27.8
39,40
[Mn(EDTA-BOM)(H2O)]2-
9.30
52.0
8.37
73
24.7
41
[Mn(EDTA-BOM2)(H2O)]2-
13.0
40.0
11.08
53
35.3
41
Mn(1,4-DO2A)(H2O)]-
113
9.00
4.60
481
4.4
40
40
[Mn(DO1A)(H2O)]596
2.00
2.20
128
13.9
a
Complexes selected from the compilation of references in Gale, E.M.; Zhu, J.; Caravan, P.J. J. Amer.
Chem. Soc. 2013, 135, 18600-18608.
108
Table 3.30. Calculateda relaxation parameters for complexes in Table 3.29
a
Calculated using the parameters in Table 3.29 in Eqns 3.4-3.10.
For [Mn(DOTAM)]2+, there are no protonation equilibria in the pH range 3 to
8 and the relaxivity is essentially pH-independent at 1.04 ± 0.03 mM-1s-1. This value
is consistent with, and has been previously assigned to,12 an essentially outer sphere
mechanism for relaxivity.43 The relatively low relaxivity has been rationalized on the
basis of the eight-coordinate geometry of the Mn(II) ion, which is coordinatively
saturated and cannot interact directly with water by an associative pathway. 12 In terms
of Equation 3.2, neither q (= 0) nor Ti1M changes significantly with the changes in pH.
For [Mn(HxDOTA)]x-2 and [Mn(HxDOTP)]x-6, the observed relaxivity vs pH
profiles were fit to expressions of the form given in Equation 2.2. The resulting
effective r1i values are reported in Table 3.9. Graphs showing the residuals for the
effective relaxivities are shown in Figure 3.27. For [Mn(HxDOTA)]x-2, both the fully
deprotonated (x=0) and mono-protonated species (x=1) have identical effective
109
relaxivities (2.3 mM-1s-1). This value is somewhat higher than that previously
reported in the literature42 for a complex of Mn(II) and H4DOTA, which was obtained
under different conditions. In this work, NMRD profiles were obtained at a
significantly lower temperature (25°C), at only one pH value (6.4), and on a mixture
of metal ion with excess ligand rather than a dissolved sample of the isolated
complex. The data in Table 3.9 suggest that both [Mn(DOTA)]2- and [Mn(HDOTA)]have the same coordination number in solution and that they both relax bulk water
protons by the same mechanisms, most likely by a combination of outer sphere and
transient water binding pathways. The relaxivity of Mn(H2DOTA) remained
indeterminate since its region of predominance is strongly correlated with the
decomplexation equilibrium and the relative contributions cannot be deconvoluted by
the fitting routine.
110
Figure 3.27. Measured r1 (black) and effective r1 (red) vs pH for
[Mn(HxDOTA)]x-2 (top) and [Mn(HxDOTP)]x-6 (bottom). The effective r1 values
were calculated from Equation 3.4.
111
The large inflection in the relaxivity vs pH curve corresponds to decomplexation of
the metal ion below pH 4 (see Figure 3.28). The increase in r1 is due to free
[Mn(H2O)6]2+ ions and the relaxivity below pH 2 is essentially identical to that of a
Mn(II) solution at the same concentration. This interpretation is supported by
measurements of
Figure 3.31.
17
17
O transverse relaxivities (r2) as a function of pH as shown in
O T2 values are sensitive to water exchange (as described in Section
1.9) and 1H relaxivities reflect contributions from both exchange
Table 3.31. Effective 1H relaxivities (20 MHz, 37°C) for Mn(HxDOTA)]x-2 and
[Mn(HxDOTP)]x-6 species.
Species
Effective r1 (mM-1s-1)
[Mn(DOTA)]22.32 ± 0.10
[Mn(HDOTA)]-
2.31 ± 0.29
Mn(H2DOTA)
a
[Mn(DOTP)]6-
1.61 ± 0.38
[Mn(HDOTP)]
5-
2.53 ± 0.84
4-
3.03 ± 0.60
3-
2.82 ± 0.36
2-
4.36 ± 0.61
[Mn(H2DOTP)]
[Mn(H3DOTP)]
[Mn(H4DOTP)]
[Mn(H5DOTP)]
2.64 ± 0.98
Mn(H6DOTP)
8.51 ± 0.48
[Mn(H7DOTP)]+
6.32 ± 0.26
-
a
Indeterminate, see text.
mechanisms.43,44 For example, [Mn(H2O)6]2+, for which water exchange is the
dominant relaxation mechanism, has a pH independent 17O r2 of 3326 ± 608 mM-1s-1
at 54.23 MHz and 23°C. Under the same conditions, [Cr(H2O)6]3+, which is
112
substitution inert and can only relax bulk water by prototropic exchange, has a much
lower 17O r2 average value of 471 ± 224 mM-1s-1 from pH 1.29 to 3.45.45 In general,
if the water residence time is longer than the proton residence time, then prototropic
exchange contributes to the overall relaxivity.
The 17O r2 of [Mn(DOTAM)]2+ has an average pH independent value 506.1 ±
600.7 mM-1s-1, comparable to that for [Cr(H2O)6]3+. This relatively small value for r2
is consistent with a small outer sphere contribution to the
the
17
17
O relaxivity. In contrast,
O r2 value for [Mn(HxDOTA)]x-2 is strongly pH-dependent. At high pH values
where only [Mn(DOTA)]2- is present, the
17
O relaxivity is very low, but larger than
that observed for [Mn(DOTAM)]2+. As the pH is lowered below 5, there is a large
increase in the 17O relaxivity, which parallels the increase in 1H r1 values. In addition,
at the lowest pH values the
17
O r2 value is very close to that for [Mn(H2O)6]2+
solutions. In terms of Equation 3.3, there is a large change in q as the ligand
decomplexes at low pH and Mn2+(aq) dominates the speciation.
Mn(H6DOTP) exhibits the most complex pH-dependent relaxivities of any of
the complexes. Figure 3.30 shows the 1H relaxivity data for the complex superim-
113
Figure 3.28. 1H relaxivity data superimposed on the speciation diagram for
[Mn(HxDOTA)]x-2 at 1 mM (red= Mn2+(aq), magenta=Mn(H2DOTA),
green=[Mn(HDOTA)]- and blue=[Mn(DOTA)]2-).
posed on its speciation diagram. (Note: This was chosen over the in-situ version or
Model 2 because the r1 data was acquired using the pre-formed complex, the solution
IR and
17
O/1H relaxivities can be more easily interpreted, and at pH 3 when there is
an r1 enhancement Model 2 (Appendix B) shows 100% Mn2+ which is not likely
given the stability constants and other data presented). Interpreted in terms of the
speciation diagram, it is clear that the relaxivity changes correlate with specific
changes in protonation states. Table 3.9 gives protonation state-specific relaxivities
obtained from fitting the observed relaxivities to the species distribution using
Equation 2.2.
114
The 1H relaxivity of [Mn(HxDOTP)]x-6 at the highest measured pH value (9.84) is low
(1.65 ± 0.18 mM-1s-1). These results are consistent with a relatively high coordination
number and little (or slow) direct water access to the metal site. The 17O relaxivity at
high pH is also low and thus consistent with this interpretation. The first inflection in
the 1H relaxivity occurs at pH 8.34 and correlates with the increased predominance of
[Mn(H2DOTP)]4-. The relatively small increase in r1 at pH 8.34 correlates with the
first protonation of a metal-bound –PO32- group. The increase in relaxivity is,
however, relatively modest and suggests that water access to the metal has been
enhanced giving rise to an effective increase in q and/or a small decrease in a
dynamically averaged metal-proton distance. The
17
O relaxivity also supports this
conclusion since the increase in 1H r1 is paralleled by a small increase in the
17
O r2
value.
An additional possible contributor to both the 1H and
17
O relaxivities is a
second coordination sphere effect46,47, which has been demonstrated both
computationally48,49 and experimentally25,50 for a number of complexes of Gd(III)
with phosphonate ligands. Second sphere effects arise from water molecules that are
not bound directly to the metal ion, but have an increased residence time relative to
bulk water. The increased residence time is most often ascribed to hydrogen bonding
interactions with ligand groups and a specific exchange mechanism has been
proposed for phosphonate-based pendant arms (see Appendix F for a diagram of this
mechanism).25 These contributions are generally treated with the same formalism as
inner sphere exchange, although the effect is usually much smaller. As described in
115
Sections 1.7-1.9 second-sphere mechanisms can contribute to the overall relaxivity. If
optimized maybe they can plan an even larger role.
One of the most significant features of phosphonates is exactly their ability to
form electrostatic interactions and extended networks of hydrogen bonds, which
stems from their hydrogen-bond donor and acceptor groups.5152
116
Figure 3.29. 17O r2 relative relaxivities in red and 1H r1 relative relaxivities in blue for
[Mn(DOTAM)]2+ (top), [Mn(HxDOTA)]x-2 (middle) and [Mn(HxDOTP)]x-6 (bottom).
Relaxivities are reported relative to the value for Mn2+(aq).
117
The amphoteric nature of the phosphonate arms allows for the exchange of protons
between the single bound water of the complex (or a proton on the ligand) and the
bulk water, and allows for a unique pH response that is both acid and base catalyzed.
Our data do not provide a means of distinguishing specifically between inner sphere
and second sphere exchange, but do support an interpretation of changing q and/or
rMn-H with changes in protonation state.
The largest inflection in the 1H relaxivities occurs as the pH is lowered below
5, near the [Mn(H6DOTP)]/[Mn(H5DOTP)]- predominance equilibrium. This pH
equilibrium represents the first pH at which a fully protonated –PO(OH)2 appears in
the solution IR spectrum.
Figure 3.30. Speciation diagram superimposed on the 1H relaxivity data for
[Mn(HxDOTP)]x-6 (gray=[Mn(DOTP)]6-, light blue=[Mn(HDOTP)]5-, magenta=
[Mn(H2DOTP)]4 -, gold=[Mn(H3DOTP)]3-, green= [Mn(H4DOTP)]2-,
blue=
118
[Mn(H5DOTP)]1-,
olive=Mn(H6DOTP),
purple=[Mn(H8DOTP)]2+).
There is a simultaneous increase in
17
cyan=[Mn(H7DOTP)]+
and
O r2 values, indicating an increase in water
access to the metal ion. These results may reflect a weakening of phosphonate
binding to the metal ions as the overall protonation of the complex increases or a
change in structure resulting in a loss of Mn(II) from the ring (see above). The trends
in 1H and
17
O relaxivities in this region are different, however. The
17
O relaxivity
never exceeds that of [Mn(H2O)6]2+, while the 1H relaxivity is greater than that of
[Mn(H2O)6]2+ in the pH range 2 to 3. In particular, the effective relaxivity of
Mn(H6DOTP) is 8.51 mM-1s-1. According to the speciation diagram in Figure 3.16,
there is a negligible amount of [Mn(H2O)6]2+ present in this range and the complex
remains intact. Since the 1H and
17
O relaxivities for Mn(H6DOTP) is significantly
higher than those for the other species, water must have much better access to the
metal in Mn(H6DOTP). In addition, the observation that the 1H relaxivity is higher
than that for [Mn(H2O)6]2+ while the
17
O relaxivity is not implies that there is a
significant prototropic exchange pathway in addition to a water exchange pathway
that contributes to the overall observed 1H relaxivity. At even lower pH values, the 1H
relaxivity decreases and reflects contributions from higher protonation states.
Interpreted in terms of Equation 3.3, the evidence is consistent with the addition of a
significant new exchange pathway (prototropic exchange) as the pH is lowered in
addition to an increase in the effective q.
119
It has been previously noted that the maximum second sphere contribution to
1
H relaxivity for phosphonate pendant arms appears to occur when half of the
phosphonates are in the conjugate acid form and half are in the conjugate base form.
Thus the large prototropic exchange contribution in the Mn(H6DOTP) complex can
be rationalized in terms of a phosphonate-promoted second sphere prototropic
exchange at a coordinated water molecule (Appendix F).
3.6 Conclusion
The models for the speciation and relaxivities of the three Mn(II) complexes
described above are consistent with the experimental evidence. When more than one
chemically reasonable speciation model fits experimental titration data, other
techniques (in this case, pH-dependent solution IR spectroscopy) must be employed
to narrow the possibilities to one or a few that are consistent with all the data. A
reliable speciation diagram may then provide the basis for assigning species-specific
values for relaxivities.
The three complexes display distinctly different pH-dependent relaxivity
profiles that are related to changes in protonation state and to the binding constants
for the complexes. The differences may be ascribed to the pKa values of the pendant
arm functional groups, with amides providing the apparently most stable binding and
carboxylates the least stable binding at low pH. In contrast to the carboxylates, the
phosphonate pendant arms may exist in one of three different protonation states,
giving rise to the more complex pH dependence of the complex.
120
These conclusions suggest some general design principles for potential
contrast agents based on Mn(II). For example, it appears that amide pendant arm
functional groups impart significant stability to the complex at physiological pH
values while carboxylates provide pH-dependent coordinating ability.
The
phosphonates also appear to enhance overall stability and may provide sites for
enhanced hydrogen bonding to the bulk water and prototropic exchange.
The
development of cyclen-based ligands with mixed types of pendant arms may provide
complexes that can incorporate several of these properties and experiments are
currently underway exploring variants of the ligands described here.53
[Mn(DOTAM)]2+, Mn(H2DOTA), and Mn(H6DOTP) are unlikely to be
directly useful as clinical contrast agents. Their thermodynamic and kinetic stabilities
under physiological conditions, as well as their toxicities have yet to be investigated.
In addition, their relaxivities at physiological pH are much lower than those of the
established Gd(III) contrast agents. These complexes do, however, provide insights
into the types of chemical mechanisms that can contribute to relaxivities in a series of
complexes of structurally similar ligands. The results described suggest that new,
more promising candidates may be found by incorporating multiple functionalities
into the ligand to provide both thermodynamic stability and pH-responsiveness. The
possibility of designing new systems that exhibit both enhanced prototropic exchange
and water exchange pathways for relaxivity provides the basis for a chemical
approach to achieving higher relaxivities for Mn(II) complexes.
121
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with excess ligand rather than a dissolved sample of the isolated complex.
43
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50
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Cyclic Tetra-Aza Tetraacetic Acids.Talanta, 1992, 39, 249-254.
53
SAH Manuscript in Preparation
124
Chapter 4
Future Directions
125
The following experiments are not yet complete and provide interesting
results worth investigating further: The comparison of the pH-dependent r2 and r1
values for [Mn(HxDOTA)]x-2, [Mn(HxDOTP)]x-6 and Mn(H2O)62+ and the kinetic
isotope effect of the relaxation times of [Mn(H2O)6]2+ and of [Cr(H2O)6]3+.
4.1 R2 and R1 pH-Dependence Comparison
In solution, the rotational motion of water molecules will be temperature
dependent. Most water molecules (bulk water) will be rotating very rapidly. However,
some water molecules will be rotating relatively slowly as they will be relatively
fixed in orientation; either bound directly to the metal center or locked in a secondsphere or hydrogen-bonded network.
When water molecules are fixed in orientation the local magnetic field is
different from the B0.1 Protons in this vicinity therefore, will precess at a slightly
different frequency (local field inhomogeneity). This results in dephasing of
transverse magnetization. This causes the fixed water molecules to cause a T2
relaxation.1 Only when there is a large number of fixed water molecules will there be
significant T2 shortening (with no effect on the T1) like in large molecules or when
there is aggregation.2 In fact the r2 and r1 1H relaxivities for Mn(HxDOTA)]x-2 and
Mn(HxDOTP)]x-6 are pH-dependent. And the following shows how hydrogen-bonding
networks (second-sphere effects discussed in Section 1.9 and 3.5) can possibly play a
role at low pH to slow down the rotational motion and increase r2.
126
r1
30
r2
25
r1,2 (mM-1s-1)
20
15
10
5
0
2
4
6
8
10
12
pH
Figure 4.1. The comparison of r2 and r1 1H relaxivities for Mn(HxDOTA)]x-2 at
7mM, 37 ºC and 20 MHz.
Figure 4.1 shows the comparison of the longitudinal and transverse
relaxivities for Mn(HxDOTA)]x-2 as a function of pH. Below pH 4 the r2 values are
much higher than the r1 values and above pH 4 the r1 and r2 values are the same.
Figure 4.2 shows the comparison of the longitudinal and transverse
relaxivities for Mn(HxDOTP)]x-6 as a function of pH. Below pH 6 the r2 values are
much higher than the r1 values and above pH 6 the r1 and r2 values are the same.
Both Mn(HxDOTA)]x-2 and Mn(HxDOTP)]x-6 show a pH-dependence in the
R2/R1 ratio. Although R2/R1 ratios were not explicitly calculated, one can see the
127
difference at low pH compared to high pH. It should be noted that the T2 values for
H2O have a pH-dependence3 and all future work should include this analysis.
Interestingly, [Mn(H2O)6]2+ does not show a pH-dependence for this r2 and r1
comparison. This might not be the case however, when the T2 values for water as a
function of pH are measured and subtracted. The r2 value is constant at 32 mM-1s-1
and the r1 value is constant at 7.00 mM-1s-1.
If in fact, the pH-dependence of the ratio for Mn(HxDOTA)]x-2 and
Mn(HxDOTP)]x-6 are not a result of a change in rotational correlation time as a
function of pH, then it is likely due to a change in the coordination number and/or the
protonation state of the complex. This is because of the result for [Mn(H2O)6]2+,
where the data does not change as a function of pH. [Mn(H2O)6]2+ has a constant
coordination number and protonation state in solution, if its data does not change then
this suggests that there is something going on with Mn(HxDOTA)]x-2 and
Mn(HxDOTP)]x-6 .
128
50
r1
r2
40
r1,2 (mM-1s-1)
30
20
10
0
1
2
3
4
5
6
7
8
9
10
pH
Figure 4.2. The comparison of r2 and r1 1H relaxivities for Mn(HxDOTP)]x-6 at 7mM,
37 ºC and 20 MHz.
129
50
r1
r2
45
40
r1,2 (mM-1s-1)
35
30
25
20
15
10
5
1.5
2.0
2.5
3.0
3.5
4.0
pH
Figure 4.3. The comparison of r2 and r2 1H relaxivities for Mn(H2O)62+ at 37 ºC, 7
mM and 20 MHz.
4.1.2 Relaxation Time as a Function of Concentration for Mn(H6DOTP)
Because the relaxivity of Mn(H6DOTP) was higher than that of free Mn2+ (aq)
at low pH it was first thought that maybe there was a change in the rotational
correlation time as a result of aggregation. Specifically because after the R2/R1 ratio
was analyzed, the likely cause of the difference is a change in the rotational
correlation time.
130
Figure 4.4. Taken from “Spin-Dynamics”4 showing the variation of T1 and T2 with
correlation time, for intramolecular dipole-dipole relaxation.
As demonstrated in Figure 4.4, at very short rotational correlation times, the
values of T1 and T2 are equal. This is called the extreme narrowing limit5. As the
correlation time increases, these values become very different. For this reason it was
thought that maybe Mn(HxDOTP)]x-6 at low pH was aggregating and causing an
increase in relaxivity. It should also be noted that this prediction says that the
reciprocal of the relaxation times should be 1/T1 ≤ 1/T2 which means r2 would be
greater than r1. This was in fact observed in the data shown in Figures 4.1 and 4.2 at
low pH.
Therefore the relaxation time (1/T1) as a function of concentration at low pH
was analyzed (slope equals r1 based on Equation 1.3). If the relationship is linear then
131
this rules out aggregation. If the high relaxivity at low pH were due to aggregation,
the increase in aggregate would give the higher relaxivity. When the concentration of
complex is increased, then the amount of aggregate formed is also increased. This
would result in a relaxivity that would increase with concentration faster than the
relationship in Equation 1.3. Figure 4.5 shows that in fact this relationship is linear,
which rules out aggregation based on this concept. This is possibly because of all the
charge present on the phosphonates. Although, the previously published complex has
a lot of charge and “aggregates” in the solid-state, the presence of these charges can
invoke an extended hydrogen bond network facilitating the proton transfer effects
(discussed in Sections 1.9 and 3.5) in solution.
The 1/T2 relaxation times should in fact be investigated as a function of
concentration as well. If it is the 1/T2 that is in fact increased by this effect for the
molecules herein, then the transverse relaxation time (1/T2) should be studied as a
function of concentration.
132
60
50
1/T1 (s-1)
40
30
20
10
0
0
1
2
3
4
5
6
7
8
[mM]
Figure 4.5. The reciprocal longitudinal relaxation times of [Mn(HxDOTP)]x-6 at pH
1.43 and 7 mM as a function of concentration. (Black squares are initial values and
red circles are one week later.)
The slope of the graph in Figure 4.5 gives the relaxivity of the complex which
are 7.68 mM-1s-1 and 8.35 mM-1s-1 for the initial and 1 week later linear fits
respectively (both fits having an R2 value of 0.999 demonstrating a good fit to data).
Both are larger than free Mn2+ (aq) which shows the reproducibility of the fact that
the relaxivity is higher than the free metal ion at low pH. The increase in relaxivity
over time should also be investigated further to determine how stable the complex
really is at low pH.
133
4.2 Kinetic Isotope Effect
In order to help distinguish between water exchange and prototropic exchange
further, the kinetic isotope effect of the relaxation times of [Mn(H2O)6]2+ which is
dominated by water exchange and of [Cr(H2O)6]3+ which is substitutionally inert and
dominated by prototropic exchange was performed. This would then eventually be
extended towards the complexes studied in Chapter 3. Melton and Pollak6 have
studied the proton spin relaxation and exchange properties of hydrated chromic ions
in H2O and H2O-D2O mixtures and found an increase in viscosity when adding D2O.
Their work should be considered with any further investigation of this kinetic isotope
effect study.
Kinetic isotope effect measurements were determined at 400 MHz for protons
(1H) in 1% H2O in D2O or 61.4 MHz for deuterons (2H) in 1% D2O in H2O at 0.1 mM
concentration of [Mn(H2O)6]2+ and [Cr(H2O)6]3+. 2H is also a quadrupole nucleus like
17
O so the T2 values were experimentally measured similarly to that of the
17
O
measurements.
It was expected, that for [Mn(H2O)6]2+ there will be a smaller isotope effect.
The R2(D) relaxivity values are not affected much by the additional weight of
deuterium. The mass of water (18 g/mol) is not much different when substituted to
2
H2O (20 g/mol). However, there will likely be a larger effect for proton (1H)
exchange (1 g/mol) when substituted for a 2H (2 g/mol). This 100% mass increase
should slow down the exchange rate a lot and decrease the value of R2(D) and make
134
the R2(H)/R2(D) ratio very large. It should be noted however, that more factors go
into an R2 value than just the exchange rate (Equations 4.1 and 4.4). For
[Mn(H2O)6]2+ there should not be much of a difference in the R2(H) and R2(D) values
and its ratio should be close to 1.
Table 4.1. T2 comparison for [Mn(H2O)6]2+ and [Cr(H2O)6]3+
Solvent
T2 (s) Proton (1H)
1.48 ± 0.06
T2 (s) Deuteron (2H)
0.297 ± 0.031
[Mn(H2O)6]2+
0.021 ± 0.001
0.201 ± 0.008
[Cr(H2O)6]3+
0.107 ± 0.001
0.181 ± 0.011
Table 4.2 Relaxivity comparison [Mn(H2O)6]2+ and [Cr(H2O)6]3+
R2(H)
[Mn(H2O)6]2+ (mM-1s-1)
469
[Cr(H2O)6]3+ (mM-1s-1)
86.7
R2(D)
16.1
21.5
R2(H)/R2(D)
29.2
4.03
The results in Tables 4.1 and 4.2 show the opposite to be true. The
R2(H)/R2(D) ratio for [Mn(H2O)6]2+ is 29.2 and for [Cr(H2O)6]3+ is 4.03. This is,
however, preliminary data that shows they are at least very different.
135
One of the key concerns with this approach is that kinetic isotope effects are
not addressed in the SBM theory for relaxation and protons do not have an electronic
quadrupole moment.
If instead we look at this in terms of rates of exchange and realize that the
relaxivity terms for each isotope are:
R2 ( H ) 
cH qH
(4.1)
T2 m   H
H
and
R2 ( D) 
cD qD
(4.2)
T2 m   D
D
where c H , D are the molar concentrations of hydrogen and deuterium, q H , D are the
number of bound water molecules or protons, T2 m
H ,D
is the transverse relaxation time
of the bound water or proton and  H , D is the rate of exchange. The denominator in
Equations 4.1 and 4.2 show the terms for T2 m
H ,D
and  H , D . If we want to compare
this in terms of rates of exchange then taking R2(D)/R2(H) and solving for  H , D gives
Equation 4.3:
 D RH  c D q D  RDT2 m

 H RD  c H q H  RH T2 m H
D




(4.3)
136
In future work Equation 4.3 can be used as long as T2 m
H ,D
can be determined
for both [Mn(H2O)6]2+ and [Cr(H2O)6]3+ as long as m is small enough to be
2
ignored according to Equation 4.4 from the Swift-Connick equations7.
2
1
2
1
1 T2 m   m T2 m  m

T2
 m  m 1  T2 m 1 2  m 2

2
(4.4)

According to Equation 4.5 m depends largely on the hyperfine coupling
constant (A0/  ).
 m 
g L  B S ( S  1) B A0
3k BT

(4.5)
Hyperfine interactions between nuclear spin and electron spin play a key role
in the description of NMR relaxation of ligand nuclei in solution of paramagnetic
species.8 It has been reported that the scalar contribution to 1H relaxivity is
responsible for a non-negligible part of the inner-sphere contribution to relaxivity in a
few Mn(II) complexes such as [Mn(H2O)6]2+.9,10 Because most Mn(II) complexes lack
a significant scalar contribution to relaxivity, which is directly correlated with the
hyperfine coupling constant, then it is reasonable to say that m is small enough to
2
be ignored.
In addition, it is possible that more than transverse relaxivities will be needed
to answer this question. The rates of exchange for 1H and 2H can be observed as a
function of temperature (chemical shifts) or frequency just like with 17O11. Also, 17O
137
NMR data provide information on the water exchange kinetics of the complex, and
depend on the hyperfine coupling constant8 described above.
4.3 Temperature-Dependent 17O Transverse Relaxivities
Knowledge of the hydration state of these complexes in aqueous solution
would be very useful in narrowing down the solution structure and confirming the
proposed changes in relaxivity of each. Caravan et. al.12 have developed a simple
method to estimate the inner-sphere hydration state (number of water molecules) of
the Mn(II) ion in coordination complexes. The line width of bulk H217O is measured
in the presence and absence of Mn(II) as a function of temperature, and transverse
17
O relaxivities are calculated. It is demonstrated that the maximum 17O relaxivity is
directly proportional to the number of inner-sphere water ligands (q).
4.4 Conclusion
The comparison of r2 and r1 values and the kinetic isotope effect are very
complex problems worth further investigation.
Both Mn(HxDOTA)]x-2 and Mn(HxDOTP)]x-6 show a pH-dependence in their
r2/r1 ratios which could reflect changes in the rotational correlation times.
[Mn(H2O)6]2+ does not show a pH-dependence for this r2 and r1 comparison.
[Mn(H2O)6]2+ r1 as a function of concentration at low pH was done to test the
138
aggregation theory and results showed it is not likely. If in fact, the pH-dependence of
the ratio for [Mn(HxDOTA)]x-2 and [Mn(HxDOTP)]x-6 are not a result of a change in
rotational correlation time as a function of pH, then it is likely due to a change in the
coordination number and/or the protonation state of the complex. This is because of
the result for [Mn(H2O)6]2+, where the data does not change as a function of pH.
[Mn(H2O)6]2+ has a constant coordination number and protonation state in solution, if
its data does not change then this suggests that there is something going on with
[Mn(HxDOTA)]x-2 and [Mn(HxDOTP)]x-6. More work needs to be done towards this
experiment, including a detailed study of the relaxation times (T1 and T2) of pure deionized water as a function of pH and an experiment showing r2 as a function of
concentration at low pH for [Mn(HxDOTP)]x-6.
A kinetic isotope effect study was performed in order to further distinguish
relaxivity contribution of water exchange and prototropic exchange. [Mn(H2O)6]2+
and [Cr(H2O)6]3+ show interesting and opposite than expected R2(H)/R2(D) values.
Much further work is needed to help solve why. Including further analysis of
Equation 4.3.
139
References
Smith R.C.; Lange R.C. Understanding Magnetic Resonance Imaging. CRC Press:
1998.
2
Wild, J.M.; Woodrow, J.; van Beek, E.J.R.; Misselwitz, B.; Johnson, R. Evaluation
of rHA Labeled with Gd-DTPA for Blood Pool Imaging and Targeted Contrast
Delivery. Contrast Media Mol. Imaging 2010, 5, 39-43.
3
Meiboom, S.; Luz, Z.; Gill, D. Proton Relaxation in Water. J. Chem. Phys. 1957, 27,
1411-1412.
4
Levitt, M.H., Spin Dynamics: Basics of Nuclear Magnetic Resonance, Wiley 2008.
5
Brainard, J.R.; Szabo, A. Theory for Nuclear Magnetic Relaxation Probes in
Anisotropic Systems: Applications of Cholesterol in phospholipid vesicles.
Biochemistry, 1981, 20, 4618-4628.
6
Melton, B.F.; Pollak, V.L. Proton Spin Relaxation and Exchange Properties of
Hydrated Chromic Ions in H2O and H2O-D2O Mixtures. J. Phys. Chem. 1969, 75,
3669-3679.
7
T.J. Swift and R.E. Connick, J. Chem. Phys., 1962, 41, 2553.
8
Esteban-Gomez, D.; Cassino, C.; Botta, M.; Platas-Iglesias, C. 17O and 1H
Relaxometric and DFT Study of Hyperfine Coupling Constants in [Mn(H2O)6]2+ RSC
Adv. 2014, 4, 7094-7103.
9
Balogh, E.; He, Z.; Hsieh, W.; Liu, S.; Toth, E. Dinuclear Complexes Formed with
the Triazacyclononane Derivative ENOTE4-: High-Pressure 17O NMR Evidence of an
Associate Water Exchange on [MnII2(ENOTA)(H2O)2] Inorg. Chem. 2007, 46, 238250.
10
Bertini, I.; Briganti, F.; Xia, Z.; Luchina, C. Nuclear magnetic Relaxation
Dispersion Studies of Hexaaquo Mn(II) Ions in Water-Glycerol Mixtures, J. Magn.
Reson. 1993 101, 198-201.
11
Merbach, A.; Toth, E. The Chemistry of Contrast Agents in Medical magnetic
Resonance Imaging, John Wiley & Sons, Ltd: New York, 2001 p. 39-41.
12
Gale, E.M.; Zhu, J.; Caravan, P. Direct Measurement of the Mn(II) Hydration State
in Metal Complexes and Metalloproteins through 17O NMR Line Widths. J. Am.
Chem. Soc. 2013, 135, 18600-18608.
1
140
Appendix A- Models that fit to the titration data for [Mn(HXDOTA)]x-2
After stability constants were determined in HyperQuad, they were imported
in the program Hyss for generation of speciation diagrams. Hyss uses the stability
constants to determine the species present versus pH. The following models fit the
titration data.
Model 1 is the same model found in the literature. It does not include the
MnH2DOTA species. There is crystallographic evidence for the existence of
MnH2DOTA, so its omission may result in an incomplete model. Model 2 is a general
stepwise protonation model that includes the free ligand (fixed values for the ligand
are shown in the table below). This model is based on intuitive chemical reasoning.
The free ligand is included to account for the possibility of free Mn2+. Model 3 is
based on a cooperative 2-proton system for the deprotonation of the metal-ligand
complex, where the MnH3DOTA species is converted directly to [MnDOTA]2-,
without the [MnHDOTA]- intermediate. Model 4 does not include free ligand, only
species bound to manganese. This model is a test for the possibility that no free Mn2+
exists at any pH. Given that free Mn2+ may be the reason for the pH-dependent
relaxivity displayed by MnHxDOTA, it is of interest to test this model.
141
Species
Model 1
Model 2
Model 3
Model 4
HDOTA
12.04 ± 0.135
12.04 ± 0.135
12.04 ± 0.135
−−−−
H2DOTA
22.57 ± 0.0698
22.57 ± 0.0698
22.57 ± 0.0698
−−−−
H3DOTA
26.94 ± 0.113
26.94 ± 0.113
26.94 ± 0.113
−−−−
H4DOTA
30.44 ± 0.130
30.44 ± 0.130
30.44 ± 0.130
−−−−
MnDOTA
19.03 ± 0.0691
20.42 ± 0.0671
21.35 ± 0.217
22.14 ± 0.0596
MnHDOTA
23.44 ± 0.0181
24.31 ± 0.0372
−−−−
25.59 ± 0.245
27.54 ± 0.107
28.41 ± 0.279
28.84 ± 0.198
MnH2DOTA −−−−
All speciation diagrams below were consistent with the titration data:
Model 1
M nDOT A
100
% formation relative to Mn
Mn
MnDOTA
80
60
MnDOTAH
40
20
0
0
2
4
pH
6
142
8
Model 2
MnDOTA
100
MnDOTA
Mn
% formation relative to Mn
80
60
40
MnDOTAH
20
MnDOTAH2
0
2
4
6
8
pH
Model 3
MnDOTA
100
Mn
% formation relative to Mn
80
MnDOTA
60
40
20
MnDOTAH2
0
2
4
6
pH
143
8
Model 4
MnDOTA
100
MnDOTA
% formation relative to Mn
80
MnDOTAH2
60
40
20
MnDOTAH
0
2
4
6
8
pH
Figures of the fits of the four models:
Blue diamonds indicate the titration data points. The red dashed line represents the
calculated values from the fit. Red diamonds indicate titration data that were not
included in the fit since only one species is present. The important data for an
equilibrium constant determination represent a mixture of at least two species, so only
those points are included in the refinement. Solid lines refer to the percent formation
of the species indicated by the legend to the right of the figure.
144
Model 1
Mn2+
[MnHDOTA][MnDOTA]2-
Model 2
Mn2+
MnH2DOTA
[MnHDOTA][MnDOTA]2-
Model 3
145
Mn2+
MnH2DOTA
[MnDOTA]2-
Model 4
MnH2DOTA
[MnHDOTA][MnDOTA]2-
146
Appendix B- Models Used to Fit Pre-Formed [Mn(HxDOTP)]x-6 Titration Data
The following chemically reasonable models were used to fit the titration data
of the pre-formed complex.
Equilibrium equations for [Mn(HxDOTP)]x-6.
2+
8-
6-
1) Mn + DOTP = Mn(DOTP)
2) Mn2+ + DOTP8- + H+ = Mn(HDOTP)53) Mn2+ + DOTP8- + 2H+ = Mn(H2DOTP)44) Mn2+ + DOTP8- + 3H+ = Mn(H3DOTP)35) Mn2+ + DOTP8- + 4H+ = Mn(H4DOTP)26) Mn2+ + DOTP8- + 5H+ = Mn(H5DOTP)7) Mn2+ + DOTP8- + 6H+ = Mn(H6DOTP)
8) Mn2+ + DOTP8- + 7H+ = Mn(H7DOTP)+
9) DOTP8- + H+ = (HDOTP)710) DOTP8- + 2H+ = (H2DOTP)611) DOTP8- + 3H+ = (H3DOTP)512) DOTP8- + 4H+ = (H4DOTP)413) DOTP8- + 5H+ = (H5DOTP)314) DOTP8- + 6H+ = (H6DOTP)215) DOTP8- + 7H+ = (H7DOTP) 16) DOTP8- + 8H+ = H8DOTP
x 6
In each case,  (MnH x DOTP ) 
and  (Hx DOTP
x 8
Model 1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Model 2
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
[MnH x DOTP x 6 ]
,
[Mn 2 ][H  ]x [DOTP 8- ]
[H x DOTP x-8 ]
)  x
[H ] [DOTP 8- ]
Model 1 is a general stepwise protonation model that includes all protonation states of
the complex as well as of the free ligand up to H8DOTP.
Model 2 is similar to Model 1 except for the exclusion of Mn(H7DOTP)+.
147
Each model gives an acceptable fit to the titration data and the logβ values obtained
are reported in Table ii.
Table B1. Log β values for fits of [Mn(HXDOTP)]x-6 titration data to the models
described above.
Species
Model 1
Model 2
6a
Mn(DOTP)
25.22 ± 0.08
21.63 ± 0.02
Mn(HDOTP)533.85 ± 0.02
30.26 ± 0.02
4Mn(H2DOTP)
41.87 ± 0.01
38.29 ± 0.02
Mn(H3DOTP)348.95 ± 0.02
45.35 ± 0.01
2Mn(H4DOTP)
54.25 ± 0.02
50.58 ± 0.01
Mn(H5DOTP)
58.56 ± 0.03
b
Mn(H6DOTP)
62.58 ± 0.03
b
+
Mn(H7DOTP )
65.41 ± 0.08
------------(H2DOTP)628.78
28.78
5(H3DOTP)
37.84
37.84
4(H4DOTP)
45.46
45.46
(H5DOTP)351.31
51.31
2(H6DOTP)
56.28
56.28
a. For Model 1, negligible amounts of Mn2+ are present. Thus the values of logβ
cannot be accurately determined from the titration data, but differences in logβ values
correspond to pKa values for the complex. b. Species not present in high enough
concentration to give a reasonable value.
148
Figures of the fits of the models:
Blue diamonds indicate the titration data points. The red dashed line represents the
calculated values from the fit. Solid lines refer to the percent formation of the species
indicated by the legend to the right of the figure.
Model 1
MnDOTPtitration2
100
80
70
60
pH
8
50
40
6
30
20
% formation relative to Mn
10
Mn2+
Mn(H7DOTP)+
Mn(H6DOTP)
Mn(H5DOTP)Mn(H4DOTP)2Mn(H3DOTP)3Mn(H2DOTP)4Mn(HDOTP)5Mn(DOTP)6-
% formation relative to Mn
90
Mn2+
Mn(H6DOTP)
Mn(H5DOTP)Mn(H4DOTP)2Mn(H3DOTP)3Mn(H2DOTP)4Mn(HDOTP)5Mn(DOTP)6-
10
4
0
Obs-calc pH
for selected
data.
sigma=2.7261
Volume
of base
added
0.2
0.1
0
-0.1
-0.2
Model 2
MnDOTPtitration2
100
0
2
10
4
titre volume
6
8 90
80
70
60
pH
8
50
40
6
30
20
10
4
0
Obs-calc pH for selected data. sigma=1.4866
Volume of base added
0.2
0.1
0
-0.1
-0.2
0
2
4
titre volume
149
6
8
Speciation Diagrams for the Models in Table B1.
Model 1
Model 2
150
Appendix CMeasured 1H longitudinal relaxation times (T1) , 20 MHz, 37°C
[Mn(DOTAM)]2+ (3.56
mM)
pH
T1 (ms)
2.51
245 ± 9
4.26
281 ± 1
5.40
264 ± 4
6.79
246 ± 5
8.57
230 ± 4
2.51
245 ± 9
[Mn(HxDOTA)]x-2 (1.00
mM)
pH
T1 (ms)
1.55
139.6 ± 0.3
1.69
144 ± 1
1.79
139.8 ± 0.7
1.90
138.7 ± 0.3
1.99
142.3 ± 0.3
2.05
139 ± 1
2.19
140 ± 1
2.29
141.7 ± 0.8
2.42
145.4 ± 0.7
2.48
151 ± 2
2.56
159 ± 1
2.64
171 ± 2
2.74
194 ± 2
3.07
270 ± 1
3.29
300.2 ± 0.4
3.36
316 ± 2
3.43
323.2 ± 0.7
3.52
331.3 ± 0.9
3.61
348 ± 2
3.72
359.2 ± 0.8
3.83
369 ± 4
3.84
376 ± 1
3.97
370.3 ± 1
4.31
389 ± 2
4.32
370 ± 1
4.39
394 ± 4
5.00
378 ± 5
6.02
366 ± 2
6.58
388 ± 2
7.50
399 ± 2
151
[Mn(Hx DOTP)]x-6
(7.00 mM)
pH
T1 (ms)
1.04
22.70 ± 0.03
2.02
21.13 ± 0.04
2.34
20.54 ± 0.05
2.70
20.12 ± 0.03
3.00
19.93 ± 0.04
3.42
19.72 ± 0.09
3.60
20.62 ± 0.04
3.81
24.13 ± 0.07
3.95
23.45 ± 0.03
4.06
33.57 ± 0.08
4.42
29.84 ± 0.05
5.02
36.58 ± 0.07
5.21
39.0 ± 0.1
5.50
48.7 ± 0.4
6.02
44.1 ± 0.1
6.39
46.4 ± 0.1
6.80
47.3 ± 0.2
6.98
47.2 ± 0.1
7.49
49.0 ± 0.1
7.75
53.28 ± 0.07
8.46
58.6 ± 0.1
8.90
70.5 ± 0.2
9.84
85.1 ± 0.2
Measured 17O transverse relaxation times (T2), 54 MHz, 23.7°C
[Mn(DOTAM)]2+ (0.11
mM)
pD
T2 (ms)
3.21
2.261 ± 0.287
8.24
2.127 ± 0.202
12.39
2.179 ± 0.235
[Mn(HxDOTA)]x-2 (0.50
mM)
pD
T2 (ms)
1.99
0.582 ± 0.044
2.31
0.459 ± 0.082
2.76
0.672 ± 0.082
3.01
0.934 ± 0.059
3.49
1.26 ± 0.11
4.10
1.70 ± 0.18
4.73
2.30 ± 0.27
6.06
2.07 ± 0.19
6.33
2.11 ± 0.22
7.02
2.30 ± 0.25
9.78
2.26 ± 0.22
11.78
2.38 ± 0.30
152
[Mn(Hx DOTP)]x-6
(0.20 mM)
pD
T2 (ms)
1.99
1.35 ± 0.07
2.39
1.31 ± 0.06
2.44
1.25 ± 0.01
2.57
1.13 ± 0.03
2.89
1.24 ± 0.07
3.29
1.23 ± 0.04
3.30
1.15 ± 0.03
3.51
1.30 ± 0.07
3.57
1.09 ± 0.04
3.84
1.11 ± 0.04
3.96
1.25 ± 0.06
5.09
1.37 ± 0.07
5.29
1.14 ± 0.03
5.44
1.28 ± 0.03
5.84
1.43 ± 0.05
6.02
1.60 ± 0.06
6.32
1.57 ± 0.04
6.67
1.60 ± 0.06
6.93
2.08 ± 0.07
7.36
2.03 ± 0.09
7.62
1.75 ± 0.05
7.94
1.75 ± 0.06
7.94
1.64 ± 0.06
8.83
2.16 ± 0.10
9.40
2.14 ± 0.10
9.45
1.73 ± 0.08
9.58
2.14 ± 0.08
9.73
2.13 ± 0.04
10.09
2.33 ± 0.10
Appendix D- Solution IR of Zn(DOTA)2- at pD 7.54 in D2O
153
Appendix E- Full NMR spectrum of Figure 3.7 1H NMR of Zn(H2DOTA) at 90 °C
and pD 7.5 (300 MHz, D2O) δ ppm 3.30 (s, 8 H) 3.09 (m, 8 H) 2.86 (m, 8 H).
154
Appendix F- How the phosphonates in Gd(DOTA-4AmP) transfer protons
between the coordinated water molecule and the bulk solvent taken from
Kalman et. al.
Schematic representation, viewed down the Gd-OH2 axis, of how the phosphonates in
GdLH23- transfer protons between the coordinated water molecule and the bulk
solvent. The relaxed protons of the coordinated water molecule (shown in red) are
removed from the water molecule by the deprotonated phosphonates, which act as
bases. They are then replaced by unrelaxed protons from the bulk water (shown in
blue), which are supplied by the monoprotonated phosphonates that are acting as
acids.1
1
Kalman, F.K.; Woods, M.; Caravan, P.; Jurek, P.; Spiller, M.; Tirsco, G.; Kiraly, R.;
Brucher, E. Sherry, A.D. Potentiometric and Relaxometric Properties of a
Gadolinium-based MRI Contrast Agent for Sensing Tissue pH. Inorg. Chem. 2001,
46, 5260-5270.
155