The Dynamics of Water Evaporation
from Proteins
Thesis submitted for the degree of "Doctor of Philosophy"
By
Michal Steinberg
Submitted to the Senate of the Hebrew University
May/2008
This work was carried out under the supervision of
Professor R. Benny Gerber
1
Publications from doctoral research
1. Steinberg, M. Z.; Breuker, K.; Elber, R.; Gerber, R. B., The dynamics of water
evaporation from partially solvated cytochrome c in the gas phase. Physical
Chemistry Chemical Physics 2007, 9, (33), 4690-4697.
2. M Z Steinberg, R Elber, R. E., F W McLafferty, R B Gerber and K Breuker, Early
structural evolution of native Cytochrome c after solvent removal. ChemBioChem
2008, 9, (15), 2417-2423.
2
Table of Contents
Abstract
…………………………………………………………….. 5
Chapter One – Introduction
I.
Background
II.
Objectives of research
………………………………………... 8
……………………………………………………….. 9
………………………………………. 20
Chapter Two – Methods ……………………………………………… 22
I.
Molecular Dynamics ………………………………………………. 23
II.
Force Field
III.
SHAKE algorithm
IV.
Cutoff of the electrostatic potential
V.
MOIL ………………………………………………………………. 33
………………………………………………………. 26
………………………………………………. 31
………………………………. 32
Chapter Three – Results …………………………………………….... 35
I.
The dynamics of water evaporation from partially solvated cytochrome
c in the gas phase
………………………………………………. 36
a. System and Methods
………………………………………. 40
i. The Force Field
………………………………………. 40
ii. Model of the initial state ………………………………. 40
iii. Dynamics ………………………………………………. 43
b. Results
………………………………………………………. 44
i. Protein temperature as a function of time ………………. 44
ii. Water evaporation rate
………………………………. 46
iii. Water coordination numbers
………………………. 49
iv. Lifetime of pair of water molecules
3
………………. 50
v. Water Diffusion Coefficient at the protein
vi. Structural properties of the protein
………. 51
………………. 52
vii. Structural changes with time during the evaporation
dynamics ………………………………………………. 56
c. Conclusions
II.
………………………………………………. 58
Early structural evolution of native Cytochrome c after solvent
removal
………………………………………………………. 59
a. Computational procedures
b. Results
………………………………………………………. 63
i. Reorientation of charged sidechains
………………. 63
ii. Effect of initial charge distribution
…………...….. 66
iii. Changes in RMSD
c. Conclusions
III.
………………………………. 61
…………………………...….. 68
………………………………………………. 69
NECD cleavage of Cytochrome c: Computational study and
experiments
………………………………………………………. 70
a. Methods
………………………………………………………. 71
b. Results
………………………………………………………. 73
c. Conclusions
………………………………………………. 78
Chapter Four – Concluding Remarks …………………………...…… 80
References …………………………………………………………… 85
4
Abstract
The study of the effect of water on biological macromolecules is important for the
understanding of electrospray mass spectrometry experiments. In electrospray
ionization (ESI), electrically charged nanoscale droplets are formed from solution of,
for example, proteins. The evaporation of solvent then leads to dry protein ions that
can be analyzed by the mass spectrometer. In the work presented in this thesis
computational methods are used for the study of different aspects of the electrospray
mass spectrometry experimental process. These aspects include the evaporation
process from a partially solvated protein, the effect of dehydration on non covalent
interactions in the protein and the structural changes of the protein resulting from
desolvation of the protein.
For the evaporation of water from a protein surface the dynamics of water evaporating
from native Cytochrome c covered by a monolayer of water is studied by molecular
dynamics (MD) simulation at constant energy conditions. A model of the initial
conditions of the process is introduced and physical properties of the system were
calculated. The temperature of the protein was found to drop by about 100K during
the 400ps of the simulations. This sharp drop in temperature due to evaporation
causes the water evaporation rate to decrease by about an order of magnitude, leaving
the protein with 50% to 90%, depending on the initial temperature of the system, of
the initial number of water molecules.
5
The structural changes of the protein were considered through calculations of the
radius of gyration and the root mean square (RMS) of the protein. A variation of 0.4
Å in the radius of gyration, together with an RMS value of less than 3 Å, indicates of
only minor changes in the overall shape of the protein. The water coordination
number of the solvation shell was found to be much smaller than that for bulk water.
The mobility of the water was found to be high at the beginning of the simulations
and to drop as the simulation progresses and the temperature decreases. Incomplete
desolvation of protein ions was also observed in recent experiments where there was
not enough heating of the system.
It is believed that covalent bonds are generally preserved during and after the phase
transition, from solution into the gas phase, that take place in electrospray ionization
experiments. However, it is less clear to what extent non covalent interactions are
affected by the new gaseous state. Atomic-level computational data, obtained from
MD simulations, on structural rearrangements of native Cytochrome c immediately
after solvent removal, is reported in this work. The first structural changes after
desolvation occur surprisingly early, on a timescale of picoseconds. For the time
segment of up to 4.2 ns investigated here, no significant breaking of native
noncovalent bonds was observed. However, formation of new noncovalent bonds that
involve charge residues at the protein surface are found. This formation of new
noncovalent bonds results in a transiently stabilized intermediate structure with a
global fold that is essentially the same as in solution. It was also found that
reorientation of charged sidechains is governed by the initial charge distribution and
proceeds in such a way as to minimize the charge asymmetry of the protein and
therefore its dipole moment in the gas phase.
6
Native electron capture dissociation (NECD)1 is a mass-spectrometric method that
occurs during “gentle” ESI, without external electron addition. A new theoretical
approach based on MD simulations is presented here for the prediction of NECD
fragmentation patterns. Backbone cleavage is assumed to depend on the distance
between the heme group and the residues framing the given cleavage site, as well as
the proximity of a proton sourcing from a protonated sidechain to the same cleavage
site. Site specific cleavage yields were calculated for gaseous Cytochrome c.
Comparison with data from NECD experiments corraborats both the mechanistic
postulations and the computational predictions. It also suggests that global structural
changes take place on a millisecond timescale not covered by the MD simulations.
This new theoretical approach can be useful for other proteins as well and is therefore
a general interpretation tool for NECD experiments for better understanding of
protein structure in the gas phase.
7
CHAPTER
ONE
8
Introduction
I. Background
The fundamental aspects of protein structure and folding in solution have been studied
for decades2-5, yet numerous questions are still unanswered. Most of these questions
relate to the effect of a protein's environment on structure and stability. In
experiments of proteins in solution it is very difficult to separate the contribution of
solvent from intrinsic protein stability. A different approach in addressing the effect
of hydration is to completely remove any solvent and study the structure and
energetics of the protein, in the gas phase, by itself1. This raises a number of new
questions:
1. What is the protein structure in the compete absence of solvent, and do
single minimum energy gas-phase structure exist?
2. Can protein in the gas phase fold and unfold, and what are the energetics of
gas-phase folding process?
3. If folding is possible, what is the major driving force, and on what
timescalse does it occur?
4. Does the protein structure change during the desolvation process, and how
many water molecules are necessary for maintaining the solution phase structure?
In the work described in this thesis computational methods are used to provide tools
of interpretation and analysis of the new experimental studies of proteins in the gas
phase, in order to answer these questions. The experimental methods are described
bellow followed by the description of the system studied.
9
It was not possible to study gaseous proteins because of their negligible volatility,
until the late 1980s. Thermal desorption requires temperatures at which proteins
degrades before entering the gas phase. More recent desorption methods such as fastatom bombardment (FAB)6 also turned out to be unsuitable for the intact desorption
of large proteins. The situation has changed dramatically with the introduction of the
"soft" desorption/ionization methods, matrix-assisted laser desorption/ionization
(MALDI)7-9 and electrospray ionization (ESI) that was developed by John Bennett
Fenn for which he was rewarded by the Nobel Prize at 200210. Although MALDI is
capable of transferring very large protein ions into the gas phase, the matrix crystal is
quite an artificial environment for a protein11. Most studies on gaseous protein ion
conformers use ESI, which directly transfers proteins from liquid solution into the gas
phase and therefore controls protein conformation in the condensed phase. Examples
for ESI studies include desorption/ ionization by ESI of ribosomes12 and other large
biomolecular complexes13, 14, and even viruses15.
ESI is a technique used in mass spectrometry to produce ions. It is especially useful in
producing ions from biological macromolecules because it overcomes the propensity
of these molecules to fragment when ionized. In ESI, a liquid, containing the
substance to be studied dissolved in a large amount of solvent, is pushed through a
very small capillary16. The substance to be studied, the analyte, exists as an ion in
solution either in its anion or cation form. This liquid is pushed out of the capillary
and forms an aerosol, a mist of small droplets of about 10 m across, due to charge
repulsions. Electrospray droplets start off highly charged, and as they shrink through
evaporation the Coulomb repulsion forces approach the force of surface tension that
10
holds droplet together. The droplet then becomes unstable and disintegrates into
several droplets of smaller radius (figure 1). This process is called Coulombic fission
because it is driven by repulsive Coulombic forces between charged molecules. The
process repeats itself until the analyte is a lone ion in the droplet. There is still debate
about the exact mechanism of the process, particularly of the last stage, when lone
ions form. An uncharged carrier gas such as nitrogen is used to help nebulize the
liquid and evaporate the neutral solvent in the droplets. The lone ions then move to
the mass analyzer of a mass spectrometer.
Figure 1: Electrospray Ionization (ESI).
There are two major competing theories about the final production of lone ions, the
charged residue model (CRM) and the ion evaporation model (IEM)17. The Charged
Residue Model suggests that electrospray droplets undergo evaporation and
disintegration cycles, with each initial droplet leading to a multitude of much smaller
"daughter" droplets. Each final "daughter" droplet contains on average one (or more)
11
molecule of analyte. When the last solvent molecules evaporate from such droplet the
analyte molecule is left with the charges that the droplet carried. The Ion Evaporation
(Desorption) Model suggests that as the droplet reaches a certain radius the field
strength at the surface of the droplet becomes great enough to push or desorb ions
directly out of the droplet. Characteristically, the fission event corresponds to an
almost negligible loss in droplet mass, but a significant drop in charge. It has been
suggested that both models probably occur for different analytes/solvents and in the
limit of both models they have a tendency to converge. That is to say that the
distinction between a droplet containing an analyte molecule and an analyte molecule
surrounded by a layer of solvent eventually disappears and coulombic fission looks a
lot like ion evaporation. The real question is scale and timing but the techniques to
definitively determine this are not yet available.
In mass spectrometry, electron capture dissociation (ECD) is a method of fragmenting
gas phase ions for tandem mass spectrometric analysis (structural elucidation)18. ECD
involves the introduction of low energy electrons, with energy in the range of 1 ev to
a few ev, to trapped gas phase ions. While methods such as with Collisionally
Activated Dissociation (CAD) or Infrared Multiphoton Dissociation (IRMPD)
introduce internal vibrational energy in some way or another ECD does not.
12
Figure 2: ECD is belived to take place when (1) There is a proton attack on the
backbone. (2) There is a free electron available in the system.
ECD cleavages the protein backbone N-C! bond to yield complementary c/z• fragment
ion pairs (~90%) (figure 2). In an alternative pathway a• and y fragment ions (~10%)
are formed. It was postulated that the energy available from charge recombination
(~6eV) produces localized excitation far in excess of that randomized over the
thousands of vibrational degrees of freedom of the protein ion19. For proteins as large
as cytochrome c, the excess energy (<3eV) was insufficient to cause thermal
unfolding of the gaseous ions, so that ECD affects only backbone cleavage but causes
no significant conformational change20. Thus the ECD spectrum of (M + nH)n+
protein ions shows c/z• (or a•/y) fragment ions only if they are not held together by
noncovalent bonding. The unseparated fragments will instead appear as reduced
13
molecular ions, (M + nH)(n-1)+•
20-22
. In a Typical ECD experiment for probing the
higher-order protein structure, ions formed by ESI are transferred through
differentially pumped vacuum stages into the trapped ion cell (<10-9 mbar) of a
Fourier Transform Mass Spectrometer (FTMS). There the ion population is allowed to
thermally equilibrate for ~40 s with cell and vacuum chamber via blackbody infrared
radiation23 prior to the irradiation with low energy (<0.5 eV) electrons20, 21.
The c/z• ions are unique products of reaction with electrons (figure 2). The
observation of c ions in ESI spectra of Cytochrome c protein without added electrons
was therefore unexpected. This new phenomenon, in this contex, which is related to
ECD is Native Electron Capture Dissociation (NECD)1. NECD is a massspectrometric method for the structural investigation of noncovalent interactions in
native proteins24. In contrast to conventional ECD techniques, NECD occurs during
“gentle” ESI, without external electron addition. NECD is believed to take place when
a protein dimer is formed in the solution and therefore requires sufficiently high
solution concentrations (~75 M). Charge partitioning in protein dimer dissociation
can apparently be so asymmetric that it causes intermolecular electron transfer and
cleavage of the protein backbone. Unlike ECD where cleavage is observed at all amid
bonds in the protein in NECD cleavage is observed only at sites that are in contact
with the heme. Residue-specific information on structural changes of the native
protein following transfer into the gas phase can therefore be extracted.
14
Figure 3: Electrospray experimental system of Prof. McLafferty in Cornell. Protein in
solution is sprayed into the system though the emitter to form small droplets (right
side of the scheme). The droplets are heated at the heat capillary to remove the solvent
from the protein. The protein is pumped into the magnet chamber where it is
cleavaged and analyzed by the mass spectrometer.
The protein, Cytochrome c was chosen to be studied in this thesis for a number of
reasons. (1) It is an extensively studied protein with data both from experiments in
solution25 and gas phase26 as well as from theory27-29. (2) A solution structure of horse
heart (Equine) Cytochrome c that was solved by NMR technique is available30. (3)
Cytochrome c is the first and only protein at the moment for which NECD data are
available1. (4) While theoretical interpretation and analysis seems desirable, there are
no NECD computational studies of Cytochrome c. (5) Cytochrome c is a relatively
small protein of about 100 amino acids, making it easier to calculate.
15
Cytochrome c is an electron-transfer protein which contains a heme moiety, with the
iron ion cycling between the oxidation states 2 and 3 during biological function31, 32. It
is a soluble protein and is an essential component of the electron transfer chain
associated with the inner membrane of the mitochondrion. Cytochrome c is a highly
conserved protein across the spectrum of species, found in plants, animals, and many
unicellular organisms. As it happens the cytochrome C in humans is slightly different
from the cytochrome C in bacteria, but it still functions the same way. This, along
with its small size, of about 100 amino acid residues makes it useful in studies of
evolutionary divergence. The protein has been studied for the glimpse it gives into
evolutionary biology. Both chickens and turkeys have the identical Cytochrome c
molecule (amino acid for amino acid) within their mitochondria, whereas ducks
possess molecules differing by one amino acid. Similarly, both humans and
chimpanzees have the identical molecule, while rhesus monkeys possess cytochromes
differing by one amino acid.
16
Figure 4: Horse heart Cytochrome c with it's six !-Helixes. The protein contains a
heme c group with an iron atom centered at the porphyrin ring (in pink).
Horse heart Cytochrome c, please see figure 4, has 104 amino acids and a heme group
which is covalently bonded to the protein via thioether linkages at Cysteine 14 and
Cysteine 17. The iron in its FeII or FeIII state is located at the center of the heme
embedded in the porphyrin ring system (figure 5). The structure of the protein contains
6 !-helices formed by 39 residues which comprise 37% of the protein, while it doesn't
contain any "-sheets. At pH 5 the net charge of the protein, according to calculated
pKa values of the ionizable residues in native (FeIII) Cytochrome c33 is plus six.
Meaning that all Aspartic and Glutamic acid residues, both heme propionates and the C-
17
terminus are deprotonated, all Lysine and Arginine residues are protonated, and the
Histidine residues are uncharged. For ESI in positive mode, the number of charges
depends on the state of the protein in solution and is therefore also plus six.
Figure 5: Heme group of Cytochrome c, which is called heme c. The Iron is located at the
center of the porphyrin ring. Heme c is covalently bonded to the protein Cysteines via
thioether linkages.
Equine Cytochrome c is the first protein studied by NECD method to reveal structural
properties of the protein in the gas state. In this work Molecular Dynamics (MD)
simulations were used for the study of the structural changes of Cytochrome c at the
different stages of the NECD experiment. In MD atoms and molecules are allowed to
interact for a period of time under the classical laws of dynamics, giving a view of the
motion of the atoms. MD simulations require the availability of a potential function,
or a description of the terms by which the particles in the simulation interact. This is
usually referred to as the force field. Potentials may be defined at many levels of
18
physical accuracy; those most commonly used are based on a classical description of
particle-particle interactions that can reproduce structural and conformational changes
but usually cannot reproduce chemical reactions. MD serves as an important tool in
protein dynamics and in structure determination and refinement. More details on the
force field employed and the conditions used in the simulations can be found in the
methods section of this work.
In the first stage of the Electrospray experiment droplets of protein in solution are
sprayed into a lower pressure chamber. This is when the evaporation of solvent starts.
This evaporation process was studied by MD simulations of equine Cytochrome c
covered by a monolayer of water, at constant energy conditions. The properties of the
water as well as the temperature and structural changes of the protein during
desolvation were analyzed from these simulations. This study is described in details in
chapter three, section I, of this thesis.
Chapter three, section II, of this thesis focuses on the structural changes of the
Cytochrome c protein after dehydration. For the purpose of this study MD simulations
at constant energy conditions were pursued starting from the NMR native structure of
the protein. A new approach for calculations of cleavage sites in NECD is described
in chapter three, section III.
19
II. Objectives of research
ESI is emerging as a very popular and important tool for the study of biological
molecules in the gas phase. The goal of this work is to study ESI by theoretical
methods in order to answer the following questions:
(1) What are the properties of water molecules at the protein surface as they
emerge at the first stages of ESI? How mobile are the water molecules at the
ESI droplets? Are they arranged uniformly on the protein surface, or do they
form patches around hydrophilic areas?
(2) What is the timescale for the desolvation of the protein for different
experimental conditions such as initial temperature, heat capillary temperature
or pressure of the gas carrying the droplets (usually air)?
(3) What happens to the energy and temperature of the protein upon the
evaporation of solvent from its surface? Can optimal experimental conditions,
such as heat capillary temperatures, be estimated from these numbers in order
to achieve full evaporation on one hand and maintain stable protein
conformation on the other hand?
(4) What happens to the protein structure during desolvation? Does the protein
conserve its original solution structure or does the protein structure change
during the hydration of water from its surface? If the protein structure changes
which are the first parts of the protein to move and what are the timescales of
these structural changes? Some effort have been made by Mark Ratner on the
study of the effect of ion net charge on the compactness, stability and
hydration of unsolvated Cytochrome c ions, and qualitative agreement was
found with results from ion mobility experiments, which showed that the
20
lower charge states are geometrically more compact and stable than the higher
charge states, and that the compact ions absorb more water molecules28,
29
.
However, dehydration processes were not considered in these studies.
(5) Can very fast structural changes of the protein be used in order to learn about
much longer processes such as longer timescale structural modifications and
cleavage patterns in NECD? The electron transfer mechanism in ECD was
previously studied by Jack Simons using ab initio calculations. These studies
show that a positive charge allows direct dissociative attachments to occur34.
These studies did not address questions on the structural changes of the protein
that are involved in the cleavage process.
21
CHAPTER
TWO
22
Methods
I. Molecular Dynamics35, 36
In Molecular Dynamics (MD) Newton's second law of motion is used to generate
configurations of the system that results in a trajectory that specifies how the positions
and velocities of the particles in the system vary with time. Newton's seconds law
(F=ma) can be written as follows:
d 2 xi
dt 2
Fxi
mi
(1)
This equation describes the one dimensional motion of a particle of mass mi along
coordinate xi. Fxi is the force acting on the particle in the xi direction. The force on an
atom depends on its position relative to the other atoms in the system.
Time integration is used in MD to generate trajectories in the case analytical potential
function. The idea is that the particles path is broken down into many small segments
that are separated in time by a fixed time #t. The time #t is chosen to be very small so
that the forces on the particles can be assumed to remain constant through this time
interval. There are many algorithms for integrating the equations of motion all of
which assume that the positions and derivatives (velocities, accelerations, etc.) can be
approximated as Taylor series expansions in #t. The most widely used algorithm and
the one used in the simulations described in this thesis is the Verlet algorithm37. The
basic idea of the Verlet algorithm is that two third-order Taylor expansions for the
positions r(t), one forward and one backward in time can be written (equations 2 and
3). Calling v the velocities, a the accelerations, and b the third derivatives of r with
respect to t, one can write:
23
1
r ! t $ # t " r ! t " $ # tv ! t " $ # t 2 a ! t " $
2
(2)
1
r ! t % # t " r ! t " % # tv ! t " $ # t 2 a ! t " %
2
(3)
Adding these two equations gives:
r !t $ # t "
2r ! t " $ # t 2a ! t " % r ! t % # t " $
(4)
Assuming that the positions at time t and time t-#t are known as well as the
acceleration at time t the new position at time t+#t can be calculated from equation
(4). At the beginning of the simulation there is only one set of positions, at t=0. The
position at t=0-#t is therefore calculated by a Taylor series (equation (3)), truncated
after the first term, r(0-#t)=r(0)-#tv(0).
The velocities of the particles at time t+#t can be calculated from the difference
between equation (2) and equation (3) as follows:
v ! t " = &(r ! t $ # t " $ r ! t % # t " ') /2# t
(5)
As the calculation of the velocities requires the positions at time t-#t as well as the
positions at time t+#t, this calculation can be done only after the positions have been
computed at the next step.
While, in this thesis, the initial coordinates of the system are obtained from
experimental data, the initial velocities are assigned by random sampling from a
Maxwell-Boltzmann distribution at the temperature of interest. According to
Maxwell-Boltzmann Gaussian distribution the probability at temperature T that an
atom i of mass mi has a velocity vix in the x direction is:
24
& 1 mi vix2 '
mi
exp , %
2+ k BT
( 2 k BT )
* ! vix "
(6)
The temperature of the simulated system is calculated from the kinetic energy of the
particles in the system in the following way:
N
Kinetic Energy = .
i 1
mi vi2
2
(7)
Assuming that the energy distribution is fast and the system is in quasi equilibrium
stat the kinetic energy of the system can be also calculated from:
Kinetic Energy =
kb T
! 3N % N c "
2
(8)
Where N is the number of particles and Nc is the number of constrains, so that 3N-Nc
is the number of degrees of freedom.
The temperature can be calculated from the last two equations to give:
T
2
/
k b ! 3N % N c "
N
.
i 1
mi vi2
2
(9)
The time step is chosen so that it will be small enough to maintain accuracy of the
calculation which can be checked by the conservation of energy. The best timestep is
determined by the vibrations involved in the system. If there are fast vibrations in the
system as a result of light atoms or high temperatures small timesteps are required. In
25
general a timestep of 1ps is commonly used in simulations of biological
macromolecules. In the simulations described in this thesis smaller timesteps of 0.2 ps
to 0.5 ps were used in order to maintain high level of energy conservation. In some of
the calculations SHAKE algorithm was used in order to enable simulations with larger
time steps. A more detailed description of the SHAKE algorithm is presented in
section III.
The first MD simulation was performed by Alder and Wainwright in 195738 using the
hard-sphere model. Rahman was the first to perform MD simulations using
continuous potentials at 196439. In these simulations the motions of all particles are
coupled together under the influence of an analytical potential. Protein MD
simulations though were done for the first time only at 1977. These simulations were
carried by McCammon, Gelin and Karplus on the bovine pancreatic trypsin inhibitor
(BPTI)40, which is a small protein containing 58 amino acid residues. Since this work
protein simulation has become a very popular field and many programs has been
developed for such simulations. Among these programs one can find AMBER41,
CHARMM42, GROMACS43, TINKER44, MOIL45 and more. All simulations
described in this thesis were performed using MOIL which is described in more
details in section V.
II. Force Field35
The force field refers to the functional form and parameter sets used to describe the
potential energy of a system of particles. Force field functions and parameter sets are
26
derived from both experimental work and high-level quantum mechanical
calculations. "All-atom" force fields provide parameters for every atom in a system,
including hydrogen. In some cases groups such as CH2, CH3, NH3+, etc. are treated as
a single particle in order to reduce computational efforts. Such is the case in the
calculations described in this work.
The basic functional form of a force field encapsulates both bonded terms relating to
atoms that are linked by covalent bonds, and nonbonded (also called "noncovalent")
terms describing the long-range electrostatic and van der Waals forces. The specific
decomposition of the terms depends on the force field, but a general form for the total
energy can be written as:
V(r) = V(r)covalent + V(r)non-covalent
(10)
Where the components of the covalent and noncolvalent contributions are given by
the following summations:
V(r)covalent=V(r)bond+V(r)angle+V(r)dihedral+V(r)torsion
(11)
Figure 6 bellow shows the schematics of the different terms of the covalent
interactions and their commonly used potentials. Figure 7 bellow shows the
schematics of the different terms of the non covalent interactions and their commonly
used potentials.
27
(a-1)
(a-2)
(b-2)
(b-1)
(c-2)
(d-2)
(c-1)
(d-1)
Figure 6: Potential of the covalent bonds. (a-1) visualization of the bond spring. (a-2)
Bond spring harmonic potential. (b-1) Visualization of the angle potential. (b-2)
Angle harmonic potential. (c-1) visualization of the improper dihedral. (c-2) dihedral
harmonic potential. (d-1) visualization of the torsion angle. (d-2) torsion periodic
potential.
28
V(r)non-covalent = V(r)electrostatic + V(r)van-der-Waals
(12)
Figure 7: Potential of the covalent bonds. Upper left: Visualization of the van der
Waals potential. Upper right: The van der Waals potential described by a LennardJones potential. Lower left: Visualization of the electrostatic potential. Lower right:
The electrostatic potential described by the Coulomb potential.
The bond and angle terms are usually modeled as harmonic oscillators in force fields
that do not allow bond breaking. The torsion term is a sum over cosine functions that
indicate where are spherical groups, which may prevent smooth rotations around the
bond, located and how large they are. The nonbonded terms are very computationally
expensive because they include many more pairwise interactions per atom. The van
der Waals term is usually computed with a Lennard-Jones potential and the
electrostatic term with Coulomb's law.
29
In addition to the functional form of the potentials, a force field defines a set of
parameters for each type of atom. For example, a force field would include distinct
parameters for an oxygen atom in a carbonyl functional group and in a hydroxyl
group. The typical parameter set includes values for atomic mass, van der Waals
radius, and partial charge for individual atoms, and equilibrium values of bond
lengths, bond angles, and dihedral angles for pairs, triplets, and quandruplets of
bonded atoms, and values corresponding to the effective spring constant for each
potential. The force field also provides information about special groups often found
in biological molecules. An example for such a group is the heme group often found
in electron transfer proteins such as Cytochrome c which is studied in this work. The
aromatic property of the heme group requires special parameters for accurate
description of the interactions of its atoms.
There are various force fields models for describing the potential of water molecules.
The simple models use three, four or five charge sites and vibrationally rigid water
molecules. In cases where there are strong electric field gradients, force field models
that explicitly include polarization effects of the water are considered to be more
appropriate46. This explicit inclusion of polarization term is believed to better
reproduce the behavior of water in non liquid phases (e.g. solid and vapor) and at the
interface between different phases. The dipole moment of an isolated water molecule
in such a model should therefore be closer to the gas-phase value rather than the value
in liquid water47. Polarization effects in these models are introduced ether by an
isotropic molecular polarisability contribution, atom-centered polarizabilities or by
the variable charge model48. The incorporation of polarisability significantly increases
the computational effort required for the simulation. Due to the high computational
30
effort required for the use of a polarisable water model combined with the fact that
polarization effects are unlikely to affect the main findings of the work described in
this thesis where water molecules are considered in the liquid phase, all simulations
described in this thesis were done with the TIP3P model49. TIP3P is a very popular
non-polarisable three point model where the partial positive charges on the hydrogen
atoms are exactly balanced by an appropriate negative charge located on the oxygen
atom.
III. SHAKE algorithm50:
The SHAKE algorithm was first introduced by Ryckaert Ciccotti and Berendsen50 and
is the most commonly used method for applying geometry constrains in MD
simulations. The SHAKE algorithm is based on Holonomic constraints51 where the
forces of constraints are perpendicular to the virtual displacements and do no virtual
work. When simulating flexible molecules the high frequency motions of bond
vibrations are usually of less interest than the lower frequency modes, which often
correspond to major conformational changes. Fixing the bond lengths and sometimes
even the angles to a specific value is therefore used for filtering rapid vibrations and
allowing simulations with larger time step which result in speeding up the
calculations. In constrained dynamics the equations of motion are solved while
simultaneously satisfying the imposed constrain. SHAKE is therefore a modification
of the Verlet algorithm for integrating the equations of motion where particle
velocities are first calculated for the unconstrained system and then modified to meet
each constraint. The most common use of SHAKE is for constraining bonds involving
hydrogen atoms due to their much higher vibrational frequencies.
31
IV. Cutoff of the electrostatic potential:
The charges in a molecule are distributed according to the electronegativity of the
different elements in the system which is represented by fractional point charges.
These point charges are designed to reproduce the elctrostatic properties of the
molecule. The electrostatic interaction is calculated as a sum of interactions between
pairs of point charges using Coulomb's law. Coulomb's law states that the magnitude
of the electrostatic force (F) between two point charges (q1, q2), is directly
proportional to the product of the magnitudes of each charge and inversely
proportional to the square of the distance between the charges, so that:
F
1
4+0 0
/
q1 / q2
r2
(13)
Where r is the distance between the charges, calculated between the two nuclear
centers of the two point charges, and $0 is a constant called the permittivity of free
space. A positive force implies a repulsive interaction, while a negative force implies
an attractive interaction52.
For an accurate calculation of the electrostatic potential it is necessary to sum over all
pairs of particles in the system. In the case of large systems like proteins this
procedure is very computationally consuming. An approximation is many times used
in order to reduce the computational efforts of calculating the electrostatic force. This
32
approximation is justified by the fact that that the protein is a dielectric medium which
cause screening and therefore, exponential extinguishing of the force like in water. In
this approximation a cutoff is used so that the electrostatic potential between particles
that are separated by a larger distance than this cutoff is ignored. This results in
computation of fewer interactions and therefore in speeding up of the calculations. In
this work there was no use in the cutoff of electrostatic interactions in order to
maintain a high level of energy conservation of the calculations.
V. MOIL45:
MOIL is a molecular modeling software designed and developed by Ron Elber and
co-workers45. MOIL is a suite of programs aiming at studying proteins and other
biologically important macromolecules. MOIL is designed to be used to compute the
time evolution (trajectory X(t)) of a large (composed of thousands of atoms) and
inhomogeneous system. MOIL uses the initial coordinates and velocities as well as
the potential energy function U(X) in order to solve the differential equations of
motion using the Verlet algorithm. MOIL force field is a combination of two other
force fields: AMBER41 and OPLS95. In MOIL groups such as CH2, CH3, NH3+, etc.
are treated as a single particle in order to reduce computational efforts. The water
potential in MOIL is TIP3P49 which is a three point non polarized potential.
MOIL is a public domain program written in Fortran 77. One of the advantages of
MOIL is that the code itself is free to download so one may modify the code for his
own use. For the purpose of this work MOIL was modified to allow freezing of water
33
molecules that have evaporated from the protein. The water molecules velocity was
set to zero once its distance from the center of mass of the protein was higher than
60Å.
34
CHAPTER
THREE
35
Results
The results section will be divided into three parts describing simulations of
Cytochrome c at different stages of the electrospray ionization experiments. In the
first part (I) the protein is studied when surrounded by water. The focus here is to
learn on the behavior of a droplet containing the protein in solution when sprayed into
a vacuum environment. In the second part (II) the protein is studied in gas phase, with
no water molecules at its surface. Structural changes of the protein are observed on
very fast timescals of the order of picoseconds. The electrical properties of the protein
are considered through these structural changes. In the third part (III) a new model is
proposed for cleavage prediction in NECD experiments. Comparison with
experimental data corroborates the computational predictions, and suggests that
certain global structural changes occur on the timescale of milliseconds.
I. The dynamics of water evaporation from partially
solvated cytochrome c in the gas phase53
A detailed atomic-level description of the mechanisms by which water molecules
affect proteins is important for the understanding of protein structure and stability.
Because detailed protein structures in the gas phase are not yet available, the most
promising approach for studying the effect of hydration on protein structure and
stability is to start with the known structure in aqueous solution, and follow possible
changes upon evaporation of the water. This can be done in computational studies as
reported here, or in electrospray ionization (ESI)10, 54 experiments. Two models for
36
the formation of solvent-free ions in ESI experiments have been suggested: the ion
evaporation model (IEM)55, and the charge residue model (CRM)56,
57
. In both
models, the electrically charged droplets from ESI first undergo multiple fissions to
form very small droplets58-61. The IEM suggests that partially solvated ions are ejected
from small droplets (~10 nm radius), whereas the CRM proposes solvent evaporation
from even smaller droplets (<3 nm radius)62. However, little is known to date about
the final stages of ion desolvation in ESI. Computational studies on the evaporation of
water from biological macromolecules could substantially increase our understanding
of the desolvation process in ESI.
ESI of biomolecules from non-denaturing solutions ("native ESI") is believed to
proceed via CRM63-65, suggesting that their native structure is preserved at least until
the very last stages of ion desolvation. However, native electron capture dissociation
(NECD)1 experiments on equine Cytochrome c revealed different degrees of local
stability for different regions of the protein in the transition from solution to gas
phase. This order of regional stability was essentially the reverse of the order in
solution, which was attributed to the loss of hydrophobic bonding and the
strengthening of electrostatic interactions in the absence of bulk water24. While the
reversed order of local stability necessitates unfolding of the native Cytochrome c
structure in the gas phase, experiments have not provided an exact time scale for this
process. Ion mobility studies on the +7 to +10 ions of Cytochrome c stored in an ion
trap at 300ºK showed unfolding transitions on a millisecond timescale but with
induction periods of ~30 ms66. A possible reason for these induction periods was
attributed to ion cooling below the ambient temperature and conformational freezing
as a result of solvent evaporation during the ESI process66,
37
67
. Partially hydrated
peptides68,
69
and proteins70 in electrospray experiments have also been reported.
Liquid water beam desorption mass spectrometry is another experimental technique
where conformational freezing is indicated. This technique has recently been used by
Abel et al for the study of macrobiomolecules in the gas phase71. The issues of
conformational freezing and partial hydration are addressed in the present work by
computational studies on equine Cytochrome c.
Our understanding of electrospray experiments of native biological systems can
greatly benefit from theoretical modeling72-76. Efficient methodology that retains the
atomically detailed description of the large system of a biological macromolecule is
desired. This is the Molecular Dynamics (MD)40,
77
approach. Mao, Ratner and
Jarrold27-29 have studied by MD the effect of ion net charge on the compactness29,
stability27 and hydration28 of unsolvated Cytochrome c ions, and found qualitative
agreement with results from ion mobility experiments which showed that the lower
charge states are geometrically more compact and stable than the higher charge states,
and that the compact ions absorb more water molecules78,
79
. The +3 to +8 ions
exhibited collision cross section values close to those predicted for the native
Cytochrome c structure78,
80, 81
. In a similar approach using MD calculations and
collision cross sections from ion mobility experiments, Bowers and coworkers
concluded that G-quadruplex structures can be conserved in a solvent-free
environment82. Orozco et al83, 84 have studied complexes of DNA with minor groove
binders in the gas phase by MD. They found that solvent evaporation does not change
the gross structural, energetic and dynamic features of the DNA, and does not produce
dissociation of the drug from the DNA. The study of completely desolvated proteins
in the gas phase by MD has recently been reviewed by Arteca, Reimann, and Tapia85.
38
Protein Hydration was previously studied theoretically86. Previous studies of
hydration levels of Myoglobin87, 88 by MD suggest that a moderate water coverage of
~350 water molecules for Myoglobin is needed in order to conserve native structural
properties of the protein. Merzel and Smith89-91 studied by MD the density of water
molecules that surround a protein. They found that the density of the first water layer
around a protein is higher than the density of bulk water.
Evaporation of water molecules from a surface of a protein involves breaking of
noncovalent bonds between water and protein atoms as well as between different
water atoms. Thus the evaporation process not only models the final stages of ESI, but
also gives detailed insight into the interaction of a protein with its environment. This
work also improves of the understanding of the local noncovalent forces at different
regions of the protein surface. Valuable information on protein interaction with water
molecules has been also obtained from experiments in solution92-94.
In the present investigation the evaporation of water from Cytochrome c is studied
computationally. Molecular Dynamics simulations of Cytochrome c covered with a
monolayer of water were carried out in order to answer the following questions. How
do the water molecules arrange around the protein? How mobile are the water
molecules? How is the kinetic energy partitioned between the protein and the water
molecules during the evaporation process? What happens to the temperature of the
protein during the desolvation process?
39
In the electrospray experiments the droplets containing the protein are transferred
through the heat capillary which is a chamber containing low pressure of carrying gas.
This chamber is been heated from the outside and the heat from its surface is
transferred to the protein through the low pressure carrying gas and causes
desolvation of the protein. The conditions inside this heat capillary are nether of
constant temperature (much higher density of carrying gas would be necessary for
creating constant temperature conditions) nor of constant energy (an absence of
carrying gas would be necessary for creating constant energy conditions). Since the
exact conditions inside the heat capillary are not known one of the extreme condition
of constant energy was chosen for the aim of the current study.
Equine Cytochrome c is an electron transfer protein composed of 104 amino acids and
a covalently attached heme group. Cytochrome c is a useful model for water
evaporation studies as it has been extensively studied in solution25 and in the gas
phase26.
I.a. System and Methods:
I.a.1. The Force Field
The MOIL suite of programs45 was used in the atomistic detailed simulations. The
MOIL force field is based on AMBER41 and OPLS95 force fields. In MOIL only
polar hydrogen atoms are treated explicitly in the dynamics. Covalently bound
hydrogen atoms such as in the CHn groups are described as part of an “extended
atom”. Water molecules were explicitly represented by the TIP3P model49.
40
I.a.2. Model of the initial state
The model adopted here corresponds to a protein covered with a thin layer of water,
initially taken to be at a selected temperature. This model droplet is not coupled to a
thermal bath. Evaporation events therefore occur necessarily at the expense of internal
energy of the system. Different initial temperatures were used in order to explore the
effect of internal energy on water evaporation.
Figure 8: Native Cytochrome c (shown as cartoons without the heme group)
surrounded by 182 water molecules (shown by red balls for the oxygen and white
balls for the hydrogens). Left: Water arrangement after relaxation. Right: Water
arrangement without relaxation.
All simulations in this work are based on the NMR structure of native oxidized (FeIII)
horse heart Cytochrome c which was solved by Banci et al30 (protein data bank entry
1AKK). The native structure was covered with 182 water molecules to form an
approximate monolayer of water by two different procedures. In the first procedure
the protein was placed in a water box of 30Å×30Å×30Å with 201 water molecules.
The system was then partially relaxed by a 10 psec simulation at 10°C with no
geometric constraints and at constant energy. After the initial relaxation all water
41
molecules that escaped the surface of the protein were removed. The resulting initial
water distribution is non-uniform as the water molecules aggregate near the charges
on the surface and leave patches of non charged areas uncovered. In the second
procedure the protein was placed in a water box and without any relaxation. All water
molecules more than 4.65 Å away from any protein atom were removed. The 4.65 Å
cutoff was chosen so 182 water molecules would remain on the protein surface to give
the same amount of water molecules as in the first procedure. The initial structure
formed by this method is characterized by a more uniform water arrangement around
the protein but in a less stable structure. The relaxed water conformation is more
realistic as it allows the water molecules to be located at the energetically favorable
locations on the protein surface like they would in nature. These two initial structures
are shown in Figure 8.
In the relaxed initial conformation (Figure 8, left) the hydration shell of 182 water
molecules is not a uniform monolayer but a patchwork of water clusters, covering
primarily the charged groups such as the protonated lysine and arginine residues and
the deprotonated aspartic acid and glutamic acid residues while leaving other areas of
the surface uncovered. The water molecules are arranged such that their density is
higher on the exposed areas of the alpha helices and lower in the loop regions.
The two structures in Figure 8 were used as starting structures for the MD
simulations. The different initial kinetic energies used in the calculations correspond
to temperatures ranging from 60°C to 170°C. Charge sites were assigned according to
calculated pKa values of the ionizable residues in native (FeIII) Cytochrome c96 at pH
42
5 (for details, see reference of K. Breuker, 200633). Briefly, all Aspartic and Glutamic
acid residues, both heme propionates and the C-terminus are deprotonated, all Lysine
and Arginine residues are protonated, and the Histidine residues are uncharged to give
a net charge of +6.
I.a.3. Dynamics
The evaporation of water molecules from the surface of Cytochrome c was studied by
Molecular Dynamics simulations. The simulations were done in vacuum conditions at
constant energy. Two different options of the SHAKE algorithm50 in MOIL were
used. The light SHAKE freezes only vibrations of bonds that contain hydrogen atoms.
The regular SHAKE freezes fast vibrations of all bonds.
Ten different trajectories of 400 picoseconds were simulated with different initial
conditions. Seven trajectories were computed for the relaxed water conformation with
initial temperatures of 354ºK, 379ºK, 380ºK, 399ºK, 421ºK, 447ºK and 470ºK. Light
SHAKE was used for the higher temperatures and regular SHAKE was used for the
lower temperatures where it was found to better conserve the energy. The time step in
all the simulations was 0.2 femtoseconds. This is significantly lower than the 1
femtosecond step used in most MD simulations but was necessary to maintain a high
level of energy conservation of the order of 0.1 kcal/mol. No cutoff distance for nonbonded interactions was used.
43
The quantitative properties of the evaporation process computed in this work include
the temperature of the system, the temperature of the protein, the evaporation rate, the
water diffusion coefficients, the RMS of the protein and the radius of gyration of the
protein.
I.b. Results
I.b.1. Protein temperature as a function of time
The temperature of the protein is computed based on the kinetic energy of all atoms in
the protein. The system is assumed to be in equilibrium, though strictly speaking it is
not. After a short time of a few hundred femtoseconds it is assumed that the system
reaches a partial equilibrium state with respect to the kinetic energy. The temperature
is therefore computed by:
T
2 Average Kinetic Energy
*
3
K Boltzmann
44
(14)
Figure 9: Protein temperature vs. time for different initial temperatures, Ti
The drop in protein temperature during the evaporation process is shown in Figure 9.
The cooling of the system upon evaporation of water molecules is due to the fact that
the breaking of water – protein non covalent bonds occurs at the expense of kinetic
energy of the system. In addition, the evaporating water molecules carry kinetic
energy with them which also decreases the temperature of the protein. This MD result
is in qualitative agreement with "native" protein electrospray experiments by Loo70
(Figure 10). The mass spectra provide evidence that in the absence of sufficient
external heating, the protein remains partially hydrated in the electrospray experiment
process. In the top panel of Figure 10 the temperature of the metal capillary through
which the protein ions enter the mass spectrometer was about 100°C. The broad shape
of the peaks was attributed to water molecules that remained attached to the protein
since the higher the number of water molecules attached to the protein the higher the
mass of the system is. A broad shape of the peaks is therefore a result of a distribution
of proteins with different number of water molecules attached to their surface and
45
therefore, a distribution of masses. For the bottom spectrum in Figure 10, a
temperature of 200°C was applied. The resulting sharp peaks in this case indicate a
much higher degree of protein desolvation. Preliminary results from MD simulations
at constant temperature conditions (not shown here) show that additional heating of
the protein/water system at room temperature can lead to full desolvation of the
protein. A full report of this is in preparation.
Figure 10: "Native" electrospray mass spectra of streptavidin (from reference 70).
The protein solution is electrosprayed into a metal capillary that can be heated to
assist desolvation. With a capillary temperature of 100°C (top spectrum), desolvation
is incomplete as evidenced by the broad peaks in the m/z spectrum. Increasing the
temperature to 200°C (bottom spectrum) greatly improves the desolvation process,
and the resulting peaks are sharpened.
I.b.2. Water evaporation rate
The evaporation rate as a function of time is plotted in Figures 11 and 12 for different
initial temperatures. In Figure 11 the evaporation rate is plotted for Cytochrome c
46
covered with 182 water molecules that were relaxed around the surface of the protein
by a short MD. In this case the water molecules were located on the surface at
energetically favorable positions near charge sites and were more stable with respect
to detachment from the surface.
Figure 11: Water evaporation rate vs. time for different initial temperatures, Ti, for
native Cytochrome c covered with 182 water molecules that were relaxed around the
protein. The figure at the top right shows the number of water molecules left on the
protein surface vs. time for different initial temperatures, Ti.
In Figure 12 the evaporation rate is plotted for Cytochrome c covered with 182 water
molecules that were more uniformly arranged on the protein surface. In this case the
water molecules were not relaxed to energetically stable sites on the surface of the
protein and were therefore less attached to the surface. It is clear from the two graphs
that the evaporation rates for the unrelaxed water molecules are higher than the
evaporation rate for the relaxed water molecules. In both cases the evaporation rate
increases for higher initial temperatures, though after an initial “ballistic” period all
47
rates become similar rather quickly. Limited statistics forbids more precise
conclusions.
Figure 12: Water evaporation rate as a function of time for different initial
temperatures, Ti, for native Cytochrome c covered with 182 water molecules that
were uniformly arranged around the protein. The figure at the top right shows the
number of water molecules left on the protein surface vs. time for different initial
temperatures, Ti.
Because the temperature of the system drops during the evaporation process, the
evaporation rate decreases until it becomes so small that the water molecules are
frozen on the surface of the protein on the time scale of the simulation. The amount of
water molecules left on the surface was found to be smallest for the hottest trajectory
with non relaxed water conformation for which only 87 out of the initial 182 water
molecules were left attached. The number of water molecules that remained on the
surface is largest for the coldest trajectory (Ti=354ºK) with the relaxed water
conformation. A total of 163 out of the 182 water molecules originally covering the
48
surface of the protein remained attached in this case. This provides an indication of
how different the water loss can be for different initial structure and energy.
I.b.3. Water coordination numbers
The coordination number of a water molecule is defined as the number of neighboring
water molecules with an oxygen-oxygen distance of 3.1Å or less. The water
coordination number was approximately the same for all trajectories reported here.
Figures 13 and 14 illustrate the difference between surface and bulk water. The water
coordination number was calculated to have a maximum probability of one for water
on the protein surface, and a maximum probability of four for bulk water.
Coordination number of water interface, on the surface of a water box, was also
calculated and was found to have maximum probability at two and maximum
coordination number of four. The reason for the coordination number of water around
the protein to peak as low as at one is that on some areas of the protein surface groups
of water molecules can be found together in other areas single water molecule
(meaning, with zero neighbors) can be attached to the surface. The maximum
coordination number of water on the surface of the protein is seven which is much
higher than that of water interface (which is four) and closer to that of bulk water
(which is eight). These high coordination numbers result from these areas on the
protein surface where groups of water molecules are attached close together. These
areas are usually attributed to charges on the protein surface.
49
Population
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
Coordination Number
Figure 13: Histogram for coordination of water on the surface of Cytochrome c from
an average over all times of the trajectory.
Population
0.4
0.3
0.2
0.1
0
0
2
4
6
8
Coordination Number
Figure 14: Histogram for coordination of bulk water calculated with the "pure water
box" of the Moil package.
I.b.4. Lifetime of pair of water molecules
A water pair is defined when two water molecules are 4Å apart or closer. The
histogram of the number of water pairs, averaged over all the ten trajectories, as a
function of the lifetime is plotted in Figure 15. The lifetime of a water – water pair is
50
of no more than a few tens of picoseconds, indicating rapid movements of the water
Log (Number of Pairs)
molecules on the protein surface.
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
5
15
25
35
45
55
65
Pair LifeTime (psec)
Figure 15: The log of the number of water pairs as a function of lifetime. Note that the
relaxation deviates from exponential behavior.
I.b.5. Water Diffusion Coefficient at the protein
The Diffusion Coefficient was calculated from the mean square displacement
function97:
6 Dt
&( r !1 $ t " % r !1 " ')
2
(15)
Where t is the time offset that was taken to be 1psec and % is a specific time, <…>
denotes an average over time origins % and over a species of molecules of interest, and
r(%) is the position of the molecule at time %.
The diffusion coefficient depends on the temperature. As a result of the drop in
temperature during the evaporation process the diffusion coefficient drops with time.
The diffusion coefficient are therefore calculated at time intervals of 10 picoseconds
and plotted as a function of temperature for the different trajectories in Figure 16. The
51
dependence of the diffusion coefficient on the temperature was found to be the same
for trajectories of the same initial structure regardless of the initial temperature. The
two trajectories of Figure 9 are therefore examples of the two different initial
structures.
Figure 16: The diffusion coefficient (in m2/sec), on a logarithmic scale, vs. the inverse
of the temperature, for different initial temperatures, Ti. The blue line and dots
correspond to a trajectory that was started from a non relaxed water conformation and
therefore shows higher diffusion rates than the one calculated for the red data which
corresponds to a trajectory calculated from a relaxed water conformation.
It is clear from Figure 16 that the diffusion coefficient does not depend only on
temperature but also on the initial state of the system. The trajectories with the nonrelaxed water conformation have higher diffusion coefficients than the trajectories
with the relaxed water conformation. The reason for the latter is that the water in the
non relaxed water conformation are less attached to the protein and are therefore more
free to move around the surface of the protein.
The regular diffusion coefficient is defined for equilibrium conditions which do not
apply here. Yet the system does reach a quasi steady state after a few hundred
femtoseconds. The activation energy for diffusion can be calculated from
52
equation(16) and was found to range from 4.7 ± 0.3 kcal/mol to 7.3 ± 0.3 kcal/mol
depending on the initial conditions. The highest effect of the initial conditions is at the
beginning of the trajectory before the system reaches quasi equilibrium, when the fit
to a straight line is poorest.
%
D
D0e
Ea
K bT
2 log ! D " log ! D0 " %
Ea
KbT
(16)
Where, D is the diffusion coefficient, D0 is the Diffusion constant at T & infinite
temperature, Ea is the activation energy Kb is the Boltzmann constant and T is the
temperature.
Since the surface of the protein is not uniform, with regards to electrostatic forces and
steric effects, there is a distribution of barriers for diffusion. This may lead to a
distribution of diffusion coefficients corresponding to different regions of the surface.
I.b.6. Structural properties of the protein
The structural properties of the protein were analyzed by two means, the Radius of
gyration of the protein and the root mean square (RMS) of the protein.
Radius of gyration
The Radius of Gyration was calculated from:
Rg
.m r
.m
2
i i
i
53
(17)
Where mi is the mass of atom i and ri is the distance of atom i from the center of mass.
Water molecules were not taken into account in these calculations.
The Radius of gyration was roughly constant throughout the simulations with an
average value of 12.64 Å for which the standard deviation was 0.4 Å.
RMS of the protein
The conformational changes of the protein are described by the all atom Root Mean
Square (RMS) deviation from the initial structure:
RMSi
1
ND
ND
&( r3 ! t " % r3 ! t " ')
.
3
i
0
2
(18)
1
Where r3(ti) and r3(t0) are the coordinate sets of the i'th structure and the initial
structure and ND is the number of atoms in the protein.
As can be seen from Figure 17, the change in the protein's RMS hardly exceeds 3Å
which means that the structural changes are relatively small, and the overall shape of
the protein is maintained during the simulations.
54
Figure 17: The all atom RMS of the protein for the trajectory started at 439°K
Comparison between the initial structure of the protein and the final structure can be
seen in figure 18. It can be visualized from the figure that there are barely any
changes in the backbone structure of the protein.
Figure 18: Native Cytochrome c (shown as cartoons without the heme group)
surrounded by 182 water molecules (shown by red balls for the oxygen and gray balls
for the hydrogens). Left: Initial structure. Right: Final structure, after simulation of
400 psec.
55
The conclusion from the radius of gyration, RMS analysis and visualization of the
structure is that the overall structural changes of the protein upon desolvation are
small.
Lysine side chains are very long and flexible. They are mostly found on the surface of
the protein due to the charge at the end of their long "tail" that is stabilized by
solvation by water. These side chains were found to move and stretch more than other
parts of the protein. This property is described in more details in the next section.
I.b.7. Structural changes with time during the evaporation dynamics
Different kinds of evaporation mechanisms are evident from the simulations. Most of
the time the evaporation process involves a single water molecule but in some rare
events evaporation of a dimer occurs. Figure 19 below shows snapshots of the system
at different times of the simulation. At the beginning the system is dense as the water
molecules are close to the surface of the protein. As the simulation proceeds the water
molecules that are not yet evaporated are positioned further away from the surface of
the protein. The whole system seems to expand. At the end of the simulation the
remaining water molecules are mostly located around the charge sites of the lysine
side chains. The lysine side chains are long and flexible, and in solution their charged
ends tend to point away from the protein surface. Water molecules aggregate near the
charged end of the lysines and stabilize the charge.
56
(a)
(b)
(c)
Figure 19: Snapshots of the system at different times of the simulation. Native
Cytochrome c (shown as cartoons) surrounded by 182 water molecules (shown by red
57
balls for the oxygen and white balls for the hydrogens) with the heme group (shown
in green) and the lysine side chains (shown in balls and stick format). (a) The initial
state. The water molecules here are very dense on the surface of the protein. (b) After
200 picoseconds. The arrangement of the water molecules expands to longer distances
from the surface of the protein. (c) After 400 picoseconds. Most of the remaining
water molecules are attached to the –NH3+ groups of the Lysine sidechains which
point away from the surface of the protein.
I.c. Conclusions
Mass spectrometric methods and in particular electrospray ionization techniques have
emerged in recent years as indispensable tools for the study of biological
macromolecules in the gas phase. So far only limited understanding is available of the
mechanisms involved in ESI. In the present study an attempt was made to deal with
an important aspect of ESI, namely the evaporation of water from the surface of the
protein following the formation of nano droplets. The molecular dynamics
simulations carried out here show several characteristics of this evaporation process.
First when starting with a monolayer of hydration water and realistic initial
temperatures, only a limited fraction of the water (10-50%) evaporates under energy
conservation conditions. The early loss of water molecules leads to rapid cooling on
the order of up to ~100ºK during the first 100 picoseconds, after which the remaining
water molecules are "frozen" on the surface. It also seems that there are no major
structural changes of the protein during the evaporation stage. Another observation is
that the remaining sub monolayer involves water molecules of low coordination. The
results are relevant for the interpretation of electrospray experiments in which the
energy that drives the desolvation process comes from the initial temperature of the
58
hydrated protein. Heating the protein by infrared radiation and/or collisions with gas
molecules during the electrospray process appears to be essential for complete
desolvation of proteins. As electrospray ionization is conducted at atmospheric
pressure, energy is supplied via collisions in all experimental studies, although to
different extents. Work in progress studies the evaporation of water from proteins
under constant temperature conditions.
II. Early structural evolution of native Cytochrome c after
solvent removal98
The structural study of biomolecules by mass spectrometry (MS) has recently
emerged as a promising alternative to conventional condensed-phase methods such as
nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography. There is
evidence that aspects of native protein99-101 and nucleic acid102-104 structure can be
retained after solvent removal in electrospray ionization (ESI)10 mass spectrometry
experiments. However, atomic-level detail of biomolecular structure in the gas phase
is not yet available. Reported here is computational data on structural changes of
native protein structure immediately after desolvation. Equine (FeIII)Cytochrome c
was chosen as model system, because it is well characterized in solution, and has also
been studied in gas phase experiments105. Equine Cytochrome c is a 104-residue
electron transfer protein with a covalently bound heme group; in solution, all charged
residues are surface exposed, with the charges pointing away from the protein surface
for efficient solvation in water (Figure 20)30.
59
Figure 20: NMR structure (pdb entry 1AKK)[5] of native equine (FeIII)Cytochrome
c, (a) N-terminal helix (residues 1-14), C-terminal helix (90-104), and '-loop (18-34)
in dark gray, (b) charged residues in dark gray.
ESI produces gas phase ions directly from solution, and accumulating evidence
suggests that the charge residue model (CRM)56, 57 is the dominating process in ESI of
native proteins63-65,
106-109
. It is assumed that solvent evaporation from nm-sized
droplets containing only one protein ion each results in the formation of gaseous ions.
Studies from the previous chapter of the desolvation process show no appreciable
changes of the native (FeIII)Cytochrome c structure during water evaporation53.
Moreover, the last water molecules to evaporate were found to aggregate around
charged sites, thereby shielding any intramolecular charge-charge and chargedipole
interactions in the largely desolvated structure. Reported here are MD simulations of
equine (FeIII)Cytochrome c in the complete absence of solvent, with focus on the
very first structural changes caused by dehydration.
60
II.a. Computational procedures
Atomistic detail Molecular Dynamics40 simulations were performed with MOIL45, a
modeling package for simulations of biological molecules. All simulations were
carried out under constant energy conditions in vacuo (no solvent water), with the
NMR structure of native equine (FeIII)Cytochrome c (pdb entry 1AKK) as starting
structure. To match conditions in NECD experiments (pH 5 of ESI solution), charge
sites were assigned according to calculated pKa values of ionizable residues in native
equine (FeIII)Cytochrome c, for details, see reference 10. No cutoff distance for nonbonded interactions was used in any of the simulations. Also no SHAKE algorithm
was used to ensure that all degrees of freedom were included in the calculations.
MD simulations were carried out starting from the 1AKK structure that was assigned
ten different initial atom velocity distributions, each of which represents a Boltzmann
distribution at 300 K. The ten resulting trajectories had timesteps of 0.2 fs and a total
length of 20 ps. Frames were saved every 20 steps, resulting in a frame every 4 fs.
For identification of salt links, distances between all nitrogens of lysine and arginine
sidechains carrying a positive charge, and all oxygens of glutamic and aspartic acid
carrying a negative charge were measured. A salt link between two residues of
opposite charge was defined when the distance between positive and negative charges
was smaller than 3 Å. For identification of ionic hydrogen bonds involving positively
charged sidechains ((+)iHBs), the distances between all nitrogens of lysine and
arginine sidechains carrying a positive charge, and all backbone amide oxygen or
61
nitrogen atoms were measured. A (+)iHBs was defined between a positively charged
sidechain and the backbone when the distance between charged nitrogen and
backbone heteroatom was smaller than 3 Å. For identification of ionic hydrogen
bonds involving negatively charged sidechains (-)iHBs, the distances between all
oxygens of glutamic and aspartic acid sidechains carrying a negative charge, and all
backbone amide oxygen or nitrogen atoms were measured. A (-)iHB was defined
between a negatively charged sidechain and the backbone when the distance between
charged oxygen and backbone heteroatom was smaller than 3 Å.
The geometrical centers of positive and negative charges were calculated as follows.
For the positive charge center, individual charge vectors originating from an arbitrary
reference point and pointing to the positive charges were multiplied by the
corresponding charge values (1 for all sites except for the heme iron, which was 3).
The vectorial sum of the resulting vectors was divided by the total number of positive
charges to give a vector pointing to the center of positive charges. The vector pointing
to the center of negative charges was calculated in the same manner. Subtraction of
the vector pointing to the center of negative charges from the vector pointing to the
center of positive charges gave the vector Z (equation 19), whose length (in Å) and
orientation is independent of the reference point chosen.
!"
Z
!"
. rp / q p
p
.q
%
p
!"
r
. n / qn
n
.q
n
p
n
62
(19)
Where rp represents a vector pointing to a positive charge indexed p, rn represents a
vector pointing to a negative charge indexed n, qp is the value of the positive charge
indexed p and qn is the absolute value of the negative charge indexed n.
For specification of Z orientation, two angles, ( and ), were defined with respect to
the plane spanned by three out of the four heme nitrogen atoms (the distance between
the fourth nitrogen atom and this plane was very small throughout all simulation,
about 0.1 Å on average, so that our reference plane is essentially the heme plane).
Here ( is the angle between Z and its orthogonal projection onto the plane, and ) is
the rotation angle of Z around a vector perpendicular to the plane.
II.b. Results
II.b.1. Reorientation of charged sidechains
Visual inspection of the protein structures from relatively short time (0-20 ps) and
highly resolved MD simulations showed that the first structural rearrangements after
desolvation generally involve charged sidechains. Most of these were found to rapidly
collapse onto the protein surface, illustrated in Figure 21 for protonated K79 forming
an ionic hydrogen bond with the amide oxygen of Y48.
63
Figure 21: Rapid formation of an ionic hydrogen bond, shown here for protonated
K79 and amide oxygen of Y48, (a) NMR structure 1AKK, (b) Molecular Dynamics
snapshot after 15 ps simulation time.
Attractive interactions of charged residues in proteins include charge-charge (salt
link) and charge-dipole (ionic hydrogen bond) interactions. The MD data for the
number of salt links (SL) and ionic hydrogen bonds involving positively, (+)iHB, as
well as negatively, (-)iHB, charged sidechains were therefore analyzed. Positive
charges in Cytochrome c are located on the NH3+ group of the lysine and on the NH2+
groups of the arginine sidechain as well as on the iron. The negative charges in
Cytochrome c are located on the COO- groups of the glutamic acid and aspartic acid
sidechain. Figure 22 shows that the number of salt links increases from 6 in the
solution structure to an average value of 17.3 within the first 10 ps. Within the same
time span, the number of ionic hydrogen bonds involving positively and negatively
charged sidechains increases from 0 to 11.6 on average, and from 5 to 6.3,
respectively. The number of positively and negatively charged sidechains in native
Cytochrome c at pH 5 is 21 and 12, respectively33, meaning that some of the charged
sidechains participate in more than one electrostatic interaction.
64
Figure 22: Number of (a) salt links, (b) ionic hydrogen bonds involving protonated
sidechains, and (c) ionic hydrogen bonds involving deprotonated sidechains for ten
trajectories (black lines) versus simulation time; average values shown as red lines.
The average number of electrostatic interactions increases exponentially with
simulation time, with rate constants of 1.497·1012 ± 0.020·1012 s-1, 0.533·1012 ±
0.004·1012 s-1, and 0.523·1012 ± 0.012·1012 s-1 for SL, (+)iHB, and (-)iHB formation,
respectively. Plateau values from the exponential fits are 17.2, 11.7, and 6.1 for SL,
(+)iHB, and (-)iHB formation, respectively, very close to the above average values for
10 ps simulation time. Considering error limits, the rate constants for (+)iHB and ()iHB formation are the same, whereas salt link formation proceeds about 2.8 times
faster. This finding is consistent with the longrange potential of charge-charge
interactions (1/r distance dependence), and the shorter-range potential of charge-
65
dipole interactions (1/r2 or 1/r4 distance dependence, depending on whether the
dipole is fixed or freely rotating)110.
II.b.2. Effect of initial charge distribution
Next we asked whether the new sidechain interactions formed randomly, or if
sidechain reorientation was affected by the overall distribution of charges. Native
equine (FeIII)Cytochrome c has a relatively large electric dipole moment of 1.08·10-27
C·m, mainly as a result of the inhomogeneous distribution of negatively charged
residues on the protein surface111, 112. However, calculation of electric dipole moments
is rather complex for proteins113, and our primary interest is in the distribution of
charges. A Z-vector that originates from the geometrical center of all negative
charges, and points to the center of all positive charges, with its length being a direct
measure of the protein's charge asymmetry (Figure 4a,b) was therefore introduce. Zvector orientation was calculated with respect to a plane spanned by three of the
heme’s nitrogen atoms, and described by two angles; ( and ) (please see
methodology section for details).
66
Figure 23: Distance between positive and negative charge centers for (a) NMR
structure 1AKK and (b) representative MD structure after 2.756 ps simulation time,
charged residues shown as balls and sticks; (c) length of Z-vector, and angles (b) (
and (c) ) of Z-vector orientation for ten trajectories (black lines) versus simulation
time; average values shown as red lines.
67
Z-vector length decreases exponentially with simulation time from 5.0 Å for the
native structure to an average value of 3.4 Å after 10 ps, whereas its orientation did
not change significantly (Figure 23c-e). The rate constant for the decrease in vector
length is 0.949·1012 ± 0.008·1012 s-1, about halfway between those for salt link and
ionic hydrogen bond formation. This indicates that all newly formed electrostatic
interactions contribute to the rapid decrease of Z-vector length. Apparently,
reorientation of all charged sidechains is governed by the initial charge distribution,
and proceeds in such a way as to minimize the protein's charge asymmetry and
therefore its dipole moment in the gas phase.
II.b.3. Changes in RMSD
Figure 24 shows root mean square deviations (RMSD) from the starting structure
1AKK for positively charged basic residues and C!-atoms for all trajectories. The
average RMSD of positively charged residues for the short trajectories increases
exponentially with a rate constant of 0.860·1012 ± 0.003·1012 s-1, between that for
SL and (+)iHB formation. After about 10 ps, the RMDS plateaus at 3.4 Å. Similar
results are found for the C!-atoms, for which the average RMSD increases with a
slightly smaller rate constant of 0.826·1012 ± 0.002·1012 s-1. The plateau value for
simulation times >10 ps is also smaller, 2.8 Å, consistent with substantial
reorientation of the charged residues while largely preserving the native backbone
fold. The plateaus found for both sidechain and C!-RMSD values from all
simulations suggest that after a short phase (~10 ps) of sidechain reorientation,
intermediate gas phase structures stabilized by new electrostatic interactions formed
in ESI.
68
(a)
(b)
Figure 24: Root mean square deviation from NMR structure 1AKK for all trajectories
for (a) positively charged residues and (b) C! atoms.
II.c. Conclusions
The MD simulations reported here reveal that the very first structural changes after
desolvation of a native protein structure generally involve charged sidechains. Rather
than breaking of noncovalent bonds, rapid formation of salt links and ionic hydrogen
bonds on the protein surface was observe. These new interactions do not form
randomly, but are directed in a way that significantly reduces the protein's dipole
moment. Apparently, any global structural changes caused by desolvation are
preceded by rearrangements of charged sidechains, resulting in transiently stabilized
structures with a backbone fold that is essentially the same as that in solution. These
newly formed electrostatic interactions could be responsible for transient stabilization
of the native fold after removal of bulk water, making possible the detection by mass
spectrometry of increasingly large and complex biomolecular architectures99, 101, 104.
On the other hand, arresting the formation of electrostatic interactions after
desolvation by heating and/or solution additives makes possible "top-down"
characterization of proteins as large as 200 kDa114 by electrospray techniques.
69
III. NECD cleavage of Cytochrome c: Computational study
and experiments98
Native electron capture dissociation (NECD)1 has recently provided residue-specific
information on structural changes of native equine Cytochrome c following transfer
into the gas phase24. The NECD data revealed a sequential unfolding mechanism, with
the terminal helices and the '-loop unfolding first (Figure 20a). It was found by
Englander and co workers that in solution the terminal helices are the last to unfold115,
116
. A new computational approach is presented in this work for the calculation of
cleavage sites in the protein backbone at the absence of water. NECD experiments
complemented with these computational data reveal atomic-level insight into the
effect of gaseous environment on protein structure.
In the proposed NECD mechanism1, backbone cleavage of gaseous Cytochrome c
ions occurs when (i) a proton is in close proximity to the cleavage site and (ii)
residues next to the cleavage site are in contact with the protein's heme group, which
is thought to transfer an electron. In native equine (FeIII)Cytochrome c30, 25 out of its
104 residues have noncovalent contact with the heme, including hydrophobic
interactions of 18 residues, hydrogen bonding with the heme propionates of 4
residues, coordinative bonding with the heme iron of H18 and M80, and an unspecific
T40/heme interaction. According to the proposed mechanism, NECD cleavage can
occur next to any of these residues, provided that contact with the heme is retained on
transfer into the gas phase, and a nearby positive charge is available. The formation of
ionic hydrogen bonds involving positively charged sidechains and amide oxygen
(Figure 21b) or nitrogen53 places charge in exactly the right position for NECD.
70
III.a. Methods
Atomistic detail Molecular Dynamics (MD) simulations were performed with MOIL45. All
simulations were carried out under constant energy conditions in vacuo (no solvent water),
with the NMR structure of native equine (FeIII)Cytochrome c1130 as starting structure. To
match conditions in NECD experiments (pH 5 of ESI solution), charge sites were assigned
according to calculated pKa values of the ionizable residues in native equine33. No cutoff
distance for non-bonded interactions was used in any of the simulations. Also no
SHAKE algorithm was used to ensure that all degrees of freedom were included in the
calculations.
Two sets of MD simulations were carried out. For the first set, the starting structure
1AKK was assigned ten different initial atom velocity distributions, each of which
represents a Boltzmann distribution at 300 K. The ten resulting trajectories had
timesteps of 0.2 fs and a total length of 20 ps. Frames were saved every 20 steps,
resulting in a frame every 4 fs. This first set of simulations is referred to as the short
and highly resolved simulations. For the second set of simulations, a short (0.5 ps)
MD simulation of the starting structure 1AKK was performed at 30 K to sample
slightly different initial structures (allatom RMSD <0.9 Å compared to 1AKK) for the
dynamics. Structures extracted from this trajectory were used as initial structures to
generate 10 trajectories with a starting temperature of 300 K; the simulations were run
with timesteps of 0.25 or 0.5 fs. Frames were saved every 10000 steps, resulting in
frames every 2.5 or 5 ps. The total lengths of the simulations in the second set varied
between 350 ps and 4.2 ns. This second set of simulations is referred to as the longer
71
simulations with moderate time resolution. The timesteps used in all the MD
simulations are smaller than the 1 fs step typically used for proteins, but were
necessary to maintain a high level of energy conservation.
For calculation of site-specific proton scores, distances between all charge-carrying
nitrogen atoms of lysine or arginine residues and the backbone amide oxygen or
nitrogen associated with a given cleavage site were measured for each frame. When
any of these distances was less than 3 Å, a score of one was assigned to the cleavage
site, and a score of zero otherwise. Proton scores of all frames considered were added,
divided by the number of frames, and multiplied by 100 to give %-values. Site
specific heme scores were calculated in a similar way, except that the cutoff distance
for protein/heme contacts was 5 Å (this was neccessary because MOIL treats CH3
groups as single atoms) and that individual score values were 0.5 and 0 instead of 1
and 0 (this accounts for the fact that each cleavage site is framed by two amino acids,
each of which can be in contact with the heme). For increased statistics in Figures 25
and 26, scores were calculated from eleven frames from each trajectory and time
indicated (frame at the time indicated, plus the five preceding and five subsequent
frames, covering time intervals of 40 fs; the 0 ps calculation used the 1AKK structure
and 10 subsequent frames), resulting in 110 frames for each time indicated. For
calculation of score values in Figure 28, 25010 frames from the short simulations
(time range 10-20 ps) and 8308 frames from the longer simulations were used.
72
III.b. Results:
Reproducing the experimentally observed protein backbone cleavage from the MD
simulations is impossible due to the fact that they use conventional harmonic
potentials for covalent bond representation. Nevertheless, it is possible to connect
experimental NECD data with the MD results by analyzing the latter for the proposed
requirements for backbone cleavage1 (i) a proton is in close proximity to the cleavage
site and (ii) residues next to the cleavage site are in contact with the protein's heme
group. For this purpose, two parameters are introduced, the "proton score" (P) and the
"heme score" (H). The proton score is a measure of how frequently a proton is in
proximity to a given cleavage site (for details on its calculation see the methods
section). The heme score is a measure of how frequently the residues framing a given
cleavage site are in close proximity to the heme (for details on its calculation see the
methods section). The score analysis was performed separately for all backbone sites
in the protein.
73
Figure 25: Site-specific proton score (P) versus cleavage site for simulation times 0,
0.5, 1, 2, 5, 10, and 20 ps.
Figure 25 shows site-specific proton scores for simulation times 0 to 20 ps. The
proton score for the native structure (0 ps) is zero for all sites as all charged residues
are exposed to solvent and point away from the protein surface (Figures 20b, 23a).
With increasing simulation time, the proton score increases rapidly as a consequence
of ionic hydrogen bond formation. Consistent with the plateau in number of ionic
hydrogen bond for simulation times >10 ps (Figure 22b), the proton scores at 10 and
20 ps are very similar. The site-specific heme score, on the other hand, does not
change significantly for simulation times of up to 20 ps (Figure 26), consistent with
the backbone fold being largely preserved throughout the simulations.
74
Figure 26: Site-specific heme score (H) versus cleavage site for simulation times 0,
0.5, 1, 2, 5, 10, and 20 ps.
To include both hypotheses (i) and (ii) from the proposed mechanism in the model for
prediction of NECD cleavages, the proton and heme scores were multiplied to obtain
predicted sitespecific NECD yields. Multiplication of the scores tests if both are high
for efficient cleavage under the assumption that both are independent. Figure 27
shows root mean square deviations (RMSD) from the starting structure 1AKK for
positively charged basic residues and C!-atoms for all trajectories. The average
RMSD of positively charged residues for the short trajectories increases exponentially
with a rate constant of 0.860·1012 ± 0.003·1012 s-1. After about 10 ps, the RMDS
plateaus at 3.4 Å. Data from the longer trajectories all lie in the range 3.4 ± 0.9 Å for
simulation times >10 ps (dashed lines in Figure 27a). Similar results are found for the
C!-atoms, for which the average RMSD increases with a slightly smaller rate constant
75
of 0.826·1012 ± 0.002·1012 s-1. The plateau value for simulation times >10 ps is also
smaller, 2.8 Å, consistent with substantial reorientation of the charged residues while
largely preserving the native backbone fold. C!-RMSD values from the longer
trajectories all lie in the range 2.8 ± 0.9 Å for simulation times >10 ps (dashed lines in
Figure 27b). The plateaus found for both sidechain and C!-RMSD values from all
simulations suggest that after a short phase (~10 ps) of sidechain reorientation,
intermediate gas phase structures stabilized by new electrostatic interactions formed
in ESI. For increased statistics in our NECD prediction, data for which C!-RMSD
values were in the range 2.8 ± 0.9 Å were therefore combined, i.e., all frames from the
short trajectories for simulation times >10 ps and data from the long trajectories of up
to 4.2 ns.
\
Figure 27: Root mean square deviation from NMR structure 1AKK for all trajectories
(black solid lines) of (a) positively charged residues and (b) C - atoms for simulation
times of up to 4.7 ns. Solid red lines are average values for the short (0-20 ps) MD
simulations.
76
The site-specific proton and heme score from this analysis is shown in Figure 28a and
b, respectively. Neither score alone shows particularly good agreement with
experimental NECD data (Figure 28d). Comparison between our computational
cleavage prediction (Figure 28c) and the experimental results (Figure 28d)1, on the
other hand, shows good agreement for most sites of the protein. This includes
cleavage after residue 12 (cleavage site 12), six adjacent cleavages at sites 35-40, five
cleavages at sites 45- 49, two cleavages at sites 51 and 52, cleavage at sites 59, 68, 79,
and three cleavages at sites 82 84. However, computation also predicts NECD
products from cleavage in the N-terminal helix, the !-loop, and the C-terminal helix
regions that were not observed experimentally (Figure 28d). The absence of these
products and the disappearance at higher inlet capillary temperatures of additional
predicted products in the NECD experiment is consistent with partial unfolding of the
native Cytochrome c structure the inlet capillary24 such that the corresponding
residues no longer have contact with the heme when NECD occurs (zero heme
score)117. Unfolding leading to NECD has a temperature-dependent timescale in the
low millisecond range (The time that takes for the protein to pass through the inlet
capillary). The native structure however, has been little modified by reorientation of
the charged sidechains on a low picosecond timescale.
77
Figure 28: Site-specific (a) heme score (H), (b) proton score (P), and (c) NECD score
predicted from MD data (N), and (d) experimental NECD yield from reference 1.
III.c. Conclusions:
A new computational approach based on MD simulations is reported here. The
predicted cleavage sites show good agreement with experimental results for most sites
of the protein. Disagreement was found for regions that undergo major structural
changes in the experiment, on a timescale not covered by the MD simulation
presented in this work. The MD simulations provide important atomic-level
78
information on the initial structural changes after desolvation, such as the rapid
formation of ionic hydrogen bonds and salt bridges. These newly formed electrostatic
interactions could be responsible for transient stabilization of the native fold after
removal of bulk water, making possible the detection by mass spectrometry of
increasingly large and complex biomolecular architectures.
79
CHAPTER
FOUR
80
Concluding Remarks
In conclusion of this work on computational study of biological macromolecules in
mass spectrometric experiments the main results and findings are examined below.
Mass spectrometric methods and in particular electrospray ionization (ESI) techniques
have proved to be extremely important tools for the study of physical aspects as well
as structural properties of biological macromolecules. Despite the extent and
increasing use of these techniques, understanding of the mechanism involved in ESI is
still limited. In the work presented in this thesis an attempt was made to better
understand some of the processes that take place at the different stages of the ESI
experiment by computational methods based on MD simulations. The study focuses
on the Cytochrome c protein because of the experimental data available for it. The
work was done in collaboration with the experimental groups of Prof. F. W.
McLafferty in Cornell University, USA and Dr. K. Breuker in the University of
Innsbruck, Austria. This collaboration helped pointing out, what stages in ESI are not
clear and where can computational study be important.
The different stages of the ESI experiments that are covered in this thesis are (i) the
desolvation process of the macromolecule, (ii) the electrical properties and the
structural changes of the protein immediately after solvent removal and (iii) the
clevage mechanism in ECD/NECD and its association with structure. The evaporation
of water from the surface of the protein following the formation of nano droples was
studied here by MD simulation initiated with the Cytochrome c protein covered by an
approximation of one monolayer of water. It was found that when realistic initial
81
temperatures are used, only a limiter fraction of water (10-50%) evaporates under
energy conservation conditions. This is due to the fact that early loss of water
molecules leads to rapid cooling on the order of up to 100 K during the first 100 ps,
after which the remaining water molecules “freeze” on the surface of the protein. No
major backbone structural changes were observed during the evaporation process and
the remaining sub monolayer involves water molecules of low coordination number.
These results are relevant to an extreme case of electrospray experiments were very
little energy is provided to facilitates the evaporation process. Heating of the system is
essential for complete desolvation of proteins. Future work on this project may
include the study of the evaporation process where energy is applied to the system.
For example, this could be done by running simulations in constant temperature
conditions were kinetic energy is regularly applied to the system in order to keep the
temperature from dropping.
One of the main questions of ESI is to what extent does the protein structure
preserved after solvent removal from its surface. It is believed that covalent bonds are
generally preserved during and after the phase transition that take place in
electrospray ionization experiments. But it is less clear to what extent non covalent
interactions are affected by the new gaseous environment. Short MD simulations
reveal that the first structural changes after desolvation of a native Cytochrome c
protein occur very early after less than one picosecond. These structural
rearrangements generally involve charges sidechains that form new non covalent
bonds such as salt bridges and ionic hydrogen bonds. These new interactions do not
form randomly but are rather directed in a way that significant reduces the dipole
moment of the protein. Longer simulations show that after the formation of these new
82
non covalent interactions the structure of the protein stabilizes and remain unchanged
for very long times of the order of nanoseconds. This means that the native backbone
structure of the protein is stabilized in the gas phase, due to these new electrostatic
interactions, making possible the study of large complexes by the ESI methods.
The mechanism in which protein cleavage takes place, in the gas phase, is an open
question. It was suggested that cleavage results from a simultaneous attack of a proton
and an electron on a peptide bond but, no proof was made on this suggested
mechanism. In this work, a new computational approach for cleavage site prediction,
based on the above suggested mechanism, is introduced. Comparison of the predicted
cleavage sites for Cytochrome c with NECD experimental data for the same protein
show good agreement, indicating high certainty of the proposed mechanism.
Comparison between the computational prediction and NECD data also suggests that
global structural changes take place on a millisecond timescale not covered by the
MD simulations. The new computational approach presented in this work is general
and can be implied to any protein that undergo NECD mechanism, that is, a protein
that contains a heme group.
The work described in this thesis give explanation to some of the stages involved in
the ESI experiment, and yet there is much more that can be studied on these
processes. For example, the evaporation process studied here is in one extreme of the
experimental conditions, that is, under constant energy conditions. It would be very
interesting to study the other extreme, which is, under the conditions of constant
temperature. Combination of these two studies could give a full view of the
mechanisms involved. Another example for possible future work is the study of the
83
charge properties of the protein after desolvation at longer times, and the
understanding of whether the “dipole moment” of the protein drops at short times and
remains low or oscillates.
84
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