Enzyme Kinetics Using Isothermal
Calorimetry
Malin Suurkuusk
TA Instruments
October 2014
ITC is a powerful tool for determining enzyme
kinetics
Reactions, including enzymatic reactions, produce or absorb heat
ITC is a facile technique for characterizing enzyme kinetics, and
enzyme inhibition
Thermodynamics controls substrate recognition,
binding and catalysis
Selectively Binding
H-bonds and electrostatic interactions with specific amino acid side chains
in the active site.
Correct shape and coordination required for recognition and creating the
correct product.
Michaelis-Menten Kinetics
Pseudo first order:
The rate or velocity (v) of the reaction is given by the Michaelis-Menten
relationship:
v = d[P]/dt = (vmax[S])/(KM + [S])
vmax = maximum velocity at saturating
substrate concentration [S]
KM = value of [S] at which v = (Vmax/2)
[P] = concentration of the product
released
Enzyme turnover number (Kcat)
Kcat = vmax[E]total
Studying enzyme kinetics by ITC
The amount of heat involved in converting n moles of substrate to
product is:
Q = n ⋅ ∆H app = [P ]Total ⋅ V ⋅ ∆H app
Rearrange:
dP
1
dQ
Rate( ) =
×
dt
Vo ⋅ ∆H app dt
where d[P]/dt is the
rate of the reaction
Measuring the thermal power generated by the enzyme as it converts
substrate to product provides the reaction rate:
kcat ⋅ [ETotal ]⋅ [S ]
Rate =
K M + [S ]
KM, vmax, and kcat can be subsequently determined from a plot of v vs [S].
Two Techniques for Determining Kinetic
Parameters
1. Multiple Injection Method (MIM)
1. Two Steps
2. Single Injection Method (SIM)
Multiple Injection Method (MIM) Titration A:
Determine Rate
250 mM Sucrose 3.7 nM invertase, 100 mM NaAc pH 5.6
[S] is known and [E]
is eventually limiting.
Vmax region
[S]cell final > Km
Steady State
conditions Required.
>5 % of the
substrate is
depleted prior
to the next
injection.
MIM Titration A: Determine Rate
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1. Determine the differential power prior to the first injection.
2. Determine baseline/differential power after the injection (dQ/dt). The injection is NOT the
event.
The baseline shifts because of the continuous turnover
MIM Titration B: Determine Enthalpy
4.5 mM Sucrose 5 µM invertase, 100 mM NaAc pH 5.6 (3 uL injections 25°C)
Enzyme is not limited
and all substrate is
converted into product.
Enthalpy similar to
previously published
values on an
isoperibolic
calorimeter (Huttle,
Oehlschlager, Wolf
Thermochimica Acta. 325 (1999)
1-4).
Proton coupled
equilibria could exist.
(∆HBH: Fukada and Takahashi.
Proteins 33(1998)159-166)
∆ HITC = ∆HR + ∆ HBH
Michaelis-Menten and Lineweaver-Burk Plots
kcat = Vmax/Etotal
KM agrees with published value of 49 mM, using traditional UV-Vis and colorimetric probe
(Combes and Monsan. Carbohydrate Research, 117 (1983) 215-228).
When is MIM Limited?
Cases when the
incremental method
is not ideal:
Low dQ/dt
dQn/dt = 0.06 µJ/s
KM = 4 µM kcat =15 s-1
Todd and Gomez.
Analytical
Biochemistry.
296.(2001) 179-187.
SIM
Good agreement
even with small dQ/dt!
Single Injection Method (SIM) Kinetics
Usually a moderate concentration of the substrate
is used (mM or µM) and a relatively high
concentration in of enzyme is in the syringe (µM or
nM).
Reverse Option
To avoid starting the reaction early, use a buffer plug
ɣ
The heat flow (dQ/dt)
(dP/dt), rate
Enzyme
Most experimental time < 1 hr.
Instrument response time consideration: reaction
completion times at least one order of magnitude
greater than the instrumental response time.
This typically means use more substrate
Total
injection
Buffer
plug
Substrate
SIM: Determining the Best Conditions
2.5 mM
37 µM Invertase, 5µL (8 µL
total) titrated into varying
concentrations of sucrose
100 mM Glycine Buffer pH
5.65
0.25 mM
0.025 mM
Enzyme into substrate
Buffer into substrate
Negatives: 1. relatively rapid
turnover, on a similar order of
magnitude as the mixing. 2.
Significant amount of the heat
generated is from dilution, errors
in the enthalpy.
Determining the Enthalpy
The substrate, here in the cell, is completely
turned over into product.
Normalize the area to the moles of substrate.
(∆Happ)
Background correct (blue)
SIM: Determining [S] and rate
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Substrate is being consumed at a rate proportional to dQ/dt.
Method 1 : Common model used: dQ/dt = dHappVk[S0] exp(-kt)
Obtain the fractional rate, which will give the fractional remainder
of [S], example of how to obtain this:
= αn and [S]n = (1-αn)*[S0]
Downside – partial analysis of curve, only the decay
Method 2: Use Alternative Modeling
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Points above are not actual data point intervals.
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Method 2: Information Geometry and Data Fitting
Example
Typical problems with fitting algorithms:
1. Narrow Boundaries Widths
2. Local Minima
Geodesic Levenberg-Marquardt
• Fast convergence
• Robust to initial guesses
• Avoids manifold boundaries
• Open source FORTRAN package
Work completed with M. Transtrum and L. Hansen. BYU, Provo, UT
Geodesic Minimization and Time Constant
correction
Simultaneous fit to 3 data sets
Michaelis-Menten kinetics (invertase
into sucrose)
Fitting parameters with and without time
constant
Parameter
tau > 0
tau = 0
tau
64.5
0.0
KM (M-1)
0.050
0.080
∆H (kJ/mol)
13.0
12.4
All of the parameters in the table
are calculated simultaneously
Work completed with M. Transtrum and L. Hansen. BYU, Provo, UT.
Kinetics in the ITC - Summary
Advantages of evaluating kinetic information via ITC:
Complex systems (study crowding effects –
conditions mimic cell protein concentrations (250 mg/mL BSA),
Olsen 2006)
Cloudy systems
No need for labels
Continuous assay
Inhibition Studies work also
Two Different Techniques
MIM
SIM
Enzyme inhibition, SIM
2.5
A
heat rate / µW
2
1.5
1
0.5
0
0
1000
1500
2000
2500
3000
3500
4000
time / s
20
18
B
16
14
rate / s-1
Blue: 10 µL 5.1 x 10-7 M trypsin injected
into 950 µL 1.44 x 10-4M BAEE
Red: plus 1.36 x 10-4 M benzamidine
Total heat identical (∆H = -6.33 kcal/mol
BAEE)
(-) inhibitor: KM = 4.17 µM; Vmax = 0.091
µMol/s, kcat = 17.8 s-1
(+) inhibitor: KM = 35.1 µM; Vmax = 5.9 x
10-4 µMol/s, kcat = 0.11 s-1, Ki = 18.4 µM
500
12
10
8
6
4
2
0
0
20
40
60
80
[S] / µM
100
120
140
High Solid Content – TAM Assay
Bioethanol application
Optimize degradation of cellulosic biomass
Cellulosic substrates: Avicel & pretreated corn stover (PCS)
Major Difficulties for Traditional Methods
1. Cellulose Hydrolysis: A Complex Enzyme system
cellobiohydrolases (CBH) – attacks end of polymer, creates cellobiose
endoglucosidases (EG) – creates ends by attacking glucosidic bonds
Beta-glucosidases (BG) – converts cellobiose to glucose
2. 29% solids (w/w)
3. High viscosity
Olsen, S. et al. Appl. Biochem Biothechnol (2011) 163:626-635)
TAM ITC vs NanoITC
Removable cell
Flexible volume (from 0.5 ml
to 20 ml, depending on
reaction vessel)
Flexible reaction vessels (1,4
or 20 ml) and stirrers (single
propeller, double propeller,
paddle, turbine)
Visualisation possible
Separate stirrer and injection
needle
Less sensitive and slower
response
Fixed-in-place cell
Fixed constant volume
(950 or 190 µL)
Injection needle and
stirrer in one
More sensitive and
faster response
TAM ITC is more flexible in experimental control,
but lacks the higher sensitivity Nano ITC offers
High Solid Content – TAM Assay
CE = rate/enzyme
PCS
enzyme limitation
t to 16% conversion
Large Graph
1. Substrate limited: Low CE with
high enzyme. Insufficient ends
available
2. Enzyme limited: EG created more
ends for CBH attack
Substrate limitation
Inset: CE under identical substrate concentrations
1. Separate time dependent contributions from slowdown rate
(irreversible enzyme inactivation)
2. Time required to reach conversion is either identical in CE or
increases (Avicel, not shown), which means that it is not enzyme
inactivation overtime causes the slow-down.
Olsen, S. et al. Appl. Biochem Biothechnol (2011) 163:626-635)
Isothermal Calorimetry
1
dP
dQ
×
Rate( ) =
dt
Vo ⋅ ∆H app dt
A global technique for enzymatic reactions