Enzyme Kinetics Using Isothermal Calorimetry

Malin SuurkuuskTA InstrumentsOctober 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

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

The rate or velocity (v) of the reaction is given by the Michaelis-Mentenrelationship:

v = d[P]/dt = (vmax[S])/(KM + [S])

Pseudo first order:

Studying enzyme kinetics by ITC

� The amount of heat involved in converting n moles of substrate to product is:

Rearrange:

� Measuring the thermal power generated by the enzyme as it converts substrate to product provides the reaction rate:

[ ] appTotalapp HVPHnQ ∆⋅⋅=∆⋅=

dt

dQ

HVdt

dPRate

appo

×∆⋅

=1

)(

[ ] [ ][ ]SK

SEkRate

M

Totalcat

+

⋅⋅=

where d[P]/dt is the

rate of the reaction

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)

� [S] is known and [E] is eventually limiting.

� [S]cell final > Km

� Steady State conditions Required.� >5 % of the

substrate is depleted prior to the next injection.

Vmax region

Multiple Injection Method (MIM) Titration A: Determine Rate

� 250 mM Sucrose � 3.7 nM invertase, 100 mM NaAc pH 5.6

MIM Titration A: Determine Rate

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

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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 isoperiboliccalorimeter (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

� KM agrees with published value of 49 mM, using traditional UV-Vis and colorimetric probe

(Combes and Monsan. Carbohydrate Research, 117 (1983) 215-228).

kcat = Vmax/Etotal

When is MIM Limited?

� Cases when the incremental method is not ideal:� Low dQ/dt

� KM = 4 µM kcat =15 s-1

Todd and Gomez. Analytical Biochemistry. 296.(2001) 179-187. SIM

� Good agreement even with small dQ/dt!

dQn/dt = 0.06 µJ/s

Single Injection Method (SIM) Kinetics

� Usually a moderate concentration of the substrateis 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

� The heat flow (dQ/dt) (dP/dt), rate

� 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

Buffer plug

Total injection

Enzyme

Substrateɣ

37 µM Invertase, 5µL (8 µL total) titrated into varying concentrations of sucrose100 mM Glycine Buffer pH 5.65

2.5 mM

0.025 mM

0.25 mM

SIM: Determining the Best Conditions

� 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.

Enzyme into substrate

Buffer into substrate

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)

Qn

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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SIM: Determining [S] and rate

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 (invertaseinto 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

Work completed with M. Transtrum and L. Hansen. BYU, Provo, UT.

� All of the parameters in the table are calculated simultaneously

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

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/molBAEE)

(-) 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

A

0

0.5

1

1.5

2

2.5

0 500 1000 1500 2000 2500 3000 3500 4000

time / s

hea

t ra

te / µ

W

B

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100 120 140

[S] / µM

rate

/ s

-1

High Solid Content – TAM Assay

Bioethanol applicationOptimize degradation of cellulosic biomassCellulosic substrates: Avicel & pretreated corn stover (PCS)

Major Difficulties for Traditional Methods

1. Cellulose Hydrolysis: A Complex Enzyme systemcellobiohydrolases (CBH) – attacks end of polymer, creates cellobioseendoglucosidases (EG) – creates ends by attacking glucosidic bondsBeta-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

Olsen, S. et al. Appl. Biochem Biothechnol (2011) 163:626-635)

PCS

Inset: CE under identical substrate concentrations1. 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.

CE

= r

ate

/enzym

e

t to 16% conversion

Substrate limitation

enzyme limitation

Large Graph1. Substrate limited: Low CE with

high enzyme. Insufficient ends available

2. Enzyme limited: EG created more ends for CBH attack

Isothermal Calorimetry

dt

dQ

HVdt

dPRate

appo

×∆⋅

=1

)(

A global technique for enzymatic reactions