Enzyme Kinetics Using Isothermal Calorimetry. Malin Suurkuusk TA Instruments October 2014

Transcription

1 Enzyme Kinetics Using Isothermal Calorimetry Malin Suurkuusk TA Instruments October 2014

2 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

3 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.

4 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 = (v max [S])/(K M + [S]) v max = maximum velocity at saturating substrate concentration [S] K M = value of [S] at which v = (V max /2) [P] = concentration of the product released Enzyme turnover number (K cat ) K cat = v max [E] total

5 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 Rate( ) dt = V o 1 H app dq 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: Rate = k cat K [ ETotal ] [ S] + [ S] K M, v max, and k cat can be subsequently determined from a plot of v vs [S]. M

6 Two Techniques for Determining Kinetic Parameters 1. Multiple Injection Method (MIM) 1. Two Steps 2. Single Injection Method (SIM)

7 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. V max region [S] cell final > K m Steady State conditions Required. >5 % of the substrate is depleted prior to the next injection.

8 MIM Titration A: Determine Rate 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

9 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. ( H BH : Fukada and Takahashi. Proteins 33(1998) ) H ITC = H R + H BH

10 Michaelis-Menten and Lineweaver-Burk Plots k cat = V max /E total K M agrees with published value of 49 mm, using traditional UV-Vis and colorimetric probe (Combes and Monsan. Carbohydrate Research, 117 (1983) ).

11 When is MIM Limited? Cases when the incremental method is not ideal: Low dq/dt dq n /dt = 0.06 µj/s K M = 4 µm k cat =15 s -1 Todd and Gomez. Analytical Biochemistry. 296.(2001) SIM Good agreement even with small dq/dt!

12 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 The heat flow (dq/dt) ɣ (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

13 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 Enzyme into substrate Buffer into substrate 0.25 mm mm 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.

14 Determining the Enthalpy The substrate, here in the cell, is completely turned over into product. Normalize the area to the moles of substrate. ( H app ) Background correct (blue)

15 SIM: Determining [S] and rate Substrate is being consumed at a rate proportional to dq/dt. Method 1 : Common model used: dq/dt = dh app Vk[S 0 ] exp(-kt) Obtain the fractional rate, which will give the fractional remainder of [S], example of how to obtain this: = α n and [S] n = (1-α n )*[S 0 ] Downside partial analysis of curve, only the decay Method 2: Use Alternative Modeling Q n Points above are not actual data point intervals.

16 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

17 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 K M (M -1 ) H (kj/mol) All of the parameters in the table are calculated simultaneously Work completed with M. Transtrum and L. Hansen. BYU, Provo, UT.

18 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

19 Enzyme inhibition, SIM A heat rate / µw Blue: 10 µl 5.1 x 10-7 M trypsin injected into 950 µl 1.44 x 10-4 M BAEE Red: plus 1.36 x 10-4 M benzamidine Total heat identical ( H = kcal/mol BAEE) (-) inhibitor: K M = 4.17 µm; V max = µmol/s, k cat = 17.8 s -1 (+) inhibitor: K M = 35.1 µm; V max = 5.9 x 10-4 µmol/s, k cat = 0.11 s -1, K i = 18.4 µm rate / s time / s B [S] / µm

20 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: )

21 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

22 High Solid Content TAM Assay CE = rate/enzyme PCS enzyme limitation Substrate 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 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: )

23 Isothermal Calorimetry dp Rate( ) dt = V o 1 H app dq dt A global technique for enzymatic reactions