Prof. R. Shanthini 23 Sept 2011 Enzyme kinetics and associated reactor design: Determination of the kinetic parameters of enzyme-induced reactions CP504 – Lecture 4 - learn about the meaning of kinetic parameters - learn to determine the kinetic parameters - learn the effects of pH and temperature on reaction rates - learn about inhibited enzyme kinetics - learn about allosteric enzymes and their kinetics

Prof. R. Shanthini 23 Sept 2011 E + S ESE + P k1k1 k2k2 k3k3 which is equivalent to S P [E] S for substrate (reactant) E for enzyme ES for enzyme-substrate complex P for product Simple Enzyme Kinetics (in summary)

Prof. R. Shanthini 23 Sept 2011 where r max = k 3 C E0 and K M = f(rate constants) - r S r max C S = K M + C S r P = Simple Enzyme Kinetics (in summary) S P [E] r max is proportional to the initial concentration of the enzyme K M is a constant

Prof. R. Shanthini 23 Sept r S r max C S = K M + C S CsCs r max 2 KMKM -r s Catalyzed reaction uncatalyzed reaction Simple Enzyme Kinetics (in summary)

Prof. R. Shanthini 23 Sept 2011 How to determine the kinetic parameters r max and K M ? Carry out an enzyme catalysed experiment, and measure the substrate concentration (C S ) with time. From the data, we could calculate the substrate utilization rate (-r s ) as follows: tCsCs - r s r max C S = K M + C S - r S

Prof. R. Shanthini 23 Sept 2011 How to determine the M-M kinetics r max and K M ? Carry out an enzyme catalysed experiment, and measure the substrate concentration (C S ) with time. From the data, we could calculate the substrate utilization rate (-r s ) as follows: tCsCs - r s 050(50-45)/ (45-41)/ r max C S = K M + C S - r S

Prof. R. Shanthini 23 Sept 2011 r max C S = K M + C S - r S We could rearrange to get the following 3 linear forms: = - r S CSCS r max KMKM 1 + CSCS = - r S 1 r max KMKM 1 + CSCS 1 = - r S r max KMKM - CSCS - r S (15) (14) (16)

Prof. R. Shanthini 23 Sept 2011 = - r S CSCS r max KMKM 1 + CSCS (14) CSCS - r S CSCS 1 r max - K M The Langmuir Plot

Prof. R. Shanthini 23 Sept 2011 = - r S CSCS r max KMKM 1 + CSCS (14) CSCS - r S CSCS 1 r max - K M The Langmuir Plot Determine r max more accurately than the other plots.

Prof. R. Shanthini 23 Sept 2011 (15) - r S 1 KMKM r max - K M The Lineweaver-Burk Plot = - r S 1 r max KMKM 1 + CSCS 1 CSCS 1 1

Prof. R. Shanthini 23 Sept 2011 (15) - r S 1 KMKM r max - K M The Lineweaver-Burk Plot = - r S 1 r max KMKM 1 + CSCS 1 CSCS Gives good estimates of r max, but not necessarily K M - Data points at low substrate concentrations influence the slope and intercept more than data points at high C s

Prof. R. Shanthini 23 Sept 2011 (16) - r S KMKM K M The Eadie-Hofstee Plot CSCS -r S r max = - r S r max KMKM - CSCS - r S

Prof. R. Shanthini 23 Sept 2011 (16) - r S KMKM K M The Eadie-Hofstee Plot CSCS -r S r max = - r S r max KMKM - CSCS - r S - Can be subjected to large errors since both coordinates contain (-r S ) - Less bias on point at low C s than with Lineweaver-Burk plot

Prof. R. Shanthini 23 Sept 2011 C S (mmol/l) -r S -(mmol/l.min) Data: Determine the M-M kinetic parameters for all the three methods discussed in the previous slides.

Prof. R. Shanthini 23 Sept 2011 r max = 1 / slope = 1 / = 0.63 mmol/l.min K M = r max x intercept = 0.63 x = 2.93 mmol/l

Prof. R. Shanthini 23 Sept 2011 r max = 1 / intercept = 1 / = 0.51 mmol/l.min K M = r max x slope = 0.51 x = 1.78 mmol/l

Prof. R. Shanthini 23 Sept 2011 r max = intercept = 0.54 mmol/l.min K M = - slope = 1.89 mmol/l

Prof. R. Shanthini 23 Sept 2011 The Langmuir Plot The Lineweaver- Burk Plot The Eadie- Hofstee Plot r max KMKM R2R2 Comparison of the results

Prof. R. Shanthini 23 Sept 2011 The Langmuir Plot The Lineweaver- Burk Plot The Eadie- Hofstee Plot r max KMKM R2R2 94.9%84.6%66.2% Comparison of the results

Prof. R. Shanthini 23 Sept 2011 The Langmuir Plot The Lineweaver- Burk Plot The Eadie- Hofstee Plot r max KMKM R2R2 94.9%84.6%66.2% Determine r max more accurately than the other plots Gives good estimates of r max, but not necessarily K M Can be subjected to large errors Comparison of the results

Prof. R. Shanthini 23 Sept The effects of pH and temperature on reaction rate Most enzymes function over a broad range of pHs and temperatures. However, they have an optimal pH and temperature for peak activity. In general, enzyme activities increase with increasing temperatures; however, as temperatures get higher, enzymes begin to denature. Most enzymes are also sensitive to pH. As with temperature, the optimal pH for an enzyme depends on the environment in which it normally functions.

Prof. R. Shanthini 23 Sept 2011 The effects of temperature on reaction rate Temperature (deg C) Reaction rate Optimal for most human enzymes Optimal for some thermophillic bacterial enzymes

Prof. R. Shanthini 23 Sept 2011 The effects of pH on reaction rate pH Reaction rate Optimal for pepsin (a stomach enzyme) Optimal for trypsin (an intestinal enzyme)

Prof. R. Shanthini 23 Sept 2011 Effect of shear

Prof. R. Shanthini 23 Sept 2011 Complex enzyme kinetics - learn about inhibited enzyme kinetics - learn about allosteric enzymes and their kinetics

Prof. R. Shanthini 23 Sept 2011 Inhibited enzyme reactions Inhibitors are substances that slow down the rate of enzyme catalyzed reactions. There are two distinct types of inhibitors: - Irreversible inhibitors form a stable complex with enzymes and reduce enzyme activity (e.g. lead and cadmium) - Reversible inhibitors interact more loosely with enzymes and can be displaced.

Prof. R. Shanthini 23 Sept 2011 Inhibited enzyme reactions Inhibitors are also classified as competitive and non-competitive inhibitors.

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition A competitive inhibitor has a chemical and structural similarity to the substrate. It competes with the substrate for the position at the active site of the enzyme. The rate of the reaction slows down because the active site is occupied by the competitive inhibitor, making the active site less accessible to the substrate.

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition Competitive inhibitors (denoted by I) compete with substrate to occupy the active site of the enzyme. E + S ESE + P k1k1 k2k2 k3k3 E + I EI k4k4 k5k5 r P = k 3 C ES (17) C E0 = C E + C ES + C EI where (18)

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition Assuming rapid equilibrium, we get k 1 C E C S = k 2 C ES k 4 C E C I = k 5 C EI k2k2 k1k1 K M = C E C S C ES = k5k5 k4k4 K I = C E C I C EI = (19) (20)

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition Combining (17) to (20), we get k 3 C E0 C S r P = r max C S = K M,app + C S (21) K M (1 + C I / K I ) + C S where K M,app = K M (1 + C I / K I ) (22) K M = k 2 / k 1 (6) (5) r max = k 3 C E0 K M,app > K M

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition - r S 1 - K M The Lineweaver-Burk Plot r max 1 CSCS K M, app 1 C I = 0 (no inhibitor) C I > 0

Prof. R. Shanthini 23 Sept 2011 Competitive inhibition In the presence of a competitive inhibitor, the maximal rate of the reaction (r max ) is unchanged, but the Michaelis constant (K M ) is increased.

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition Non-competitive inhibitor binds to the enzyme, but not on the active site. It therefore does not compete with the substrate. However, non-competitive inhibitor causes the enzyme’s active site to change shape and as a result, the substrate can no longer bind to it, decreasing the rate of the reaction.

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition E + S ESE + P k1k1 k2k2 k3k3 E + I EI k4k4 k5k5 EI + S EIS k6k6 k7k7 ES + I ESI k8k8 k9k9

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition k2k2 k1k1 = K M = We could drive the rate equation (given on the next page) assuming the following: k7k7 k6k6 = K IM k5k5 k4k4 = K I = k9k9 k8k8 = K MI

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition r P = r max,app C S K M + C S (23) where K M = k 2 / k 1 (6) (5) r max = k 3 C E0 r max,app < r max r max,app = (1 + C I / K I ) r max (24)

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition - r S 1 - K M The Lineweaver-Burk Plot r max 1 CSCS 1 1 C I = 0 (no inhibitor) C I > 0 r max,app 1

Prof. R. Shanthini 23 Sept 2011 Non-competitive inhibition In the presence of a non-competitive inhibitor, the maximal rate of the reaction (r max ) is lower but the Michaelis constant (K M ) is unchanged.

Prof. R. Shanthini 23 Sept 2011 Sigmoid/Hill kinetics A particular class of enzymes exhibit kinetic properties that cannot be studied using the Michaelis-Menten equation. The rate equation of these unique enzymes is characterized by Sigmoid/Hill kinetics as follows: r P = r max C S n K + C S n (25) n = 1 gives Michaelis-Menten kinetics n > 1 gives positive cooperativity n < 1 gives negative cooperativity The Hill equation Hill coefficient Hill constant

Prof. R. Shanthini 23 Sept 2011 Sigmoid/Hill kinetics Examples of the “S-shaped” sigmoidal/Hill curve, which is different from the hyberbolic curve of M-M kinetics. n = 2 n = 4 n = 6

Prof. R. Shanthini 23 Sept 2011 Sigmoid kinetics 1 - θ CSnCSn K + C S n (26) For an alternative formulation of Hill equation, we could rewrite (25) in a linear form as follows: θ ln = n ln(C S ) – ln ( K ) r max θ = = rPrP

Prof. R. Shanthini 23 Sept 2011 “Food for Thought” Problem 3.13 from Shuler & Kargi: The following substrate reaction rate (-r S ) data were obtained from enzymatic oxidation of phenol by phenol oxidase at different phenol concentrations (C S ). By plotting (-r S ) versus (C S ) curve, or otherwise, determine the type of inhibition described by the data provided? C S (mg/l) -r S (mg/l.h)

Prof. R. Shanthini 23 Sept 2011 Substrate inhibition Cover it next time

Prof. R. Shanthini 23 Sept 2011 Uncompetitive inhibition Cover it next time

Prof. R. Shanthini 23 Sept 2011 Allosteric enzyme Cover next time in relation to competitive inhibition