Overview of Kinetics [P] t = ν = k[s] Velocity of reaction Conc. of reactant(s) Rate of reaction M/sec Rate constant sec -1, M -1 sec -1 1 st order reaction-rate depends on concentration of one reactant S P [P] t = ν = k[s] 2 nd order reactions may Depend on two reactants S 1 + S 2 P [P] t = ν = k[s 1] S 2
Review of Kinetics Most of the time reactions obtain equilibrium k 1 and k -1 are the rate constants for forward And reverse reactions K eq = [P] eq [S] eq = k 1 k 1 Kinetic rate constants are useful in determining equilibrium chemistry When equilibrium is reached: rate of forward and reverse reactions are the same.
Determination of rates and rate constants Method of initial rates (V o ) at different [S] o to determine rate constants -measure V o very early in the reaction -very little product has formed (equilibrium is not a factor) Figure 7.2 [S] o
Enzyme Kinetics E = enzyme S = substrate P = product ES = enzyme substrate complex k 1 = rate constant for ES binding -IF k 1 is very large, binding is very favorable k 2 = rate constant for P formation from ES - IF k 2 is very large, conversion to product is fast. This enzymatic reaction depends upon both the [E] and [S]
Enzyme Kinetics - A more common reaction scheme or mechanism involves a reversible binding of E and S. Define a dissociation constant (K d ), measure of S binding to E. K d = k 1 k 1 If k 1 >> k -1, S binding is very favorable. A small value for K d means binding is favorable
Enzyme kinetics terminology [S] substrate concentration V o initial velocity of a reaction. A significant amount of substrate has not yet been converted to product. V max maximal velocity of a reaction. Addition of more substrate will not increase the rate of the reaction. K M The concentration of substrate at which the rate of the reaction is half-maximal
A commonly observed behavior for enzyme catalyzed reactions showing the change in V o as [S] is changed This region is zero order in [S] This region is 1 st order in [S] This behavior can be described mathematically by the Michaelis-Menten equation Vo= V max[s] K M +[S]
k 2 (called k cat ) is a measure of the number of substrate molecules converted to product per second per enzyme molecule k cat is called catalytic constant and is determined at high [S] k cat /K M is a rate measure of catalytic efficiency for the conversion of E + S E + P
Turnover numbers (k cat ) CO 2 + H 2 O HCO 3 - (1.7 microseconds (ms) per reaction) Chymotrypsin catalyzes peptide cleavage (0.01 sec per cleavage)
Experimental method for determining V max and K M Figure 7.5 Plot the reciprocal of The Michaelis-Menten Equation. A linear equation is generated
Allosteric enzymes and regulation These complex metabolic pathways must be regulated. Figure 7.7
Regulation of metabolic pathways In Feedback Inhibition, high concentration of the product of a pathway controls the rate of its own synthesis by inhibiting an early step Flux through the pathway is regulated depending on the concentration of Product (K below) In Allosteric Activation, high concentration of a metabolite early in the pathway activates enzymes for synthesis of the final product. Flux through the pathway is regulated depending on the concentration of Metabolites (F and I below)
Feed-Forward Activation - Metabolite early in the pathway activates an enzyme further down the pathway B is an allosteric activator
Figure 7.11 Effect of regulators on aspartate transcarbamoylase CTP ATP relaxes the enzyme (R state favored) Binding of substrates more favored CTP makes enzyme more tense (T state favored) binding of substrates less favored
Regulation by covalent modification Enzyme activity can be modified by covalent attachment and removal of groups on the polypeptide chain reversible phosphorylation Pyruvate dehydrogenase catalyzes a reaction that link glycolysis and the citric acid cycle. Phosphate is removed from serine residue reactivated form Phosphate is attached to serine residue Inactive form
Assignment Read Chapter 7 Read Chapter 8 Topics not covered: Concerted and Sequential models Section 7.4 Enzymes can be studied one molecule at a time.