# CHAPTER 6 - TRANSPORT AND KINETICS

## B:  Kinetics of Simple and Enzyme-Catalyzed Reactions

BIOCHEMISTRY - DR. JAKUBOWSKI

4/10/16

 Learning Goals/Objectives for Chapter 6B:  After class and this reading, students will be able to write appropriate chemical and differential equations for the rate of disappearance of reactants or appearance of products for 1st order, pseudo first order, second order, reversible first order reactions draw and interpret graphs for integrated rate equations (showing reactant or product concentrations as a function of time) and initial rate equations (showing the initial velocity vo as a function of reactant ; derive kinetic rate constants from data and graphs of integrated rate and initial rate equations; write appropriate chemical, differential equations, and initial rate equations for the rate of disappearance of reactants or appearance of products for simple enzyme catalyzed reaction; differentiate between rapid and steady state assumptions; simplify the initial rate equation containing rate constants for an enzyme catalyzed reactions to one replacing the rate constants with kcat and KM, and give operational and mathematical definitions of those constants;

# B7.  Meaning of Kinetic Constants

It is important to get a "gut-level" understanding of the significance of the rate constants.  Here they are:

• Km:  The Michaelis constant with units of molarity (M), is operationally defined as the substrate concentration at which the initial velocity is half of Vmax.  It is equal to the dissociation constant of E and S only in if E, S and ES are in rapid equilibrium.  It can be thought of as an "effective" Kd in other cases.

• kcat:  The catalytic rate constants, with units of s-1 is often called the turnover number.  It is a measure of how many bound substrate molecules turnover or form product in 1 second.  This is evident from equation v0 = kcat[ES]

• kcat/Km:  Under condition when [S] << Km, the Michaelis-Menten equation becomes v0 = (kcat/KM)[E0][S].  This really describes a biomolecular rate constant, with units of M-1s-1, for conversion of free substrate to product.  Some enzyme have kcat/Km values around 108, indicating that they are diffusion controlled.  That implies that the reaction is essentially done as soon as the enzyme and substrate collide. The constant kcat/Km is also referred to as the specificity constant in that it describes how well an enzyme can differentiate between two different competing substrates.  (We will show this mathematically in the next chapter.)

 Km values enzyme substrate Km (mM) catalase H2O2 25 hexokinase (brain) ATP 0.4 D-Glucose 0.05 D-Fructose 1.5 carbonic anhydrase HCO3- 9 chymotrypsin glycyltyrosinylglycine 108 N-benzoyltyrosinamide 2.5 b-galactosidase D-lactose 4.0 threonine dehydratase L-Thr 5.0 kcat values enzyme substrate kcat (s-1) catalase H2O2 40,000,000 carbonic anhydrase HCO3- 400,000 acetylcholinesterase acetylcholine 140,000 b-lactamase benzylpenicillin 2,000 fumarase fumarate 800 RecA protein (ATPase) ATP 0.4
 Enzymes with kcat/Km values close to diffusion controlled (108 - 109 M-1s-1) enzyme substrate kcat (s-1) Km (M) kcat/Km (M-1s-1) acetylcholinesterase acetylcholine 1.4 x 104 9 x 10-5 1.6 x 108 carbonic anhydrase CO2 1 x 106 1.2 x 10-2 8.3 x 107 HCO3- 4 x 105 2.6 x 10-2 1.5 x 107 catalase H2O2 4 x 107 1.1 4 x 107 crotonase crotonyl-CoA 5.7 x 103 2 x 10-5 2.8 x 108 fumarase fumarate 8 x 102 5 x 10-6 1.6 x 108 malate 9 x 102 2.5 x 10-5 3.6 x 107 triose phosphate isomeraser glyceraldehyde-3-P 4.3 x 103 4.7 x 10-4 2.4 x 108 b-lactamase benzylpenicillin 2.0 x 103 2 x 10-4 1 x 108