Quimica

Chapter 4

Enzyme Kinetics: Theory and Practice
Alistair Rogers and Yves Gibon

4.1 Introduction
Enzymes, like all positive catalysts, dramatically increase the rate of a given reaction. Enzyme kinetics is principally concerned with the measurement and mathematical description of this reaction rate and its associated constants. For many steps in metabolism, enzyme kinetic properties havebeen determined, and this information has been collected and organized in publicly available online databases (www.brenda.uni-koeln.de). In the first section of this chapter, we review the fundamentals of enzyme kinetics and provide an overview of the concepts that will help the metabolic modeler make the best use of this resource. The techniques and methods required to determine kinetic constantsfrom purified enzymes have been covered in detail elsewhere [4, 12] and are not discussed here. In the second section, we will describe recent advances in the high throughput, high sensitivity measurement of enzyme activity, detail the methodology, and discuss the use of high throughput techniques for profiling large numbers of samples and providing a first step in the process of identifying potentialregulatory candidates.

4.2 Enzyme Kinetics
In this section, we will review the basics of enzyme kinetics and, using simple examples, mathematically describe enzyme-catalyzed reactions and the derivation of their key constants. However, first we must turn to the mathematical description of chemical reaction kinetics.

A. Rogers (B) Department of Environmental Sciences, Brookhaven NationalLaboratory, Upton, NY 11973-5000, USA e-mail: arogers@bnl.gov

J. Schwender (ed.), Plant Metabolic Networks, DOI 10.1007/978-0-387-78745-9 4, C Springer Science+Business Media, LLC 2009

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A. Rogers and Y. Gibon

4.2.1 Reaction Rates and Reaction Order
4.2.1.1 First-Order Irreversible Reaction The simplest possible reaction is the irreversible conversion of substance A to product P(e.g., radioactive decay). A −→ P
k1

(4.1)

The arrow is drawn from A to P to signify that the equilibrium lies far to the right, and the reverse reaction is infinitesimally small. We can define the reaction rate or velocity (v) of the reaction in terms of the time (t)-dependent production of product P. Since formation of P involves the loss of A, we can also define v in terms of thetime-dependent consumption of substance A, where [A] and [P] are the concentrations of the substance and product, respectively. v= δ[A] δ[P] =− = k1 [A] δt δt (4.2)

The transformation of substance A to product P is an independent event and therefore is unaffected by concentration. As substance A is transformed to product P, there is less of substance A to undergo the transformation, and therefore theconcentration of substance A will decrease exponentially with time (Fig 4.1A). The rate constant (k1 ) of this reaction is proportional to the concentration of A and has the unit s−1 .This type of unimolecular reaction is known as a first-order reaction because the rate depends on the first power of the concentration. Integration of Eq. (4.2) from time zero (t0 ) to time t gives ln or [A] = e−k1 t [A]0(4.4) [A] = − k1 t [A]0 (4.3)

where [A]0 is the starting concentration at t0 . Eq. (4.4) describes how the concentration of A decreases exponentially with time as shown in Fig. 4.1A. When the ln[A] is plotted against time (Fig. 4.1B), a first-order reaction will yield a straight line, where the gradient is equal to –k1 . 4.2.1.2 First-Order Reversible Reaction Few reactions in biochemistry areas simple as the first-order reaction described above. In most cases, reactions are reversible and equilibrium does not lie far to one side.

4 Enzyme Kinetics Fig. 4.1 A first-order reaction showing the decrease of substance A over time expressed as the concentration of A ([A], Panel A) and in a semi-logarithmic plot (ln[A], Panel B)

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A

[A]

B

ln [A]

gradient = – k1

Time...