Introduction and Definitions

An enzyme reaction in its simplest form can be written as

Substrate A reacts with enzyme E to form an enzyme-substrate complex EA. From this, product is formed in a consecutive irreversible step, and the enzyme can enter into a new reaction cycle. To each reaction step belongs a specific rate constant k. It is marked with a positive figure (k1, k2, k3,.) in the forward direction and with a negative one (k-1, k-2, k-3,.) in the backward. Upon a more detailed examination of this apparently simple reaction, however, additional steps must be considered:

Initially, substrate and enzyme form in a rapid equilibrium a loose association complex EA. Rearrangement in the following step by interaction of the substrate with the residues of the catalytic center yields a tight transition state complex E*A. This state is prepared to convert the substrate into the product forming a tight E*P complex, which turns into a loose association complex EP before dissociating into free product and enzyme. The whole reaction sequence appears quite symmetrical and can be run through from the forward direction, but similarly from the backward direction, P acting as substrate and A as product. In contrast to the upper simple scheme with two reaction steps and three rate constants, 5 reaction steps with 10 rate constants must be considered for a more exact description of the same reaction.

Closer observation of an enzyme reaction can reveal an even more complicated situation. In fact, in most enzyme reactions more components are involved, such as two or more substrates (A, B, C,.) and products (P, Q, R,.), cofactors, and, as regulating components, inhibitors and activators (both also called effectors):

To unravel such complicated mechanisms, sophisticated theoretical treatments and extensive methodical approaches are required. The first aim is to simplify the scheme. Actually, each individual step can be assigned to two different types: equilibrium and kinetic steps. Both types need their special treatment. Each reaction starts with binding of a ligand to the enzyme, forming an equilibrium. Such binding steps can individually be investigated by special binding methods. On the other hand, the conversion of substrate to product is followed by kinetic methods. Combination of both approaches, possibly including methods to detect conformational changes, serves to uncover the central steps of the scheme. Finally, by combining all the detailed results, the complete mechanism can be developed.

This consideration shows that kinetic studies alone are not sufficient to describe an enzyme reaction thoroughly, as every kinetic step is preceded by a binding step. Binding, as an equilibrium reaction, can only be investigated in the complete absence of any kinetic process, and the theoretical treatments as well as the methods for both reaction types are principally different. Therefore, before going into enzyme kinetics, equilibria are discussed. Because of the strict absence of kinetic processes, this treatment is not restricted to enzymes but is applicable to any specific binding process. In this respect, binding is understood as the specific interaction between two compounds. The ligand, usually a low-molecular-mass compound such as a substrate, inhibitor, activator, inducer, hormone, interacts with a larger target, such as a protein, receptor, or DNA. In Chapters 1 and 2, for the target, the term macromolecule is used synonymously with the term enzyme (both abbreviated as E), while Chapters 3-10 on enzyme kinetics deal only with enzymes. For specific interaction with the ligand, the macromolecule must possess a distinct region, a specific binding site, in contrast to unspecific binding, which can occur at any appropriate region at the surface of the macromolecule, such as ionic or hydrophobic groups. The various mechanisms for equilibria between different ligands and macromolecules are described under the term multiple equilibria.

The principal differences between equilibrium and kinetic investigations are summarized in Table 1. Equilibria are time independent and, consequently, they can principally be measured without time limit, while kinetic measurements are bound to the relatively short reaction time. However, the fact that biological substances, especially enzymes, are not very stable under experimental conditions demands short measure times also for equilibrium studies. In contrast to enzyme reactions, where the chemical conversion of substrate to product can be used as detection signal, reversible binding causes no intrinsic change in the features of the components, so it is difficult to find a clear signal for detecting an equilibrium. Due to the mostly weak signal, high amounts of the macromolecule are required, because the share of binding is directly proportional to the macromolecule concentration. Kinetic experiments, in contrast, need only catalytic (i.e., very low) amounts of the enzyme. The requirements for purity of the macromolecule are also different. For binding measurements, where the knowledge of the molar concentration of the macromolecule is essential, high purity is required. For enzyme kinetic determinations, on the other hand, the enzyme must be active but not necessarily pure, as long as there are no disturbing influences, such as side reactions. Finally, there are also differences in the constants. From equilibrium treatments, thermodynamic constants, the association, or dissociation constants are derived, while kinetic studies yield the more complex kinetic constants. Both types of constants, however, are composed of rate constants, which are valid for both approaches, and even with kinetic studies dissociation constants, such as the inhibition constants, can be obtained. Taken together, it can be stated that equilibrium studies are easier in the theoretical treatment but more difficult in the experimental procedure, while in comparison experimental determination of enzyme kinetics is easier, but the theoretical approach is more complex. The easier methodological access is the reason for the broader application of enzyme kinetics.

Table 1 Differences between equilibrium and kinetic studies

A special area is the treatment of fast reactions. This field can similarly be differentiated into kinetic methods, which directly observe fast reactions, that is, the continuous and stopped flow methods, and in techniques dealing with equilibria, such as relaxation methods (although the deviation from equilibrium is a kinetic process). These techniques allow to analyze complex mechanisms from a particular viewpoint and, besides the fact that fast processes become accessible, individual rate constants can be determined, rendering this approach as a valuable completion of equilibrium and kinetic studies with conventional methods.

For all areas treated in this book, a uniform nomenclature is applied. For example, discussions of equilibrium that are based on thermodynamics deal usually with association constants, while enzyme kinetics prefers dissociation constants (the Michaelis constant is related to a dissociation constant). Both types of constants describe principally the same equilibrium, only in a reversed sense. In this book, dissociation constants are used throughout because the main emphasis is on enzyme kinetics. The terms A, B, C, and so on are used for any ligand, including substrates, which specifically bind to a macromolecule or an enzyme. If it is necessary to discriminate between distinct types of ligands, divergent terms are used, such as I for inhibitors. Enzyme products are designated as P, Q, R, and so on. The macromolecule, with or without enzymatic activity, is E. Generally, the NC-IUB recommendations (Nomenclature Committee of the International Union of Biochemistry, 1982) and the IUPAC rules (International Union of Pure and Applied Chemistry, 1981) are considered. Concentrations are indicated by square brackets ([A], [E], etc.). The reference list below specifies a selection of text books relevant to the various fields treated in this book.

References

1. Bisswanger, H. (2004) Practical Enzymology, Wiley-VCH Verlag GmbH, Weinheim.
2. Cornish-Bowden, A. (1976) Principles of Enzyme Kinetics, Butterworth, London, Boston.
3. Cornish-Bowden, A. (2004)...