The steady state
The steady state:
All of the chemical processes considered to this point have been single-step reactions, but reality is not so simple, and this is particularly important for considering enzyme-catalyzed reactions, because these are essentially never single-step reactions. A reaction of more than one step, such as
usually does not have simple first-order kinetics, even if it is unimolecular overall (as this one is), and similar considerations apply to reactions that are bimolecular overall, and to reactions with more than two steps. Nonetheless, in conditions where the concentration of intermediate is always very small the behavior can be simple. In such conditions a reaction may reach a state in which the concentration of intermediate does not change perceptibly during significant periods of time. The general idea is quite familiar from everyday observation of the flow of water in a basin when the outlet is left open. Initially (Figure 1.12) the level of water in the basin is too small to bring the pressure at the outlet to a value sufficient to drive the water out as fast as it enters, so the level must rise. Once the necessary pressure is reached the water flows out as fast as it enters (Figure 1) and the level remains constant as long as the external conditions remain constant. Notice that this is not an equilibrium, because there is continuous unidirectional flow through the system; instead it is a steady state. If you are not convinced you can readily verify that a basin of water will behave as described.
Although we have assumed here that the steady state is reached from below—either a low concentration of intermediate or a low level of water—it is also possible, though less likely in simple reactions, for the initial concentration of intermediate to be higher than the steady-state value, and in this case it will decrease until the same steady state is reached. The idea of a steady state was introduced by Chapman and Underhill, and developed by Bodenstein in particular. As we shall see in later chapters, it is absolutely crucial in the analysis of enzyme catalysis, because enzyme-catalyzed reactions are very often studied in conditions where the enzyme concentration is very small compared with the concentrations of the reactants, and this implies that the concentrations of all intermediates in the process are also very small.
Figure 1. (a) Fulhame supposed that a catalyst E would first react with a reactant A to produce a complex EA that would regenerate the original catalyst E at the same time as releasing product P. This is essentially the modern view of catalysis, but (b) Henri also examined the possibility that despite forming a complex the catalytic effect was due to action of the free catalyst on the reaction.
To this point we have discussed the dependence of reaction rates on concentrations as if the only concentrations that needed to be considered were those of the reactants, but this is obviously too simple: more than two centuries ago Fulhame noted that many reactions would not proceed at a detectable rate unless the mixture contained certain necessary nonreactant components (most notably water). In a major insight that did not become generally adopted in chemistry until many years later, she realized that her observation was most easily interpreted by supposing that such components were consumed in the early stages of the reaction and regenerated at the end.
Fulhame’s work was largely forgotten by the time that Berzelius introduced the term catalysis for this sort of behavior. He considered it to be an “only rarely observed force”, unlike Fulhame, who had come to the opposite conclusion that water was necessary for virtually all reactions. Both points of view are extreme, of course, but at least in enzyme chemistry the overwhelming majority of known reactions do require water. To a considerable degree the study of enzyme catalysis is the study of catalysis in aqueous solution, and as the relevant terminology will be introduced later in the book
when we need it, there is little to add here, beyond remarking that despite its age the classic book by Jencks remains an excellent source of general information on catalysis in chemistry and biochemistry, for readers who need more emphasis on chemical mechanisms than is found in the present book. Fulhame’s view that a catalyst reacts in a cyclic fashion, consumed in one step of reaction, and regenerated in a later one (Figure 1.), is now generally accepted as an explanation of catalysis, but even at the beginning of the 20th century this was not fully understood, and Henri discussed the possibility that an enzyme might form a complex with its substrate but that this complex was not part of the reaction cycle; instead, the free enzyme might act on the substrate, perhaps by emitting some sort of radiation, as suggested by Barendrecht, and shown in Figure 1b. These ideas are completely obsolete, though they are still occasionally discussed, for example by Schnell and co-workers, but they led Henri to enunciate a principle, now called homeomorphism, that remains vital for kinetic analysis: the fact that a particular equation generates an equation consistent with experimental observations does not demonstrate that the equation is correct, because two or more mechanisms may lead to indistinguishable kinetic equations.