Enzymes that conform to simple Michaelis–Menten kinetics are called Michaelis–Menten enzymes. These enzymes are not regulated in the cell, and their activity is governed simply by mass action: if substrate is present, they catalyze. Most enzymes in the cell are Michaelis–Menten enzymes.

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As important as catalysis is to the functioning of a cell, catalysis alone is not sufficient. The vast array of reaction pathways also need to be regulated so that the biochemical pathways function in a coherent fashion. Figure 7.7A is a street map of part of Paris. Every day, hundreds of thousands of vehicles travel these streets. Although the streets of Paris are notoriously difficult to navigate by car, imagine how much more difficult navigation would be without stop signs, stoplights, and traffic police. The metabolic map shown in Figure 7.7B shows that metabolic traffic also is immensely complex, and, like street traffic, metabolic traffic requires regulation. An effective means of regulating metabolic pathways is to regulate enzyme activity. Enzymes that regulate the flux of biochemicals through metabolic pathways are called allosteric enzymes, for reasons to be discussed shortly. Key features of allosteric enzymes include the regulation of catalytic activity by environmental signals, including the final product of the metabolic pathway regulated by the enzyme; kinetics that are more complex than those of Michaelis–Menten enzymes; and quaternary structure with multiple active sites in each enzyme.

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Let us begin our consideration of allosteric enzymes by imagining what control processes would be useful for the efficient functioning of metabolic pathways.

We begin by examining a hypothetical metabolic pathway:

There are five reactions in this metabolic pathway, catalyzed by five distinct enzymes, denoted e₁ through e₅. As is typical in real metabolic situations, the end product F is needed in limited amounts and cannot be stored. The initial reactant A is valuable and should be conserved unless F is needed. Finally, B, C, D, and E have no biological roles except as chemical intermediates in the synthesis of F. This last condition means that the first reaction, A → B, is the committed step in this pathway; after this reaction has taken place, B is committed to conversion into F. How can the production of F be regulated to meet the cellular requirements without making more than is needed?

In the simplest situation, when sufficient F is present, F can bind reversibly to e₁, the enzyme catalyzing the committed step, and inhibit the reaction, an effect called feedback inhibition.

Feedback inhibition is a common means of biochemical regulation. Feedback inhibitors usually bear no structural resemblance to the substrate or the product of the enzyme that they inhibit. Moreover, feedback inhibitors do not bind at the active site but rather at a distinct regulatory site on the allosteric enzyme. Allosteric (from the Greek allos, meaning “other,” and stereos, meaning “structure”) enzymes are sonamed because they are regulated by molecules that bind to sites other than the active site. Allosteric enzymes always catalyze the committed step of metabolic pathways.

Another level of complexity is required when metabolic pathways must communicate with one another. Consider the pathway shown in Figure 7.8 for the synthesis of K from two separate pathways producing F and I. How can these pathways be coordinated to produce the appropriate amount of K? Compound K might inhibit enzymes e₁ and e₁₀ by feedback inhibition, inasmuch as these two enzymes control the committed step for each of the two required pathways. But, in this case, a second wasteful situation could arise: if more F were produced than I, some of the F molecules would be wasted because there would not be enough I to bind to F. Thus, how might the concentrations of F and I be balanced? Compound F could stimulate e₁₀ but inhibit e₁ to balance the amount of I with F. Likewise, compound I could inhibit e₁₀ but stimulate e₁. Thus, allosteric enzymes can recognize inhibitor molecules as well as stimulatory molecules.

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Allosteric enzymes are distinguished by their response to changes in substrate concentration in addition to their susceptibility to regulation by other molecules. A typical velocity-versus-substrate curve for an allosteric enzyme is shown in Figure 7.9. The curve differs from what is expected of an enzyme that conforms to Michaelis–Menten kinetics because of the sharp increase in V₀ in the middle of the curve. The observed curve is referred to as sigmoidal because it resembles the letter S.

Thus far, we know two properties that are unique to allosteric enzymes: (1) regulation of catalytic activity and (2) sigmoidal kinetics. Is there a relation between these two unique characteristics of allosteric enzymes? Indeed there is, and the relation is best elucidated by first examining a model for how sigmoidal kinetics might be displayed.

We will consider one possible model, called the concerted model or the MWC model after Jacques Monod, Jefferies Wyman, and Jean-Pierre Changeux, the biochemists who developed it. The model is based on several premises. First, allosteric enzymes have multiple active sites on different polypeptide chains. Second, the enzyme can exist in two distinct conformations or states. One state, designated R for relaxed, is the active conformation, which catalyzes reactions. The other state, designated T for tense, is significantly less active. In the absence of substrate or signal molecules, R and T are in equilibrium, with T being the more stable state and thus the more common state. The T/R ratio, which is called the allosteric constant (L₀), is in the hundreds for a typical allosteric enzyme. However, the difference in stability is small enough that thermal jostling of the cellular environment provides enough energy to occasionally power the spontaneous conversion of a T form into an R form. Third, the concerted model also requires that all of the subunits or active sites of the enzyme must be in the same state; that is, all must be T or all must be R. No hybrids are allowed. This requirement is called the symmetry rule. Finally, substrate (S) binds more readily to the R form of the enzyme than to the T form.

How can we use this information to explain the sigmoidal nature of allosteric kinetics? Consider a population of allosteric enzymes with each enzyme containing four active sites on four subunits. Because it is more stable, most of the enzymes will be in the T state. The binding of S to the T form is difficult; thus, there will be little activity at low substrate concentrations (Figure 7.10). However, if the substrate concentration is increased, eventually enough S will be present so that, when a relaxed form of the enzyme spontaneously appears, S will bind to it. Because of the symmetry rule, if one S binds to the R form, all of the four potential active sites become trapped in the R form. Consequently, the next S to bind the enzyme will not have to unproductively collide with the many T forms, because R forms of the enzymes are accumulating owing to the binding of the initial S to the enzyme. The binding of substrate disrupts the T ⇋ R equilibrium in favor of R. This behavior is called cooperativity and accounts for the sharp increase in V₀ of the velocity-versus-substrate concentration curve.

What is the physiological significance of cooperativity, seen as a sigmoidal kinetics? Allosteric enzymes transition from a less active state to a more active state within a narrow range of substrate concentration. The benefit of this behavior is illustrated in Figure 7.11, which compares the kinetics of a Michaelis–Menten enzyme (blue curve) to that of an allosteric enzyme (red curve). In this example, the Michaelis–Menten enzyme requires an approximately 27-fold increase in substrate concentration to increase V_o from 0.1 V_max to 0.8 V_max. In contrast, the allosteric enzyme requires only about a 4-fold increase in substrate concentration to attain the same increase in velocity. The activity of allosteric enzymes is more sensitive to changes in substrate concentration near K_M than are Michaelis–Menten enzymes with the same V_max. This sensitivity is called a threshold effect: below a certain substrate concentration, there is little enzyme activity. However, after the threshold has been reached, enzyme activity increases rapidly. In other words, much like an “on or off” switch, cooperativity ensures that most of the enzyme is either on (R state) or off (T state). The vast majority of allosteric enzymes display sigmoidal kinetics.

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How can we explain the signal-sensing capabilities of allosteric enzymes with the concerted model? The regulatory molecules alter the equilibrium between T and R forms. That is, they change the relative proportion of enzymes in the T and R states. A positive effector binds to the R form at a regulatory site, distinct from the active site, and stabilizes this form, thus increasing the concentration of R and making an R and S interaction more likely. A negative effector binds to T and stabilizes it; a negative effector increases the concentration of T and thereby decreases the likelihood of an R binding to an S. Figure 7.12 shows the effects of a positive and a negative regulator on the kinetics of an allosteric enzyme. The positive effector lowers the threshold concentration of substrate needed for activity, whereas the negative effector raises the threshold concentration. The effects of regulatory molecules on allosteric enzymes are referred to as heterotropic effects. Heterotropic effectors shift the sigmoidal curve to the left (activators) or right (inhibitors). In contrast, the effects of substrates on allosteric enzymes are referred to as homotropic effects. Homotropic effects account for the sigmoidal nature of the kinetics curve.

It is all but impossible to overestimate the importance of allosteric enzymes in biological systems. They respond immediately and specifically to chemical signals produced elsewhere in the cell. They are receivers and transducers of chemical information, allowing cross talk between metabolic pathways, not only within the cell, but also between cells and organs. The complexity of biological systems is due to the sensing of the environment by allosteric enzymes.

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In the concerted model, an allosteric enzyme can exist in only two states, T and R; no intermediate or hybrid states are allowed. An alternative model posits that the subunits of the allosteric enzyme undergo sequential changes in structure. The binding of substrate to one site influences the substrate binding to neighboring sites without necessarily inducing a transition encompassing the entire enzyme (Figure 7.13). The sequential model more readily accommodates negative cooperativity, in which the binding of one substrate decreases the affinity of other sites for the substrate. The results of studies on a number of allosteric proteins suggest that many behave according to some combination of the sequential and concerted models.