Introduction to Molecular Biology: From Cells to Atoms - Anthony Rees, Michael Sternberg 2002

Proteins
Regulation of Enzyme Activity

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Fig. 13.1.

The kinetic properties of many, but not all, Enzymes can be explained within the framework of the Michaelis-Menten model. According to this model, a substrate S binds to an enzyme E with a rate constant k₁. The resulting enzyme-substrate complex E—S can either dissociate back into E and S with a rate constant k₂ or convert into a product P and free enzyme with a rate constant k₃:

The model assumes that the product cannot be converted back into the substrate, which holds true for the Cytology/cytology/16.html">Early stages of the reaction when the product concentration is low. The reaction velocity v is related to the Substrate Concentration [S] by the following equation:

where V_mах is the maximum reaction velocity achieved when all enzyme molecules are bound to the substrate, and

K_M, the Michaelis constant, is numerically equal to the substrate concentration at which the reaction velocity is half of the maximum value. K_M is a measure of the affinity of a given substrate for the enzyme (in cases where k₃ « k₂), which in turn reflects the strength of substrate binding to the Active Site. The plot of v versus [S] is a hyperbola.

The Lineweaver-Burk double-reciprocal plot. There is an alternative way to represent the Michaelis-Menten Equation using the double-reciprocal plot proposed by Lineweaver and Burk. Let us rewrite the equation as

If we plot 1/v versus 1/[S], we obtain a straight line with a slope of K_M/V_max, intercepting the 1/v axis at 1/V_max. Using this form of the Michaelis-Menten equation makes it easy to determine The values of V_max and K_M. Competitive and noncompetitive inhibitors can be distinguished from one another by how they alter the kinetic Properties of the enzyme system. This is most easily illustrated using the Lineweaver-Burk plot (Fig. 13.2). If enzyme behavior obeys the Michaelis-Menten equation, this property will be retained in the presence of an inhibitor of either type. However, upon The addition of a competitive or noncompetitive inhibitor, the double-reciprocal plot will change, with The Nature of the changes depending on the type of inhibitor.

Fig. 13.2.

Competitive Inhibitors increase the K_м of the reaction but have no effect on V_max. Since a competitive inhibitor competes for the Active Site of the enzyme, its effect is essentially equivalent to substrate dilution. Consequently, achieving a reaction velocity equal to half of V_max now requires a higher substrate concentration (which, as is known, is numerically equal to K_м). Because the inhibitory effect can be overcome by increasing the substrate concentration, V_max remains unchanged.

Noncompetitive inhibitors decrease V_max but do not affect K_м. Since inhibitors of this type do not interfere with substrate binding to the active site, the value of K_м remains unchanged. The Mechanism of inhibition involves lowering the rate at which the substrate within the enzyme-substrate complex is converted into the product; therefore, noncompetitive inhibition results solely in a decrease in V_max.

ENZYME ACTIVITY REGULATION can be carried out in A wide variety of ways, such as zymogen (proenzyme) activation, covalent modification, feedback inhibition, cooperative effects, or allosteric effects.

A zymogen is an inactive enzyme precursor. For a zymogen to be converted into an active enzyme, a specific part (or parts) of its polypeptide chain must be cleaved off. For example, within the Serine protease family, chymotrypsinogen and trypsinogen are the zymogens of Chymotrypsin and Trypsin, respectively.

Covalent modification refers to the covalent addition or removal of a small chemical group to or from an enzyme, which regulates its activity. Such modifications typically either switch a completely inactive enzyme form into an active one or, conversely, inactivate a fully active enzyme. For instance, Glycogen synthase from mammalian Cells, which converts glucose into glycogen, is inactivated following the covalent addition of a phosphate group to the side chain of one of its serine residues and is reactivated upon the removal of the phosphate.

Feedback inhibition is typical of enzyme systems in which a substrate undergoes several sequential transformations, with each reaction catalyzed by a distinct enzyme (see, for example, enzymes E₁ - E₄ in Fig. 13.3). Inhibition occurs when the end product T blocks an earlier stage in the reaction chain. For this to happen, product T must either structurally resemble P (i.e., act as a competitive inhibitor) or bind to another region of the enzyme, thereby regulating its activity (i.e., act as a noncompetitive inhibitor).

Fig. 13.3

Cooperative effects are characteristic of multisubunit Proteins, including enzymes. When a cooperative effect is present, the kinetic properties of the enzyme are no longer described by the Michaelis-Menten equation: the plot of v versus [S] in this case is a sigmoidal curve rather than a hyperbola, and the Lineweaver-Burk plot ceases to be a straight line (Fig. 13.1). Furthermore, a small increase in substrate concentration leads to a significant surge in reaction velocity. Various models have been proposed to explain this effect, the most prominent being the Monod-Wyman-Changeux model (the Symmetry model) and the Koshland-Némethy-Filmer model (the sequential model).

Fig. 13.4.

The concerted model assumes that each multimeric enzyme complex can exist in at least two different states with distinct quaternary structures, wherein all subunits share the identical tertiary Structure within any given state. The simplest model considers two states in equilibrium with one another. In one of these states, the protein exhibits a high affinity for the substrate (the R-state, derived from relaxed), while in the other, its affinity is low (the T-state, derived from tense). The added substrate will preferentially bind to the R-conformers of the enzyme, whereas its binding to the T-conformer induces strain within the enzyme subunits, triggering a simultaneous transition of all subunits into the R-state (where such strain is absent). This concerted transition preserves the molecular symmetry of each multimeric molecule. As more substrate is added, an increasing number of molecules shift from the T-state to the R-state. This equilibrium shift in the presence of the substrate accounts for the positive cooperativity effect. As a result of this effect, the plot of $v$ versus [S] adopts a sigmoidal shape (see the previous page).

The sequential model postulates that individual subunits of a multimeric molecule can simultaneously adopt different tertiary structures. In this mechanism, substrate binding to one subunit can induce a conformational change in the Tertiary Structure of an adjacent subunit (or subunits), thereby increasing (positive cooperativity) or decreasing (negative cooperativity) their affinity for the substrate. Allosteric Regulation (from the Greek allos, meaning "other", and stereos, meaning "solid" or "space") is an effect observed when small molecules (effectors) bind to the enzyme outside the active site and alter the reaction rate. Such regulation can be homotropic—when a substrate molecule interacting with the enzyme alters its affinity for molecules of the same substrate—or heterotropic—when the substrate affinity is altered through interaction with a molecule structurally distinct from the substrate. Both homotropic and heterotropic effectors can act as either activators or inhibitors. An allosteric activator acting on an enzyme described by the concerted model will bind preferentially to the R-conformer, thereby stabilizing this state. Consequently, the activator increases the initial concentration of R-conformers relative to T-conformers and, in turn, enhances the enzyme's affinity for its substrate (positive cooperativity). Conversely, an allosteric inhibitor preferentially binds and stabilizes the enzyme in the T-state, thereby reducing the enzyme's affinity for its substrate (negative cooperativity). Overall, The Role of allosteric effectors is either to broaden (in the case of inhibitors) or to narrow (in the case of activators) the range of substrate concentrations over which the enzyme is capable of increasing the reaction rate.