8885dc061952/2/042:50 PM Page195mac76mac76:385reb 6.2 How Enzymes Work erate the reactions, they organize and control them so action rates are linked to the activation energy, AG.A that much of the energy released is recovered in other basic introduction to these thermodynamic relationships chemical forms and made available to the cell for other is the next step in understanding how enzymes work tasks. The reaction pathway by which sucrose(and other An equilibrium such as S P is described by sugars) is broken down is the primary energy-yieldin equilibrium constant, Keg, or simply K (p. 26).Un pathway for cells, and the enzymes of this pathway al- der the standard conditions used to compare biochem low the reaction sequence to proceed on a biologically ical processes, an equilibrium constant is denoted Ke useful time scale (or k) Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates. A reaction intermediate is From thermodynamics, the relationship between Ke any species on the reaction pathway that has a finite and AG can be described by the expression chemical lifetime (longer than a molecular vibration 10-3 seconds). When the S P reaction is catalyzed △G"°=- RT In k y an enzyme, the Es and EP complexes can be con- where R is the gas constant, 8. 315 J/mol- K, and T'is sidered intermediates, even though S and P are stable the absolute temperature, 298 K(25C) Equation 6-3 chemical species (Eqn 6-1); the Es and EP complexes is developed and discussed in more detail in Chapter 13 occupy valleys in the reaction coordinate diagram(Fig. The important point here is that the equilibrium con 6-3). Additional, less stable chemical intermediates of- stant is directly related to the overall standard free- ten exist in the course of an enzyme-catalyzed reaction. energy change for the reaction ( Table 6-4). A large The interconversion of two sequential reaction inter- negative value for AG reflects a favorable reaction mediates thus constitutes a reaction step. When several equilibrium-but as already noted this does not mear steps occur in a reaction, the overall rate is determined the reaction will proceed at a rapid rate by the step (or steps )with the hignea. In a simple case, centration of the reactant(or reactants)and by a rate The rate of any reaction is determined by the con- the rate-limiting step is the highest-energy point in constant, usually denoted by k. For the unimolecular the diagram for interconversion of S and P In practice, reaction S-P, the rate (or velocity) of the reaction, and for many enzymes several steps may have similar time-is expressed by a rate equation, cts per unit the rate-limiting step can vary with reaction conditions, V--representing the amount of s that activation energies, which means they are all partially (6-4) Activation energies are energy barriers to chemical In this reaction, the rate depends only on the concen- reactions. These barriers are crucial to life itself. The rate tration of s. This is called a first-order reaction. The at which a molecule undergoes a particular reaction factor k is a proportionality constant that reflects the decreases as the activation barrier for that reaction in- probability of reaction under a given set of conditions molecules would revert spontaneously to much simpler rate constant and has units of reciprocal time, such ass y w creases. Without such energy barriers, complex macro- (pH, temperature, and so forth). Here, k is a first-ordo molecular forms, and the complex and highly ordered If a first-order reaction has a rate constant k of 0.03s- structures and metabolic processes of cells could not ex- ist. Over the course of evolution, enzymes have devel- oped lower activation energies selectively for reactions TABLE 6-4 Relationship between Keg and AG that are needed for cell survival Reaction Rates and Equilibria Have Precise 一6 Thermodynamic Definitions 28.5 Reaction equilibria are inextricably linked to the stan- 10 228 dard free-energy change for the reaction, AG, and re- 11.4 *In this chapter, step and intermediate refer to chemical species in 0.0 the reaction pathway of a single enzyme-catalyzed reaction. In the 5.7 context of metabolic pathways involving many enzymes(discussed in 11.4 Part ID), these terms are used somewhat differently. An entire enzy. 10 1 Latic reaction is often referred to as a"step"in a pathway, and the product of one enzymatic reaction(which is the substrate for the next enzyme in the pathway) is referred to as an"intermediat ote: The relationship is calculated from AG=-RI In Keg(Eqn 6-3)erate the reactions, they organize and control them so that much of the energy released is recovered in other chemical forms and made available to the cell for other tasks. The reaction pathway by which sucrose (and other sugars) is broken down is the primary energy-yielding pathway for cells, and the enzymes of this pathway al￾low the reaction sequence to proceed on a biologically useful time scale. Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates.* A reaction intermediate is any species on the reaction pathway that has a finite chemical lifetime (longer than a molecular vibration, ~10
13 seconds). When the S P reaction is catalyzed by an enzyme, the ES and EP complexes can be con￾sidered intermediates, even though S and P are stable chemical species (Eqn 6–1); the ES and EP complexes occupy valleys in the reaction coordinate diagram (Fig. 6–3). Additional, less stable chemical intermediates of￾ten exist in the course of an enzyme-catalyzed reaction. The interconversion of two sequential reaction inter￾mediates thus constitutes a reaction step. When several steps occur in a reaction, the overall rate is determined by the step (or steps) with the highest activation energy; this is called the rate-limiting step. In a simple case, the rate-limiting step is the highest-energy point in the diagram for interconversion of S and P. In practice, the rate-limiting step can vary with reaction conditions, and for many enzymes several steps may have similar activation energies, which means they are all partially rate-limiting. Activation energies are energy barriers to chemical reactions. These barriers are crucial to life itself. The rate at which a molecule undergoes a particular reaction decreases as the activation barrier for that reaction in￾creases. Without such energy barriers, complex macro￾molecules would revert spontaneously to much simpler molecular forms, and the complex and highly ordered structures and metabolic processes of cells could not ex￾ist. Over the course of evolution, enzymes have devel￾oped lower activation energies selectively for reactions that are needed for cell survival. Reaction Rates and Equilibria Have Precise Thermodynamic Definitions Reaction equilibria are inextricably linked to the stan￾dard free-energy change for the reaction, G, and re￾zy action rates are linked to the activation energy, G‡ . A basic introduction to these thermodynamic relationships is the next step in understanding how enzymes work. An equilibrium such as S P is described by an equilibrium constant, Keq, or simply K (p. 26). Un￾der the standard conditions used to compare biochem￾ical processes, an equilibrium constant is denoted K eq (or K): K eq =  [ [ P S] ]  (6–2) From thermodynamics, the relationship between Keq and G can be described by the expression G 
RT ln K eq (6–3) where R is the gas constant, 8.315 J/mol
K, and T is the absolute temperature, 298 K (25 C). Equation 6–3 is developed and discussed in more detail in Chapter 13. The important point here is that the equilibrium con￾stant is directly related to the overall standard free￾energy change for the reaction (Table 6–4). A large negative value for G reflects a favorable reaction equilibrium—but as already noted, this does not mean the reaction will proceed at a rapid rate. The rate of any reaction is determined by the con￾centration of the reactant (or reactants) and by a rate constant, usually denoted by k. For the unimolecular reaction S n P, the rate (or velocity) of the reaction, V—representing the amount of S that reacts per unit time—is expressed by a rate equation: V  k[S] (6–4) In this reaction, the rate depends only on the concen￾tration of S. This is called a first-order reaction. The factor k is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature, and so forth). Here, k is a first-order rate constant and has units of reciprocal time, such as s
1 . If a first-order reaction has a rate constant k of 0.03 s
1 , zy 6.2 How Enzymes Work 195 *In this chapter, step and intermediate refer to chemical species in the reaction pathway of a single enzyme-catalyzed reaction. In the context of metabolic pathways involving many enzymes (discussed in Part II), these terms are used somewhat differently. An entire enzy￾matic reaction is often referred to as a “step” in a pathway, and the product of one enzymatic reaction (which is the substrate for the next enzyme in the pathway) is referred to as an “intermediate.” K eq G (kJ/mol) 10
6 34.2 10
5 28.5 10
4 22.8 10
3 17.1 10
2 11.4 10
1 5.7 1 0.0 101
5.7 102
11.4 103
17.1 TABLE 6–4 Note: The relationship is calculated from G 
RT ln K eq (Eqn 6–3). Relationship between K eq and G 8885d_c06_195 2/2/04 2:50 PM Page 195 mac76 mac76:385_reb: