Figure 3–45 Small changes in the number of weak bonds can have drastic effects on a binding interaction. This example illustrates the dramatic effect of the presence or absence of a few weak noncovalent bonds in a biological context. Consider 1000 molecules of A and 1000 molecules of B in a eukaryotic cell. The concentration of both will be about 10–9 M. If the equilibrium constant (K ) for A + B AB is 1010, then one can calculate that at equilibrium there will be If the equilibrium constant is a little weaker at 108, which represents a loss of 11.9 kilojoule/mole of binding energy from the example above, or 2–3 fewer hydrogen bonds, then there will be 270 A molecules 270 B molecules 730 AB molecules 915 A molecules 915 B molecules 85 AB molecules 0.5Vmax catalyzing only a single type of reaction. Thus, hexokinase adds a phosphate group to D-glucose but ignores its optical isomer L-glucose; the blood-clotting enzyme thrombin cuts one type of blood protein between a particular arginine and its adjacent glycine and nowhere else, and so on. As discussed in detail in Chapter 2, enzymes work in teams, with the product of one enzyme becoming the substrate for the next. The result is an elaborate network of metabolic pathways that provides the cell with energy and generates the many large and small molecules that the cell needs (see Figure 2–63).
Substrate Binding Is the First Step in Enzyme Catalysis
For a protein that catalyzes a chemical reaction (an enzyme), the binding of each substrate molecule to the protein is an essential prelude. In the simplest case, if we denote the enzyme by E, the substrate by S, and the product by P, the basic reaction path is E + S → ES →EP → E + P. There is a limit to the amount of substrate that a single enzyme molecule can process in a given time. Although an increase in the concentration of substrate increases the rate at which product is formed, this rate eventually reaches a maximum value (Figure 3–46). At that point the enzyme molecule is saturated with substrate, and the rate of reaction (Vmax) depends only on how rapidly the enzyme can process the substrate molecule. This maximum rate divided by the enzyme concentration is called the turnover number. Turnover numbers are often about 1000 substrate molecules processed per second per enzyme molecule, although turnover numbers between 1 and 10,000 are known.
The other kinetic parameter frequently used to characterize an enzyme is its Km, the concentration of substrate that allows the reaction to proceed at one-half its maximum rate (0.5 Vmax) (see Figure 3–46). A low Km value means that the enzyme reaches its maximum catalytic rate at a low concentration of substrate and generally indicates that the enzyme binds to its substrate very tightly, whereas a high Km value corresponds to weak binding. The methods used to characterize enzymes in this way are explained in Panel 3–2 (pp. 142–143).
Enzymes achieve extremely high rates of chemical reaction—rates that are far higher than for any synthetic catalysts. There are several reasons for this efficiency. First, when two molecules need to react, the enzyme greatly increases the local concentration of both of these substrate molecules at the catalytic site, holding them in the correct orientation for the reaction that is to follow. More importantly, however, some of the binding energy contributes directly to the catalysis. Substrate molecules must pass through a series of intermediate states of altered geometry and electron distribution before they form the ultimate products of the reaction. The free energy required to attain the most unstable intermediate state, called the transition state, is known as the activation energy for the reaction, and it is the major determinant of the reaction rate. Enzymes have a much higher affinity for the transition state of the substrate than they have for the stable form.
rate of reaction