Enzyme Kinetics PDF

# Enzyme Kinetics ## Introduction to enzyme kinetics Living systems depend on chemical reactions which, on their own, would occur at extremely slow rates. Enzymes are catalysts which reduce the needed activation energy so these reactions proceed at rates that are useful to the cell. ## Product accu...

# Enzyme Kinetics ## Introduction to enzyme kinetics Living systems depend on chemical reactions which, on their own, would occur at extremely slow rates. Enzymes are catalysts which reduce the needed activation energy so these reactions proceed at rates that are useful to the cell. ## Product accumulation is often linear with time In most cases, an enzyme converts one chemical (the substrate), into another (the product). A graph of product concentration vs. time follows three phases as shown in the following graph: - At very early time points, the rate of product accumulation increases over time. Special techniques are needed to study the early kinetics of enzyme action, since this transient phase usually lasts less than a second (the figure greatly exaggerates the first phase). - For an extended period of time, the product concentration increases linearly with time. - At later times, the substrate is depleted, so the curve starts to level off. Eventually the concentration of product reaches a plateau and doesn't change with time. It is difficult to fit a curve to a graph of product as a function of time, even if you use a simplified model that ignores the transient phase and assumes that the reaction is irreversible ## Enzyme velocity as a function of substrate concentration If you measure enzyme velocity at many different concentrations of substrate, the graph generally looks like this:  Enzyme velocity as a function of substrate concentration often follows the Michaelis-Menten equation: $Velocity = V = \frac{V_{max}[S]}{[S] + K_M}$ ## The meaning of $K_M$: To understand the meaning of $K_M$, you need to have a model of enzyme action. The simplest model is the classic model of Michaelis and Menten, which has proven useful with many kinds of enzymes. $E + S \rightleftharpoons ES \longrightarrow E + P$ The substrate (S) binds reversibly to the enzyme (E) in the first reaction. In most cases, you can't measure this step. What you measure is production of product (P), created by the second reaction. The rate of product formation equals the rate at which ES turns into E + P, which equals $k_2$ times [ES]. This equation isn't helpful, because we don't know ES. We need to solve for ES in terms of the other quantities. This calculation can be greatly simplified by making two reasonable assumptions. First, we assume that the concentration of ES is steady during the time intervals used for enzyme kinetic work. That means that the rate of ES formation, equals the rate of ES dissociation (either back to E + S or forward to E + P). Second, we assume that the reverse reaction (formation of ES from E + P) is negligible, because we are working at early time points where the concentration of product is very low. $Rate of ES formation = Rate of ES dissolution$ $k_1[S][E_{free}] = k_{-1}[ES] + k_2[ES]$ We also know that the total concentration of enzyme, $E_{total}$, equals ES plus E. So the equation can be rewritten. $k_1[S]([E_{total}] - [ES]) = k_{-1}[ES] + k_2[ES]$ Solving for ES: $[ES] = \frac{k_1[E_{total}][S]}{k_1[S] + k_{-1} + k_2} = \frac{[E_{total}][S]}{[S] + K_M}$ The velocity of the enzyme reaction therefore is: $Velocity = k_2[ES] = k_2\frac{[E_{total}][S]}{[S] + K_M}$ Finally, define $V_{max}$ (the velocity at maximal concentrations of substrate) as $k_2$ times $E_{total}$, and $K_M$, the Michaelis-Menten constant, as $(k_{-1} + k_2)/k_1$. Substituting: $Velocity = V = \frac{V_{max}[S]}{[S] + K_M}$ Note that $K_M$ is not a binding constant that measures the strength of binding between the enzyme and substrate. Its value includes the affinity of substrate for enzyme, but also the rate at which the substrate bound to the enzyme is converted to product. Only if $k_2$ is much smaller than $k_1$ will $K_M$ equal a binding affinity. The Michaelis-Menten model is too simple for many purposes. The Briggs-Haldane model has proven more useful: $E + S \rightleftharpoons ES \longrightarrow E + P$ Under the Briggs-Haldane model, the graph of enzyme velocity vs. substrate looks the same as under the Michaelis-Menten model, but $K_M$ is defined as a combination of all five of the rate constants in the model. ## Assumptions of enzyme kinetic analyses Standard analyses of enzyme kinetics (the only kind discussed here) assume: - The concentration of enzyme remains constant during the time intervals used for enzyme kinetic work. - The reverse reaction (formation of ES from E + P) is negligible. - The enzyme concentration is very low, enabling a steady-state assumption. - The data are collected during the [linear part of] the graph where the reaction is linear with time.