Enzyme Catalysis Heterogeneous and Homogeneous

Describes reactions of enzymes and their kinetics

1. 1 Enzyme catalysis . Enzymes are homogeneous biological catalysts. These ubiquitous compounds are special proteins or nucleic acids that contain an active site , which is responsible for binding the substrates , the reactants, and processing them into products. As is true of any catalyst, the active site returns to its original state after the products are released. Many enzymes consist primarily of proteins, some featuring organic or inorganic co-factors in their active sites. However, certain RNA molecules can also be biological catalysts, forming ribozymes . A very important example of a ribozyme is the ribosome , a large assembly of proteins and catalytically active RNA molecules responsible for the synthesis of proteins in the cell.

2. 2 Enzyme catalysis . Two models that explain the binding of a substrate to the active site of an enzyme. Lock-and-key model , the active site and substrate have complementary 3D structures and dock perfectly without the need for major atomic rearrangements. Induced fit model , binding of the substrate induces a conformational change in the active site. The substrate fits well in the active site after the conformational change has taken place.

3. 3 Based on transition state theory, the rate of a reaction is dependent on the energy difference between the initial state and the highest energy transient state along the reaction pathway. Thus, rate enhancements by enzymes must be mediated by a decrease in the energy of the highest energy transition state. A decrease in the energy of the highest energy transition state can be accomplished; The enzyme stabilizes the transition state . The same transition The enzyme allows a different pathway for the process . In the enzyme- catalyzed process, the highest energy transition state (which does not exist in the non- catalyzed process) has a lower energy than the energy of the transition state for the non- catalyzed process. Enzyme Kinetics

4. 4 Consider a reaction in which S is converted to P, either as a simple chemical reaction or as an enzyme-catalyzed process. Instead of merely stating S→P, for transition state theory we need to add an additional term: In each case, the reaction pathway passes through an identical transition state, X ‡ (in the uncatalyzed pathway, this species is not bound to the enzyme, but it is the same species in both cases). In each case in the scheme above, the rate constant shown is the one for the slowest step in the forward direction reaction. Enzyme Kinetics

5. 5 Enzyme Kinetics The energy level diagram below demonstrate the binding of the substrate and dissociation of the product from the enzyme explicitly. Note that the ES complex is lower in energy than the free S, which is why this complex forms spontaneously. David L. Nelson, Lehninger Principles of Biochemistry, IV Edition, W. H. Freeman ed.

6. 6 Enzyme Kinetics Using the principles of transition state theory, we can derive an equation for the rate enhancement mediated by the enzyme. Note that the rate constant is related to the difference in energy of between the initial state and the transition state. Arrhenius equation: If the rate constant for the catalyzed reaction is divided by that of the uncatalyzed reaction: Simplifies to

7. 7 Enzyme Kinetics At equilibrium K eq and ∆G° are related. Rearranging the standard equation for ∆G° to solve for Keq, we obtain: Comparing catalyzed and uncatalyzed K eq , Thus, the ratio of the rate constant for the catalyzed reaction to that of the uncatalyzed reaction is equal to the ratio of the equilibrium constant for the binding of the enzyme to the transition state to that for the binding to the substrate.

8. 8 Enzyme Kinetics

9. 9 The Michaelis–Menten Mechanism of Enzyme Catalysis The principal features of many enzyme-catalysed reactions are as follows : For a given initial concentration of substrate, [S] , the initial rate of product formation is proportional to the total concentration of enzyme, [E] . For a given [E] and low values of [S] , the rate of product formation is proportional to [S] . For a given [E] and high values of [S] , the rate of product formation becomes independent of [S] , reaching a maximum value known as the maximum velocity , v max

10. 10 The Michaelis–Menten mechanism accounts for these features. According to this mechanism, an enzyme–substrate complex is formed in the first step and either the substrate is released unchanged or after modification to form products: Consider the following reaction mechanism: This mechanism leads to the Michaelis– Menten equation for the rate of product formation; where K m = ( k a ′ + k b )/ k a is the Michaelis constant , characteristic of a given enzyme acting on a given substrate. The Michaelis–Menten Mechanism of Enzyme Catalysis

11. 11 The Michaelis–Menten Mechanism of Enzyme Catalysis Derivation of Equation: The rate of product formation according to the Michaelis–Menten mechanism is: The concentration of the enzyme–substrate complex is obtained by invoking the steady-state approximation and writing; Simplifies to: where [E] and [S] are the concentrations of free enzyme and substrate, respectively. Now the Michaelis constant can be defined as: K M has the same units as molar concentration

12. 12 The Michaelis–Menten Mechanism of Enzyme Catalysis To express the rate law in terms of the concentrations of enzyme and substrate added, we note that: [E] =[E] + [ES]. In addition, because the substrate is typically in large excess relative to the enzyme, the free substrate concentration is approximately equal to the initial substrate concentration and we can write [S] ≈ [S] . It then follows that; The Michaelis-Menten equation is then obtained by substituting [ES] is the rate The Michaelis–Menten Equation

13. 13 Significance of Michaelis–Menten constant, K m Experimental observation show that: When [S] << K M , the rate is proportional to [S] When [S] >> K M , the rate reaches its maximum value and is independent of [S] .

14. 14 Significance of Michaelis–Menten constant, K m Substitution of the definitions of K M and v max into the Michaelis –Menten equation; Rearranging the equation in linear form; A Lineweaver–Burk plot for the analysis of an enzyme-catalysed reaction that proceeds by a Michaelis–Menten mechanism and the significance of the intercepts and the slope.

15. 15 The Catalytic Efficiency of Enzymes The turnover frequency , or catalytic constant , of an enzyme, k cat , is the number of catalytic cycles (turnovers) performed by the active site in a given interval divided by the duration of the interval. This quantity has units of a first-order rate constant and, in terms of the Michaelis–Menten mechanism, is numerically equivalent to k b , the rate constant for release of product from the enzyme–substrate complex. It follows from the identification of k cat with k b and from: Thus:

16. 16 The Catalytic Efficiency of Enzymes The catalytic e ffi ciency , ε(epsilon), of an enzyme is the ratio k cat / K M . The higher the value of ε, the more efficient is the enzyme. We can think of the catalytic activity as the effective rate constant of the enzymatic reaction. From K M = ( k a ′ + k b )/ k a and eqn k cat equation, it follows that; The efficiency reaches its maximum value of k a when k b >> k a ′. Because k a is the rate constant for the formation of a complex from two species that are diffusing freely in solution, the maximum efficiency is related to the maximum rate of diffusion of E and S in solution .

17. 17 Determining the Catalytic Efficiency of an Enzyme The enzyme carbonic anhydrase catalyses the hydration of CO2 in red blood cells to give bicarbonate (hydrogen carbonate) ion: CO 2(g) + H 2 O (l) → HCO 3− (aq) + H + (aq) The following data were obtained for the reaction at pH = 7.1, 273.5 K, and an enzyme concentration of 2.3 nmol dm −3 Atkins, Physical Chemistry , 8 th Ed.

18. 18 Determining the Catalytic Efficiency of an Enzyme Solution: Draw a straight line graph to determine K M and V max . Atkins, Physical Chemistry , 8 th Ed.

19. 19 Determining the Catalytic Efficiency of an Enzyme...

20. 20 Determining the Catalytic Efficiency of an Enzyme... Atkins, Physical Chemistry , 8 th Ed.