Biochemistry 462a - Enzyme Kinetics Reading - Chapter 8 Practice problems - Chapter 8: (not yet assigned); Enzymes extra problems Introduction Enzymes are Biological Catalysis A catalyst is a substance that increases the rate (velocity) of a chemical reaction. Most biological catalysts are proteins. The material acted upon by the catalyst is the substrate. Although a catalyst participates in the reaction process, it is unchanged after the process is complete. A catalyst increases the rate at which a reaction reaches equilibrium but does not alter K eq or G o' for the reaction. A thermodynamically favorable process is not made more favorable by the presence of a catalyst. A thermodynamically unfavorable process is not made favorable by the presence of a catalyst. Kinetics The Rate Constant For the irreversible reaction A B. This is a first order reaction (there is only a single reactant). The velocity (v) or reaction rate is given by the rate of formation of product or the rate of disappearance of reactant. The velocity (v) or reaction rate is, where k= the rate constant. For the reaction A + B products, v = k[a][b]. This is a second order reaction (there are two reactants). 1
Reaction Rate Theory What determines the rate of a reaction? For every reaction there is a highenergy transition state through which the reactants must pass in order for the reaction to occur. The height of the energy barrier, G o, determines the rate of the reaction. k=qe (- Go /RT) Q is a collection of constants. Catalysis A catalyst functions by lowering the activation energy for a reaction by amount = G o. A catalyst does not alter the G for the reaction. G o = H o -T S o - a catalyst can accelerate a reaction by affecting either H o or S o, or both. Strong binding of the transition state to the catalyst lowers H o - makes it more negative. Proximity and orientation of the substrates on the catalyst favor formation of the transition state by reducing S o. Enzymes Enzymes are highly effective catalysts that carry out complex chemical transformations under mild conditions (water, neutral ph). Enzymes show great specificity with regard to the reactions they catalyze and the substrates they react with. Enzymes can be regulated. Enzymes carry out their catalytic role by binding the substrate to a specific area of the protein called the active site (Companion: Enzymes/Enzyme Kinetics). 2
Several amino acid side chains comprise the active site. Coenzymes are small organic molecules, derived from vitamins that participate in the chemical reactions catalyzed by many enzymes. Coenzyme Vitamin Reaction Mediated Biotin Biotin Carboxylation Cobalamin B 12 Alkylation Coenzyme A Pantothenic acid Acyl Transfer Flavin Riboflavin Oxidation-Reduction Lipoic Acid Lipoamide Acyl Transfer Nicotinamide Niacin Oxidation-Reduction Pyridoxal Phosphate Pyridoxal Amino Group Transfer Tetrahydrofolate Folate One-Carbon Group Transfer Thiamine Pyrophosphate Thiamine Aldehyde Transfer Summary of factors responsible for the rate enhancement seen with enzyme catalysis Uncatalyzed reactions in solution can be slow because o They involve the formation of unstable positive and negative charges in the transition state. o They frequently require several molecules to be brought together with a concomitant loss of entropy. These difficulties are lessened with enzymes because o Strategically placed acids, bases, metal ions, or dipoles that are part of the structure of the enzyme stabilize charges. o o Covalent catalysis is used to give reaction pathways of lower energy. Entropy losses are minimized because the necessary catalytic groups are part of the enzyme structure. These features are paid for in two ways. o The original synthesis of the enzyme costs energy, although the enzyme is used repeatedly. o The enzyme-substrate binding energy is used to immobilize the substrate at the active site and hold it next to the catalytic groups. This binding energy is inherently available for use but it is generally not utilized in uncatalyzed reactions. Enzyme Kinetics The simplest enzyme mechanism involves the following two steps 3
The rate of the enzymatic reaction is: In order to derive a useful equation describing this reaction we make the steady-state assumption, which assumes that over most of the reaction course [ES] is small and does not change, i.e., d[es]/dt=0. Using this assumption, one can derive the Michaelis-Menten equation. Plotting Kinetic Data The Michaelis-Menten equation describes a rectangular hyperbola. The enzyme is characterized by two constants: K M and V max o V max is the maximal rate of the reaction which occurs when [S] >> o K M K M is the substrate concentration that gives 1/2 maximal velocity. 4
For determination of K M and V max a linear transformation, the Lineweaver-Burk plot, is useful. Turnover Number The turnover number of an enzyme, k cat, is the maximal velocity per enzyme molecule per unit of time. Enzyme Efficiency We can rewrite the rate equation as When [S] << K M, then k cat /K M is a second order rate constant, and is a measure of the efficiency of the enzyme at low [S]. The maximal value of k cat /K M is 10 8-10 9, which is diffusion-controlled. Enzyme Substrate k cat (sec -1 ) K M (M) k cat / K M (M -1 ) (sec -1 ) Catalase H 2 O 2 4.0x10 7 1.1 4.0x10 7 Carbonic anhydrase Acetylcholine esterase CO 2 1.0x10 4 1.2x10-2 8.3x10 7 Acetylcholine 1.4x10 4 9.0x10-5 1.6x10 8 Fumarase Fumarate 8.0x10 2 5.0x10-6 1.6x10 8 For different substrates, k cat /K M is also the best way to determine the specificity of an enzyme. 5
For hydrolysis of a peptide bond by the proteolytic enzyme chymotrypsin, the nature of the R 1 sidechain is critical.. R 1 k cat / K M (M -1 sec -1 ) Gly 1.3x10-1 Val 3.6x10 2 Leu 3.0x10 3 Phe 1.0x10 5 The Phe-containing substrate is best! Enzyme Regulation Amount of enzyme (transcriptional). Amount of substrate. Control of activity. o Allosteric regulation. o Covalent modification. o Inhibitors. Allosteric Regulation (remember hemoglobin!!). Multisubunit enzymes Homoallostery - cooperative substrate binding and activation. 6
Heteroallostery - regulation by effector molecules, which can be positive or negative. Allosteric effectors bind at a site different from the active site.allosteric effectors can activate (favor R state) or inhibit (favor T state). Reversible covalent modification is widely used to regulate enzyme activity. Phosphorylation of a Ser is a common reaction. Irreversible covalent modification. Many enzymes are made as inactive precursors, zymogens. Activation of the zymogen involves proteolytic cleavage and in this case (trypsinogen) removal of a peptide fromthe amino terminus. 7
Enzyme Inhibitors The use of enzyme inhibitors can often provide valuable information about an enzymatic mechanism. Many drugs are based on the use of enzyme inhibitors, e.g., penicillin inhibits an enzyme involved in bacterial cell wall synthesis. A competitive inhibitor competes with the substrate for binding at the active site, increasing Km. A noncompetitive inhibitor binds to a site other than the active site and inhibits product formation. Noncompetitive inhibitors decrease velocity, including Vmax, by decreasing kcat. 8
Covalent Inhibition Irreversible or covalent inhibition involves chemical modification of the protein. Effect of ph ph is not an important regulatory mechanism, but the effect of ph can be highly informative about the mechanism. Changing ph can increase or decrease the rate. This ph-rate profile suggests that a deprotonated histidine is involved in the catalytic step. 9
This ph-rate profile suggests that a protonated lysine is involved in the catalytic step. Note that the apparent pka derived from inspection of kinetic data may be significantly different than the actual pka of the sidechain. More sophisticated analysis is required to obtain an accurate estimation of the pka in the enzyme. 10