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CHAPTER 1 ENZYME KINETICS AND APPLICATIONS CHAPTER 1 ENZYME KINETICS AND APPLICATIONS Kinetics of Enzyme Catalyzed Reactions Applied Enzyme Catalysis Chapter 1.1 The Kinetics of Enzyme Catalyzed Reactions Introduction Classification of enzymes according to the reaction catalyzed and how enzymes work. Enzymes There are many chemical compounds in the living cell. How they are manufactured and combined at sufficient reaction rates under relatively mild temperature and pressure? How does the cell select exactly which reactants will be combined and which molecule will be decomposed? Catalysis by ENZYME Enzymes •Enzymes are biological catalysts that are protein molecules in nature- react in mild condition •They are produced by living cells (animal, plant, and microorganism) and are absolutely essential as catalysts in biochemical reactions. •Almost every reaction in a cell requires the presence of a specific enzyme– related to its particular protein structure. •A major function of enzymes in a living system is to catalyze the making and breaking of chemical bonds. •Therefore, like any other catalysts, they increase the rate of reaction without themselves undergoing permanent chemical changes. •The catalytic ability of enzymes is due to its particular protein structure. •A specific chemical reaction is catalyzed at a small portion of the surface of an enzyme, which is known as the active site. •Some physical and chemical interactions occur at this site to catalyze a certain chemical reaction for a certain enzyme. Catalysts A catalyst is unaltered during the course of a reaction and functions in both the forward and reverse directions. In a chemical reaction, a catalyst increases the rate at which the reaction reaches equilibrium. For a reaction to proceed from starting material to product, the chemical transformations of bond-making and bond-breaking require a minimal threshold amount of energy, termed activation energy. Generally, a catalyst serves to lower the activation energy of a particular reaction. Enzyme Enzyme is protein or nucleic acid. Catalyze biochemical reactions breaking, forming and rearranging bonds. Specificity Dictated by the enzyme active site. Some active sites allow for multiple substrates. Cofactors/Coenzyme (Non protein group) Vitamin derivatives, metals (minerals) can bind as cosubstrates or remain attached through multiple catalytic cycles Cofactors: metal ions, Mg, Zn, Mn, Fe. Coenzyme: complex organic molecule, NAD, FAD, CoA or some vitamins Holoenzyme = apoenzyme + cofactor Enzymes Proteins that assist in chemical reactions may be Enzymes Enzymes are catalysts Specific because of conformational shape Catalyst: chemical that changes the rate of a reaction without being consumed Recycled (used multiple times) Enzymes reduce the activation energy of a reaction Amount of energy that must be added to get a reaction to proceed The activation energy for the decomposition of hydrogen peroxide varies depending on the type of catalysis. Type of catalysis Activatio n energy Uncatalyzed reaction at 20°C 18 kcal/mol Enzymatically catalyzed (catalase) 7 kcal/mol Chemically catalysed (by collodial platinum) 13 kcal/mol Enzyme lower the activation energy of the reaction by binding the substrate and forming an enzymes-substrate complex. Important terms (Enzyme) active site - a region of an enzyme comprised of different amino acids where catalysis occurs or a small portion of the surface of an enzyme which a specific chemical reaction is catalyzed substrate - the molecule being utilized and/or modified by a particular enzyme at its active site co-factor - organic or inorganic molecules that are required by some enzymes for activity. These include Mg2+, Fe2+, Zn2+ and larger molecules termed co-enzymes like nicotinamide adenine dinucleotide (NAD+), coenzyme A, and many vitamins. Important terms (Enzyme) holoenzyme - a complete, catalytically active enzyme including all co-factors OR an enzyme containing a nonprotein group apoenzyme - the protein portion of a holoenzyme minus the co-factors OR the protein part of holoenzyme (holoenzyme=apoenzyme+cofactor) isozyme - (or iso-enzyme) an enzyme that performs the same or similar function of another enzyme that occur in several different molecular forms. Nomenclature of enzyme Originally enzymes were given nondescriptive names such as: rennin : curding of milk to start cheese-making processor pepsin : hydrolyzes proteins at acidic pH trypsin : hydrolyzes proteins at mild alkaline pH The nomenclature was later improved by adding the suffix ase to the name of the substrate with which the enzyme functions, or to the reaction that is catalyzed, for example: Nomenclature of enzyme Alcohol dehydrogenase Glucose isomerase Glucose oxidase Lactic acid dehydrogenase Enzyme reactions are different from chemical reactions, as follows: 1. An enzyme catalyst is highly specific, and catalyzes only one or a small number of chemical reactions. A great variety of enzymes exist, which can catalyze a very wide range of reactions. 2. The rate of an enzyme-catalyzed reaction is usually much faster than that of the same reaction when directed by nonbiological catalysts at mild reaction condition. 3. A small amount of enzyme is required to produce a desired effect. 4. Enzymes are comparatively sensitive or unstable molecules and require care in their use. Enzymatic Reaction Principles Biochemically, enzymes are highly specific for their substrates and generally catalyze only one type of reaction at rates thousands and millions times higher than nonenzymatic reactions. Two main principles to remember about enzymes are a) b) they act as CATALYSTS (they are not consumed in a reaction and are regenerated to their starting state) and they INCREASE the rate of a reaction towards equilibrium (ratio of substrate to product), but they do not determine the overall equilibrium of a reaction. Reaction Rates The rate of the reaction is determined by several factors including the concentration of substrate, temperature and pH. For most standard physiological enzymatic reactions, pH and temperature are in a defined environment (pH 6.9-7.4, 37oC). This enzymatic rate relationship has been described mathematically by combining the equilibrium constant, the free energy change and first or second-order rate theory. Keq = e−∆Go/RT The net result for enzymatic reactions is that the lower the activation energy, the faster the reaction rate, and vice versa. Specificity Most synthetic catalyst are not specific i.e., they will catalyze similar reactions involving many different kinds of reactants. While enzymes are specific. They will catalyze only one reaction involving only certain substances. Binding Energy The interaction between enzyme and its substrate is usually by weak forces. In most cases, van der Waals forces and hydrgen bonding are responsible for the formation of ES complexes. The substrate binds to a specific site on the enzyme known as the active site. Classification of Enzyme Enzymes fall into 6 classes based on function 5. Oxidoreductases: which are involved in oxidation, reduction, and electron or proton transfer reactions Transferases : catalysing reactions in which groups are transferred Hydrolases : which cleave various covalent bonds by hydrolysis Lyases : catalyse reactions forming or breaking double bonds Isomerases : catalyse isomerisation reactions 6. Ligases : join substituents together covalently. 1. 2. 3. 4. SIMPLE ENZYME KINETICS •Enzyme kinetics deals with the rate of enzyme reaction •Kinetic studies of enzymatic reactions provide information about : (1)the basic mechanism of the enzyme reaction and (2) other parameters that characterize the properties of the enzyme. •The rate equations developed from the kinetic studies can be applied in : (1)calculating reaction time, (2) yields, and (3) optimum economic condition, which are important in the design of an effective bioreactor. Assume that a substrate (S) is converted to a product (P) with the help of an enzyme (E) in a reactor as: If you measure the concentrations of substrate and product with respect to time, the product concentration will increase and reach a maximum value, whereas the substrate concentration will decrease as shown in Figure 2.1 The rate of reaction can be expressed in terms of either the change of the substrate Cs or the product concentrations CP as follows: Brown (1902) proposed that an enzyme forms a complex with its substrate. The complex then breaks down to the products and regenerates the free enzyme. The mechanism of one substrate-enzyme reaction can be expressed as: One of the original theories to account for the formation of the enzymesubstrate complex is the "lock and key" theory. The main concept of this hypothesis is that there is a topographical, structural compatibility between an enzyme and a substrate which optimally favors the recognition of the substrate as shown in Figure 2.3. The reaction rate equation can be derived from the preceding mechanism based on the following assumptions: 1. The total enzyme concentration stays constant during the reaction, 2. The amount of an enzyme is very small compared to the amount of substrate. Therefore, the formation of the enzyme substrate complex does not significantly deplete the substrate. 3. The product concentration is so low that product inhibition may be considered negligible. The simplest model describing this interaction is the lockand-key model, in which the enzyme represents the lock and substrate represents the key. In multisubstrate, enzyme-catalyzed reactions, enzymes can hold substrates such that reactive regions of substrates are close to each other and to the enzyme’s active site, which is known as the proximity effects (nearest in distance). Also, enzymes can hold substrates at certain positions and angles to improve the reaction rate, which is known as the orientation effect. Multisubstrate enzyme catalyst reaction Alteration of active site by activator Enzyme Kinetics Enzymes are protein catalysts that, like all catalysts, speed up the rate of a chemical reaction without being used up in the process. A mathematical model of the kinetics of single – substrate-enzyme-catalyzed reaction was first developed by V.C.R. Hendry (1902), and by L. Michaelis and M.L. Menten (1913). Kinetics of simple enzyme catalyzed reaction are often refered to Michaelis-Menten or saturation kinetics. This model are based on data from batch reactors with constant liquid volume in which the the initial substrate,[S0], and enzyme [E0], concentration are known. An enzyme solution has a fixed number of active sites to which substrate can bind. At high substrate concentrations, all these sites may be occupied by substrates or the enzyme is saturated. Two major approaches used in developing a rate expression for enzyme catalyzed reactions are , (1) rapid-equilibrium approach and (2) quasisteady-state approach. Both quasi-steady state approximation and the assumption of rapid equilibrium share the same few steps in deriving a rate expression, Rate of product formation: Rate of variation of the ES complex: Since the enzyme is not consumed, the conservation equation yields, An assumption is required to achieve an analytical solution Vm = k2[Eo] Quasi-steady-state Approximation Briggs and Haldane first proposed Quasi-steadystate assumption In a batch reactor at closed system, [E0] is considered very small compared S Therefore, d(ES)/dt ≈0 From equation d ES k1 [ S ][ E ] k 1 k 2 ES ----1 dt k1 [ E ][ S ] ES k1 k2 ----2 Quasi-steady-state Approximation • Substituting , [ES], , and solve equation 2 for [ S ][ E0 ] ES k k 1 2 [S] k1 ----3 Production formation kinetics, d[ S ] d[ P] v k 2 [ ES ] ----4 dt dt • Substitute equation 3 into 4, k 2 [ E0 ][ S ] v k1 k2 / k1 [ S ] ----5 Quasi-steady-state Approximation Substituting, Vm k2 [ E0 ] and Vm [ S ] v Km [ S ] k 1 k 2 Km k1 ----6 There is difference between Michaelis-Menten and Quasisteady-state constant. [K’m=k-1/k1] Since Km results from the more general derivation, we will use it in the rest of our discussion Enzyme-catalysed reactions display saturation kinetic Determination of Rate Parameters for Michaelis-Menten Type Kinetics Lineweaver-Burk plot Eadie- Hofstee plot Hanes-Woolf plot Batch kinetics Lineweaver-Burk plot From equation 6, Double reciprocal plot Vm [ S ] v Km [ S ] slope Y-intercept Lineweaver-Burk plot gives good estimates on Vm but not necessarily on Km (error relates with substrate conc) Eadie–Hofstee plot Vm [ S ] From equation 6, v Km [ S ] Rearranged equation 6, plot v versus v/[S] gives a line of slope –Km and y-axis intercept of Vm Can be subject to large errors since both coordinates contain v, but less bias on points at low [S] Hanes–Woolf plot Rearrangement of equation 6 yields, slope intercept This plot is used to determine Vm more accurately. Batch kinetics Integration of equation 6 and rearranged yields, 1 [ So ] 1 [ So ] [ S ] Vm ln t [S] Km t Km slope Y-intercept 1 [ So ] ln t [S] [ So ] [ S ] t Models for More Complex Enzyme Kinetics Allosteric Enzymes Allostery @ cooperative binding The binding of one substrate to enzyme facilitates binding of other substrate molecules Vm [ S ] n v K" m [ S ] n Where, n = cooperativity coefficient Modulation and Regulation of Enzyme Activity enzyme-substrate inhibitors systems classify by their influence on the Michaelis-Menten equation parameters Vm and Km Reversible inhibitors are termed competitive if their presence increases the value of Km but does not alter Vm. On the other hand, by rendering the enzyme or the enzyme-substrate complex inactive, a noncompetitive inhibitor decreases the Vm of the enzyme but does not alter the Km value. Inhibited enzyme kinetic •Certain compound may bind to enzymes and reduce their activities ~ enzyme inhibitors •Enzyme inhibitions may be irreversible ( heavy metal: lead, cadium, mercury–form a stable complex with enzyme and reduce enzyme activity) or reversible (EDTA and citrate) •Three major class of reversible enzyme inhibitioncompetitive, noncompetitive and uncompetitive inhibitions. •Competitive- compete with substrate for active site of the enzyme Competitive enzyme inhibition scheme can be described as: K’m,app The effect of such inhibitors can be countered or reversed by increasing the substrate concentration. •Noncompetitive inhibitors bind on site other than the active site, reduce enzyme affinity to the substrate • Can be described by: Rate equation: Overcome by adding reagents to block binding of inhibitor Uncompetitive inhibition Inhibitors binds to the ES complex only and have no affinity for the enzyme itself Rate of reaction, v Vm, app [ S ] K ' m ,app [ S ] The net effect is reduction in both Vm and K’m values. Substrate inhibition High substrate concentrations may cause inhibition in some enzymatic reaction Effect of pH and temperature -Enzyme are active only over small range of pH due to: the active site functional group charges (ionic form) the three dimensional shape of enzyme are pHdependent -these ionic group on active sites must be in a suitable form (acid or base) to function. -Variation in pH of medium result in changes of: Ionic form of the active site Activity of enzyme, hence the reaction rate Affect the maximum reaction rate, Km and enzyme stability -Scheme to describe pH dependence of the enzymatic reaction rate for ionizing enzymes. - Variation of enzyme activity with pH for 2 different enzymes -Some cases, the substrate may contain ionic groups, and the pH of medium affects the affinity of substrate to enzyme. (How to determine pH optimum?) -Refer to Eq. 3.44& Eq. 3.45 ascending descending The rate varies according to Arrhenius equation Thermal denaturation occurred Variation of reaction rate with temperature The rate, v k2 [ E ] k2 Ae Ea / RT kd is the denaturation constant, k d Ad e Ea / RT Enzyme denaturation is much faster than enzyme activation. Variation in T affect both Vm and Km