Topic 10 Enzymes II Thermodynamics & Kinetics PDF

BTEN 2315 CHEN 1314 Biochemistry TOPIC 10 ENZYMES II: THERMODYNAMICS AND KINETICS  OUTLINE ENZYMES II: THERMODYNAMICS AND KINETICS THERMODYNAMICS OF ENZYME REACTION  ACTIVATION ENERGY AND TRANSITION STATE  GIBBS FREE ENERGY OF ENZYME RE...

BTEN 2315 CHEN 1314 Biochemistry TOPIC 10 ENZYMES II: THERMODYNAMICS AND KINETICS  OUTLINE ENZYMES II: THERMODYNAMICS AND KINETICS THERMODYNAMICS OF ENZYME REACTION  ACTIVATION ENERGY AND TRANSITION STATE  GIBBS FREE ENERGY OF ENZYME REACTION ENZYME KINETICS  ENZYME VELOCITY  ENZYME UNITS  EFFECT OF SUBSTRATE CONCENTRATION  EFFECT OF ENZYME CONCENTRATION  EFFECT OF TEMPERATURE  EFFECT OF PH  MICHAELIS-MENTEN MODEL OF ENZYME KINETICS  ALLOSTERIC ENZYME KINETICS THERMODYNAMICS OF ENZYME REACTIONS  THERMODYNAMICS OF ENZYME REACTION A Review The First Law of Thermodynamics, a mathematical statement of the law of conservation of energy, states that the total energy (internal energy, sometimes denoted by U) of a system and its surroundings is a constant: However, the disadvantage is, it cannot be used to predict whether a reaction can occur spontaneously, as some spontaneous reactions have a positive ΔE. The Second Law of Thermodynamics states that a process can occur spontaneously only if the sum of the entropies of the system and its surroundings increases (or that the universe tends towards maximum disorder), that is: But using entropy as a criterion of whether a biochemical process can occur spontaneously is difficult, as the entropy changes of chemical reactions are not readily measured.  These difficulties are overcome by using a different thermodynamic function, free energy (G), proposed by Josiah Willard Gibbs which combines the First and the Second Laws of Thermodynamics: ΔG is the free energy of a system undergoing a transformation at constant pressure (P) and temperature (T), ΔH is the change in enthalpy (heat content) of this system, and ΔS is the change in the entropy of this system. The enthalpy change is: The volume change (ΔV) is small for nearly all biochemical reactions, and so ΔH is nearly equal to ΔE. Since, Therefore, Thus, the ΔG of a reaction depends both on the change in internal energy (Δ E) and on the change in entropy (ΔS) of the system Continue… The change in free energy ΔG of a reaction is a valuable criterion of whether that reaction can occur spontaneously:  a reaction can occur spontaneously only if ΔG is negative;  a system is at equilibrium if ΔG is zero;  a reaction cannot occur spontaneously if ΔG is positive whereby an input of energy is required to drive such a reaction;  the ΔG of a reaction is independent of the path of the transformation;  ΔG provides no information about the rate of a reaction.  Therefore:  ΔG > 0 the reaction is non-spontaneous  ΔG = 0 the reaction is at equilibrium  ΔG < 0 the reaction is spontaneous ACTIVATING ENERGY AND TRANSITION STATES The energy changes that take place during the course of a biochemical reaction are shown in Fig. 1. In all reactions there is an energy barrier that has to be overcome in order for the reaction to proceed. Continue…. This energy barrier is the energy needed to transform the substrate molecules into the transition state – an unstable chemical form part-way between the substrates and the products. The transition state has the highest free energy of any component in the reaction pathway. The Gibbs Free Energy of Activation (ΔG‡) is equal to the difference in free energy between the transition state and the substrate (Fig. 1). An enzyme works by stabilizing the transition state of a chemical reaction and decreasing ΔG‡ (Fig. 1). The enzyme does not alter the energy levels of the substrates or the products. Thus an enzyme increases the rate at which the reaction occurs, but has no effect on the overall change in energy of the reaction. GIBBS FREE ENERGY OF ENZYME REACTION The change in Gibbs free energy (ΔG) dictates whether a reaction will be energetically favorable or not. Fig. 1 shows an example where the overall energy change of the reaction makes it energetically favorable (i.e. the products are at a lower energy level than the substrates and ΔG is negative). It should be noted that ΔG is unrelated to ΔG‡. The ΔG of a reaction is independent of the path of the reaction, and it provides no information about the rate of a reaction since the rate of the reaction is governed by ΔG‡. Continue….. A negative ΔG indicates that the reaction is thermodynamically favorable in the direction indicated (i.e. that it is likely to occur without an input of energy) A positive ΔG indicates that the reaction is not thermodynamically favorable and requires an input of energy to proceed in the direction indicated. In biochemical systems, this input of energy is often achieved by coupling the energetically unfavorable reaction with a more energetically favorable one (coupled reactions). It is often convenient to refer to ΔG under a standard set of conditions, defined as when the substrates and products of a reaction are all present at concentrations of 1.0 M. Reactions that take place at a constant pH of 7.0 has a slightly different value for ΔG, and this is called ΔGo’. Continue… An example of an energetically favorable reaction which has a large negative ΔGo’ and is commonly used to drive less energetically favorable reactions is the hydrolysis of ATP to ADP and Pi: A real example of coupled reaction is given below, whereby it is the first reaction step in the glycolysis: ENZYME KINETICS  ENZYME KINETICS Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, e.g., its role in metabolism. A chemical reaction usually reached a state of dynamic equilibrium, where at this point, although new molecules of substrate and product are continually being transformed and formed, the ratio of substrate to product remains at a constant value. Consider the reaction: The rate of the forward reaction is 10-4 s-1 and the rate of the reverse reaction is 10-6 s-1. At equilibrium the ratio of the concentrations of the substrate and product gives a constant value, known as the equilibrium constant (K). K for a given reaction is defined as: Note: The square brackets indicate concentration Continue… K is also given by the ratio of the forward reaction rate (kf) and the reverse reaction rate (kb): Thus, for the above reaction at equilibrium, there is 100 times more of product B than there is of substrate A, regardless of whether there is enzyme present or not. Enzymes do not alter the equilibrium position of a reaction, but accelerate the forward and reverse reactions to the same extent. Enzymes accelerate the attainment of the equilibrium position but do not shift its position. For the hypothetical reaction shown above, in the absence of added enzyme the reaction may take over an hour to reach the equilibrium position, whereas in the presence of enzyme the equilibrium position may be reached in less than 1 s. ENZYME VELOCITY The rate of an enzyme-catalyzed reaction is often called its velocity, reported as values at time zero or initial velocity, V0 (µmol min-1) The rate is fastest at the point where no product is yet present because the substrate concentration is greatest before any substrate has been transformed to product. This is because enzymes may be subjected to feedback inhibition by their own products and/or because with a reversible reaction the products will fuel the reverse reaction. Experimentally V0 is measured before more than approximately 10% of the substrate has been converted to product in order to minimize such complicating factors. Continue… A typical plot of product formed against time for an enzyme-catalyzed reaction shows an initial period of rapid product formation which gives the linear portion of the plot (Fig. 1). This is followed by a slowing down of the enzyme rate as substrate is used up and/or as the enzyme loses activity. V0 is obtained by drawing a straight line through the linear part of the curve, starting at the zero time-point, whereby the slope of this straight line is equal to V0. ENZYME UNITS Enzyme activity may be expressed in a number of ways, the commonest is by the initial rate (V 0 ) of the reaction being catalyzed (e.g. µmol of substrate transformed per minute or µmol min-1). The two standard units of enzyme activity that can be used:  Enzyme unit (U) -- An enzyme unit is that amount of enzyme which will catalyze the transformation of 1 µmol of substrate per minute at 25oC under optimal conditions (pH and temperature) for that enzyme.  Katal (kat) -- is defined as that catalytic activity which will raise the rate of a reaction by one mole per second in a specified system. It is possible to convert between these different units of activity: 1 µmol min-1 = 1 U = 16.67 nanokat. Total activity refers to the total units of enzyme in the sample (weight given). Specific activity is the number of enzyme units per milligram of protein (Units mg-1). The specific activity is a measure of the purity of an enzyme; during the purification of the enzyme its specific activity increases and becomes maximal and constant when the enzyme is pure. EFFECT OF SUBSTRATE CONCENTRATION ON ENZYME ACTIVITY The normal pattern of dependence of enzyme rate on substrate concentration ([S]) is that at low substrate concentrations a doubling of [S] will lead to a doubling of the initial velocity (V0). However, at higher substrate concentrations the enzyme becomes saturated, and further increases in [S] lead to very small changes in V0, because at saturating substrate concentrations, effectively all of the enzyme molecules have bound substrate. At the saturation point, the overall enzyme rate is now dependent on the rate at which the product can dissociate from the enzyme, and adding further substrate will not affect this. The shape of the resulting graph when V 0 is plotted against [S] is called a hyperbolic curve (Fig. 2). EFFECT OF ENZYME CONCENTRATION ON ENZYME ACTIVITY In situations where the substrate concentration is saturating (i.e. all the enzyme molecules are bound to substrate), a doubling of the enzyme concentration will lead to a doubling of V0. This gives a straight line graph when V 0 is plotted against enzyme concentration (Fig. 3) Increasing the enzyme concentration 3X or 4X will results in 3X and 4X V0 respectively Fig.3 Effect of enzyme concentration EFFECT OF TEMPERATURE ON ENZYME ACTIVITY Temperature affects the rate of enzyme-catalyzed reactions in two ways: 1. First effect of rise in temperature is the increase of the thermal energy of the substrate molecules.  This raises the proportion of substrate molecules with sufficient energy to overcome the Gibbs free energy of activation (ΔG ‡ ) and hence increases the rate of the reaction. 2. Second effect comes into play at higher temperatures, whereby increasing the thermal energy of the molecules which make up the protein structure of the enzyme itself will increase the chances of breaking the multiple weak, noncovalent interactions (H-bonds, van der Waals forces, etc.) which hold the 3-D of the enzyme together.  Ultimately this will lead to the denaturation (unfolding) of the enzyme.  Even small changes in the 3-D shape of the enzyme can alter the structure of the active site and lead to a decrease in catalytic activity. The overall effect of a rise in temperature on the reaction rate of the enzyme is a balance between these two opposing effects. Continue… A graph of temperature plotted against V0 will therefore show a curve, with a well-defined temperature optimum (Fig. 3a). For many mammalian enzymes this is around 37 o C, but there are also organisms which have enzymes adapted to working at considerably higher or lower temperatures. Fig. 3a. The effect of temperature on enzyme activity.+ EFFECT OF PH ON ENZYME ACTIVITY Each enzyme has an optimum pH at which the rate of the reaction that it catalyzes is at its maximum. Small deviations in pH from the optimum value lead to decrease activity due to changes in the ionization of groups at the active site of the enzyme. Larger deviations in pH lead to the denaturation of the enzyme protein itself, due to interference with the many weak non-covalent bonds maintaining its three-dimensional structure. A graph of V 0 plotted against pH will usually give a bell-shaped curve (Fig. 3b). Many enzymes have a pH optimum of around 6.8, but there is great diversity in the pH optima of enzymes, due to the different environments in which they are adapted to work. For example, the digestive enzyme pepsin is adapted to work at the acidic pH of the stomach (around pH 2.0). Fig. 3b. The effect of pH on enzyme activity.  MICHAELIS–MENTEN MODEL IN ENZYME KINETICS Enzyme kinetics is the study of the rates of chemical reactions that are catalysed by enzymes. Studying an enzyme's kinetics can reveal:  the catalytic mechanism of this enzyme,  its role in metabolism,  how its activity is controlled,  how drugs/chemicals might inhibit the enzyme. In 1913, Michaelis–Menten used the following mathematical model to explain the concept of enzyme catalysis of single-substrate-enzyme-catalyzed reactions:  The enzyme (E), combines with its substrate (S) to form an enzyme–substrate complex (ES).  The ES complex can dissociate again to form E and S, or can proceed chemically to form E and the product P. Continue…. The rate constants k1, k2 and k3 describe the rates associated with each step of the catalytic process. It is assumed that there is no significant rate for the backward reaction of enzyme and product (E + P) being converted to ES complex. [ES] remains approximately constant until nearly all the substrate is used, hence the rate of synthesis of ES equals its rate of consumption over most of the course of the reaction; that is, [ES] maintains a steady state. From the observation of the properties of many enzymes it was known that V0 at low substrate concentrations is directly proportional to [S]. However, at high substrate concentrations the velocity tends towards a maximum value, that is the rate becomes independent of [S] (Fig. 4a). Fig. 4a. The relationship between substrate concentration [S] and initial reaction velocity (V0 ). (a) A direct plot, Continue…. This maximum velocity is called Vmax (µmol min-1). The initial velocity (V0) is the velocity measured experimentally before more than approximately 10% of the substrate has been converted to product. Michaelis and Menten derived an equation to describe these observations, and the equation is as follows: The equation describes the hyperbolic curve as in Figure 4 a In deriving the equation, Michaelis and Menten defined a new constant, Km, the Michaelis constant (unit is M): Km is a measure of the stability of the ES complex, being equal to the sum of the rates of breakdown of ES over its rate of formation. Continue…. For many enzymes k2 is much greater than k3. Under these circumstances Km becomes a measure of the affinity of an enzyme for its substrate since its value depends on the relative values of k1 and k2 for ES formation and dissociation, respectively. A high Km indicates weak substrate binding (k2 predominant over k1). A low Km indicates strong substrate binding (k1 predominant over k2). K m can be determined experimentally by the fact that its value is equivalent to the substrate concentration at which the velocity is equal to half of Vmax. Linearization of the Michaelis-Menten Plot V max and K m , the kinetic properties of any enzyme can be determined experimentally by measuring V0 at different substrate concentrations (see Fig. 4). However, if the Michaelis-Menten plot is used, the estimation of values from the hyperbolic regression plot will be made impossible, because Vmax (and hence Km) is only achieved at an infinite substrate concentration. Many researchers have manipulated the Michaelis-Menten equation to linearize the plot so that the estimations of the Vmax and Km can be made simpler. Two mathematical linearization manipulations by two different group of scientist are given as follows: 1. Lineweaver-Burk Plot - A double reciprocal of 1/V0 against 1/[S]. 2. Eadie-Hofstee Plot – A plot of of V0/[S] against V0. Whichever linearization plot is to be used, is a matter of preference, whereby each has their pros and cons. 1. Lineweaver–Burk Plot To determine Vmax and Km accurately, Lineweaver–Burk manipulate the Michaelis-Menten equation mathematically. Lineweaver-Burk suggested a double reciprocal or Lineweaver–Burk plot of 1/V0 against 1/[S] is made (Fig. 4b). Equation derivatized Fig. 4. The relationship between substrate concentration [S] and initial reaction velocity (V0) (a) A direct plot (b) A Lineweaver-Burk double-reciprocal plot. Continue… About the Lineweaver–Burk plot of 1/V0 against 1/[S]  The plot gives a straight line, with the intercept on the y-axis equal to 1/Vmax and the intercept on the x-axis equal to 1/Km.  The slope of the line is equal to Km/Vmax  The practical significance - the Lineweaver–Burk plot is also a useful way of determining how an inhibitor binds to an enzyme (Discussed in Topic 12). 2. Eadie-Hofstee Plot This is another method of a mathematical linearization equation of Michaelis-Menten equation (besides Lineweaver-Burk plot). The K m and V max can also be determined from an Eadie-Hofstee plot of V0/[S] against V0 The manipulation of Michaelis-Menten equation by Eadie-Hofstee gives: Equation derivatized Fig 5 Eadie-Hofstee plot of enzyme kinetics In this plot, the intercept on the x-axis equals Vmax and the slope of the line is equal to 1/Km. ALLOSTERIC ENZYMES KINETICS (NON MICHAELIS-MENTEN ENZYME KINETICS) Not all enzyme follows the Michaelis-Menten kinetics. Some enzymes consist of multiple subunits and multiple active sites, thus, have more than one substrate-binding site, and they are categorized as allosteric enzymes. The binding of one substrate to the enzyme facilitates the binding of other substrate molecules. This behavior is known as allostery or cooperative binding. The rate expression in this case is: where n = cooperativity coefficient and n > 1 indicates positive cooperativity Allosteric enzymes often display Sigmoidal plots of V 0 vs [S], rather than the Hyperbolic plots as predicted by the Michaelis-Menten equation. Thus allosteric enzymes are often multi-subunit proteins, with one or more active sites on each subunit. The binding of substrate at one active site induces a conformational change in the protein that is conveyed to the other active sites, altering their affinity for substrate molecules. E.g. Aspartate transcarbamoylase is an allosteric enzyme because the binding of substrate to one active site can affect the properties of other active sites in the same enzyme molecule. Two models to describe the mechanism of action of allosteric enzymes: 1. Concerted (Symmetry) Model by Monod, Wyman and Changeux  In the Concerted model, T-state subunits are in a tense state and relatively inactive, while R-state subunits are in a relaxed, active state with higher affinity for the substrate. In the absence of bound substrate the equilibrium favors the T-state. As substrate binds to every active site in the T-state, the equilibrium shifts towards the R-state. All of the subunits modify the conformation of enzymes in a concerted manner. 2. Sequential Model by Koshland, Nemethy and Allous  In the Sequential model, substrate binding induces a conformational modification in a cooperative way and the subunit interactions arise by the influence in which these conformational changes have on neighboring subunits. Neither model can describe the cooperative nature of allosteric binding of substrate to the enzymes satisfactorily; instead both models can be used interchangeably to properly describe the mechanism of action of any particular allosteric enzymes. Two models to describe the mechanism of action of allosteric enzymes Hyperbolic curve Sigmoid curve  1 0 pic o ofT d En Any questions? ‫ل اﻟﺣـﻣد‬ ‫ﻟﮫ‬