BioC 3021 Notes - Lecture 6: Enzyme Characteristics and Thermodynamics PDF

BioC 3021 Notes Robert Roon Lecture 6: Enzyme Characteristics and Thermodynamics Slide 1. Enzyme Characteristics and Thermodynamics Today we’ll look the basic character of enzymes and the thermodynamic aspects of enzyme catalysis. We will look at how enzym...

BioC 3021 Notes Robert Roon Lecture 6: Enzyme Characteristics and Thermodynamics Slide 1. Enzyme Characteristics and Thermodynamics Today we’ll look the basic character of enzymes and the thermodynamic aspects of enzyme catalysis. We will look at how enzymes are constructed and how the laws of thermodynamics govern enzyme activity. Slide 2. Enzyme Characteristics One of the primary functions of protein molecules is to serve as enzymes. Enzymes are catalysts that speed up the rate of biochemical reactions without themselves being permanently altered in the course of reaction. Almost all enzymes are protein molecules, and for many years it was thought that only proteins could serve as enzymes. However, (note the parenthetical term “or nucleic acid”) about 20 years ago Sidney Altman and Tom Cech discovered that certain nucleic acids can also serve as enzymes, and so there are a few exceptions to this (enzyme equals protein) rule. In our discussions of enzymes, we will generally assume that we are dealing with protein molecules. One unusual feature of enzymes is their high degree of specificity. Enzyme catalyzed reactions are often exquisitely sensitive to small changes in the chemical structure of reactant (substrate) molecules, something that is not generally true of normal chemical reactions. We will deal with how such specificity is achieved as we consider the mechanisms of enzyme reactions. Enzyme catalyzed reactions often respond to substrate levels in ways that are uncharacteristic of normal chemical reactions. Reaction rates can increase dramatically by increasing substrate at low substrate concentrations. Rates often plateau at higher substrate levels, at which point enzymes become virtually 1 BioC 3021 Notes Robert Roon insensitive to further increases in substrate concentration. Enzyme molecules are highly specific toward reactants and products. They exhibit high sensitivity to changes in temperature, pH, substrate concentration, cofactor availability, and ionic environment. Slide 3. Classification of Enzymes Although there are thousands of different enzymes, most enzymatic reactions fall into one of the six major categories. -Oxidoreductases are involved in oxidation-reduction reactions. We will see many of these enzymes in the pathways that we study, because most anabolic pathways involve reduction and most catabolic pathways involve oxidation. -Transferases catalyze the transfer of groups from one substrate to another. These are common in the assembly of the four major classes of macromolecules—lipids, carbohydrates, proteins and nucleic acids. -Hydrolases are involved in the addition of water to a bond to promote bond cleavage. Such reactions are common in stage one of catabolism—the digestion of polymers into their component monomers. -Lyases catalyze the addition of a group to the two carbons of a double bond or the loss of a group in the formation of a double bond. We will see examples of lyases in the TCA cycle and in fatty acid oxidation and biosynthesis. -Isomerases are involved in the interconverson of isomers. There are isomerases in the glycolysis pathway and in the TCA cycle. -Ligases catalyze the formation of a new bond between two substrates with the participation of ATP. The enzyme that joins discontinuous lagging strands of DNA is a ligase. 2 BioC 3021 Notes Robert Roon Slide 4. Enzyme Kinetics Enzymes are biological catalysts that speed the rates of reactions under mild conditions. Unlike most uncatalyzed chemical reactions, enzyme reactions occur rapidly at normal environmental temperatures. Enzymes function under moderate pH conditions and at low reactant concentrations. The rates of many enzyme reactions are extremely high compared to the equivalent uncatalyzed chemical reactions. For example, the enzyme carbonic anhydrase raises the rate of carbon dioxide hydration by a factor of 107. Enzymes achieve such rate enhancements by providing an alternate reaction pathway with a lowered energy of activation. Slide 5. Pathway of an Enzyme Catalyzed Reaction The figure shows the simplest formulation of the kinetic events that occur in an enzyme catalyzed reaction. In this diagram, an enzyme (E) binds its substrate (S), S being the reacting molecule or reactant, to form an enzyme-substrate complex (ES). A biochemical reaction then takes place in the enzyme-substrate complex. The product (P) is then released, and the enzyme is free to participate in another round of catalysis. Note that the E at the left and the E at the right of the reaction are identical molecules. The double-headed arrows indicate that, for many enzymes, these reactions are readily reversible. The reaction show here is monomolecular; that is, it involves only one substrate. However, many biochemical reactions involve two or more substrates, and the kinetics are much more complex. It is also important to note that even monomolecular reactions are more complicated than shown here, if one considers that there are also other complexes formed in the course of reaction—for example, an enzyme-product 3 BioC 3021 Notes Robert Roon complex (EP) is also part of the reaction, as are various complexes with reaction intermediates. Slide 6. The Active Site of an Enzyme The active site of an enzyme occupies a small niche on the surface of the protein, which is comprised of amino acid side chains from various parts of the primary sequence. There are two features to enzyme activity—binding and catalysis. The substrate is bound to the active site by weak interactions with various side chains of the enzyme. The specificity of substrate binding depends on geometric and chemical complementarities between substrate and the active site amino acid residues. The interactions between enzyme and substrate include ionic bonds, hydrogen bonds, hydrophobic interactions, and van der Waals forces. The key to enzyme catalysis is that the reaction pathway and the energy level of the transition state are altered by interactions between the substrate and some of the active site amino acid side chains. Interactions with these amino acids include such things as acid-base catalysis, nucleophilic and electrophylic interactions, hydrophobic effects, ionic stabilization of charged intermediates, and, in some cases, the formation of a covalent bond between substrate and the enzyme. Slide 7. The Lock and Key Hypothesis There are two hypotheses that are used to explain substrate binding. The lock and key hypothesis states that the enzyme active site is an exact complement to the substrate at all times. The substrate fits immediately in the active site like a key in a lock. Taken to its extreme, this hypothesis would suggest that the shape of the active site remains absolutely the same before and after the substrate is bound. 4 BioC 3021 Notes Robert Roon Slide 8. The Induced Fit Hypothesis The induced fit hypothesis states that the shape of the active site changes in the presence of the substrate to yield a precise fit. According to this model, interactions between the substrate and active site amino acids induce conformational changes in the shape of the active site. In actual fact, both of these hypotheses have some validity. All enzymes undergo some changes in active site topography when the substrate is bound, but the enzymes vary considerably in the degree of change that occurs upon substrate binding. Slide 9. Induced Fit with Hexokinase The enzyme hexokinase provides a dramatic example of induced fit. The active site of hexokinase undergoes a significant alteration in its conformation when its substrate, glucose, is bound. In the absence of glucose, the active site exists as an open cleft. In the presence of glucose, the site undergoes a significant transformation in which the cleft closes around and envelopes the substrate. Slide 10. Effect of Temperature on Enzyme Activity Temperature has a significant effect on enzyme activity. In general, enzyme reactions are more sensitive than equivalent chemical reactions to changes in temperature. At lower temperatures, the rates of enzyme reactions increase markedly as the temperature is raised. This sensitivity to temperature is sometimes measured as a Q10—the increase in activity for a ten degree rise in temperature. The Q10 for enzyme reactions is generally higher than it is for chemical reactions. Enzymes are subject to inhibition at higher temperatures. Enzyme activity increases with temperature up to some optimal temperature range, but then decreases as the temperature is raised even higher. Above a certain critical temperature, enzymes completely lose activity because they are irreversibly denatured. 5 BioC 3021 Notes Robert Roon Slide 11. Effect of pH on Enzyme Activity Most enzymes are highly sensitive to changes in pH. There is generally a pH range in which optimal activity is observed. At pH values below or above this optimal range, enzyme activity decreases, and at pH extremes most enzymes are denatured. As with temperature, the effects of pH on enzyme reactions are more pronounced than on most chemical reactions. That is because in addition to effects on the substrate, the pH influences the shape and charge of the active site, which in turn changes the functionality of the enzyme in catalysis. Slide 12. Enzyme Specific Activity The catalytic activity of an enzyme relates to the ability to convert substrate (S) to product (P). Catalytic activity is generally measured as µmole of product/minute (Enzyme Units). Specific activity describes the ratio of enzyme activity to the amount of protein present, and is measured as Enzyme Units/mg of protein. The specific activity of an enzyme is generally relatively low in a crude biological extract and increases as the enzyme is purified. One indication that an enzyme preparation has reached homogeneity is that the specific activity does not increase when further purification procedures are attempted. Slide 13. Enzyme Turnover Number The turnover number (Kcat) of a reaction is given by the formula Kcat = Vmax/[Et]. The turnover number gives the number of molecules of substrate that can be converted per second per molecule of enzyme (or per enzyme active site for a multi-subunit enzyme). Turnover numbers relate to the molecules of a specific enzyme (not the total protein in a preparation), and thus unlike the specific activity that increases as an enzyme is purified, the turnover number of an enzyme is an intrinsic property that does not change with purification. 6 BioC 3021 Notes Robert Roon Slide 14. Values for Enzyme Turnover Numbers In the examples shown here, enzyme turnover numbers vary from 100 per second to 600,000 per second. There are other enzymes with turnover numbers of less than 1 per second and more than 40,000,000 per second. Slide 15. Rate Enhancements by Selected Enzymes The enhancement in reaction rate for enzyme catalysis is generally enormous. The data in our figure, which compares the rates of enzyme catalyzed and uncatalyzed reactions, show rate enhancements that range from about 106 to 1017. In the case of OMP decarboxylase, the uncatalyzed reaction would take 78 million years, whereas the catalyzed reaction occurs in seconds. One of the fastest enzymes, carbonic anhydrase, catalyzes the breakdown of one million substrate molecules per second. Slide 16. Cofactor Molecules Many enzyme reactions require small molecules called cofactors (or coenzymes) in addition to the protein structure itself. In this case, catalysis depends on three factors interacting to form an active complex—Enzyme, Substrate and Cofactor all participate in the catalytic reaction. Cofactors can be inorganic ions or organic molecules. An enzyme that lacks an essential cofactor is called an apoenzyme. The enzyme with the cofactor bound is called a holoenzyme. Organic cofactors commonly participate in oxidation-reduction reactions and in the transfer of various organic functional groups. The organic cofactors often are vitamins or contain vitamin components. By definition, these vitamin components must be provided in the diet, because humans lack the necessary metabolic pathways for their synthesis. Inorganic cofactors participate in oxidation-reduction reactions, 7 BioC 3021 Notes Robert Roon in substrate binding, and may also be needed to facilitate the correct active conformation of a protein. The inorganic cofactors must be obtained from dietary sources, and thus constitute part of the minimal nutritional requirements for human survival. Slide 17. Structure of ATP Adenosine triphosphate (ATP) is a nucleotide cofactor that contains an adenine base, ribose sugar, and three phosphate groups. When ATP is used as a cofactor in enzyme reactions, a bond between two phosphate groups (γ and β phosphates or β and α phosphates) is hydrolyzed. The hydrolysis of these phosphate bonds releases high amounts of energy. These two terminal phosphates are linked to each other and to the α phosphate by phosphoanydride bonds that release approximately 7.3 kcal per mole upon hydrolysis. Hydrolysis of the inner α phosphate, which is linked to a carbon atom by a phosphoester bond, releases much less energy upon hydrolysis and is not generally coupled to energy requiring reactions. Slide 18. Hydrolysis of ATP to ADP and Pi This slide shows the hydrolysis of ATP to ADP and inorganic phosphate (Pi). This is a cleavage between the γ and β phosphates of ATP. That hydrolysis reaction yields 7.3 kcal per mole. The energy from the phosphoanhydride bond cleavage can either be released as heat or coupled to the synthesis of some biochemical intermediate. Slide 19. Hydrolysis of ATP to AMP and PPi This slide shows the hydrolysis of ATP to AMP and inorganic pyrophosphate (PPi). ATP → AMP + PPi 8 BioC 3021 Notes Robert Roon This is called a pyrophosphate cleavage reaction. This reaction is used when ATP hydrolysis is coupled to some reaction that needs more energy than can be provided by the cleavage of a single phosphoanhydride bond of ATP to ADP and Pi. (For example, when a nucleotide is incorporated into a growing DNA or RNA strand by a polymerase, an NTP is cleaved and pyrophosphate (PPi) is released.) The release of pyrophosphate gives more energy to the system, because the pyrophosphate is then cleaved into two molecules of Pi by a pyrophosphatase enzyme. This added reaction releases an extra 8 kcal per mole and shifts the thermodynamics of ATP coupled systems in the direction of product formation. The pyrophosphate anion has the structure P2O74−, and is an acid anhydride of phosphate. The pyrophosphate can be enzymatically hydrolyzed into two molecules of inorganic phosphate by the action of a pyrophosphatase enzyme: P2O74−, + H2O → 2 HPO42− (PPi + H2O → 2 Pi) Slide 20. Energetics of the Pyrophosphate Cleavage Reaction. The enzymatic hydrolysis of pyrophosphate to inorganic phosphate effectively renders the cleavage of ATP to AMP and PPi essentially irreversible, and biochemical reactions coupled to this hydrolysis are also irreversible. From the standpoint of high energy phosphate accounting, the hydrolysis of ATP to AMP and PPi requires two high-energy phosphates (cleavage of two phosphoanhydride bonds). To reconstitute AMP into ATP requires two phosphorylation reactions. AMP + ATP → 2 ADP 2 ADP + 2 Pi → 2 ATP 9 BioC 3021 Notes Robert Roon Slide 21. Enzyme Cofactors. We have just seen how the central cofactor, ATP, can be hydrolyzed to release energy. Here is a list of other organic and inorganic cofactors that commonly participate in enzyme reactions. The organic cofactors commonly participate in oxidation-reduction reactions and in the transfer of various organic functional groups. Most of these organic cofactors have vitamin components that must be provided in the human diet. In addition to organic cofactors, there are also inorganic cofactors. Inorganic cofactors participate in oxidation-reduction reactions, substrate binding, and may also be needed to facilitate the correct active conformation of a protein. Slide 22. Vitamin Components of Organic Cofactors. Many organic cofactors have a vitamin component. Vitamins are nutritionally required compounds that an organism cannot synthesize because it lacks the necessary enzyme pathways. In humans, almost all of the organic cofactors have a vitamin component. Examples of vitamins include the niacin component of NADH and the riboflavin component of FADH2. Exceptions are the cofactors ATP and lipoic acid, which do not have vitamin components. Slide 23. The Vitamin Components and Metabolic Functions of Cofactors Here is a list of eight enzyme cofactors that have vitamin components. When we study metabolic pathways later in the course, we will see how these cofactors participate in enzyme reactions. It is a good idea to memorize these cofactors now, so that when you encounter them a metabolic context, you will understand how they work. 10 BioC 3021 Notes Robert Roon Slide 24. Nicotinamide Adenine Dinucleotide (NAD+) The Structure of Nicotinamide Adenine Dinucleotide is shown on this slide. We will encounter the coenzyme, nicotinamide adenine dinucleotide (NAD+) very frequently in our tour of biochemistry. The coenzyme functions in a variety of oxidation reduction reactions in which it can either accept two electrons and one proton (in the NAD+ form) or donate two electrons and one proton (in the NADH form). It is generally used as an acceptor of electrons and hydrogen ions (in the NAD+ form) in catabolic reactions. It also donates electrons (in the NADH form) to the electron transport system in the oxidative phosphorylation pathway. First let us consider the structure of NAD+. Most of the components of the coenzyme are involved in binding and do not participate directly in catalysis. Starting from the lower left and working clockwise, we see adenine, ribose, phosphate, phosphate—the same components and linkages that occur in ADP. That is followed by a second ribose. All of those components serve to place the remaining component, the nicotinamide ring, into the correct location and orientation in the active site of the enzyme. It is the nicotinamide ring on which the catalytic action actually occurs. Oxidation-reduction reactions involve the exchange of electrons and/or protons. The nicotinamide ring is a heterocyclic aromatic system that can accept or donate two electrons and one proton. It is shown in the oxidized form in which there is one hydrogen atom on the upper carbon and a positive charge on the ring nitrogen. In the reduced form, there are two hydrogen atoms on the upper carbon and no charge on the ring. Most oxidation-reduction reactions that involve the transfer of two electrons also involve two protons—in the case of NAD+-dependent reactions, the second proton is released into the media. The nicotinamide component of NAD+ is a vitamin. Nicotinamide 11 BioC 3021 Notes Robert Roon can be obtained directly in the diet, or it can be replaced with a carboxylic acid that exhibits the equivalent structure except that it lacks the amide nitrogen—this modified structure is referred to as niacin. If we obtain a sufficient quantity of niacin (or nicotinamide) in our diet, we can synthesize and assemble the remaining components of NAD+. Slide 25. Oxidation of a Secondary Alcohol Coupled to Reduction of NAD+ In the reaction shown, NAD+ serves as a cofactor for the oxidation of a secondary alcohol to a ketone. The hydroxyl group of the substrate loses two electrons and two protons, and is converted to a ketone. Two of those electrons and one of the protons are transferred to the nicotinamide ring, and the second proton is released into the solvent. In the process, the nicotinamide ring gains another hydrogen atom on its upper carbon. Both electrons enter the ring—one electron neutralizes the charge on the new proton and the other electron neutralizes the plus charge on the quaternary ring nitrogen. The reduced product of the reaction is referred to as NADH. This is called an oxidation-reduction reaction because the two processes are coupled—the alcohol substrate is oxidized to a ketone, and the NAD+ coenzyme is reduced to NADH plus H+. In the process of being oxidized, the alcohol loses electrons and protons. Concomitantly, the NAD+ cofactor is reduced and gains electrons and a proton. Oxidation and reduction are always coupled process—one cannot occur without the other. Slide 26. Structure of NAD+ vs NADP+ The NADP+ molecule is a variant of NAD+. The NADP+ molecule has the same chemical structure as NAD+ except that it has an extra phosphate residue on the C2’ position of a ribose ring. Similar to NAD+, the NADP+ coenzyme functions in a variety of oxidation reduction reactions, and like NAD+, it can either accept 12 BioC 3021 Notes Robert Roon or donate two electrons and one proton. In contrast to NAD+, the NADP+ molecule is generally used in its reduced form (NADPH) as a donor of electrons and hydrogen ions in anabolic reactions. Slide 27. Nicotinamide Adenine Dinucleotide Phosphate (NADP+) Here we see the structure of NADP+. It varies from NAD+ in that the lower ribose ring (the one connected to adenine) has a phosphate group on the 2’ position. Slide 28. Flavine Adenine Dinucleotide (FAD) Here is the structure of the cofactor Flavine Adenine Dinucleotide. The FAD coenzyme contains the elements of adenosine diphosphate connected to ribitol, which in turn is connected to an isoalloxazine ring system. (The ribitol isoalloxazine pair, collectively known as riboflavin, constitutes one of the B vitamins.) It is the isoalloxazine ring that is involved in catalysis. Slide 29. Reduction of FAD to FADH2 Here is an oxidation-reduction reaction in which FAD is reduced to FADH2. In the reaction shown, a reduced substrate with a single bond is oxidized to an oxidized product with a double bond. At the same time, FAD is reduced to FADH2. This oxidation-reduction reaction involves the transfer of two electrons and two protons to FAD to form FADH2. The two electrons enter the isoalloxazine ring, and the two protons sit on the two nitrogen atoms coded in blue. Slide 30. Flavine Mononucleotide (FMN) Here is the structure of the cofactor Flavine Mononucleotide. The FMN coenzyme contains phosphate connected to ribitol, which is connected to an isoalloxazine ring system. As it is with FAD, it is the isoalloxazine ring of FMN that is involved in catalysis. In fact, the mechanism of action of FMN is exactly the same as that of FAD. However, the FMN coenzyme is recognized 13 BioC 3021 Notes Robert Roon by different enzymes. Slide 31. Pathway of an Enzyme Catalyzed Reaction Here is another look at the pathway of an enzyme catalyzed reaction. The figure shows the simplest formulation of the kinetic events that occur in an enzyme catalyzed reaction. In this diagram, an enzyme (E) binds its substrate (S), S being the reacting molecule or reactant, to form an enzyme-substrate complex (ES). A biochemical reaction then takes place in the enzyme-substrate complex. The product (P) is then released, and the enzyme is free to participate in another round of catalysis. Having reviewed this basic kinetic scheme, we are now ready to segue into the thermodynamics of enzyme reactions. Slide 32. Product Formation as a Function of Time This figure shows kinetic plots of product formation vs. time for an enzyme catalyzed reaction and a chemical reaction. The upper plot (in red) shows that an enzyme catalyzed reaction produces product rapidly and then levels off at some equilibrium level. Once the reaction reaches equilibrium, the amount of product remains essentially constant. At that point, the rates of the forward and reverse reactions are equal. The lower plot (in black) shows that an uncatalyzed chemical reaction initially produces product at a slower rate. However, after an extended time, the product concentration reaches the same equilibrium value as the enzyme catalyzed reaction. This illustrates a key point. Enzymes speed reaction rates, but they do not change the reaction equilibrium. When we look at thermodynamics, we will confirm this fact— enzymes affect reaction rates, but they do not alter thermodynamic constants. Slide 33. Equilibrium Constant For any reaction, we can write an equilibrium constant. For a reaction in which aA + bB -----> cC + dD, the equilibrium constant is given by the formula: 14 BioC 3021 Notes Robert Roon K = [C]c [D]d/ [A]a [B]b What is important here is that this relationship holds true regardless of whether an enzyme is present on not. That is, Enzymes Do Not Change Reaction Equilibria. The thermodynamic constants of reactions depend on the relative energy levels of substrates and products. As long as the reactants and products of a reaction are the same, the equilibrium does not change, regardless of the reaction pathway. An enzyme can change a reaction pathway and make the reaction proceed faster, but it does not change its equilibrium. Enzymes accelerate the forward and reverse reactions to the same extent. Slide 34. Enzymes Do Not Change Reaction Equilibria This figure summarizes the conclusions from the previous slide. It is so important that we are repeating it. Enzymes Do Not Change Reaction Equilibria. The thermodynamic constants of reactions depend on the relative energy levels of substrates and products. As long as the reactants and products of a reaction are the same, the equilibrium does not change, regardless of the reaction pathway. An enzyme can change a reaction pathway and make the reaction proceed faster, but it does not change its equilibrium. Enzymes accelerate the forward and reverse reactions to the same extent. Slide 35. Free Energy of Reaction The free energy of a reaction (ΔG) is the amount of energy released or consumed by a reaction. -The energy diagram shows a thermodynamically favorable reaction (a reaction with a negative ΔG). -The difference in energy levels between A (substrate) and B (product) equals the free energy of the reaction. -The free energy of a reaction (ΔG) is a thermodynamic factor that is dependent upon the energy levels of the reaction substrate and 15 BioC 3021 Notes Robert Roon product. The intervention of an enzyme does not change these values and thus does not change the overall free energy of a reaction. -The free energy of activation is the difference between the energy level of a substrate and the activated intermediate or "transition state" of the reaction. An enzyme can provide an alternate transition state for a reaction, and thus can change the free energy of activation of a reaction. Slide 36. Free Energy Change for Reactions with Varying Energy Differences The three energy diagrams shown in this figure reflect reactions in which the substrates and products are at various energy levels. -When product B is at a lower energy level than substrate A, it denotes an energy releasing reaction with a negative ΔG. At equilibrium, there will be more product than substrate. -When product D and substrate C are at the same level, there is no energy released and the ΔG is zero. At equilibrium, there is no difference in relative concentrations of substrate and product. -When product F is at a higher energy level than substrate E, the transformation of E to F is an energy requiring reaction with a positive ΔG. At equilibrium, there will be more substrate than product. Slide 37. Energy of Activation for an Enzyme Reaction The third energy diagram shows that an enzyme can lower the activation energy of a reaction. This is how an enzyme can increase the rate of reaction. A lower energy barrier means substrate is converted into product at a faster rate. Note: an enzyme changes the energy of activation but does not change the free energy of the reaction and does not change the equilibrium or the equilibrium constant. 16 BioC 3021 Notes Robert Roon Very important, so I will say it again! Enzymes do not, not, not change the thermodynamics of a reaction. That is, enzymes do not change ΔG, the equilibrium constant Keq, the amount free energy released or required, or the net balance of substrate and product at equilibrium. Slide 38. Relationship Between the Standard Free Energy and the Equilibrium Constant The next series of figures defines standard free energy and explores the relationship between standard free energy and equilibrium constant. These two factors are inextricably related to each other by a mathematical relationship that we will define. Slide 39. Standard Free Energy The standard free energy (ΔGo) measures the energy released or consumed by a reaction when all substrates are present at 1 M concentrations under standard conditions of temperature and pressure. While this (ΔGo) is a useful value for chemists and physicists, it becomes a problem for biochemists when hydrogen ions constitute part of a reaction. A hydrogen ion level of 1M is equivalent to pH 0, and biochemical reactions generally take place at or around pH 7.0. Slide 40. Standard Free Energy (For Biologists) Because most biological reactions take place at or around pH 7.0, biologists use a modification of standard free energy (ΔGo'). The prime (') denotes the fact that the [H+] concentration is set at pH 7 (10-7 M) instead of at 1 M. Slide 41. Mathematical Relationship Between Standard Free Energy and Equilibrium Constant At equilibrium, ΔG equals zero and ΔGo' = -RTlnK'eq where K'eq is the equilibrium constant for the reaction. Note that ln is a "natural log" that can be converted to a log to the base 10 by multiplying by 17 BioC 3021 Notes Robert Roon 2.3. That is, lnX = 2.3log10X. (These days everyone wants to be natural, so I know that you all really wanted to know all about natural logs. I am not going to tell you anything about unnatural logs, because this is not that kind of course.) The point here is really that the equilibrium constant of a reaction is related to the standard free energy. Neither of these factors can be changed in the presence of an enzyme. They are both determined by the energy levels of substrate and product. One other point—because there is a negative logarithmic relationship between ΔGo' and K'eq, the following relationships exist: If ΔGo' is negative, the K'eq will be a positive number greater than one. If ΔGo' is zero, the K'eq will be equal to one. If ΔGo' is positive, the K'eq will be a positive number less than one. Slide 42. Facts Concerning Standard Free Energy -A reaction with a negative ΔG0 favors product formation at equilibrium -A reaction with a ΔG0 of zero yields equal amounts of substrate and product at equilibrium -A reaction with a positive ΔG0 favors reactant formation at equilibrium -Enzymes do not change the ΔG0 of a reaction -The ΔG0 of a reaction tells you nothing about reaction rates Slide 43. Table Comparing the Standard Free Energy and the Equilibrium Constant The table shows that for each 10-fold change in the equilibrium constant of a reaction, the standard free energy changes by a factor of 1.36. That is, the number of calories released or consumed by 18 BioC 3021 Notes Robert Roon the reaction changes by a factor of 1.36. 19