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1.6 ENZYMES
Snapshot
1. Almost every biochemical reaction is catalyzed by an enzyme. With the exception of a few catalytic RNAs, all known enzymes are proteins. 2. Many require nonprotein coenzymes or cofactors for their catalytic function. 3. Enzymes are classified according to the type of reaction they catalyze. All enzymes have formal E.C. numbers and names, and most have trivial names. 4. Enzymes are highly effective catalysts, commonly enhancing reaction rates by a factor of 105 to 1017 . 5. Enzyme-catalyzed reactions involve formation of a complex between substrate and enzyme (an ES complex). Substrate binding occurs in a pocket on the enzyme called the active site. 6. Enzymes lower the activation energy of a reaction and thereby enhance the reaction rate. The equilibrium of a reaction is unaffected by the enzyme. 7. A significant part of the energy used for enzymatic rate enhancements is derived from weak interactions hydrogen bonds and hydrophobic and ionic interactions) between substrate and enzyme. Binding energy also accounts for the exquisite specificity of enzymes for their substrates. 8. Additional catalytic mechanisms employed by enzymes include general acid-base catalysis, covalent catalysis, and metal ion catalysis. 9. Catalysis often involves transient covalent interactions between the substrate and the enzyme, or group transfers to and from the enzyme, so as to provide a new, lower-energy reaction path. 10. Most enzymes have certain kinetic properties in common. When substrate is added to an enzyme, the reaction rapidly achieves a steady state in which the rate at which the ES complex forms balances the rate at which it reacts. As [S] increases, the steady-state activity of a fixed concentration of enzyme increases in a hyperbolic fashion to approach a characteristic maximum rate, Vmax, at which essentially the entire enzyme has formed a complex with substrate. 11. Km is the substrate concentration that results in a reaction rate equal to one-half Vmax, which is characteristic for each enzyme acting on a given substrate. 12. Reversible inhibition of an enzyme is competitive, uncompetitive, or mixed. 13. Competitive inhibitors compete with substrate by binding reversibly to the active site, but they are not transformed by the enzyme. 14. Uncompetitive inhibitors bind only to the ES complex, at a site distinct from the active site. 15. Mixed inhibitors bind to either E or ES, again at a site distinct from the active site. 16. In irreversible inhibition an inhibitor binds permanently to an active site by forming a covalent bond or a very stable noncovalent interaction. 17. The activities of metabolic pathways in cells are regulated by control of the activities of certain enzymes. 18. In feedback inhibition, the end product of a pathway inhibits the first enzyme of that pathway. 19. The activity of allosteric enzymes is adjusted by reversible binding of a specific modulator to a regulatory site. 20. Modulators may be the substrate itself or some other metabolite, and the effect of the modulator may be inhibitory or stimulatory. 21. The kinetic behavior of allosteric enzymes reflects cooperative interactions among enzyme subunits. 22. Other regulatory enzymes are modulated by covalent modification of a specific functional group necessary for activity. 23. The phosphorylation of specific amino acid residues is a particularly common way to regulate enzyme activity. 24. Many proteolytic enzymes are synthesized as inactive precursors called zymogens, which are activated by cleavage of small peptide fragments.assembly.
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Unit 1
Introduction
Properties of enzymes
High catalytic power High degree of specificity for substrates Accelerate chemical reactions tremendously Function in aqueous conditions at very mild temperature and pH
Nature of Enzymes
Most of the Enzymes are proteins (exception catalytic RNA i.e. Ribozymes). Denaturation or dissociation of Enzyme subunits lead to loss of catalytic function. The primary, secondary, tertiary, and quaternary structures of protein enzymes are essential to their catalytic activity. Enzymes have molecular weights ranging from about 12,000 to more than 1 million. Some enzymes require cofactor. Cofactor – can be either inorganic ions (eg. Fe2+, Mg2+, Mn2+ or Zn2+) or can be a complex of organic or metallo-organic molecule called a coenzyme. Prosthetic group - A coenzyme or metal ion that is very tightly or even covalently bound to the enzyme protein. Holoenzyme – A complete, catalytically active enzyme together with its bound coenzyme and/or metal ions. Apoprotein / Apoenzyme – Only the protein part of Holoenzyme. Function of Coenzyme – Carrier of transient functional groups
Enzyme Classification
Because of many ambiguities in the enzyme names, and the ever-increasing number of newly discovered enzymes, biochemists, by international agreement, have adopted a system for naming and classifying enzymes. This system divides enzymes into six classes, each with subclasses, based on the type of reaction catalyzed.
According to this system, each enzyme is assigned a four-part classification number and a systematic name, which identifies the reaction it catalyzes. For eg. Consider the following reaction ATP + D-glucose ADP + D-glucose 6-phosphate
The systematic name of the enzyme is ATP:glucose phosphotransferase (trivial name Hexokinase) and its E.C. number is 2.7.1.1. Of this E.C. number,
2 – denotes the class name (transferase) 7 – denotes the subclass (phosphotransferase) 1 – denotes a phosphotransferase with a hydroxyl group as acceptor
Table 1.6.1. International Classification of Enzymes
No. Class Type of reaction catalyzed
1 Oxidoreductase Transf er of electrons (hydride ions or H atoms) 2 Transf erases Group transf er reactions 3 Hydrolases Hydrolysis reactions (transf er of f unctional groups to water) 4 Lyases Addition of groups to double bonds, or formation of double bonds by removal of groups 5 Isomerases Transf er of groups within molecules to yield isomeric f orms 6 Ligases Formation of C-C, C-S, C-O and C-N bonds by condensation reactions coupled to ATP cleavage
Enzyme Catalysis
Under biological conditions, uncatalyzed reactions tend to be slow because most biomolecules are quite stable in the environment inside the cells. An enzyme provides a specific environment within which a given reaction can occur more rapidly. Some important terminologies
Active site - catalytic site of an enzyme Substrate - molecule bound in the active site & acted upon by the enzyme Ground state - starting point for forward or reverse reaction Reaction intermediate - any species on the reaction pathway that has a transient existence [ES and EP complexes] Rate-limiting step - step (or steps) with the highest activation energy (slow step)
A simple Enzymatic reaction is represented in the following way:
E = Enzyme S = Substrate P = Product ES = Enzyme-Substrate complex (transient) EP = Enzyme-Product complex (transient)
An Enzyme increases the rate of the reaction, but does not affect the reaction equilibrium.
The reaction coordinate diagram represents the energy changes associated with the progress of the reaction SP. (Figure 1.6.1.) The free energy of the system is plotted against the progress of the reaction (the reaction coordinate). Ground state is the starting point for either the forward or the reverse directions. The free energy change occurring in standard set of conditions (temperature 298 K; partial pressure of each gas 1 atm, or 101.3 kPa; concentration of each solute 1 M) is standard free energy change ΔG°. Biochemical standard free-energy change (ΔG’°) is defined as the standard free-energy change at pH Figure 1.6.1. Reaction coordinate diagram for a chemical reaction. The free energy of the system7.0. is plotted against the progress of the reaction In the above reaction coordinate diagram, the free SP. Visit: http://study.biotecnika.org for colored energy of the ground state of P is lower than that of picture.
S, i.e. ΔG’° = negative, i.e. the equilibrium favors formation of P. If ΔG’° = positive, then equilibrium favors formation of S. Even if ΔG’° is negative, it does not mean that S →P conversion will occur at a detectable rate. The rate of reaction does not depend on the position of the equilibrium. The energy barrier between S and P is the energy required for alignment of reacting groups, formation of transient unstable charges, bond rearrangements, and other transformations required for the reaction to proceed in either direction. Molecules must overcome this barrier to proceed with the reaction. Transition state: The top of the energy hill where decay to the S or P state is equally probable. (Note: Transition state is not an intermediate species, not to be confused with ES or EP)
Unit 1 Activation energy (ΔG‡): The difference between the energy levels of the ground state and the transition state. Higher activation energy corresponds to a slower reaction, and vice versa. So, to lower the activation energy, a catalyst is added. Catalysts enhance reaction rates by lowering activation energies. (Figure 1.6.2.) Enzymes accelerate the interconversion of S and P. The enzyme is not used up in the process, and the equilibrium point is unaffected. However, with the use of enzymes, the equilibrium is reached faster. In the reaction coordinate diagram comparing an enzyme uncatalyzed and a catalyzed reaction, the ES and EP intermediates occupy minimum energy. ΔG‡cat is the activation energy for an enzyme catalyzed reaction and is lower than ΔG‡uncat which is the activation energy for an enzyme uncatalyzed reaction. Reaction intermediate: any species on the reaction pathway that has a finite chemical lifetime (longer than a molecular vibration, ~10-13 seconds). In the above reaction coordinate diagram, ES and EP can be considered as reaction intermediates. The interconversion of two sequential reaction intermediates thus constitutes a reaction step. In a multi-step reaction, the overall rate of reaction is determined by the step/s with the highest activation energy. This step/s is the Rate Limiting Step. Equilibrium constant (K’eq) for a SP interconversion at equilibrium is, From thermodynamics, the relationship between
K’eq and ΔG’° can be described by the expression
Figure 1.6.2. Reaction coordinate diagram comparing enzyme catalyzed and uncatalyzed reactions. In the reaction S nP, the ES and EP intermediates occupy minima in the energy progress curve of the enzyme-catalyzed reaction. The terms G‡uncat and G‡cat correspond to the activation energy for the uncatalyzed reaction and the overall activation energy for the catalyzed reaction, respectively. The activation energy is lower when the enzyme catalyzes the reaction.
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where R = gas constant, 8.315 J/mol*K T = absolute temperature, 298 K (25 °C) The equilibrium constant is directly related to the overall standard free energy change for the reaction. A large negative value for ΔG’° reflects favorable reaction equilibrium (but does not mean rate of reaction is high).
For a unimolecular reaction, S P, the rate (or velocity) of reaction (V) represents the amount of S that reacts per unit time. This is expressed by the rate equation:
Where k = rate constant, [S] = concentration of Substrate
This is a first order reaction as rate of reaction is only dependent on the concentration of substrate. k has units of reciprocal time (eg. s-1). If a reaction rate depends on the concentration of two different compounds, or if the reaction is between two molecules of the same compound, the reaction is second order and k is a second-order rate constant, with units of M-1s-1. The rate equation then becomes
where k = Boltzmann constant and h = Planck’s constant.
The relationship between the rate constant k and the activation energy ΔG‡ is inverse and exponential (i.e. a lower activation energy has a faster reaction rate).
Enzyme catalytic power and specificity
The rate enhancements brought about by catalysts are in the range of 5 to 17 orders of magnitude.
Enzymes can lower the activation energy partly by rearrangement of covalent bonds during an enzymecatalyzed reaction. Catalytic functional groups on an enzyme may form a transient covalent bond with a substrate and activate it for reaction, or a group may be transiently transferred from the substrate to the enzyme in the active site of enzyme. Enzymes can lower the activation energy partly by weak, noncovalent interactions between enzyme and substrate. The interactions that stabilize a protein structure are the same ones that are involved in interaction between E and S to form ES complex. Formation of each weak interaction in the ES complex is accompanied by release of a small amount of free energy that provides a degree of stability to the interaction.
Binding Energy (ΔGB): Energy derived from enzyme-substrate interaction
Binding energy is a major source of free energy used by enzymes to lower the activation energies. The enzyme active site is not complementary to the substrate, but to the transition states through which substrates pass as they are converted to products. Consider a hypothetical reaction, in which a metal stick (S) is to be broken into 2 pieces (P). Before the stick is broken, it must first be bent (the transition state). In both stickase examples, magnetic interactions take the place of weak bonding interactions between enzyme and substrate. (Figure 1.6.3.) An imaginary enzyme (stickase) is designed to catalyze breakage of a metal stick. Stickase with a magnet-lined pocket complementary in structure to the stick (the substrate) stabilizes the substrate. Bending is impeded by the magnetic attraction between stick and stickase. An enzyme with a pocket complementary to the reaction transition state helps to destabilize the stick, contributing to catalysis of the reaction. The binding energy of the magnetic interactions compensates for the increase in free energy required to bend the stick. The binding energy that provides energy for catalysis also gives an enzyme its specificity. Specificity of an enzyme: the ability to discriminate between a substrate and a competing molecule. If an enzyme active site has functional groups arranged such that a variety of weak interactions are optimized with a particular substrate in the transition state, then enzyme will not be able to interact to the same degree with any other molecule.
Specificity is derived from the formation of many weak interactions between the enzyme and its specific substrate molecule. Following are 4 physical and thermodynamic factors that contribute to the activation energy (ΔG‡) and the mechanisms used by enzymes to counter them. 1. A reduction in entropy, in the form of decreased freedom of motion of two molecules in solution To counter this enzymes provide the binding energy that holds the substrates in the proper orientation to react. Substrates can be precisely aligned on the enzyme, with many weak interactions between E and S, clamping the substrate molecules into the proper positions.
Unit 1 2. The solvation shell of hydrogen-bonded water that surrounds and helps to stabilize most biomolecules in aqueous solution To counter this enzyme forms weak bonds with the substrate. This results in desolvation of the substrate. 3. The distortion of substrates that must occur in many reactions. The binding energy involving weak interactions formed only in the reaction transition state helps to compensate thermodynamically for any distortion, primarily electron redistribution that the substrate must undergo to react. 4. The need for proper alignment of catalytic functional groups on the enzyme. The enzyme itself usually undergoes a change in conformation when the substrate binds. This is called as Induced fit (Koshland). Induced fit brings specific functional groups on the enzyme into the proper position to catalyze the reaction.
Mechanisms of enzyme catalysis 1. General acid-base catalysis
Unstable charged intermediates generated in a reaction immediately breakdown to constituent reactants. Such intermediates can be stabilized by the transfer of protons to or from the substrate or intermediate to form a species that breaks down more readily to products. Specific Acid-Base catalysis: For non-enzymatic reactions, proton transport is from water molecules or weak proton acceptors or donors.
Figure 1.6.3. An imaginary enzyme (stickase) designed to catalyze breakage of a metal stick. Reaction coordinate diagram s (right) show the energy consequences of complementarity to substrate versus complementarity to transition state. (a) S to P conversion without enzyme stickase (b) S to P conversion with enzyme stickase complementary to substrate (c) S to P
conversion with enzyme stickase complementary to the transition state. Visit: http://study.biotecnika.org for colored picture.
Unit 1 General Acid-Base catalysis: proton transfers mediated by other classes of molecules (other than water). Weak organic acids acts as proton donors and weak organic bases act as proton acceptors.
2. Covalent catalysis
A transient covalent bond is formed between the enzyme and the substrate. Consider the following hydrolysis reaction:
In the presence of a covalent catalyst (an enzyme with a nucleophilic group X:) the reaction becomes
This new pathway has lower activation energy as compared to the 1st uncatalyzed pathway. Many amino acid side chains and the functional groups of some enzyme cofactors can serve as nucleophiles. The transient covalent bond formed between E and S can activate substrate for further reaction.
Metal ion catalysis
Ionic interactions are formed between an enzymebound metal and a substrate. This helps to orient the substrate for reaction or stabilize the charged reaction transition states. Metals can also mediate oxidation-reduction reactions by reversible changes in the metal ion’s oxidation state. (Nearly a third of all known enzymes require one or more metal ions for catalytic activity). Most enzymes use a combination of several catalytic strategies to bring about catalysis. For example, chymotrypsin uses both general acidbase catalysis and covalent catalysis. The first step in the reaction catalyzed by chymotrypsin is the acylation step. The hydroxyl group of Ser195 is the nucleophile in a reaction aided by general base catalysis (the base is the side chain of His57).
Figure 1.6.4. Covalent and general acid-base catalysis. The first step in the reaction catalyzed by chymotrypsin is the acylation step. The hydroxyl group of Ser195 is the nucleophile in a reaction aided by general base catalysis (the base is the side chain of His57). This provides a new pathway for the hydrolytic cleavage of a peptide bond. Catalysis occurs only if each step in the new pathway is faster than the uncatalyzed reaction.
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Enzyme kinetics
Enzyme kinetics: A study of the mechanism of an enzyme-catalyzed reaction to determine the rate of the reaction and how it changes in response to changes in experimental parameters. Substrate concentration [S] is a key factor which determines the rate of the reaction. In an experimental set up it is difficult to study the effect of substrate concentration on rate of reaction as the substrate depletes with the reaction progress. A simplified approach is to measure the initial rate/velocity (Vo), when [S] is much greater than the concentration of enzyme, [E]. If only the beginning of the reaction is monitored (often the first 60 seconds or less), changes in [S] can be limited to a few percent, and [S] can be regarded as constant. The Vo can be plotted as a function of [S] and the following plot is observed. (Figure 1.6.5.) At low [S], Vo increases linearly with [S]. At high [S], increase in Vo decreases with respect to increase in [S]. Finally at very high [S] concentration, plateau-like V0 region is formed which is close to the maximum velocity, Vmax. The maximum initial rate of the catalyzed reaction (Vmax) is observed when at very high substrate concentrations, the enzyme is saturated i.e. all E is present in the form of ES and free E is very small.
The initial period when the E is 1st mixed with large concentration of S, during which the concentration of S builds up. (very short period, lasts only a few microseconds) Steady state: [ES] (and the concentrations of any other intermediates) remains approximately constant over time. Derivation of Michaelis-Menten Equation: (rate equation for 1 substrate-enzyme catalyzed reaction) Consider the following reaction,
Where, k1 = rate constant for formation of ES
k-1 = rate constant for breakdown of ES
k2 = rate constant for formation of E + P
Figure 1.6.5. Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction.
k-2 can be ignored as in the initial stages of reaction, concentration of P is negligible, so P→S is negligible.
V0 is determined by the breakdown of ES to form product, which is determined by [ES].
[ES] is difficult to measure, so an alternative term has to be found out. If Et is the total enzyme concentration then,
Concentration of bound E = [ES]
Concentration of unbound E = Et – [ES] The rates of formation and breakdown of ES are determined by their respective rate constants.
Steady state Assumption is that at steady state rate of ES formation is equal to the rate of ES breakdown.
The left side is multiplied out and the right side is simplified to give
Adding the term k1[ES][S] to both sides of the equation and simplifying gives
Solving this equation for [ES]:
Further simplifying and combining the rate constants into one expression:
The term (k2 + k-1)/k1 is defined as the Michaelis constant, Km. So the equation becomes,
Expressing V0 in terms of [ES] and substituting [ES] in the equation Vo = k2 [ES],
The maximum velocity occurs when the enzyme is saturated (i.e. when [Et] = [ES] ), Vmax = k2[Et].
Substituting this in the above equation we get the Michaelis-Menten equation:
Consider a special case where, Vo is exactly one half of Vmax. Then the Michaelis-Menten equation becomes,
On dividing by Vmax we get,
Solving for Km, we get Km + [S] = 2[S], or
Definition of Km: Km is equivalent to the substrate concentration at which Vo is one-half Vmax. The dependence of initial velocity on substrate concentration can be explained with the graph provided below. It is a simple graphical method for obtaining an approximate value for Km.
Lineweaver- Burk Plot : The Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics.
Interpreting Vmax and Km:
Km can vary greatly from enzyme to enzyme, and even for different substrates of the same enzyme. It is sometimes used (often inappropriately) as an indicator of the affinity of an enzyme for its substrate. Actual meaning of Km changes depending upon the experimental conditions. For reactions with two steps, When k2 is rate limiting, k2 k-1
Figure 1.6.7. A double-reciprocal or Lineweaver-Burk plot. Figure 1.6.6. Dependence of initial velocity on substrate concentration.
Unit 1 Km reduces to k-1 /k1, which is defined as the dissociation constant, Kd , of the ES complex. Where these conditions hold, Km does represent a measure of the affinity of the enzyme. for its substrate in the ES complex. However, this scenario does not apply for most enzymes. Sometimes k2 k-1 , then Km = k2 /k1 In other cases, when k2 and k-1 are comparable Km is a complex function of all three rate constants k1, k2 and k-1. The quantity Vmax also varies greatly between different enzymes. If an enzyme reacts by two-step mechanism, the Vmax = k2[Et] If we consider a three step reaction such as,
Then, Vmax = k3[Et] So, a more general rate constant (kcat) is defined to describe the limiting rate of any enzyme-catalyzed reaction at saturation. If the reaction has several steps and one is clearly rate limiting, kcat is equivalent to the rate constant for that limiting step. For example, for a two step reaction, kcat = k2 For a three step reaction kcat = k3, and so on. The modified Michaelis-Menten equation
The constant kcat is a first-order rate constant and hence has units of reciprocal time. It is also called the turnover number. Turnover number: It is equivalent to the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule when the enzyme is saturated with substrate. Comparing catalytic mechanisms and efficiencies using kcat and Km: When [S] << Km,
Becomes
The above equation is a second order rate equation. The term kcat/Km is the Specificity constant. It is a second-order rate constant with units of M-1s-1. It is the rate constant for the conversion of E +
S to E + P.
Bimolecular Substrate – Enzyme catalyzed reaction:
Enzymatic reactions with two substrates usually involve transfer of an atom or a functional group from one substrate to the other. These reactions proceed by one of several different pathways. In some cases, both substrates are bound to the enzyme concurrently at some point in the course of the reaction, forming a noncovalent ternary complex. The substrates bind in a random sequence or in a specific order which is shown in the diagram below. If we perform steady-state kinetic analysis of bisubstrate reactions which involves formation of ternary complex then, the double reciprocal plot obtained for such a reaction is as follows (Intersecting lines indicate that a ternary complex is formed in the reaction):
Figure 1.6.8. The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can bind in either order.
Unit 1 In other cases, the first substrate is converted to product and dissociates before the second substrate binds, so no ternary complex is formed. An example of this is the Ping-Pong, or double-displacement, mechanism Figure 1.6.9. An enzyme-substrate complex forms, a product as depicted in diagram below. leaves the complex, the altered enzyme forms a second complex If we perform steady-state kinetic with another substrate molecule, and the second product leaves, analysis of bisubstrate reactions regenerating the enzyme. Substrate 1 may transfer a functional which does not involve formation of group to the enzym e (to form the covalently modi fied E’), which ternary complex then, the double is subsequently transferred to substrate 2. This is called a Pingreciprocal plot obtained for such a Pong or double-displacement mechanism. reaction is as follows (parallel lines indicate a Ping-Pong or double-displacement pathway)
Enzyme inhibition
Enzyme inhibitors are molecular agents that interfere with catalysis, slowing or halting
Figure 1.6.10. Steady-state kinetic analysis of bisubstrate reactions. In these double-reciprocal plots, the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S], generating several separate lines. (a) Intersecting lines indicate that a ternary complex is formed in the reaction; (b) parallel lines indicate a Ping-Pong (double-displacement) pathway. Figure 1.6.11. Mechanism of competitive inhibition.
enzymatic reactions. Enzymes can be reversibly or irreversibly inhibited.
Reversible Inhibition:
There are three types of reversible inhibition Competitive inhibition Uncompetitive inhibition Mixed inhibition
Figure 1.6.12. Kinetics of competitive inhibition.
Unit 1
Competitive Inhibition:
A competitive inhibitor (I) competes with the substrate for the active site of an enzyme. (I) occupies the active site and prevents binding of substrate to enzyme. Many competitive inhibitors are similar in structure to substrate. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation becomes
Because the inhibitor binds reversibly to the enzyme at the same active site as that of substrate, the inhibitor can be removed from competition simply by increasing the concentration of the substrate. So Vmax for this reaction remains the same. But the [S] at which Vo = half Vmax, the apparent Km, increases in the presence of inhibitor by the factor α. (Km increases as inhibitor reduces affinity of E to the
S). The double-reciprocal plot is as shown in Figure
1.6.12.
Uncompetitive inhibition:
Uncompetitive inhibitor binds at a site distinct from the substrate active site and Inhibitor (I) binds only to the ES complex. In the presence of an uncompetitive inhibitor, the Michaelis-Menten equation is altered to
Figure 1.6.13. Mechanism of uncompetitive inhibition.
At high concentrations of substrate, Vo approaches
Vmax/α’. Thus, an uncompetitive inhibitor lowers the measured
Vmax. Apparent Km also decreases, because the [S] required to reach one-half Vmax decreases by the factor α’. (Apparent
Km decreases because, as I binds only to ES complex, it appears as if it is increasing the affinity between E and S). The double reciprocal plot is as shown in Figure 1.6.14.
Mixed Inhibition:
Figure 1.6.14. Kinetics of uncompetitive inhibition.
Unit 1 Mixed inhibitor binds at a site distinct from the substrate active site, but it binds to either E or ES. The rate equation describing mixed inhibition is A mixed inhibitor usually affects both Km and Vmax. Vmax decreases by the factor α’. Km can either increase or decrease depending upon whether I binds to E or ES. If I binds only to E, then Km increases. If I binds only to ES then Km decreases. The double reciprocal plot is as follows:
Non-competitive Inhibition: Non-competitive inhibition is a special case of mixed inhibition where α = α’ The double reciprocal plot is In the rate equation of mixed inhibition
Figure 1.6.15. Mechanism of mixed inhibition.
If we substitute α = α’, Vmax decreases by a factor of α (or α’), but Km remains the same.
Irreversible inhibition:
Irreversible inhibitors bind covalently with or destroy a functional group on an enzyme that is essential for the enzyme’s activity, or form a particularly stable noncovalent association.
Suicide inactivators:
A Special class of irreversible inhibitors which are relatively un reactive until they bind to the active site of a specific enzyme. Such a compound gets converted to a very reactive compound when combined irreversibly with the enzyme. These compounds are also called mechanism-based inactivators, because they hijack the normal enzyme reaction mechanism to inactivate the enzyme.
Dependence of Enzyme activity on pH
Enzymes have an optimum pH (or pH range) at which their activity is maximal. At higher or lower pH, activity decreases. Comparing the pH activity profile of 2 enzymes: Pepsin, which hydrolyzes certain peptide bonds of proteins during digestion in the stomach, has a pH optimum of about 1.6. The pH of gastric juice is between 1 and 2 Glucose 6-phosphatase of hepatocytes (liver cells), with a pH optimum of about 7.8, is responsible for releasing glucose into the blood. The normal pH of the cytosol of hepatocytes is about 7.2.
Regulatory enzymes
In cells, many enzymes work together to carry out a given metabolic process. In such systems, the product of one enzyme becomes the substrate for the next enzyme. The regulatory enzymes exhibit increased or decreased catalytic activity in response to certain signals.
Figure 1.6.16. Kinetics of mixed inhibition.
Unit 1 In most multi-enzyme systems, the first enzyme of the sequence is a regulatory enzyme. Allosteric enzymes function through reversible, noncovalent binding of regulatory compounds called allosteric modulators or allosteric effectors, which are generally small metabolites or cofactors Other enzymes are regulated by reversible covalent modification. Metabolic systems have at least two other mechanisms of enzyme regulation: 1. Some enzymes are stimulated or inhibited when they are bound by separate regulatory proteins. 2. Some are activated when peptide segments are removed by proteolytic cleavage; unlike effector-mediated regulation, regulation by proteolytic cleavage is irreversible. Allosteric enzymes undergo conformational changes in response to modulator binding. Conformational changes induced by one or more modulators interconvert more active and less-active forms of the enzyme. The modulators for allosteric enzymes may be inhibitory or stimulatory. Often the modulator is the substrate itself; regulatory enzymes for which substrate and modulator are identical are called homotropic. When the modulator is a molecule other than the substrate, the enzyme is said to be heterotropic. Each regulatory site is specific for its modulator. Enzymes with several modulators generally have different specific binding sites for each. In homotropic enzymes, the active site and regulatory site are the same.
Figure 1.6.17. Kinetics of Non-competitive Inhibition
Feedback Inhibition:
In some multienzyme systems, the regulatory enzyme is specifically inhibited by the end product of the pathway whenever the concentration of the end product exceeds the cell’s requirements. The rate of production of the pathway’s end product is thereby brought into balance with the cell’s needs. Build-up of the end product slows the entire pathway. In the the conversion of L-threonine to L-isoleucine in bacterial systems, the first enzyme, threonine dehydratase, is inhibited by isoleucine, the product of the last reaction of the series. This is an example of heterotropic allosteric inhibition.
Kinetic properties of Allosteric enzymes:
Kinetic properties of Allosteric enzymes differ from MichaelisMenten kinetics.
Figure 1.6.18. Feedback inhibition. The conversion of Lthreonine to L-isoleucine.
Unit 1 Allosteric enzymes do show saturation with substrate but for some allosteric enzymes, plots of Vo versus [S] produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non-regulatory enzymes. In this plot the value of [S] at Vo=halfVmax is not referred to as Km, instead the term [S]0.5 or K0.5 is used. Sigmoid kinetic behavior generally reflects cooperative interactions between protein subunits. For most Homotropic allosteric enzymes, the substrate acts as a positive modulator (an activator) and the binding of one molecule of substrate to one binding site alters the enzyme’s conformation and enhances the binding of subsequent substrate molecules. In sigmoid kinetics, a small change in the concentration of a modulator can be associated with large changes in activity. For heterotropic allosteric enzymes, an activator may cause the curve to become more nearly hyperbolic, with a decrease in K0.5 but no change in Vmax, resulting in an increased reaction velocity at a fixed substrate concentration. Other heterotropic allosteric enzymes respond to an activator by an increase in Vmax with little change in K0.5. A negative modulator (an inhibitor) may produce a more sigmoid substrate-saturation curve, with an increase in K0.5.
Covalent Modification of Regulatory enzymes:
Methylation – Methyl accepting chemotaxis protein of bacteria Transmembrane sensor protein in bacteria permits a bacterium to swim toward an attractant (such as a sugar) in solution and away from repellent chemicals. The methylating agent is S-adenosylmethionine (adoMet). ADP-ribosylation – Diptheria toxin – ADP-ribosylation of eEF2 (inhibition of protein synthesis) Cholera toxin - ADP-ribosylation of G protein (inhibition of signaling pathway) Phosphorylation - This mode of covalent modification is central to a large number of regulatory pathways. Protein Kinases: Attach phosphoryl groups to specific amino acid residues of a protein Phosphatases: remove phosphoryl groups Regulation by phosphorylation is seen in glycogen phosphorylase (Mr 94,500) of muscle and liver, which catalyzes the following reaction
Figure 1.6.19. Sigmoidal curve for allosteric enzymes.
Figure 1.6.21. Vmax is altered and K0.5 is nearly constant. Figure 1.6.20. Effect of Positive and Negative Modulator on an Allosteric enzyme reaction curve.
Glycogen phosphorylase occurs in two forms: the more active phosphorylase a and the less active phosphorylase b. Phosphorylase has two subunits, each with a specific Ser residue that is phosphorylated at its hydroxyl group. The phosphoryl groups can be hydrolytically removed by a separate enzyme called phosphorylase phosphatase: In this reaction, phosphorylase a is converted to phosphorylase b by the cleavage of two serine phosphate covalent bonds, one on each subunit of glycogen phosphorylase. Phosphorylase b can in turn be reactivated—covalently transformed back into active phosphorylase a—by another enzyme, phosphorylase kinase, which catalyzes the transfer of phosphoryl groups from ATP to the hydroxyl groups of the two specific Ser residues in phosphorylase b:
Breakdown of Glycogen in liver and skeletal muscles is regulated by variation in the ratio of a and b forms of glycogen phosphorylase.
Figure 1.6.22. Regulation of glycogen phosphorylase activi ty by covalent modification.
Regulation of enzyme activity by proteolytic cleavage of enzyme precursor:
Inactive precursor called a zymogen is cleaved to form the active enzyme. Eg. Proteases of the stomach and pancreas:
Chymotrypsin and trypsin are initially synthesized as chymotrypsinogen and trypsinogen. Cleavage exposes the enzyme active site.
Figure 1.6.24. Activation of zymogens by proteolytic cleavage. Activation of Trypsin. Figure 1.6.23. Activation of zymogens by proteolytic cleavage. Activation of Chymotrypsin.
Unit 1 Proteases are inactivated by inhibitor proteins that bind very tightly to the enzyme active site. For e.g., pancreatic trypsin inhibitor (Mr 6,000) binds to and inhibits trypsin.
Critical thinking Questions 1. Suppose a mutant enzyme binds a substrate 100-fold as tightly as does the native enzyme. What is the effect of this mutation on the catalytic rate if the binding of the transition state is still unaffected? 2. What is a simple means of determining whether a recently discovered proteolytic enzyme is a thiol protease? 3. The HIV 1 protease, like other retroviral proteases, is a dimer of identical subunits rather than a single chain twice as large. What is the selective advantage to the virus of a dimeric arrangement? 4. You have isolated a dimeric enzyme that contains 2 identical active sites. The binding of substrate to one active site decreases the substrate affinity of the other active site. Which allosteric model best accounts for this negative cooperativity? 5. Antithrombin III forms an irreversible complex with thrombin but not with prothrombin. What is the most likely reason for this difference in reactivity?
