Unit IV Biocatalysts PDF

UNIT-IV Biocatalysis The basis of metabolism, Nomenclature of enzymes, Enzyme kinetics, Mechanism of enzymatic catalysis, Active site, Activators and inhibitors, Coenzymes, Isoenzymes, Michaelis-Menten equation, Km and Vmax value, Regulation of en...

UNIT-IV Biocatalysis The basis of metabolism, Nomenclature of enzymes, Enzyme kinetics, Mechanism of enzymatic catalysis, Active site, Activators and inhibitors, Coenzymes, Isoenzymes, Michaelis-Menten equation, Km and Vmax value, Regulation of enzyme activity (single-substrate and multi-substrate reactions).  THE BASIS OF METABOLISM The Chemical Reactions that keep the organisms aliveis collectively called as METABOLISM-Chemical reactions of life Synthesis Making Energy Preparing tissues Breaking down waste Synthesis of Proteins Sending hormones DNA replication Without enzymes the chemical reactions wouldn’t have been fast enough to sustain  THE BASIS OF METABOLISM Does Enzymes change the Gibbs Free Energy ? All chemical reactions require some amount of energy to get them started. OR Enzymes Lower a Reaction’s It is First push to start reaction. Activation Energy This energy is called activation energy. How much energy is utilized Thermodynamic quantity Free energy ,entropy,enthalpy Kinetics- Rate of Rxn speed of reactions  Enzymes Affect Rxn Rates, Not Equilibria Any reaction, such as S P, can be described by a reaction coordinate diagram, in which the free energy change during the reaction is plotted as a function of the progress of the reaction The free energy change (∆G’0) (and equilibrium position) of the reaction is determined by the difference in ground state free energies of S and P. The rate of the reaction is dependent on the height of the free energy barrier between S and P. At the top of this hump is the transition state. The transition state is not a chemical species with any significant stability, and should not be confused with a reaction intermediate. Rather it is a fleeting molecular moment in which events such as bond breakage, bond formation, and charge development have proceeded to the point at which decay to either substrate or product is equally likely. The difference between the energy levels of the ground state and the transition state is the activation energy, ∆G‡. The rate of the reaction is inversely and exponentially proportional to the value of ∆G‡.  Enzymes Affect Rxn Rates, Not Equilibria Like other catalysts, enzymes enhance reaction rates by lowering activation energies They have no effect on the position of reaction equilibria. The example shown is for an enzyme which follows the simple enzymatic steps of E + S ⇄ ES ⇄ EP ⇄ E + P. (E-enzyme; S-substrate; P-product; ES-transient complex between the enzyme and substrate; EP-transient complex between the enzyme and product). In the presence of the enzyme, three peaks occur in the reaction coordinate diagram. Whichever peak is the highest signifies the rate-limiting step of the overall reaction., BINDING ENERGY PROVIDED BY THE INTERACTION OF THE ENZYME WITH THE TRANSITION STATE CONTRIBUTES STRONGLY TO LOWERING THE ACTIVATION ENERGY OF THE REACTION, AND ACCELERATING ITS RATE.  Relationship Between K’eq and ∆G’0 To describe the free energy changes for reactions, chemists define a standard set of conditions (temperature 298˚K; partial pressure of each gas = 1 atm; concentration of each solute 1 M) and express the free energy change for a reacting system under these conditions as ∆G0, the standard free energy change. Because biochemical systems commonly have H+ concentrations far below 1 M, biochemists define a biochemical standard free energy change, ∆G’0, the standard free energy change at pH 7.0. The equilibrium constant for a reaction (K’eq) under standard biochemical conditions is mathematically linked to the standard free energy change for a reaction, ∆G’0, via the equation ∆G’0 = -2.303 RT log K’eq. In this equation, R is the gas constant, 8.315 J/mol.K, and T is the absolute temperature, 298˚K (25˚C). The numerical values for ∆G’0 as a function of K’eq are tabulated Note that a large negative value of ∆G’0 reflects a favorable equilibrium in which the ratio of products to reactants is much greater than 1/1.  Transition State Complementarity Explains Rate Enhancement The importance of transition state complementarity to rate enhancement can be illustrated using an example of a hypothetical “stickase” which catalyses the breakage of a metal stick, and binds to the sick via magnetic interactions. In the uncatalyzed reaction, (Part a), the stick must first be bent to a transition state structure before being broken. Due to the high activation energy barrier of the bent stick transition state, the overall reaction (which has a negative free energy change) is relatively slow. If the stickase were precisely complementary to the metal bar (Part b), the rate of the reaction would not be improved as the enzyme actually would stabilize the structure of the stick. Under these conditions, the ES complex corresponds to a trough in the reaction coordinate diagram from which the substrate would have difficulty escaping. Transition State Complementarity Explains Rate Enhancement However, if the stickase were more complementary to the transition state of the reaction (Part c), then the increase in free energy required to draw the stick into a bent and partially broken conformation would be offset, or paid for, by the magnetic interactions (binding energy) between the enzyme and the substrate in its transition state. This energy payment translates into a lower net activation energy and a faster reaction rate. Real enzymes work on an analogous principle. Some weak interactions are formed in the ES complex, but the full complement of such interactions between the substrate and enzyme is formed only when the substrate reaches the transition state. The free energy (binding energy) released by the formation of these interactions partially offsets the energy required to reach the top of the energy hill. The summation of the unfavorable (positive) activation energy ∆G‡ and the favorable (negative) binding energy ∆GB results in. a lower net activation energy Even on the enzyme, the transition state is not a stable species but is a brief point in time that the substrate spends atop an energy hill. The enzyme-catalyzed reaction is much faster than the uncatalyzed process because the hill is much smaller. The important point is that weak binding interactions between the enzyme and the substrate provide a substantial driving force for enzymatic catalysis Contributions of Binding Energy to Reaction Specificity and Catalysis For a reaction to take place, significant physical and thermodynamic factors contributing to ∆G‡ must be overcome. These include 1) the entropy (freedom of motion) of molecules in solution, which reduces the possibility that they will react together, 2) the solvation shell of hydrogen-bonded water molecules that surrounds and helps to stabilize most biomolecules in solution, 3) the distortion of substrates that must occur in many reactions 4) the need for proper alignment of catalytic functional groups on the enzyme. All of these factors can be overcome due to the binding energy released on interaction of the enzyme with the transition state. Binding energy also gives an enzyme its specificity, which is the ability of an enzyme to discriminate between its substrate and a competing molecule with a similar structure. Contributions of Binding Energy to Reaction Specificity and Catalysis The mechanism by which binding energy compensates for physical and thermodynamic factors that impede reaction rates are as follows. 1) Entropy reduction: The restriction in the motions of two substrates that are about to react is one benefit of binding them to an enzyme. Binding energy holds the substrates in the proper orientation to react--a substantial contribution to catalysis, because productive collisions between molecules in solution can be exceedingly rare. Studies have shown. that constraining the motion of two reactants can produce rate enhancements of many orders of magnitude 2) Desolvation: Formation of weak bonds between the enzyme and substrate results in the desolvation of the substrate. The removal of bound water molecules from the substrate removes water molecules which otherwise might impede the reaction 3) Substrate distortion: Binding energy involving weak interactions formed only in the reaction transition state helps to compensate thermodynamically for any distortion, primarily electronic redistribution, that the substrate must undergo to react. 4) Catalytic group alignment: Enzymes typically undergo changes in conformation when the substrate binds that are induced by multiple weak interactions with the substrate. The alignment of catalytic functional groups is referred to as induced fit, and it serves to bring specific functional groups on the enzyme into the proper position to catalyze the reaction. The Most Important Properties Of An Enzyme Are: 1.Catalytic Property 2.Specificity 3.Reversibility 4.Sensitiveness to heat and temperature and pH Catalytic Property: Enzymes have extra-ordinary catalytic power. They are active in very small quantities. A small amount of enzyme is enough to convert a large quantity of substrate. The enzymes remain unchanged after the reaction. The turnover number of enzymes ranges from 0.5 to 600000. Turn over number is the number of substrate molecules converted by one molecule of enzymes per second when its active site is saturated with substrate. Specificity: Enzymes are very specific in their action. Particular enzymes act on particular substrates only. Enzymes are also specific to a particular type of reaction. In some rare cases, the specificity may not be too strong. Enzymes show different types of specificity as follows: Bond Specificity: It is also called as relative specificity. Here the enzymes are specific for a bond. eg; peptidase is specific or peptide bond, lipase is specific for ester bond in a lipid. Group Specificity: It is also called structural specificity. Here the enzymes are specific for a group. eg; pepsin hydrolyse the peptide bonds in with the amino group belongs to aromatic amino acids. Substrate Specificity: It is also called absolute specificity. Here the enzyme acts only on a particular substrate. eg; arginase acts only on arginine; carbonic anhydrase acts only on carbonic acid. Optical Specificity: It is also called stereo-specificity. This is the highest specificity shown by an enzyme. Here the enzymes are specific not only to the substrate but also to its optical configuration. e.g. L amino acid oxidase acts only L-amino acids, not on D-amino acids. Similarly, the alpha-amylase act only on alpha-14 glycosidic linkage of starch and glycogen. It is not able to hydrolyse the beta-14 glycosidic linkage of cellulose. Co-factor Specificity: This shows that enzymes are not only specific to the substrate but also specific to its co-factors. Geometric Specificity: Here the specificity is very less. Some enzymes will work with a small range of similar substrates having similar structural geometry. e.g. alcohol dehydrogenase can oxidise methanol and n-propanol to aldehydes.  Enzyme Structure SIMPLE ENZYMES Composed only of protein CONJUGATED ENZYMES Composed of: – Apoenzyme Conjugate enzyme without its cofactor The apoenzyme can’t catalyze its reaction Protein part of a without its cofactor. conjugated enzyme – The combination of the apoenzyme with the cofactor makes the conjugated enzyme functional. – Coenzyme (Cofactor) Holoenzyme = apoenzyme + cofactor Non-protein part of a – The biochemically active conjugated enzyme. Enzyme Nomenclature Suffix of an enzyme –ase – Lactase, amylase, lipase or protease Denotes an enzyme Enzymes are named according Some digestive enzymes have the suffix –in to the – Pepsin, trypsin & chymotrypsin These enzymes were the first ones to be studied type of reaction they catalyze and/or their substrate Prefix denotes the type of reaction the enzyme catalyzes – Oxidase: redox reaction – Hydrolase: Addition of water to break one Substrate = the reactant upon component into two parts which the specific enzyme acts Substrate identity is often used together – Enzyme physically binds to the with the reaction type substrate – Pyruvate carboxylase, lactate dehydrogenase Enzyme Substrat Enzyme/substrate  ENZYME CLASSIFICATION E.C. Number The Enzyme Commission Number (EC Number) is a numerical EC 1. Oxidoreductases classification scheme for enzymes, based on the chemical reactions they catalyze. EC 2. Transferases The chemical reaction catalyzed is the specific property that distinguishes one enzyme from another. EC 3. Hydrolases EC numbers specify enzyme-catalysed reactions. EC 4. Lyases The EC numbers are assigned by the Nomenclature Committee of the International Union of Biochemistry and Molecular EC 5. Isomerases Biology (IUBMB). EC 6. Ligases Systemic Nomenclature Every enzyme consists of a code of the letters “EC” followed by Each enzyme has classification four numbers separated by periods.The first digit defines the general type of reaction catalysed by the enzyme and ranges from number consisting of four digits: one to six. The second figure indicates the subclass. Example, EC: (2.7.1.1) HEXOKINASE The third figure gives the sub-subclass. The fourth figure is the serial number of the enzyme in its sub- subclass. Enzyme Class Reaction Catalyzed Examples in Metabolism Oxidoreductase Redox reaction (reduction & oxidation) Examples are dehydrogenases catalyse reactions in which a substrate is oxidised or reduced Transferase Transfer of a functional group from 1 Transaminases which catalyze the transfer of amino group or kinases which molecule to another catalyze the transfer of phosphate groups. Hydrolase Hydrolysis reaction Lipases catalyze the hydrolysis of lipids, and proteases catalyze the hydrolysis of proteins Lyase Addition / removal of atoms to / from Decarboxylases catalyze the removal of carboxyl groups double bond Isomerase Isomerization reaction Isomerases may catalyze the conversion of an aldose to a ketose, and mutases transfer functional group from one atom to another within a substrate. Ligase Synthesis reaction (Joining of 2 Synthetases link two smaller molecules are form a larger one. molecules into one, forming a new chemical bond,coupled with ATP hydrolysis) THE TABLE EXPLAINS THE FUNCTIONS OF ENZYMES AND HOW THEY ARE CLASSIFIED AND NAMED. Factors Affecting Enzyme Activity Enzyme activity Measure of the rate at which an enzyme converts substrate to products in a biochemical reaction 4 factors affect enzyme activity: Temperature pH Substrate concentration: [substrate] Enzyme concentration: [enzyme]  Temperature (t) Stoker 2014, Figure 21-6 p753 With increased t the EKIN increases – More collisions – Increased reaction rate Optimum temperature (tOPT) is the t, at which the enzyme exhibits maximum activity – The tOPT for human enzymes = 370C When the t increases beyond tOPT – Changes in the enzyme’s tertiary structure occur, inactivating & denaturing it (e.g. fever) Little activity is observed at low t  pH Stoker 2014, Figure 21-7 p753 Optimum pH (pHOPT) is the pH, at which the enzyme exhibits maximum activity Most enzymes are active over a very narrow pH range – Protein & amino acids are properly maintained – Small changes in pH (low or high) can result in enzyme denaturation & loss of function Each enzyme has its characteristic pHOPT, which usually falls within physiological pH range 7.0 - 7.5 Digestive enzymes are exceptions: – Pepsin (in stomach) – pHOPT = 2.0 – Trypsin (in SI) – pHOPT = 8.0  Substrate Concentration Stoker 2014, Figure 21-8 p754 If [enzyme] is kept constant & the [substrate] is increased – The reaction rate increases until a saturation point is met At saturation the reaction rate stays the same even if the [substrate] is increased – At saturation point substrate molecules are bound to all available active sites of the enzyme molecules Reaction takes place at the active site – If they are all active sites are occupied the reaction is going at its maximum rate Each enzyme molecule is working at its maximum capacity Enzyme Concentration Stoker 2014, Figure 21-9 p755 If the [substrate] is kept constant & the [enzyme] is increased – The reaction rate increases – The greater the [enzyme], the greater the reaction rate RULE: – The rate of an enzyme-catalyzed reaction is always directly proportional to the amount of the enzyme present In a living cell: – The [substrate] is much higher than the [enzyme] Enzymes are not consumed in the reaction Enzymes can be reused many times  Enzyme Active Sites Enzymes greatly increase the rates of biological reactions by providing a specific environment within which a reaction can occur more rapidly. Enzyme-catalyzed reactions take place within the confines of a pocket on the enzyme called the active site. The reactant molecule is referred to as the substrate. The surface of the active site is lined with amino acid residues with substituent groups that bind to the substrate and catalyze its chemical transformation. Often, the active site encloses the substrate, sequestering it from solution.  Lock-and-Key Model Induced Fit Model In the lock-and-key model of enzyme action: In the induced-fit model of enzyme action: - the active site has a rigid shape - the active site is flexible, not rigid - only substrates with the matching shape can fit - the shapes of the enzyme, active site, and substrate adjust to maximumize the fit, - the substrate is a key that fits the lock of the which improves catalysis active site - there is a greater range of substrate This is an older model, however, and does not specificity This model is more consistent with a wider work for all enzymes range of enzymes  Complementary Shapes of Enzymes and Substrates The active site of an enzyme has a surface contour that is complementary in shape to its substrate (and products). This is illustrated for the two substrates of the enzyme dihydrofolate reductase in Fig. 6-4. Structural complementarity is responsible for the high specificity of enzyme reactions. The idea that the enzyme and substrate are complementary to one another was first proposed by the organic chemist, Emil Fisher, in 1894. He stated that the two components fit together like a lock and key. This proposal has greatly influenced the development of biochemistry. However, it is slightly misleading in that precise complementarity between an enzyme and its substrate would be counterproductive to efficient catalysis. Later day biochemical researchers instead realized that the enzyme must be more complementary to the reaction transition state than to the substrate per se for efficient catalysis to occur (next slide).  Mechanism Of Enzymatic Catalysis Other Contributions to Enzyme Catalysis: General Acid-base Catalysis Many biochemical reactions involve the formation of unstable charged intermediates that tend to break down rapidly to their constituent reactant species, thus slowing the reaction Charged intermediates can often 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. Catalysis, such as in organic chemistry reactions, that uses only the H+ or OH- ions present in solution is referred to a specific acid- base catalysis. Proton transfers mediated by weak acids and bases other than water, such as the functional groups in the side-chains of amino acids, is referred to as general-acid base catalysis. Amino acid side-chains that are commonly involved in general acid-base catalysis are listed  Mechanism Of Enzymatic Catalysis Other Contributions to Enzyme Catalysis: Covalent Catalysis In covalent catalysis, a transient covalent bond is formed between the enzyme and the substrate. Consider the hydrolysis of a bond between groups A and B: A-B + H2O A + B In the presence of a covalent catalyst (an enzyme with the nucleophilic group X:) the reaction becomes 1) A-B + X: A-X + B 2) A-X + H2O A + X: This alters the pathway of the reaction, and it results in catalysis if the new pathway has a lower activation energy than the uncatalyzed pathway. Both of the new steps must be faster than the uncatalyzed reaction. A number of amino acid side-chains and the functional groups of some enzyme cofactors can serve as nucleophiles in the formation of covalent bonds with substrates. These covalent complexes always undergo further reaction to regenerate the free enzyme. Other Contributions to Enzyme Catalysis: Metal Ion Catalysis Metals, whether tightly bound to the enzyme or taken up from solution along with the substrate, can participate in catalysis in several ways. Ionic interactions between an enzyme-bound metal and a substrate can help orient the substrate for reaction or stabilize 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 enzymes require one or more metal ions for catalytic activity.  Relationship Between ∆G‡ and Rxn Rate The rate of a chemical reaction is determined by the concentration of the reactant(s) and by a rate constant usually denoted by k. For the unimolecular reaction S P, the rate (or velocity) of the reaction, V--representing the amount of S that reacts per unit time--is expressed by a rate equation, V = k[S]. In this reaction, the rate depends only on the concentration of S. This is a first-order reaction. The factor k is a proportionality constant that reflects the probability of a reaction under a given set of conditions (pH, temperature, etc.). Here, k is a first-order rate constant and has the units of reciprocal time (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, then the reaction is second-order and k is a second-order rate constant, with units of M-1s-1. The rate equation then becomes V = k[S1][S2]. From physical chemistry, it can be derived that the magnitude of a rate constant is inversely and exponentially related to the activation energy, ∆G‡. Thus, a lower activation energy means a faster reaction rate.  ENZYME KINETICS Michaelis and Menten EQUATION Effect of Substrate Concentration on Reaction Rate The effect on V0 of varying [S] when the enzyme concentration is held constant. This is the appearance of a V0 vs [S] kinetic plot for a typical enzyme. At relatively low concentrations of substrate, V0 increases almost linearly with an increase in [S]. At higher substrate concentrations, V0 increases by smaller and smaller amounts in response to increases in [S]. Finally, a point is reached beyond which increases in V0 are vanishingly small as [S] increases. This plateau-like V0 region is close to the maximum velocity, Vmax.  The Role of the ES Complex The ES complex is the key to understanding the kinetic behavior of an enzyme. In 1913, Leonor Michaelis and Maud Menten, developed a kinetic equation to explain the behavior of many simple enzymes. Key to the development of their equation, is the assumption that the enzyme first combines with its substrate to form an enzyme-substrate complex in a relatively fast reversible step k1 E + S ⇄ ES k-1 k2 The ES complex then breaks down in a slower ES ⇄ E + P If the slower second reaction limits the rate of the overall reaction, the overall rate must be second step to yield the free enzyme and the k-2 proportional to the concentration of the species reaction product P: that reacts in the second step, i.e., ES. At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms, the free or uncombined form E and the combined form ES. At low [S], most of the enzyme is in the uncombined E form. Here, the rate is proportional to [S] because the direction of the first equation above is pushed toward formation of more ES as [S] increases.  The Role of the ES Complex The maximum initial rate of the catalyzed reaction (Vmax) is observed when virtually all of the enzyme is present in the ES complex and [E] is vanishingly small. Under these conditions, the enzyme is saturated with its substrate, so that further increases in [S] have no effect on rate. This condition exists when [S] is sufficiently high that essentially all the free enzyme has been converted to the ES form. When the enzyme is first mixed with a large excess of substrate, there is an initial period, the pre-steady state, during which the concentration of ES builds up. This period is usually too short to be easily observed, lasting just microseconds, and is not evident. The reaction quickly achieves a steady state in which [ES] remains approximately constant over time. The measured V0 generally reflects the steady state, even though V0 is limited to the early part of the reaction. The analysis of these initial rates is referred to as steady-state kinetics.  Michealis Menton Equation The kinetic curves expressing the relationship between V0 and [S] have the same general shape (a rectangular hyperbola) for most enzymes, which can be expressed algebraically by the MM equation. Michaelis and Menten derived this equation starting from their basic hypothesis that the rate-limiting step in enzymatic reactions is the breakdown of the ES complex to product and free enzyme. The MM equation is V0 = Vmax[S]/(Km + [S]). All these terms, [S], V0, Vmax, as well as the constant called the Michaelis constant, Km, can be readily measured experimentally. k1 k2 E + S ⇄ ES E + P. k-1 V0 is determined by the breakdown of ES to form product, which is determined by [ES] through the equation V0 = k2[ES]. Because [ES] in the above equation is not easily measured experimentally, an alternative expression for this term must be found. First, the term [Et], representing the total enzyme concentration (the sum of free and substrate-bound enzyme) is introduced. Free or unbound enzyme [E] can then be represented by [Et] - [ES]. Also, because [S] is ordinarily far greater than [Et], the amount of substrate bound by the enzyme at any given time is negligible compared with the total [S]. With these conditions in mind, the following steps lead to an expression for V0 in terms of easily measurable parameters. The kinetic curves expressing the relationship between V0 and [S] have the same general shape (a rectangular hyperbola) for most enzymes, which can be expressed algebraically by the MM equation. Michaelis and Menten derived this equation starting from their basic hypothesis that the rate-limiting step in enzymatic reactions is the breakdown of the ES complex to product and free enzyme. The MM equation is V0 = Vmax[S]/(Km + [S]). All these terms, [S], V0, Vmax, as well as the constant called the Michaelis constant, Km, can be readily measured experimentally. The derivation of the MM equation starts with the two basic steps of the formation and breakdown of ES. Early in the reaction, the concentration of the product [P] is negligible, and a simplifying assumption is made that the reaction P S (described by k-2) can be ignored. The overall reaction then reduces to k1 k2 E + S ⇄ ES E + P. k-1 V0 is determined by the breakdown of ES to form product, which is determined by [ES] through the equation V0 = k2[ES]. Because [ES] in the above equation is not easily measured experimentally, an alternative expression for this term must be found. First, the term [Et], representing the total enzyme concentration (the sum of free and substrate-bound enzyme) is introduced. Free or unbound enzyme [E] can then be represented by [Et] - [ES]. Also, because [S] is ordinarily far greater than [Et], the amount of substrate bound by the enzyme at any given time is negligible compared with the total [S]. With these conditions in mind, the following steps lead to an expression for V0 in terms of easily measurable parameters.  Validation of the MM Equation The MM equation can be shown to correctly explain the V0 vs [S] curves of many enzymes by considering limiting situations where [S] is very high or very low. At low [S], Km >> [S] and the [S] term in the denominator of the MM equation becomes insignificant. The equation simplifies to V0 = Vmax[S]/Km and V0 exhibits a linear dependence on [S], as is observed at the left side of V0 vs [S] graphs. At high [S], where [S] >> Km, the Km term in the denominator of the MM equation becomes insignificant and the equation simplifies to V0 = Vmax. This is consistent with the plateau in V0 observed at high [S] in kinetic graphs.An important numerical relationship emerges from the MM equation in the special case when V0 is exactly one-half Vmax. Here Vmax/2 = Vmax[S]/(Km + [S]). On dividing by Vmax, the equation is 1/2 = [S]/(Km + [S]). After solving for Km, we get Km + [S] = 2[S], or Km = [S]. This is a very useful, practical definition of Km. Km is equivalent to the substrate concentration at which V0 is one-half Vmax.  Double-reciprocal Plots Because the plot of V0 vs [S] for an enzyme-catalyzed reaction asymptotically approaches the value of Vmax at high [S], it is difficult to accurately determine Vmax (and thereby, Km) from such graphs. The problem is readily solved by converting the Michaelis-Menten kinetic equation to the so-called double-reciprocal equation (Lineweaver-Burk equation) which describes a linear plot from which Vmax and Km can be easily obtained. The Lineweaver-Burk equation is derived by first taking the reciprocal of both sides of the Michaelis-Menten equation 1/V0 = (Km + [S])/Vmax[S] Separating the components of the numerator on the right side of the equation gives 1/V0 = Km/Vmax[S] + [S]/Vmax[S] Which simplifies to 1/V0 = Km/Vmax[S] + 1/Vmax. The plot of 1/V0 vs 1/[S] gives a straight line, the y- intercept of which is 1/Vmax and the x-intercept of which is -1/Km.  The Meaning of the Km The Km can vary greatly from enzyme to enzyme, and even for different substrates of the same enzyme (Table 6-6). The Km is sometimes used (often inappropriately) as an indicator of the affinity of an enzyme for its substrate. The actual meaning of the Km depends on specific aspects of the reaction mechanism such as the number and relative rates of the individual steps. For example, for a reaction with two steps, Km = (k2 + k-1)/k1. If k2 is actually rate-limiting, then k2