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C r e a t i v e E n z y m e s I n c . Enzyme Kinetics Creative Enzymes Inc.

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Contents 1. General principles 2. Enzyme assays 3. Single-substrate reactions 4. Multi-substrate reactions 5. Non-Michaelis–Menten kinetics 6. Pre-steady-state kinetics 7. Enzyme inhibition 8. Chemical mechanism 9. Mechanisms of catalysis Creative Enzymes Inc. www.creative-enzymes.com

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P A R T 0 1 01 General Principles Creative Enzymes Inc. www.creative-enzymes.com

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The reaction catalysed by an enzyme uses exactly the same reactants and produces exactly the same products as the uncatalysed reaction. Like other catalysts enzymes do not alter the position of equilibrium between substrates and products. However unlike uncatalysed chemical reactions enzyme-catalysed reactions display saturation kinetics. Enzyme kinetics is the study of the chemical reactions that are catalysed by enzymes. In enzyme kinetics the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzymes kinetics in this way can reveal the catalytic mechanism of this enzyme its role in metabolism how its activity is controlled and how a drug or an agonist might inhibit the enzyme. General Principles Creative Enzymes Inc. www.creative-enzymes.com

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For a given enzyme concentration and for relatively low substrate concentrations the reaction rate increases linearly with substrate concentration the enzyme molecules are largely free to catalyse the reaction and increasing substrate concentration means an increasing rate at which the enzyme and substrate molecules encounter one another. However at relatively high substrate concentrations the reaction rate asymptotically approaches the theoretical maximum the enzyme active sites are almost all occupied by substrates resulting in saturation and the reaction rate is determined by the intrinsic turnover rate of the enzyme. Creative Enzymes Inc. www.creative-enzymes.com General Principles

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The substrate concentration midway between these two limiting cases is denoted by Km. Thus Km is the substrate concentration at which the reaction velocity is half of the maximum velocity. The two most important kinetic properties of an enzyme are how easily the enzyme becomes saturated with a particular substrate and the maximum rate it can achieve. Creative Enzymes Inc. www.creative-enzymes.com General Principles

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P A R T 0 2 02 Enzyme Assays Creative Enzymes Inc. www.creative-enzymes.com

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Spectrophotometric assays observe change in the absorbance of light between products and reactants Enzyme assays are laboratory procedures that measure the rate of enzyme reactions. Since enzymes are not consumed by the reactions they catalyse enzyme assays usually follow changes in the concentration of either substrates or products to measure the rate of reaction. There are many methods of measurement. Radiometric assays involve the incorporation or release of radioactivity to measure the amount of product made over time. The most sensitive enzyme assays use lasers focused through a microscope to observe changes in single enzyme molecules as they catalyse their reactions. Enzyme Assays Creative Enzymes Inc. www.creative-enzymes.com

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P A R T 0 3 03 Single-substrate Reactions Creative Enzymes Inc. www.creative-enzymes.com

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Enzymes with single-substrate mechanisms include isomerases such as triosephosphateisomerase or bisphosphoglycerate mutase intramolecular lyases such as adenylate cyclase and the hammerhead ribozyme an RNA lyase. However some enzymes that only have a single substrate do not fall into this category of mechanisms. Single-substrate Reactions Creative Enzymes Inc. www.creative-enzymes.com

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As enzyme-catalysed reactions are saturable their rate of catalysis does not show a linear response to increasing substrate. If the initial rate of the reaction is measured over a range of substrate concentrations denoted as S the initial reaction rate v 0 increases as S increases as shown on the right. However as S gets higher the enzyme becomes saturated with substrate and the initial rate reaches Vmax the enzymes maximum rate. The Michaelis–Menten kinetic model of a single-substrate reaction is shown on the right. There is an initial bimolecular reaction between the enzyme E and substrate S to form the enzyme–substrate complex ES. The rate of enzymatic reaction increases with the increase of the substrate concentration up to a certain level called Vmax at Vmax increase in substrate concentration does not cause any increase in reaction rate as there is no more enzyme E available for reacting with substrate S. Creative Enzymes Inc. www.creative-enzymes.com Michaelis–Menten Kinetics

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Here the rate of reaction becomes dependent on the ES complex and the reaction becomes a unimolecular reaction with an order of zero. Though the enzymatic mechanism for the unimolecular reaction can be quite complex there is typically one rate-determining enzymatic step that allows this reaction to be modelled as a single catalytic step with an apparent unimolecular rate constant Kcat. If the reaction path proceeds over one or several intermediates Kcat will be a function of several elementary rate constants whereas in the simplest case of a single elementary reaction e.g. no intermediates it will be identical to the elementary unimolecular rate constant K2. Creative Enzymes Inc. www.creative-enzymes.com Michaelis–Menten Kinetics The apparent unimolecular rate constant Kcat is also called turnover number and denotes the maximum number of enzymatic reactions catalysed per second.

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Creative Enzymes Inc. www.creative-enzymes.com Michaelis–Menten Kinetics Michaelis–Menten equation: ν0 dP/dt VmaxS/Km+S • v0 indicates the reaction rate and the activity of the enzyme • S represents substrate concentration • Vmax indicates maximum reaction rate • Km is Michaelis constant Km K-1+K2 / k1. The value of Michaelis constant is equal to the substrate concentration when the enzyme reaction rate is half of the maximum reaction rate. Km represents the affinity of the enzyme to the substrate. A high Km value indicates a weak affinity between E and S and a low km value indicates a strong affinity.

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As shown on the right this is a linear form of the Michaelis–Menten equation and produces a straight line with the equation y mx + c with a y- intercept equivalent to 1/Vmax and an x-intercept of the graph representing −1/Km. The Lineweaver–Burk plot or double reciprocal plot is a common way of illustrating kinetic data. This is produced by taking the reciprocal of both sides of the Michaelis–Menten equation. Linear Plots of the Michaelis–Menten Equation Creative Enzymes Inc. www.creative-enzymes.com Naturally no experimental values can be taken at negative 1/S the lower limiting value 1/S 0 the y-intercept corresponds to an infinite substrate concentration where 1/v1/Vmax as shown at the right thus the x-intercept is an extrapolation of the experimental data taken at positive concentrations.

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The study of enzyme kinetics is important for two basic reasons. Firstly it helps explain how enzymes work and secondly it helps predict how enzymes behave in living organisms. The kinetic constants defined above KM and Vmax are critical to attempts to understand how enzymes work together to control metabolism. Making these predictions is not trivial even for simple systems. For example oxaloacetate is formed by malate dehydrogenase within the mitochondrion. Oxaloacetate can then be consumed by citrate synthase phosphoenolpyruvate carboxykinase or aspartate aminotransferase feeding into the citric acid cycle gluconeogenesis or aspartic acid biosynthesis respectively. Being able to predict how much oxaloacetate goes into which pathway requires knowledge of the concentration of oxaloacetate as well as the concentration and kinetics of each of these enzymes. Practical Significance of Kinetic Constants Creative Enzymes Inc. www.creative-enzymes.com

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P A R T 0 4 04 Multi-substrate Reactions Creative Enzymes Inc. www.creative-enzymes.com

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Multi-substrate Reactions Creative Enzymes Inc. www.creative-enzymes.com Multi-substrate reactions follow complex rate equations that describe how the substrates bind and in what sequence. The analysis of these reactions is much simpler if the concentration of substrate A is kept constant and substrate B varied. Under these conditions the enzyme behaves just like a single- substrate enzyme and a plot of v by S gives apparent KM and Vmax constants for substrate B. If a set of these measurements is performed at different fixed concentrations of A these data can be used to work out what the mechanism of the reaction is. For an enzyme that takes two substrates A and B and turns them into two products P and Q there are two types of mechanism: ternary complex and ping–pong.

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Ternary-complex Mechanisms Creative Enzymes Inc. www.creative-enzymes.com In these enzymes both substrates bind to the enzyme at the same time to produce an EAB ternary complex. The order of binding can either be random in a random mechanism or substrates have to bind in a particular sequence in an ordered mechanism. When a set of v by S curves fixed A varying B from an enzyme with a ternary-complex mechanism are plotted in a Lineweaver–Burk plot the set of lines produced will intersect. Enzymes with ternary-complex mechanisms include glutathione S-transferase dihydrofolate reductase and DNA polymerase.

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Ping–pong Mechanisms Creative Enzymes Inc. www.creative-enzymes.com Enzymes with a ping-pong mechanism can exist in two states E and a chemically modified form of the enzyme E this modified enzyme is known as an intermediate. In such mechanisms substrate A binds changes the enzyme to E by for example transferring a chemical group to the active site and is then released. Only after the first substrate is released can substrate B bind and react with the modified enzyme regenerating the unmodified E form. When a set of v by S curves fixed A varying B from an enzyme with a ping–pong mechanism are plotted in a Lineweaver–Burk plot a set of parallel lines will be produced. This is called a secondary plot. Enzymes with ping–pong mechanisms include some oxidoreductases such as thioredoxin peroxidase transferases such as acylneuraminate cytidylyltransferase and serine proteases such as trypsin and chymotrypsin.

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Multi-substrate Reactions Creative Enzymes Inc. www.creative-enzymes.com 1 Intersecting lines indicate that a ternary complex is formed increasing S2 will increase Vmax and decrease Km. 2 Parallel lines indicate a Ping-Pong mechanism increase in S2 increases Vmax and Km at regular intervals

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P A R T 0 5 05 Non-Michaelis–Menten Kinetics Creative Enzymes Inc. www.creative-enzymes.com

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This behavior is most common in multimeric enzymes with several interacting active sites. Here the mechanism of cooperation is similar to that of hemoglobin with binding of substrate to one active site altering the affinity of the other active sites for substrate molecules. Some enzymes produce a sigmoid v by S plot which often indicates cooperative binding of substrate to the active site. This means that the binding of one substrate molecule affects the binding of subsequent substrate molecules. Non-Michaelis–Menten Kinetics Creative Enzymes Inc. www.creative-enzymes.com Positive cooperativity occurs when binding of the first substrate molecule increases the affinity of the other active sites for substrate. Negative cooperativity occurs when binding of the first substrate decreases the affinity of the enzyme for other substrate molecules.

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P A R T 0 6 06 Pre-steady-state Kinetics Creative Enzymes Inc. www.creative-enzymes.com

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This approach was first applied to the hydrolysis reaction catalysed by chymotrypsin. Often the detection of an intermediate is a vital piece of evidence in investigations of what mechanism an enzyme follows. For example in the ping–pong mechanisms that are shown above rapid kinetic measurements can follow the release of product P and measure the formation of the modified enzyme intermediate E. In the case of chymotrypsin this intermediate is formed by an attack on the substrate by the nucleophilic serine in the active site and the formation of the acyl-enzyme intermediate. In the first moment after an enzyme is mixed with substrate no product has been formed and no intermediates exist. The study of the next few milliseconds of the reaction is called pre-steady-state kinetics. Pre-steady-state kinetics is therefore concerned with the formation and consumption of enzyme–substrate intermediates such as ES or E until their steady-state concentrations are reached. Pre-steady-state Kinetics Creative Enzymes Inc. www.creative-enzymes.com In the figure to the left the enzyme produces E rapidly in the first few seconds of the reaction. The rate then slows as steady state is reached. This rapid burst phase of the reaction measures a single turnover of the enzyme. Consequently the amount of product released in this burst shown as the intercept on the y-axis of the graph also gives the amount of functional enzyme which is present in the assay.

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P A R T 0 7 07 Enzyme Inhibition Creative Enzymes Inc. www.creative-enzymes.com

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Enzyme Inhibition Creative Enzymes Inc. www.creative-enzymes.com Enzyme inhibition refers to the ability to reduce or lose the activity of the enzyme but does not cause the denaturation of the enzyme protein. Enzyme inhibition is mainly caused by changes in the chemical properties of the essential groups of the enzyme. Compounds that cause enzyme inhibition are called inhibitors. It should be noted that enzyme inhibition is different from enzyme inactivation and inhibitors are also different from denaturants. Enzyme inhibition includes reversible inhibition and irreversible inhibition.

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Reversible Inhibition Creative Enzymes Inc. www.creative-enzymes.com Reversible inhibition refers to the temporary loss of enzyme activity caused by the binding of inhibitors to enzyme proteins in a non-covalent manner. Reversible inhibitors can be removed by physical methods such as dialysis and can partially or completely restore enzyme activity. Reversible inhibition includes competitive inhibition uncompetitive inhibition non-competitive inhibition and mixed inhibition. Competitive inhibition Non-competitive inhibition

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Competitive inhibition can be overcome by sufficiently high concentrations of substrate i.e. by out-competing the inhibitor. However the apparent Km will increase as it takes a higher concentration of the substrate to reach the Km point or half the Vmax. In non-competitive inhibition Vmax will decrease due to the inability for the reaction to proceed as efficiently but Km will remain the same as the actual binding of the substrate by definition will still function properly. Creative Enzymes Inc. www.creative-enzymes.com Reversible Inhibition

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Reversible Inhibition Creative Enzymes Inc. www.creative-enzymes.com Uncompetitive inhibition Mixed inhibition

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Irreversible inhibition means that the inhibitor covalently binds to the functional group of the active center of the enzyme thus inhibiting the activity of the enzyme. Irreversible inhibitors cannot be removed by physical methods such as dialysis and restore enzyme activity. Irreversible inhibitors often contain reactive functional groups such as nitrogen mustards aldehydes haloalkanes alkenes Michael acceptors phenyl sulfonates or fluorophosphonates. These electrophilic groups react with amino acid side chains to form covalent adducts. Irreversible inhibition is different from irreversible enzyme inactivation. Irreversible inhibitors are generally specific for one class of enzyme and do not inactivate all proteins they do not function by destroying protein structure but by specifically altering the active site of their target. Irreversible Inhibition Creative Enzymes Inc. www.creative-enzymes.com

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P A R T 0 8 08 Chemical Mechanism Creative Enzymes Inc. www.creative-enzymes.com

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• Kinetic measurements taken under various solution conditions or on slightly modified enzymes or substrates often shed light on this chemical mechanism as they reveal the rate-determining step or intermediates in the reaction. • Isotopes can also be used to reveal the fate of various parts of the substrate molecules in the final products. • The chemical mechanism can also be elucidated by examining the kinetics and isotope effects under different pH conditions by altering the metal ions or other bound cofactors by site- directed mutagenesis of conserved amino acid residues or by studying the behaviour of the enzyme in the presence of analogues of the substrates. An important goal of measuring enzyme kinetics is to determine the chemical mechanism of an enzyme reaction i.e. the sequence of chemical steps that transform substrate into product. Chemical Mechanism Creative Enzymes Inc. www.creative-enzymes.com

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P A R T 0 9 09 Mechanisms of Catalysis Creative Enzymes Inc. www.creative-enzymes.com

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The favoured model for the enzyme–substrate interaction is the induced fit model. This model proposes that the initial interaction between enzyme and substrate is relatively weak but that these weak interactions rapidly induce conformational changes in the enzyme that strengthen binding. Mechanisms of catalysis include catalysis by bond strain by proximity and orientation by active-site proton donors or acceptors covalent catalysis and quantum tunnelling. Enzyme kinetics cannot prove which modes of catalysis are used by an enzyme. However some kinetic data can suggest possibilities to be examined by other techniques. For example a ping–pong mechanism with burst-phase pre-steady-state kinetics would suggest covalent catalysis might be important in this enzymes mechanism. Alternatively the observation of a strong pH effect on Vmax but not KM might indicate that a residue in the active site needs to be in a particular ionisation state for catalysis to occur. Mechanisms of Catalysis Creative Enzymes Inc. www.creative-enzymes.com

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Contact Us Creative Enzymes Inc. www.creative-enzymes.com www.creative-enzymes.com contactcreative-enzymes.com Creative Enzymes

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C r e a t i v e E n z y m e s I n c . Tnank You Creative Enzymes Inc.