Enzyme Kinetics Sadia Sayed

What is Enzyme Kinetics?  Kinetics is the study of the rates at which chemical reactions occur  Then what is Enzyme Kinetics?  Enzyme kinetics = Steady state kinetics  Thermodynamics only determines whether a process will happen spontaneously or not  Kinetics describes the way a reaction proceeds and how that journey is affected the surrounding  Remember, enzymes influence only reaction rates by lowering the activation energy  So, what is reaction rate??

Reaction Rates  The rate of any reaction is determined by the concentration of the reactant (Or reactants) 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  In this reaction, the rate depends only on the concentration of S. This is called a first-order reaction. The factor k is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature etc). Here, k is a first-order rate constant and has units of reciprocal time, such as s-1.  A reaction with a rate constant of 2,000 s-1 will be over in a small fraction of a second

Reaction Rates  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 i s a second-order rate constant with units of M-1s-1. The rate equation then becomes  From transition-state theory we can derive an expression that relates the magnitude of a rate constant to the activation energy  Where k is the Boltzmann constant and h is Planck's constant.  Relationship between the rate constant k and the activation energy ∆G‡ is inverse and exponential  A lower activation energy means a faster reaction rate

Reaction Rates  In a bimolecular reaction, if one substrate A is in much lower concentration than the other substrate B, then the reaction rate will depend on concentration of A and will appear first order in respect to A  These are called pseudo-first-order reactions  In case of zero order reactions, the rate doesn’t depend on any of the substrate concentrations (Higher substrate concentrations)

Factors Controlling Reaction Rates  In an enzyme catalyzed reaction, the following can influence the overall reaction rate 1. Substrate concentration 2. Product concentration (Feedback inhibition) 3. Inhibitors 4. Temperature 5. pH

Effect of Substrate Concentration  Substrate concentration [S] changes during the reaction, so difficult to monitor its effect  An enzyme may be present in nanomolar quantities, whereas [S] may be 5-6X  The beginning of the reaction is monitored (first 60 seconds), when change in [S] is not much and can be regarded as constant.  The initial rate /velocity, V 0 can then be monitored as a function of [S]  At relatively Iow concentrations of substrate, V 0 increases almost linearly with an increase in [S]  At higher substrate concentrations, V 0 increases by smaller and smaller amounts in response to increases in [S]  Finally, a point is reached beyond which increases in V 0 are vanishingly small as [S] increases- This plateau like V 0 region is close to the maximum velocity, V max

ES Complex  Combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis  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 form E. Here, the rate is proportional to [S]  The maximum initial rate of the catalyzed reaction, V max is observed when virtually all the enzyme is present as 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

ES Complex  So, to wrap it up- When the substrate concentration becomes high enough to entirely convert the enzyme to the ES form, the second step of the reaction becomes rate limiting and the overall reaction rate becomes insensitive to further increases in substrate concentration  This idea was expanded into a general theory of enzyme action, by Leonor Michaelis and Maud Menten in 1913

Michaelis-Menten Equation

Michaelis-Menten Equation- Conditions

Michaelis-Menten Equation- Derivation

Factors from Michaelis-Menten Equation

Graphical Representation

Lineweaver-Burk Plot

Km  Km can vary greatly from enzyme to enzyme and for different substrates of the same enzyme  The actual meaning of Km depends on specific aspects of the reaction mechanism such as the number and relative rates of the individual step  For 2 step reactions, Km= (k-1+k2)/k1  When k2 is rate-limiting, k2<<k-1, and Km reduces to k-1/k1, which is defined as the dissociation constant, Kd, of the ES complex  When k2>> k-1, and then Km= k2/k1  In other cases, k2 and k-1 are comparable and Km remains a function of all three rate constants  Experimentally, the Km for an enzyme tends to be simiIar to the cellular concentration of its substrates

Vmax

kcat

 The constant k cat, is a first-order rate constant  Also called the turnover number.  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  The kinetic parameters kcat, and Km are useful for the study and comparison of different enzymes, whether their reaction mechanisms are simple or complex  Each enzyme has values of kcat and Km that reflect the cellular environment, the concentration of substrate normally encountered in vivo by the enzyme, and the chemistry of the reaction being catalyzed  Also allow us to evaluate the kinetic efficiency of enzyme  2 enzymes catalyzing different reactions may have the same kcat yet the rates of the uncatalyzed reactions may be different and thus the rate enhancements brought about by the enzymes may differ greatly

Specificity Constant

Reactions with More than 2 Substrates  In bisubstrate reactions, 2 substrates bind to enzyme to produce 2 different products  Multiple substrate reactions are classified into 1. Sequential reactions 2. Double displacement reactions

Sequential Reactions  All substrates must bind to the enzyme before product release  In bisubstrate reaction, a ternary complex of the enzyme and both substrates form  2 types: 1. Ordered: Substrates bind the enzyme in a defined sequence 2. Random: No defined sequence of binding Enzymes having NAD+/NADH as substrates

Ordered Sequential Reactions  Lactate dehydrogenase  The coenzyme always binds first and lactate is released first  The reaction represented by W. Wallace Cleland notation  Ternary complex of enzyme and substrate to enzyme and products

Random Sequential Reactions  Formation of phosphocreatine and ADP from creatine and ATP by creatine kinase  Either of the substrates may bind first and either of the products may be released first  Involves formation of ternary complex

Double Displacement Reactions  Ping-pong reactions  One/more products are released before all the substrates bind  Substituted enzyme intermediate- Enzyme is temporarily modified  Reactions shuttling amino groups between amino acids and α -keto acids  Aspartate aminotransferase

Double Displacement Reactions  After binding aspartate, the enzyme accepts aspartates amino group to form substituted enzyme intermediate  The first product, oxaloacetate departs  The second substrate α -ketoglutarate binds the enzyme, accepts the amino group and then gets released as glutamate

Lineweaver-Burk Plot for Bi-substrate Reactions

All Enzymes Not Alike  Michaelis-Menten= Hyperbolic plot (Reaction velocity vs Substrate concentration)  Allosteric enzyme= Sigmoidal plot (Reaction velocity vs Substrate concentration)  Allosteric enzymes contain multiple subunits and multiple active sites  Binding of substrate to one active site influences the substrate binding capacity of other active sites  Substrate binding can become cooperative: Monod-Koshland model (Hemoglobin)  Activities of allosteric enzymes can be controlled by regulatory molecules reversibly bound to regulatory sites separate from active sites

References  Principles of Biochemistry, Lehninger, 5th Edition, Chapters 1, 6  Biochemistry, Stryer, 6th Edition, Chapters 1, 2, 8  Biochemistry, Voet and Voet, 4th Edition, Chapters 8, 13