Advance Enzymology BY Augustine I. Airaodion PDF

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Austin I. Airaodion is a Biochemist with a difference....

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LECTURE NOTE ON ADVANCED ENZYMOLOGY (BCH 401) BY MR AIRAODION A. I. Course Outline           

Review of General Enzymology Enzyme Kinetics The Michaelis—Menten Equation and Other Derivatives Enzyme Inhibition Multisubstrate Enzyme and Kinetic Mechanism Chemistry of Enzyme Catalysis Multienzyme Complex/ System Enzyme Assay Enzyme Purification Regulation of Enzyme Activity Application of Enzymes in Medicine ENZYME 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 enzyme's 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. Enzymes are usually protein molecules that manipulate other molecules (enzymes' substrates). These target molecules bind to an enzyme's active site and are transformed into products through a series of steps known as the enzymatic mechanism E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P These mechanisms can be divided into single-substrate and multiple-substrate mechanisms. Kinetic studies on enzymes that only bind one substrate, such as triosephosphate isomerase, aim to measure the affinity with which the enzyme binds this substrate and the turnover rate. Some other examples of enzymes are phosphofructokinase and hexokinase, both of which are important for cellular respiration (glycolysis). When enzymes bind multiple substrates, such as dihydrofolate reductase, enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. Examples of enzymes that bind a single substrate and release multiple products are proteases, which cleave one protein substrate into two polypeptide products. Others join two substrates together, such as DNA polymerase linking a nucleotide to DNA. Although these mechanisms are often a complex series of steps, there is typically one ratedetermining step that determines the overall kinetics. This rate-determining step may be a chemical reaction or a conformational change of the enzyme or substrates, such as those involved in the release of product(s) from the enzyme. Knowledge of the enzyme's structure is helpful in interpreting kinetic data. For example, the structure can suggest how substrates and products bind during catalysis; what changes occur during the reaction; and even the role of particular amino acid residues in the mechanism. Some enzymes change shape significantly during the mechanism; in such cases, it is helpful to determine the enzyme structure with and without bound substrate analogues that do not undergo the enzymatic reaction. Not all biological catalysts are protein enzymes; RNA-based catalysts such as ribozymes and ribosomes are essential to many cellular functions, such as RNA splicing and translation. The main difference between ribozymes and enzymes is that RNA catalysts are composed of nucleotides, whereas enzymes are composed of amino acids. Ribozymes also perform a more limited set of reactions, although their reaction mechanisms and kinetics can be analysed and classified by the same methods. 1

CHEMICAL KINETICS Zeroth-Order Kinetics Some reactions occur at rates that are independent of substrate concentration. In these cases, the rate of the reaction (often called the velocity of the reaction) is constant, regardless of the concentration of the participating compounds. Consider a simple reaction:

S P

For this reaction, the velocity of the reaction can be expressed as: V =

k

These equations state that at any given instant, the velocity is equal to the increase in concentration of P divided by the time interval, and that the velocity is also equal to the decrease in concentration of S divided by the time interval (note the minus sign in the –d[S]/dt expression). In this case, because the rate is independent of [ S] and [P], the velocity = k, where k is the rate constant for the reaction. These (somewhat unusual) reactions are called zeroth-order reactions. First-Order Kinetics Again, consider a simple reaction, but now a first-order reaction in which the rate depends on the substrate concentration: S P For this reaction, the velocity of the reaction can be expressed as: V = If you assume that the reverse reaction does not occur (which is a valid assumption if the initial concentration of P is zero), then at any given time, v = k [S]. For zeroth-order and first-order reactions, k is the rate constant for the reaction; k is a measure of how rapidly the reaction will occur at any concentration of S, and has the units of time-1 (usually seconds-1 or minutes-1). In a first-order reaction, the rate depends on the concentration of a single species (in this case, the reactant S). The equation v = k [S] states that velocity is a linear function of S concentration. In the graph (below) the zerothorder reaction has a constant velocity regardless of the concentration of S, while the first-order reaction velocity increases linearly with increasing S concentration.

Velocity

Zeroth Order

[S]

Another way to look at the course of these types of reactions is to consider the concentration of S as a function of time. For a zeroth-order reaction: [S]t = [S]0 – kt while for a first-order reaction:

[S]t = [S]0ekt

where [S]0 is the concentration of S at the beginning of the reaction, and [S]t is the concentration of S at time t. Plotting these equations reveals that S concentration decreases linearly with time for a zeroth-order reaction, and that S concentration decreases exponentially with time for a first-order reaction. These observations make sense: 2

[S]

for a first-order reaction, the rate of the reaction decreases as S is used up, because the rate depends on the substrate concentration [S].

Time

(Note: the following, slightly simplified, derivation of the equation for the first-order reaction is included for completeness.) The rate equation:

k[S] rearranges to:

Integrating both sides:∫

∫

kdt

gives: ln[S] − ln[S]0 = –kt

Raising both sides to the e power and rearranging gives: [S]t = [S]0 – kt Second-Order Kinetics More complicated reactions can also occur: S+R

P +Q

For these reactions: v =

and v = k[S][R]

Reactions of this type are second-order, and k is a second-order rate constant, because the rate of the reaction depends on the product of [S] and [R]. If the reaction involved the collision of two molecules of S, the velocity equation would be: v = k[S][S] = k[S]2 The order of the reaction comes from the exponent that describes the number of reactants. Second-order rate constants have units of M-1•sec-1. Real chemical reactions rarely have more than two molecules interacting at one time, because the simultaneous collision of more than two molecules is unlikely. (Note: there are a few examples of tri-molecular reactions; in most reactions that appear to involve more than two reactants, two reactants form an intermediate, which then reacts with the other compound to form the final product.) Pseudo-First-Order Kinetics Studying second-order reactions is usually more difficult than studying first-order reactions. One way around this difficulty is to create ―pseudo-first-order conditions‖. These are conditions in which the concentration of one compound is very high. If the concentration of R is very high compared to S, then the concentration of R will essentially be constant during the reaction. This allows the equation to be rewritten: v = k[S][R] = kpseudo[S]

3

The term for concentration of R did not disappear; because the concentration of R is approximately a constant, it was merely incorporated into the kpseudo first-order rate constant. Rate-Limiting Steps Many reaction pathways involve multiple steps. In most cases, one step will be appreciably slower than the others. This step is the rate-limiting step; it is the step upon which the rate of the overall reaction depends. Analysis for rate-limiting steps is important for understanding all types of reactions. In biochemistry, analysis for rate-limiting steps in metabolic pathways is especially important, because these steps tend to be the ones that act as regulated control points for the pathway. kcat is a term used for the rate constant for the overall reaction. In complex reactions with several steps, where the maximal catalytic rate depends on several rate constants, kcat is the rate constant for the rate-limiting step. kcat = turnover number = the number of product molecules formed by one enzyme molecule in one second (or, for slow enzymes, in one minute). kcat/Km is a measure of the catalytic efficiency of an enzyme; in effect, it takes into account both substrate binding and conversion to product. kcat/Km cannot be faster than the diffusion limit (E and S must collide in order to react). The Michaelis—Menten Equation The Michaelis—Menten equation illustrates in mathematical terms the relationship between initial reaction velocity Vi and substrate concentration [S]. The Michaelis constant Km is the substrate concentration at which Vi is half the maximal velocity ( ) attainable at a particular concentration of enzyme. Km thus has the dimensions of substrate concentration. The primary function of enzymes is to enhance rates of reactions so that they are compatible with the needs of the organism. To understand how enzymes function, we need a kinetic description of their activity. For many enzymes, the rate of catalysis V0, which is defined as the number of moles of product formed per second, varies with the substrate concentration [S]. The rate of catalysis rises linearly as substrate concentration increases and then begins to level off and approach a maximum at higher substrate concentrations. Consider an enzyme that catalyzes the S to P by the following pathway:

The extent of product formation is determined as a function of time for a series of substrate concentrations. As expected, in each case, the amount of product formed increases with time, although eventually a time is reached when there is no net change in the concentration of S or P. The enzyme is still actively converting substrate into product and vice versa, but the reaction equilibrium has been attained. Enzyme kinetics is more easily approached if we can ignore the back reaction. We define V0 as the rate of increase in product with time when [P] is low; that is, at times close to zero (hence, V0). Thus, V0 is determined for each substrate concentration by measuring the rate of product formation at early times before P accumulates. At a fixed concentration of enzyme, V0 is almost linearly proportional to [S] when [S] is small but is nearly independent of [S] when [S] is large. In 1913, Leonor Michaelis and Maud Menten proposed a simple model to account for these kinetic characteristics. The critical feature in their treatment is that a specific ES complex is a necessary intermediate in catalysis. The model proposed, which is the simplest one that accounts for the kinetic properties of many enzymes, is

4

An enzyme E combines with substrate S to form an ES complex, with a rate constant k1. The ES complex has two possible fates. It can dissociate to E and S, with a rate constant k—1, or it can proceed to form product P, with a rate constant k2. Again, we assume that almost none of the product reverts to the initial substrate, a condition that holds in the initial stage of a reaction before the concentration of product is appreciable. We want an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps. Our starting point is that the catalytic rate is equal to the product of the concentration of the ES complex and k2. V0 = k2 [ES]............. (1) Now we need to express [ES] in terms of known quantities. The rates of formation and breakdown of ES are given by: Rate of formation of ES = k1[E] [S] .........................

(2)

Rate of breakdown of ES = (k–1 + k2) [ES] .................

(3)

To simplify matters, we will work under the steady—state assumption. In a steady state, the concentrations of intermediates, in this case [ES], stay the same even if the concentrations of starting materials and products are changing. This occurs when the rates of formation and breakdown of the ES complex are equal. Setting the right—hand sides of equations 2 and 3 equal gives: k1[E] [S] = (k–1 + k2) [ES] ......................... (4) ................... (5)

By rearranging equation 4, we obtain

Equation 5 can be simplified by defining a new constant, Km, called the Michaelis-Menten constant: ..................

(6)

Note that Km has the units of concentration. KM is an important characteristic of interactions and is independent of enzyme and substrate concentrations. Inserting equation 6 into equation 5 yields

......................

Making [ES] the subject of formula yields

enzyme—substrate

(7)

......................

(8)

Now let us examine the numerator of equation 8. The concentration of uncombined substrate [S] is very nearly equal to the total substrate concentration, provided that the concentration of enzyme is much lower than that of substrate. The concentration of uncombined enzyme [E] is equal to the total enzyme concentration [E 0] minus the concentration of the ES complex. [E] = [E0] – [ES] .................... (9) Substituting this expression for [E] in equation 8 gives (

)

...............................

(10)

[ES] KM = [E0] [S] – [ES] [S] .................... (11) Collecting like terms i.e. [ES] [ES] Km + [ES] [S] = [E0] [S] ................... (12) [ES] (Km + [S]) = [E0] [S] ........................... (13) ............................................

(14) 5

but [ES] =

....................... V0 V0

(15)

..................... (16) .....................

According to Briggs–Haelden, Vmax = k2[E0]

(17)

The Michaelis-Menten equation is applicable to most enzymes, and is critically important to understanding enzyme action in biological systems. At least for simple systems, the Michaelis-Menten equation describes the way that the reaction velocity depends on the substrate concentration. The parameters Km and Vmax cannot be determined from a single measurement; instead, they must be determined by measuring velocity at a variety of [S]. The Meaning of Vmax and Km Vmax is the velocity observed when all of the enzyme present is fully saturated with substrate; in other words, when [ES] = [E] total. This is only completely true if the concentration of S is infinitely high (which is obviously impossible in the real world). For the simple reaction we have been discussing, Vmax = k2[E]total. For more complex reactions, Vmax = kcat[E]total, where kcat is the rate constant for the slowest step of the reaction. Note that the Vmax is not an intrinsic property of the enzyme, because it is dependent on the enzyme concentration; the actual intrinsic property is the kcat. The Michaelis-Menten equation, and the definition of Vmax have one major consequence for biological systems: the velocity is directly proportional to the enzyme concentration. This means that one simple method for increasing the velocity is to synthesize more enzyme molecules. Increased enzyme concentrations result in higher velocities at any substrate concentration. In contrast to Vmax, the parameter Km is an intrinsic parameter of the enzyme. When properly performed, measurements of Km yield constant results, regardless of enzyme concentration. Note that if [S] = Km, the Michaelis-Menten equation reduces to v = 1/2 Vmax. Therefore, Km is a measure of the ability of the substrate to interact with the enzyme. Altering Km (either by having multiple isozymes with different Km values, or by having an enzyme with a Km that can be regulated), also allows alteration in the velocity of a reaction. Another related way of looking at Km is to compare it to Kd, the equilibrium dissociation constant for formation of ES complex. The dissociation constant is a measure of affinity, with higher values indicating lower affinity. and If k2 = 0, then Km = Kd. Because, for most enzymes, k2 is relatively small compared to k–1, the Km value is often close to the Kd value. Note that k1 is a second-order rate constant, and has units of M-1•sec-1. The other rate constants are first-order, and have units of sec-1. This means that Km has units of M; in other words, both Km and Kd are expressed in concentration units. Contemplation of the Michaelis-Menten equation suggests that a low Km means a high affinity, and therefore, for a given substrate concentration, a high velocity. In contrast, a high Km means low affinity, and therefore low velocity at any [S]. Uses of Km Km can act as a measure of several useful properties of enzymes. 6

1. Measurement of Km is used to determine the substrate preferences of an enzyme. If more than one endogenous compound can act as a substrate for an enzyme, the substrate with the lowest Km is probably the preferred physiological substrate. 2. Measurement of Km is used to distinguish isozymes. Isozymes often have different affinities for the same substrate. 3. Measurement of Km is used to check for abnormalities in an enzyme: An altered Km reflects some change in the way the enzyme binds the substrate. Km is therefore sensitive to modifications to the enzyme; measurement of Km can often reveal extremely useful information regarding mutations or other changes in the structure of an enzyme. The physiological consequence of Km is illustrated by the sensitivity of some individuals to ethanol. Such persons exhibit facial flushing and rapid heart rate (tachycardia) after ingesting even small amounts of alcohol. In the liver, alcohol dehydrogenase converts ethanol into acetaldehyde. Alcohol dehydrogenase

CH3CH2OH

NAD+

+

CH3CHO +

H+ +

NADH

h concentrations, is

processed to acetate by acetaldehyde dehydrogenase. Acetaldehyde dehydrogenase

CH3CHO

+

NAD+

CH3COO– + NADH

+

2H+

Most people have two forms of the acetaldehyde dehydrogenase, a low Km mitochondrial form and a high Km cytosolic form. In susceptible persons, the mitochondrial enzyme is less active due to the substitution of a single amino acid, and acetaldehyde is processed only by the cytosolic enzyme. Because this enzyme has a high Km, less acetaldehyde is converted into acetate; excess acetaldehyde escapes into the blood and accounts for the physiological effects. Determining Vmax and Km One of the limitations of Michaelis-Menten equation is the difficulty in estimating Vmax value accurately. A cursory examination of a velocity versus [S] plot may suggest that the graph could be used to determine Km and Vmax. In practice, for any type of plot, accurately determining the values from a curve is difficult; for enzyme kinetics, it is especially difficult, because achieving v = Vmax is impossible, and because nothing about the curve states that: ―the Km is right here‖. To avoid this problem, several scientists derived linear forms of the MichaelisMenten equation. Hans Lineweaver and Dean Burk were the first to do one of these derivations, and developed the double reciprocal plot (also called the Lineweaver-Burk plot) in 1934. This plot has its deficiencies, but it is still useful, and all biochemists must be able to understand the information it presents.

Transformations of the Michaelis—Menten Equation: The Double—Reciprocal Plot The ...