A complete, balanced set of enzyme activities is of fundamental importance for maintaining homeostasis.
Numerous factors affect the reaction rate
The kinetic theory—also called the collision theory—of chemical kinetics states that for two molecules to react they must –
(1) approach within bond-forming distance of one another, or “collide”; and
(2) must possess sufficient kinetic energy to overcome the energy barrier for reaching the transition state.
It therefore follows that anything that increases the frequency or energy of collision between substrates will increase the rate of the reaction in which they participate.
Raising the temperature increases the kinetic energy of molecules. Increasing the kinetic energy of molecules also increases their motion and therefore the frequency with which they collide. This combination of more frequent and more highly energetic and productive collisions increases the reaction rate. A ten degree Centigrade rise in temperature will increase the activity of most enzymes by 50 to 100%. The Q10, or temperature coefficient, is the factor by which the rate of a biologic process increases for a 10 °C increase in temperature. For the temperatures over which enzymes are stable, the rates of most biologic processes typically double for a 10 °C rise in temperature (Q10 = 2).
Figure-1- showing the effect of temperature on enzyme catalyzed reaction.
The reaction rate increases with temperature to a maximum level, then abruptly declines with further increase of temperature (Figure-1). Because most animal enzymes rapidly become denatured at temperatures above 40oC, most enzyme determinations are carried out somewhat below that temperature. Some enzymes lose their activity when frozen.The optimal temperatures of the enzymes in higher organisms rarely exceed 50 °C, while enzymes from thermophilic bacteria found in hot springs, for instance, may still be active at 100 °C.
Changes in the rates of enzyme-catalyzed reactions that accompany a rise or fall in body temperature constitute a prominent survival feature for “cold-blooded” life forms such as lizards or fish, whose body temperatures are dictated by the external environment. However, for mammals and other homoeothermic organisms, changes in enzyme reaction rates with temperature assume physiologic importance only in circumstances such as fever or hypothermia.
2) Hydrogen Ion Concentration
The rate of almost all enzyme-catalyzed reactions exhibits a significant dependence on hydrogen ion concentration. Most intracellular enzymes exhibit optimal activity at pH values between 5 and 9 (Figure-2).The pH optimum—i. e., the pH value at which enzyme activity is at its maximum—is often close to the pH value of the cells (i. e., pH 7). However, there are also exceptions to this. For example, the proteinase pepsin , which is active in the acidic gastric lumen, has a pH optimum of 2, while other enzymes (at least in the test tube) are at their most active at pH values higher than 9 (Figure-3)
When the activity is plotted against pH, a bell-shaped curve is usually obtained (Figure-2)
Figure-2- Showing the effect of pH on enzyme catalyzed reaction
Figure-3- Except for Pepsin, acid phosphatase and alkaline phosphatase, most enzyme have optimum pH between 5 to 9
The relationship of activity to hydrogen ion concentration reflects the balance between enzyme denaturation at high or low pH and effects on the charged state of the enzyme, the substrates, or both. For enzymes whose mechanism involves acid-base catalysis, the residues involved must be in the appropriate state of protonation for the reaction to proceed. The binding and recognition of substrate molecules with dissociable groups also typically involves the formation of salt bridges with the enzyme. The most common charged groups are the negative carboxylate groups and the positively charged groups of protonated amines. Gain or loss of critical charged groups thus will adversely affect substrate binding and thus will retard or abolish catalysis.
3) Substrate concentration
The frequency with which molecules collide is directly proportionate to their concentrations. For two different molecules A and B, the frequency with which they collide will double if the concentration of either A or B is doubled. If the concentrations of both A and B are doubled, the probability of collision will increase fourfold.
For a typical enzyme, as substrate concentration is increased; vi increases until it reaches a maximum value Vmax (Figure -4)When further increases in substrate concentration do not further increase Vmax the enzyme is said to be “saturated” with substrate. If a curve is plotted,the shape of the curve that relates activity to substrate concentration (Figure-4) is hyperbolic.
At any given instant, only substrate molecules that are combined with the enzyme as an ES complex can be transformed into product. Second, the equilibrium constant for the formation of the enzyme-substrate complex is not infinitely large. Therefore, even when the substrate is present in excess, (points A and B of Figure), only a fraction of the enzyme may be present as an ES complex. At points A or B, increasing or decreasing [S] therefore will increase or decrease the number of ES complexes with a corresponding change in vi. The rate of reaction is substrate dependent (First order reaction)- Figure-4
At point C (Figure), essentially all the enzyme is present as the ES complex. Since no free enzyme remains available for forming ES, further increases in [S] cannot increase the rate of the reaction . Reaction rate therefore becomes independent of substrate concentration (Zero order reaction).
Figure-4- Showing the relationship of reaction rate with substrate concentration
4) Effect of Enzyme concentration
In order to study the effect of increasing the enzyme concentration upon the reaction rate, the substrate must be present in an excess amount; i.e., the reaction must be independent of the substrate concentration. Any change in the amount of product formed over a specified period of time will be dependent upon the level of enzyme present. Graphically this can be represented as:
Figure-5- Showing the effect of increasing or decreasing enzyme concentration on reaction rate
These reactions are said to be “zero order” because the rates are independent of substrate concentration, and are equal to some constant k. The formation of product proceeds at a rate which is linear with time. The addition of more substrate does not serve to increase the rate. In zero order kinetics, allowing the assay to run for double time results in double the amount of product (Figure-5)
The amount of enzyme present in a reaction is measured by the activity it catalyzes. The relationship between activity and concentration is affected by many factors such as temperature, pH, etc. An enzyme assay must be designed so that the observed activity is proportional to the amount of enzyme present in order that the enzyme concentration is the only limiting factor. It is satisfied only when the reaction is zero order.
Enzyme activity is generally greatest when substrate concentration is unlimiting.
5) Effect of product concentration
The enzyme activity declines when the products start accumulating. This is called product or feed back inhibition. Under certain conditions reverse reaction may be favored forming back the substrate.
6) Effect of activators and Coenzymes
The activity of certain enzymes is greatly dependent on metal ion activators and coenzymes. Vitamins act as coenzymes in a variety of reactions.
7) Effect of modulators and Inhibitors
The enzyme activity is reduced in the presence of an inhibitor and on the other hand the enzyme activity may be increased in the presence of a positive modifier.
In typical enzyme-catalyzed reactions, reactant and product concentrations are usually hundreds or thousands of times greater than the enzyme concentration. Consequently, each enzyme molecule catalyzes the conversion to product of many reactant molecules. In biochemical reactions, reactants are commonly known as substrates. The catalytic event that converts substrate to product involves the formation of a transition state, and it occurs most easily at a specific binding site on the enzyme. This site, called the catalytic site of the enzyme, has been evolutionarily structured to provide specific, high-affinity binding of substrate(s) and to provide an environment that favors the catalytic events. The complex that forms, when substrate(s) and enzyme combine, is called the enzyme substrate (ES) complex. Reaction products arise when the ES complex breaks down releasing free enzyme.
Between the binding of substrate to enzyme, and the reappearance of free enzyme and product, a series of complex events must take place. At a minimum an ES complex must be formed; this complex must pass to the transition state (ES*); and the transition state complex must advance to an enzyme product complex (EP). The latter is finally competent to dissociate to product and free enzyme. The series of events can be shown thus:
E + S <——> ES <——> ES* <——> EP <——> E + P
The kinetics of simple reactions like that above were first characterized by biochemists Michaelis and Menten. The concepts underlying their analysis of enzyme kinetics continue to provide the cornerstone for understanding metabolism today, and for the development and clinical use of drugs aimed at selectively altering rate constants and interfering with the progress of disease states.
The Michaelis-Menten equation is a quantitative description of the relationship among the rate of an enzyme- catalyzed reaction [v1], the concentration of substrate [S] and two constants, Vmax and km (which are set by the particular equation). The symbols used in the Michaelis-Menten equation refer to the reaction rate [v1], maximum reaction rate (V max), substrate concentration [S] and the Michaelis-Menten constant (km).
The Michaelis-Menten equation can be used to demonstrate that at the substrate concentration that produces exactly half of the maximum reaction rate, i.e. ½ V max the substrate concentration is numerically equal to Km. This fact provides a simple yet powerful bioanalytical tool that has been used to characterize both normal and altered enzymes, such as those that produce the symptoms of genetic diseases.
Thus, the Michaelis constant, km is the substrate concentration at which V1 is half the maximal velocity (Vmax /2) attainable at a particular concentration of enzyme. km thus has the dimensions of substrate concentration.
The dependence of initial reaction velocity on [S] and Km may be illustrated by evaluating the Michaelis-Menten equation under three conditions.
(1) When [S] is much less than km, the term km + [S] is essentially equal tokm. Replacing Km + [S] with Km reduces equation to
Since V max and km are both constants, their ratio is a constant (k). In other words, when [S] is considerably below km, V max is proportionate to k[S]. The initial reaction velocity therefore is directly proportionate to [S].
(2) When [S] is much greater than km, the term km + [S] is essentially equal to [S]. Replacing km + [S] with [S] reduces equation to
Thus, when [S] greatly exceeds km, the reaction velocity is maximal (V max) and unaffected by further increases in substrate concentration.
(3) When [S] = km
Equation states that when [S] equals km, the initial velocity is half-maximal. Equation also reveals that km is—and may be determined experimentally from—the substrate concentration at which the initial velocity is half-maximal.
Figure-6-Plot of substrate concentration versus reaction velocity
The key features of the plot are marked by points A, B and C. At high substrate concentrations the rate represented by point C the rate of the reaction is almost equal to V max and the difference in rate at nearby concentrations of substrate is almost negligible. If the Michaelis-Menten plot is extrapolated to infinitely high substrate concentrations, the extrapolated rate is equal to V max When the reaction rate becomes independent of substrate concentration, or nearly so, the rate is said to be zero order. (Note that the reaction is zero order only with respect to this substrate. If the reaction has two substrates, it may or may not be zero order with respect to the second substrate). The very small differences in reaction velocity at substrate concentrations around point C (near V max) reflect the fact that at these concentrations almost all of the enzyme molecules are bound to substrate and the rate is virtually independent of substrate, hence zero order. At lower substrate concentrations, such as at points A and B, the lower reaction velocities indicate that at any moment only a portion of the enzyme molecules are bound to the substrate. In fact, at the substrate concentration denoted by point B, exactly half the enzyme molecules are in an ES complex at any instant and the rate is exactly one half of V max At substrate concentrations near point A the rate appears to be directly proportional to substrate concentration, and the reaction rate is said to be first order.
A Linear Form of the Michaelis-Menten Equation Is Used to determine km & V max
The direct measurement of the numeric value of V max and therefore the calculation of km often requires impractically high concentrations of substrate to achieve saturating conditions. A linear form of the Michaelis-Menten equation circumvents this difficulty and permits V max and km to be extrapolated from initial velocity data obtained at less than saturating concentrations of substrate. Starting with equation,
Equation is the equation for a straight line, y = ax + b, where y = 1/vi and x = 1/[S]. A plot of 1/vi as y as a function of 1/[S] as x therefore gives a straight line whose y intercept is 1/ V max and whose slope is km / V max. Such a plot is called a double reciprocal or Lineweaver-Burk plot (Figure-7). Setting the y term of equation equal to zero and solving for x reveals that the x intercept is -1/Km.
Figure- 7-showing A Lineweaver-Burk Plot Plots of 1/v versus 1/[S] yield straight lines having a slope of Km/Vmax and an intercept on the ordinate at 1/Vmax.
An alternative linear transformation of the Michaelis-Menten equation is the Eadie-Hofstee transformation: and when v/[S] is plotted on the y-axis versus v on the x-axis, the result is a linear plot with a slope of –1/Km and the value Vmax/Km the intercept on the y-axis and as the Vmax intercept on the x-axis.
Both the Lineweaver-Burk and Eadie-Hofstee transformation of the Michaelis-Menten equation are useful in the analysis of enzyme inhibition.
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