Limiting Kinetics Of Enzyme Catalyzed Reactions Biology Essay


Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes. In enzyme kinetics the reaction rate is measured and the effects of varying the conditions of the reaction 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 a poison might inhibit the enzyme.

Enzymes are usually protein molecules that manipulate other molecules â€" the 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. 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.

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 rate-determining 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.

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General Principles

The reaction catalyzed by an enzyme uses exactly the same reactants and produces exactly the same products as the unanalyzed reaction. Like other catalysts, enzymes do not alter the position of equilibrium between substrates and products. However, unlike unanalyzed chemical reactions, enzyme-catalyzed reactions display saturation kinetics. 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 catalyze 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 and the reaction rate is determined by the intrinsic turnover rate of the enzyme. The substrate concentration midway between these two limiting cases is denoted by KM.

The two most important kinetic properties of an enzyme are how quickly the enzyme becomes saturated with a particular substrate, and the maximum rate it can achieve. Knowing these properties suggests what an enzyme might do in the cell and can show how the enzyme will respond to changes in these conditions.

What are enzymes?

Enzyme is laboratory procedures that measure the rate of enzyme reactions. Because enzymes are not consumed by the reactions they catalyze, 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. Spectrophotometric assays observe change in the absorbance of light between products and reactants; radiometric assays involve the incorporation or release of radioactivity to measure the amount of product made over time. Spectrophotometric assays are most convenient since they allow the rate of the reaction to be measured continuously. Although radiometric assays require the removal and counting of samples they are usually extremely sensitive and can measure very low levels of enzyme activity. An analogous approach is to use mass spectrometry to monitor the incorporation or release of stable isotopes as substrate is converted into product.

The most sensitive enzyme use lasers focused through a microscope to observe changes in single enzyme molecules as they catalyze their reactions. These measurements either use changes in the fluorescence of cofactors during an enzyme's reaction mechanism, or of fluorescent dyes added onto specific sites of the protein to report movements that occur during catalysis. These studies are providing a new view of the kinetics and dynamics of single enzymes, as opposed to traditional enzyme kinetics, which observes the average behavior of populations of millions of enzyme molecules.

An example progress curve for an enzyme is shown above. The enzyme produces product at an initial rate that is approximately linear for a short period after the start of the reaction. As the reaction proceeds and substrate is consumed, the rate continuously slows. To measure the initial (and maximal) rate, enzyme assays are typically carried out while the reaction has progressed only a few percent towards total completion. The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. However, equipment for rapidly mixing liquids allows fast kinetic measurements on initial rates of less than one second.

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Most enzyme kinetics studies concentrate on this initial, approximately linear part of enzyme reactions. However, it is also possible to measure the complete reaction curve and fit this data to a non-linear rate equation. This way of measuring enzyme reactions is called progress-curve analysis. This approach is useful as an alternative to rapid kinetics when the initial rate is too fast to measure accurately.

Reversible and Irreversible Inhibitions

Sometimes the effect of an inhibitor can be reversed by decreasing the concentration of inhibitor (e.g. by dilution or dialysis). The inhibition is then said to be reversible. If, once inhibition has occurred, there is no reversal of inhibition on decreasing the inhibitor concentration the inhibition is said to be irreversible; irreversible inhibition is an example of enzyme inactivation. The distinction between reversible and irreversible inhibition is not absolute and may be difficult to make if the inhibitor binds very tightly to the enzyme and is released very slowly. Reversible inhibitors that behave in a way that is difficult to distinguish from irreversible inhibition are called tight-binding inhibitors.

Limiting Kinetics of Enzyme-Catalyzed Reactions

At very low concentrations of substrate many enzyme-catalyzed reactions display approximately second-order kinetics, with rate given by the following equation:

v = kA [E]0 [A] . . . . . . . . (8)

in which the symbol kA (or, in general, kR for a reactant R) is the apparent second-order rate constant or specificity constant and [E]0, which may also be written as [E]t or [E]stoich, is the total or stoichiometric concentration of catalytic centers. (This corresponds to the total enzyme concentration only if there is a single catalytic centre per molecule.) The rationale for the subscript 0 is that the total enzyme concentration is normally the concentration at the instant of mixing, i.e. at time zero. Conversely, at very high substrate concentrations the same reactions commonly display approximately first-order kinetics (zero-order with respect to substrate):

v = k0 [E]0 . . . . . . (1)

In which k0, which may also be written as kcat is the apparent first-order rate constant. Although these limiting types of behavior are not universally observed, they are more common than Michaelis-Menten kinetics and provide a basis for classifying inhibitory and other effects independently of the need for Michaelis-Menten kinetics.

The apparent second-order rate constants kA and kB of competing substrates A and B determine the partitioning between competing reactions, regardless of whether the substrate concentrations are very small or not, and it is for this reason that the name specificity constant is proposed for this parameter of enzymic catalysis. The apparent first-order rate constant k0 is a measure of the catalytic potential of the enzyme and is called the catalytic constant.

The quantity k0[E]0 is given the symbol V and the name limiting rate. It is particularly useful when k0 cannot be calculated because the total catalytic-centre concentration is unknown, as in studies of enzymes of unknown purity, sub-unit structure and molecular mass. The symbol Vmax and the names maximum rate and maximum velocity are also in widespread use although under normal circumstances there is no finite substrate concentration at which v = V and hence no maximum in the mathematical sense. The form Vmax is convenient in speech as it avoids the need for a cumbersome distinction between 'capital V' and 'lower case v'. When a true maximum does occur (as insubstrate inhibition) the symbol vmax (not Vmax) and the name maximum rate may be used for the true maximum value of v but care should be taken to avoid confusion with the limiting rate.