Answer to Question #157095 in Physical Chemistry for Angie

Question

Assume an enzyme system, which contains a substrate, and reacts accordingly
known Michaelis-Menten mechanism. Measurements are performed at a given temperature with
substrate S and S*
(isotopically substituted substrate).
a) Measurements were performed with both substrate S and substrate S*
, separately. Give the ratios of the velocities of the two above cases (u / u*) in very small and
very large concentrations of substrates, respectively, as a function of Km and k2.
(Note: Assume that initially [S] = [S*] and [E] are common.)
b) Then assume that the study of the two substrates is done simultaneously, ie the
competing isotopic phenomena. Return the ratios of the speeds of the two again
cases in the two marginal cases, ie very small and very large concentrations of substrates. (Note: Apply steady-state management to
[ES] and… assume that initially [S] = [S*]. )

Answer 1

Enzyme kinetics is the study of the chemical reactions that are catalysed by enzymes.^[1] 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—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

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 (shown right), enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. An example 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.

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.