Parameters Affecting Enzymatic Reactions, Dissociation Constants, Michaelis Constant, Catalytic Efficiency, Hydroxylases

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Parameters Affecting Enzymatic Reactions
The rate of an enzymatic reaction depends on several factors including the reaction itself, the nature of enzyme involved, and more importantly the concentrations of substrate (S), product (P) and enzyme (E). For instance, if the concentration of the substrate is slowly increased, keeping other things constant, the rate of reaction increases till it reaches a maximum, where further increase in substrate concentration does not lead to any further increase in the rate of reaction. This maximum rate of reaction under a set of constant conditions is described as V_x. Besides substrate concentration, several other parameters have been suggested to describe fully an enzymatic reaction.

Different Parameters, Which Enzymatic Reactions

1. K_cat : the higher the better	2. K_cat/K_M.K_M (K_s) Low K_M causes substrate inhibition
3. low K_p causes products inhibition	4. 1 Umg^-1 ~ (K_cat²s^-1)
5. 1 mmol product per day

These parameters include the following: (i) dissociation constants of substrate S and product P (K_s and K_p); (ii) specific activity or the turnover number, which is quantified by k_cat and is obtained, when V_x is divided by. enzyme concentration [E]; this represents the number of substrate molecules processed per enzyme molecule per second and its value is generally 1000, although it can be much greater; (iii) Michaelis constant (K_m), which represents the substrate concentration, at which the rate of reaction is half its maximum rate V_x described above; and (iv) specificity or catalytic efficiency of enzyme, determined by maximum specificity constant (k_cat/K_m).

Enzyme Kinetics Showing Relationship Between the Rate of Enzyme Reaction and the Substrate Concentration, Km is the Substrate Concentration at which the Reaction Rate is Half Maximal

Among the above parameters, the turnover number {k_cat (s^-1)}, which describes the decomposition of enzyme-substrate complex (E-S) is a first order rate constant, and the catalytic efficiency {k_cat/K_m (M^-1s^-1)}' which describes the rate of product formation is a second order rate constant. The values of catalytic efficiencies of enzymes lie in the range of 10⁵ M^-1 s^-1 (e.g. aspartate aminotransferase) to 10⁹ M^-1 s^-1 (e.g. fumarase) and cluster around a mean value of ~10⁷ s^-1, which is common for many hydroxylases (see later for types of enzymes). The relationship of these two rate constants and that of a rate constant for the uncatalysed reaction (k_non) with the rate of product formation is shown in the following three sets of equations:

(1) ES E + S
d[P]/dt = k_cat [ES]

(2) E + S E + P
d[P]/dt = k_cat/k_m [E] [S]

(3) E P
d[P]/dt = k_non [S]

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By comparing the rate constant of an uncatalysed reaction (k_non) with that of catalysed reaction (k_cat) one can calculate the increase in reaction rate that an enzyme produces; this is described as rate enhancement and is calculated as k_cat/k_non. Another parameter termed as catalytic proficiency is, calculated as the ratio (k_cat/K_m)/k_non.

Ideally, for the economic' production at the industrial scale, the values of dissociation constants, K_s and K_p should be low, i.e., the enzyme should be subject to minimum substrate and product inhibition. In constrast, the values of turnover number (k_cat) and catalytic efficiency (k_cat/K_m) should be high to allow high rate of product formation. Specificity of an enzyme for a substrate is also important, because for general-purpose catalysis, enzymes with broader specificity would prove useful, although enzymes with narrow specificity may be more efficient.

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