Specificity constant

In the field of biochemistry, the specificity constant ( $k_{cat}/K_{M}$ ), sometimes referred to as kinetic efficiency, is a measure of how efficiently an enzyme converts substrates into products. A ranking of specificity constants can also be used as a measure of the preference of an enzyme for different substrates (i.e., substrate specificity). The higher the specificity constant, the more the enzyme "prefers" that substrate.^[1]

The Michaelis constant ( $K_{M}$ ) is equal to the substrate concentration at which the enzyme converts substrates into products at half its maximal rate and hence is related to the affinity of the substrate for the enzyme. The catalytic constant ( $k_{cat}$ ) is the rate of product formation when the enzyme is saturated with substrate and therefore reflects the maximum rate of product formation. Since the maximum rate of product formation depends on how well the enzyme and substrate bind, its upper limit is the rate of enzyme and substrate binding ( $k_{f}$ ). A kinetically perfect enzyme can bind its substrate at just below the rate of diffusion. By extension the upper limit of the catalytic constant is a little below the rate of diffusion (~10⁸M⁻¹s⁻¹). A small $K_{M}$ reflects a tighter/better interaction between the substrate and enzyme. Therefore a large specificity constant reflects better enzyme efficiency.

E+S\,{\overset {k_{f}}{\underset {k_{r}}{\rightleftharpoons }}}\,ES\,{\overset {k_{cat}}{\longrightarrow }}\,E+P

In Michaelis-Menten kinetics the steady-state assumption is that the rate of [ES] formation equals the rate of [ES] destruction ( $k_{f}[E][S]=\left(k_{r}+k_{cat}\right)[ES]$ ). This assumption is made to make it easier to write a dissociation constant: ${\frac {[E][S]}{[ES]}}={\frac {k_{r}+k_{cat}}{k_{f}}}=K_{M}$ . The maximum velocity ( $V_{max}$ ) of an enzyme is the maximum product formation times the total concentration of enzyme available ( $V_{max}=k_{cat}[E_{T}]$ ). The velocity of a reaction ( $v$ ) is the maximum velocity times the fraction of enzymes that are saturated (that are actually binding and converting substrate). The fractional saturation is equal to : ${\frac {[S]}{K_{M}+[S]}}$ . Consequently $v=V_{max}{\frac {[S]}{K_{M}+[S]}}$ . We can now derive $v=k_{cat}[E_{T}]{\frac {[S]}{K_{M}+[S]}}$ . From this equation one can write the most useful form of the Michaelis-Menten equation: ${\frac {v}{[E_{T}]}}=k_{cat}{\frac {[S]}{K_{M}+[S]}}$

References

^ Voet, D.; Voet, J.G.; Pratt, C.W. (2008). Principles of Biochemistry (3. ed. ed.). Wiley. pp. 366–372. ISBN 978-0470233962. {{cite book}}: |edition= has extra text (help)

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[voet08-1] Voet, D.; Voet, J.G.; Pratt, C.W. (2008). Principles of Biochemistry (3. ed. ed.). Wiley. pp. 366–372. ISBN 978-0470233962. {{cite book}}: |edition= has extra text (help)

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References