Energetics of enzyme catalysis. Kinetics of monomeric and oligomeric enzymes, examples. Km, kcat, catalytic efficiency of the enzyme.

Energetics of Enzyme Catalysis

Mechanism of Enzyme Catalysis

Enzymes are biological catalysts that help improve the rate of reaction without being changed in the overall process. They provide an alternative pathway with a lower energy of activation, making it easy to overcome the barrier of energy required for a chemical reaction to proceed. An enzyme catalyzed reaction leads to the formation of a stable intermediate, a structure in which the bonds are not like those in the substrate or the product, stabilizing this transitionary state and increasing its concentration, so that more of the product is formed efficiently. Accelerating the rate with which equilibrium is reached.

Michaelis-Menten Equation

Effect of Substrate Concentration on Enzyme Catalyzed Reactions

Monomeric enzymes-enzymes made up of a single polypeptide chain. These enzymes follow the Michaelis-Menten equation which describes how the rate of reaction varies with substrate concentration.

$v_{i}={V_{\max[}S] \over Km+S}$

Km is the Michaelis constant which reflects the affinity of the enzymes to the substrate.

Reaction model: ${\ce {E+S<=>[{k1}][{k_{-}1}]ES->[k2]E+P}}$

$k_{m}={\frac {k_{-}1+k_{2}}{k_{1}}}$

k-1 and k2 are dissociation constants and k1 is an association constant. The greater the tendency for an ES complex to dissociate the lower the affinity an enzyme has for its substrate, and the vice versa is true. At points A and B increasing the substrate concentration will affect the initial velocity and at C the enzyme concentration becomes a limiting factor and no further increase is [S] will increase the velocity. Fig 8-4 is a typical first order reaction, zero and second order curves are also classified.

Lineweaver plot with different inhibition mechanisms

The Lineweaver-Burk plot (also called a double-reciprocal plot) can be used to calculate Km and Vmax, as well as to determine the mechanism of action of enzyme inhibitors.

Kinetic parameters, catalytic efficiency of the enzymes

Kinetic parameters like Kcat (catalytic constant), unit reciprocal of time, and Km (binding constant) allow to evaluate the kinetic efficiency of certain enzymes. Either parameter alone is not sufficient for comparison, hence the catalytic efficiency ratio Kcat/Km.

Dissociation Constant

The inverse of km is used to estimate the dissociation constant. The value of [S] that gives half the maximum velocity is km, but when $k_{-}1\gg k_{2}$ then k-1 + k2 = k-1 and $[S]={\frac {k_{-}1+k_{2}}{k_{1}}}=K_{m}$ , therefore [S] = k1/k-1 = Kd. This is true under conditions where ES complex are rapid, otherwise in condition where k-1+k2 is not approximately equal to k-1, 1/km will underestimate 1/Kd