Catalysis, binding and enzyme-substrate complementarity

A simple derivation is given that the catalytic term k$_{\text{cat}}$/K$_{\text{S}}\dagger $ is at a maximum when the structure of the enzyme is complementary to the structure of the substrate in the transition state. In addition, at a constant substrate concentration, [S], the maximum reaction rate is obtained when k$_{\text{cat}}$ and K$_{\text{S}}$ are individually high so that K$_{\text{S}}$ is greater than [S]; the overall reaction rate decreases with decreasing k$_{\text{cat}}$ and K$_{\text{S}}$ for K$_{\text{S}}$ less than [S]. Two corollaries of this are that intermediates accumulating after the initial Michaelis complex are undesirable and also enzymes whose function is to optimize reaction rates should have evolved to exhibit K$_{\text{M}}$ values above those of accessible substrate concentrations. This could be achieved by an often 'distortionless' strain which consists either of unfavourable interactions in the enzyme substrate complex which are relieved in the transition state or increasingly favourable interactions in the transition state. A possible special role of the backbone NH groups in this context is discussed. The enzyme need not be complementary to the transition state of the substrate for catalysis to occur.