  A growing number of experimental evidence shows that it is general for a
ligand binding protein to have a potential for allosteric regulation and for
further evolution. In addition, such proteins generically change their
conformation upon binding. O. Rivoire has recently proposed an evolutionary
scenario that explains these properties as a generic byproduct of selection for
exquisite discrimination between very similar ligands. The initial claim was
supported by two classes of basic examples: continuous protein models with
small numbers of degrees of freedom, on which the development of a
conformational switch was established, and a 2-dimensional spin glass model
supporting the rest of the statement. This work aimed to clarify the
implication of the exquisite discrimination for smooth models with large number
of degrees of freedom, the situation closer to real biological systems. With
the help of differential geometry, jet-space analysis, and transversality
theorems, it is shown that the claim holds true for any generic flexible system
that can be described in terms of smooth manifolds. The result suggests that,
indeed, evolutionary solutions to the exquisite discrimination problem, if
exist, are located near a codimension-1 subspace of the appropriate genotypical
space. This constraint, in turn, gives rise to a potential for the allosteric
regulation of the discrimination via generic conformational changes upon
binding.
