Practically all biological systems rely on the ability of bio-molecules to specifically recognize each other. Examples are antibodies targeting antigens, regulatory proteins binding DNA and enzymes catalyzing their substrates. These and other molecular recognizers must locate and preferentially interact with their specific targets among a vast variety of molecules that are often structurally similar. This task is further complicated by the inherent noise in the biochemical environment, whose magnitude is comparable with that of the non-covalent binding interactions 
It was realized early that recognizing molecules should be complementary in shape, akin of matching lock and key (). Later, however, it was found that the native forms of many recognizers do not match exactly the shape of their targets. There is a growing body of evidence for conformational changes upon binding between the native and the bound states of many biomolecules, for example in enzyme-substrate 
, antibody-antigen 
and other protein-protein complexes 
. Binding of protein to DNA is also associated with conformational changes, which may affect the fidelity of DNA polymerase 
, and similar effects were observed in the binding of RNA by proteins 
. The induced deformation typically involves displacements of binding sites in the range of tens of angstroms 
. To account for these conformational changes upon binding, the induced fit scheme was suggested. In this scheme, the participating molecules deform to fit each other before they bind into a complex (). Another model, the pre-equilibrium hypothesis, assumes that the target native state interconverts within an ensemble of conformations and the ligand selectively binds to one of them ().
Models of molecular recognition.
The abundance of conformational changes raises the question of whether they occur due to biochemical constraints or whether they are perhaps the outcome of an evolutionary optimization of recognition processes. In the present work, we discuss the latter possibility by evaluating the effects of conformation and flexibility on recognition. To estimate the quality of recognition we use the common measure of specificity
, that is the ability to discriminate between competing targets. Whether conformational changes and especially the induced-fit mechanism can provide or enhance specificity has been a matter of debate 
. Various detailed kinetic schemes have been suggested and their potential effects on specificity have been discussed – however without direct relation to concrete conformational mechanisms. Here we examine these underlying effects of flexibility and conformational changes that may govern the rate constants and thus determine specificity. Our approach tries to elucidate some of these basic effects by introducing a simple statistical-mechanics model and applying it to a generalized kinetic scheme of recognition in the presence of noise. As an outcome, the flexibility of the ligand and its relative mismatch with respect to the target which optimize specificity can be evaluated.
In the binding schemes described above (), the ligand is a “switch” that interconverts between a native, inactive form and an active form that fits the target. However, in a noisy biochemical environment, one may expect both the ligand and the targets to interconvert within an ensemble of many possible conformations. Such an ensemble may be the outcome, for example, of thermally induced distortions. Consider for example a scenario in which an elastic ligand is interacting with two rigid competing targets (). All the conformations of the ligand may interact with the targets and as a result a variety of complexes, differing by the structures of the bound ligand, is formed (). Among the complexes formed, some are composed of perfectly matched ligand and target. In those complexes, specific binding energy due to the alignment of binding sites is gained. However, a complex may be formed even if the ligand does not perfectly match the target, due to non-specific binding energy. For example, the lac
repressor can bind non-specifically to DNA regardless of its sequence 
. All the complexes, the matched and the mismatched, may retain some functionality. The efficiency of the recognition process depends on the elasticity of the ligand and on the structural mismatch between the ligand native state and the main target.
Competition between two rigid targets.
The quality of recognition is measured by its specificity, which is defined as follows. Consider a ligand a
interacting with a correct target A
and an incorrect competitor B
are the dissociation constants, and νA
are the turnover numbers. Specificity is naturally defined as the ratio of the correct production rate, RA
, and the incorrect production rate, RB
, where [ ] denotes concentration. Typically, the chemical step is the rate-limiting one and the complex formation reaction is therefore in quasi-equilibrium, [aA
. Thus the specificity ξ takes the form:
If however the ligand and the targets interconvert within ensembles of many possible conformations (–), the specificity includes potential contributions from all possible complexes,
denote the conformations of the ligand and the target, respectively. Kij
is the dissociation constant of the complex formed from the i
-th ligand conformation and j
-th target conformation and vij
is the turnover number of this complex.
General molecular recognition scheme.
Equation 3 and its generalization, equation 4, reflect the dependence of the specificity on both the concentrations of complexes, determined by the dissociation constants K, and on their functionality, determined by the turnover numbers v. These parameters, K and v, depend on the flexibility and structure of the participant molecules. Evaluating this dependence allows us to estimate the optimal flexibility and structure similarity between the ligand and the main target.