Conceptual Models for Binding

Molecular binding interactions are fundamental properties of all matter. Though this statement is trivial at first sight and does not deserve special mention, it sets a bold limit to all attempts in the design of specific interactions towards the construction of selective molecular host compounds. The most promising approach towards this goal relies on idealized models that reflect just one prominent aspect of the entire interaction, making it illustrative and as such easily comprehensible. However, owing to the persuasive power of pictorial arguments, the premises of the models may be overlooked and their applicability is then stretched too far. Notorious in this respect is the famous metaphor of the lock-and-key fit in host-guest binding, coined by Emil Fischer more than a century ago to cite geometrical complementarity as the origin for substrate discrimination between various sugars and glycosidases. Beyond question, geometrical complementarity is an important feature to ascertain the mutual stickiness of specific binding partners, because it maximizes the help from the attractive van der Waals interactions which, in combination with the repulsive interactions of orbital overlap (Pauli principle), serve to sort out and reject less well-fitting competitors. The requirement of geometrical fit emerges from the steep distance dependence of the interacting surfaces which, in the case of the van der Waals attraction, follows an inverse sixth power law (van der Waals attractive interaction ~r ⁶; r = distance), whilst the repulsive interaction stemming from the Pauli constraint adheres to an even more extreme inverse 12th power law (repulsive energy ~r ¹²). The overlay of both distance dependencies gives an energetic well featuring an optimal separation, the van der Waals contact distance. In conjunction with the accumulative and monotonously attractive character of the pairwise interaction between distinct positions in host and guest, these features constitute the driving urge to form extended interface areas of minimal separation in order to maximize binding.

In quantitative terms the complementary fit model of host and guest binding refers to the energetic difference at constant temperature and pressure ∆ H_assoc (also called the exothermicity) of just two states: one mole each of host and guest molecules totally separated as opposed to the associated complex of the same components in its most favourable configuration. The model has been expanded in various directions to include other types of interaction, notably the participation of functional groups which supplemented the model with Coulomb-, dipolar/multipolar and hydrogen bonding terms, as well as contributions from the intrinsic distortions, bending and deformations affecting the distributions of electron density within the individual host and guest molecules. Though considerable improvements on the original idea were implemented over the years, and even gained in finesse by the inclusion of scaling factors to account for environmental influences (e.g. distance-dependent dielectric permittivity), the fundamental concept of enthalpy-based two-partner two-state binding remained unchanged and still dominates most attempts aimed at understanding molecular host-guest relations today.

In the description and explanation of real experimentally testable situations, the lock-and-key model claims a success story; however, in many cases - and among them are the majority of the more interesting biological examples -it fails to explain host-guest binding affinity and selectivity with reasonably ambitious satisfaction. For instance, anion binding in water very frequently shows endothermic rather than exothermic enthalpies of association, an observation that is incompatible with the naive complementarity model.

The reasons for the mediocre predictive power of simple models are fundamental and obvious: above all they suffer from the blunt comparison of binding enthalpies that emerge from the model treatment with free energies of binding ∆G_assoc that derive from the readily accessible affinities by straightforward recalculation (∆G_{assoc =} - RT 1n K_assoc). Such relations are equivalent to the neglect of the entropic contributions to binding that is justified only in the rare case if the interest in associations is restricted to the temperature regime near zero Kelvin (furnishing T∆S~O) or the entropy of association (as T∆S_assoc) is very small to render the enthalpy the dominating component. In reality this situation is considerably less frequent than commonly assumed, and in addition also depends dramatically on the polarity of the environment. Entropic factors tend to be of greater importance in intermolecular binding in the protic solvents typically required to generate anionic species as free entities in solution. For the calculation of anion binding in polar solvents around ambient temperature it is mandatory to employ free energies ∆G_assoc, although they are less accessible than plain enthalpies and eventually require the more sophisticated and lengthy calculation methods of molecular dynamics.

A second cause for the weakness of the complementarity model arises from the misconception that the binding process of host and guest is essentially the same whether it occurs in vacuum or in a condensed phase. For the latter this idea leads to the frequently voiced opinion that there is no physical contact between the host-guest partners in solution (they stay separated) if the binding free energy is zero. It follows from simple inspection of the relation ∆G°=-RT 1n K_assoc that at ∆G° =0 the association constant K_assoc equals 1, i.e. for non-zero concentrations of host and guest there is also a finite concentration of the 1:1 associate complex present. Is this binding? The case has been investigated in the context of protein denaturation by low molecular weight additives and has recently been lucidly unfolded by Schellman and Timasheff. The interaction between host and guest molecules, to the extent that the occupation of a binding site on the host matches the concentration of the guest in bulk solution, corresponds to the case of random collision and invokes the replacement of solvent from this site. Unlike the binding scenario in vacuo, the host-guest interaction in liquids is a genuine exchange process with solvent molecules that may favour or disfavour the uptake of the guest. Thus, the measurable free energy of binding ∆G°assoc is negative, and only ordinary binding isotherms are found if the interaction of the site with the incoming guest is more exergonic than the interaction of the same substructure with solvent (∆G°solv; ∆G°_assoc=∆G°guest_t-∆G° solv). An exergonic interaction of host and guest in the absolute sense is insufficient to bring about binding.