Phenomenological models and simple theories

In sharp contrast to the large number of experimental and computer simulation studies of the structure and dynamics of water in hydration layers reported in the literature and to be discussed in later chapters in this book, there have been only a few purely analytical (or model-independent) studies on the dynamics of the hydration layer found around biomolecules, within tissues and cells, and in and around self-assemblies. Some of the early theoretical studies invoked a simple 

This is a dynamic equilibrium. Bound water, however, does not remain bound for a very long time. Also, there is a distribution of the energies of binding of water molecules to the protein surface, so there is a distribution of binding energy that needs to be included in the theoretical description. For simplicity, the model considered below includes only the two state conditions of water molecules, bound and free. A more detailed description, with some amount of derivation, is given in Appendix 6.A of this chapter. 

In the implementation of the model, it is further assumed that as the bound water molecule is immobilized by the protein surface, it cannot rotate or translate. Thus, it must become free to move. The bound to free (and free to bound) transition is described as a chemical reaction. The free water molecules, on the other hand, are assumed to behave as molecules in bulk water, although their rotation and translation diffusion are generally modified due to their interaction with the protein. This surface layer of bound and free water is coupled to the bulk water outside the layer. Although this is a key feature, it is ignored in many other models. In addition, we allow the possibility of the bound water having a preferred orientation due to its interaction with the protein. 

Dynamic exchange between the bound and the fijee water molecules is described by a reaction-diffusion equation, with both rotational and translational motions 

We summarize the main results of the dynamie exchange model, as follows. 

---