A The dynamic exchange model

The dynamic exchange model (DEM) of dynamics in protein and the DNA hydration layer was originally proposed in 1997 and was subsequently further developed in several other studies [4]. It is a simple phenomenological model, based on arguments common in chemical kinetics, but serves as a starting point to address the influence of protein or DNA (or lipid, micelles) on the surrounding water molecules. 

It was assumed in the Nandi-Bagchi model [4] that water molecules at the protein surface can be categorized into three different (transient) species (i) those bound to protein polar/charged groups by two HBs, termed IBW2, (ii) those bound to protein groups by one HB, called IBWl, and (iii) lastly those that are not bound but free, termed IFW. It is also assumed that these three kinds of water molecules are in dynamic equilibrium. 

Note that here we have used a different notation as the number of species considered is greater here and the description is more elaborate than what was described in the main text. 

The equilibrivim constant for the above dynamic equilibrium between such different types of water molecules can be written as follows  

Here k 2, if, kpi are the rate constants of the exchange from one water species to another. In this way we can write the other exchange processes in the hydration layer in terms of their equilibrium constants. The equilibrium constants themselves are related to the free-energy difference between the species, by the usual thermodynamic relation, AG = —RT aK. 

---