Molecular motion in the hydration layer

An important dynamic measure of a hydration layer is provided by its survival correlation time, which is defined in the following way. First, we make a list of all the molecules present in the layer at the initial time. We can now proceed in two ways. First, we can assign decay to the hydration layer whenever any single water molecule leaves or enters the layer. We then average over all the molecules in the layer. Let us denote this fimction by Ssif). This can be defined in the following way 

The above definitions are particularly suitable for investigations in computer simulations. They can be applied also to a fictitious layer in the bulk liquid, except that in the latter case decay can happen by molecules crossing across the region -that is, by penetrating the sphere not allowed in the case of protein. In the case of the protein hydration layer, these survival correlation functions decay slowly for the hydration layer. 

The same method can be used to study density fluctuations by considering all the water molecules in the layer. Let us denote this function by iSnnCO- This is defined by 

This function measures the density fluctuation in the layer and related to the rigidity of the layer. 

The average (over the water molecules in the layer) orientational time correlation function also shows markedly non-exponential decay with a 3-7-times slower time constant than that of the bulk for lysozyme [2]. Simulation studies show that the slow molecules belong to those water molecules that had longer residence times near the lysozyme. Thus, residence time correlates with the rotational correlation time. 

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