Computation of the mean residence time of water in the hydration shells of biomolecules

An algorithm is presented within the context of the calculation of the time‐relaxation behavior of the hydration shells around atomic sites in biomolecules. We report a calculation of the time‐relaxation behavior of the first and second hydration shells of polar, hydrophobic, and charged groups in a protein, crambin. The water mean residence times around protein groups are obtained from averages over configurations sampled during a 325‐ps molecular dynamics simulation of crambin in solution. A convolution arising in the calculation of the mean relaxation time is implemented using a parallel prefix operator. A new characterization is given of the parallel prefix operator as a linear transformation, and this formulation enables us to derive efficient factorization of the convolution as a product of two parallel prefix operations. The parallel prefix operations are implemented in logarithmic time.