Abstract. Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.
The winding probability function for a biopolymer diffusing in a crowded cell is obtained with the drift coefficient f (s) involving Bessel functions of general form f (s) = kJ 2p+1 (νs). The variable s is the length along the chain and ν is a constant which can be used to simulate the frequency of appearance of a certain type of amino acid. Application of a particular case p = 3 to protein chains is carried out for different alpha helical proteins found in the Protein Data Bank (PDB). Analysis of our results leads us to an empirical formula that can be used to conveniently predict k/D and ν, where D is the diffusion coefficient of various α-helical proteins in solvents.
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