Modelling non-Markovian fluctuations in intracellular biomolecular transport

To model non-Markovian fluctuations arising in biomolecular transport, we introduce a stochastic process with memory where Brownian motion is modulated sinusoidally. The probability density function and moments of this non-Markovian process are evaluated analytically as Hida stochastic functional integrals. Comparison of graphs of computed variance vis-á-vis empirical data for protein diffusion coefficients closely match with both exhibiting emergent superdiffusive then subdiffusive behavior for longer proteins.