Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins

TL;DR

This paper introduces a fractional Gaussian noise-based model within the generalized Langevin equation to describe subdiffusion in proteins, aligning well with experimental single-molecule data and advancing nanoscale biophysics understanding.

Contribution

It presents a novel stochastic model incorporating fractional Gaussian noise for subdiffusion, with detailed spectral analysis and microscopic derivation, enhancing theoretical and experimental insights.

Findings

Model accurately explains single-molecule fluorescence data.

Spectral analysis of the stochastic equations provided.

Microscopic derivation supports the model's physical basis.

Abstract

Advances in nanotechnology have allowed scientists to study biological processes on an unprecedented nanoscale molecule-by-molecule basis, opening the door to addressing many important biological problems. A phenomenon observed in recent nanoscale single-molecule biophysics experiments is subdiffusion, which largely departs from the classical Brownian diffusion theory. In this paper, by incorporating fractional Gaussian noise into the generalized Langevin equation, we formulate a model to describe subdiffusion. We conduct a detailed analysis of the model, including (i) a spectral analysis of the stochastic integro-differential equations introduced in the model and (ii) a microscopic derivation of the model from a system of interacting particles. In addition to its analytical tractability and clear physical underpinning, the model is capable of explaining data collected in fluorescence studies on single protein molecules. Excellent agreement between the model prediction and the single-molecule experimental data is seen.