  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.
