2019/02/25 by K. L. Sebastian, Sebastian, K L
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1902.09082
openalex publication_date 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The usual Kramers theory of reaction rates in a condensed medium predict the rate to have an η-1 dependence, η being the viscosity of the medium. However, experiments on ligand binding to proteins performed long ago, showed the rate to have η-ν dependence, with ν in the range 0.4-0.8. Zwanzig \it (Journal of Chemical Physics 97, 3587 (1992)) suggested a model, in which the ligand has to pass through a fluctuating opening to bind. Thus fluctuating gate model predicted the rate to be proportional to η-1/2. Experiments performed by Xie et. al. (\it Physical Review Letters 93, 1 (2004)) showed that the distance between two groups in a protein undergoes subdiffusion. Hence in this paper, we suggest and solve a generalisation of the Zwanzig model, viz., passage through a gate that undergoes subdiffusion. Our solution shows that the rate is proportional to η-ν with ν in the range 0.5-1, and hence the model can explain the experimental observations.