(73) Modeling Protein Diffusion with Random Walk

     Diffusion is an important process in physics that manifests appear in diverse phenomena such as Brownian motion and the motion of electrons in solids. It is also an important kinetic process in biophysics, since... [ view full abstract ]

     Diffusion is an important process in physics that manifests appear in diverse phenomena such as Brownian motion and the motion of electrons in solids. It is also an important kinetic process in biophysics, since that is how cells take in nutrients and operate. Protein diffusion is unlike other types (ions, carbon dioxide, etc) because proteins are large structures that cannot diffuse freely through the cell membrane, which is the biggest barrier for protein diffusion between cells. The presence of the cell membrane causes protein diffusion to be sub-diffusive, which is slower than free diffusion. In this project, we used a continuous-time random-walk numerical simulation to compare free diffusion with hop diffusion, since the latter includes restrictive barriers in the random walk and is one of the possible conditions for protein diffusion in realistic situations. Analysis of the simulated data verified that the mean distance squared of diffusion is proportional to tⁿ, where n = 1 for free diffusion and n < 1 for protein sub-diffusion over a limited time scale. Our results confirmed Fick's law as well as the sub-diffusive nature of protein diffusion.