Heterogeneous anomalous diffusion of a virus in the cytoplasm of a living cell

Abstract

The infection pathway of a virus in the cytoplasm of a living cell is studied from the viewpoint of diffusion theory, based on a phenomenon observed by singlemolecule imaging. The cytoplasm plays the role of a medium for stochastic motion of a virus contained in an endosome as well as a free virus. It is experimentally known that the exponent of anomalous diffusion fluctuates in localized areas of the cytoplasm. Here, generalizing the fractional kinetic theory, such fluctuations are described in terms of the exponent locally distributed over the cytoplasm and a theoretical proposition is presented for its statistical form. The proposed fluctuations may be examined in an experiment of heterogeneous diffusion in the infection pathway.

Deviation of the statistical fluctuation in heterogeneous anomalous diffusion

“…[11] for a recent review). 3 In recent works [12,13], a kinetic theory has been developed in order to describe the infection pathway of the virus over 4 the cytoplasm by generalizing fractional kinetics [14] modeling anomalous diffusion in a unified way. There, the statistical 5 distribution of the fluctuations of α over the cytoplasm plays a central role.…”

“…Therefore, the result in 10 9 trajectories has been neglected in the discussions in Refs. [12,13]. (Following Refs.…”

“…In Refs. [12,13], it has been shown that it is in fact possible to theoretically derive the distribution in 30 Eq. (2) (which is continuous there) in a consistent manner (see the later discussion), supporting its realization.…”

Two-dimensional motion of Brownian swimmers in linear flows

“…To do so, we first solve (1). By using the definition of the exponential matrix, we are able to integrate (1) and obtain its explicit solution for an initial condition x (0) = x 0 as:…”

“…The motion of viruses [1] and bacteria can be affected by thermal fluctuations. Due to their size, these microorganisms may develop a random path (the so-called Brownian motion) due to collisions among molecules forming a fluid and microorganisms [2][3][4][5][6][7][8].…”