The Stochastic Nature Exhibited by Proteins inside the Cell Membrane during Cell-to-Cell Communication

SIMPLE SUMMARY: This paper presents a brief mathematical study in which the communication between cells is modelled. Understanding cell communication mathematically is useful across many medical fields from drug delivery to understanding how the body responds to infection. In this paper, the random motions of proteins are explored using stochastic differential equations. The study demonstrates the Brownian motion exhibited by proteins during cell communication. ABSTRACT: The movement of proteins through the cell membrane is essential for cell-to-cell communication, which is a process that allows the body’s immune system to identify any foreign cells, such as cells from another organism and pathogens; this movement is also essential for protein-to-protein interactions and protein-to-membrane interactions which play a significant role in drug discovery. This paper presents the stochastic nature exhibited by proteins during cell-to-cell communication. We study the movement of proteins through the cell membrane under the influence of an external force F and drag force with drag coefficient [Formula: see text]. We derive the stochastic diffusion equation, which governs the motion of the proteins; we start by describing the random motion exhibited by the proteins in terms of probability using a one-dimensional lattice model; this occurs when proteins move inside the cell membrane and bind with other proteins inside the cell membrane. We then introduce an external force and a drag coefficient into a Brownian motion description of the movement of proteins when they move outside the cell membrane and bind with proteins from other cells; this phenomenon occurs during cell communication when one cell releases messenger proteins to relay information to other cells. This, in turn, allows us to obtain the stochastic diffusion equation by applying [Formula: see text] ’s Lemma.