Computational Model for Membrane Transporters. Potential Implications for Cancer

Abstract

To explain the increased transport of nutrients and metabolites and to control the movement of drug molecules through the transporters to the cancer cells, it is important to understand the exact mechanism of their structure and activity, as well as their biological and physical characteristics. We propose a computational model that reproduces the functionality of membrane transporters by quantifying the flow of substrates through the cell membrane. The model identifies the force induced by conformational changes of the transporter due to hydrolysis of ATP, in ABC transporters, or by an electrochemical gradient of ions, in secondary transporters. The transport rate is computed by averaging the velocity generated by the force along the paths followed by the substrates. The results obtained are in accordance with the experiments. The model provides an overall framework for analyzing the membrane transport proteins that regulate the flows of ions, nutrients and other molecules across the cell membranes, and their activities.

How stickiness can speed up diffusion in confined systems

“…It is valid for a large range of values of ϕ, as shown in Fig. 2 where it is compared to numerical solution of the full transport equations (12,13). The theory also agrees with the Monte Carlo simulations of Ref.…”

“…Classic examples include Taylor dispersion in hydrodynamic flows [10], and the decrease of dispersion due to the energy barriers created by time independent potentials [11]. In a number of systems, such as porous media [12], zeolites, and biological channels [13], the motion of tracer particles is hindered by hard (technically speaking reflecting) boundaries or obstacles. The effective trapping of the tracer in this case is of entropic origin but it again leads to a reduction of late time diffusivity [14][15][16][17][18].…”

“…Squares: data obtained by numerical integration of Eqs. (12), (13). Triangles: results of stochastic simulations of the stochastic process r(t) associated to the Fokker-Planck equations (1,2).…”

Enhancing particle transport in deformable micro-channels

“…[32][33][34][35][36] In many cases, however, channels can change shape due to variations in the pressure of the medium in which they are immersed, forces exerted by particles passing through them, or the existence of external sources of energy and electrochemical gradients, as in the case of ion channels and transporters where the energy supplied comes from ATP hydrolysis. 19,37,38 Transport in flickering pores may give rise to the appearance of resonances. 39,40 It has also been shown that channel deformations can cause resonances and anti-resonances that may have an impact on transport properties.…”

“…39,40 It has also been shown that channel deformations can cause resonances and anti-resonances that may have an impact on transport properties. 37,[41][42][43] The question, therefore, arises as to whether there are optimal conditions for transport in this case that take into account the fact that the canals cannot be considered isolated from the environment. This is precisely the aim of this article.…”