Biomolecule transport across biomembranes in the presence of crowding: Polymer translocation driven by concentration and disorder gradients

The transport of biomolecules across biomembranes occurs in a complex environment where the fluid on both sides of the membrane contains many inclusions. We investigate the translocation of a polymer through a nanopore in such crowded environments via computer simulations. Modeling intracellular and extracellular inclusions as spherical obstacles, the emergence of an entropic driving force is demonstrated for (i) a gradient in the number of obstacles on either side of the pore and (ii) having the obstacles in an ordered arrangement on one side and disordered on the other. With a directional preference of $\approx 90\%$ of events occurring towards the disordered side and a reduction in the translocation time of $\approx 30\%$, the latter case represents a manifestation of entropic trapping. Simple estimates for the magnitude of the driving force are developed for both cases. The effect of allowing the obstacles to move as well as systems containing opposing concentration and disorder gradients are also explored. Demonstrating a robust conclusion that translocation to lower obstacle densities and higher degrees of disorder will be accelerated, these results suggest that accounting for such effects will be critical in developing a realistic model of in vivo translocation.

Figure 1

Simulation setup for the ordered-disordered system.

Figure 2

Results for the obstacle concentration gradient: (a) Directional preference as a function of the grid spacing $a_C$ (upper axis) and estimated free energy (lower axis); (b) the associated mean translocation times (solid lines indicate translocation in the preferred direction). For the order-disorder case: (c) The fraction of events to the disordered side; (d) the mean translocation time to the disordered side. The results for the force model: (e) The directional preference for different polymer lengths; (f) the incremental mean first passage time $t_0$. For the case of the mobile obstacles: (g) Directional preference as a function of the mean obstacle displacement on cis; (h) the translocation times. The error bars were generated from 10 to 20 sets of 100 events each. Wherever not explicitly shown, error is within the data points.

Figure 3

Results for the opposing entropic driving forces cases. (a) and (b) display the directional preference and translocation time for a fixed disorder gradient but varying concentration gradient. (c) and (d) display the equivalent data for a fixed concentration gradient but varying degree of disorder across the pore. Wherever not explicitly shown, error is within the data points.