Our major goal is to develop a comprehensive continuum diffusion model of solute and blocker dynamics in a membrane channel. Water-filled pores of biological channels usually have complex geometry that only rarely can be approximated by a cylinder. This leads to the so-called entropic wells and barriers in theoretical description of transport through such structures. To address these problems, we have been working in several directions. The most important recent advances were to apply our analytical approach to investigate new aspects of diffusion in confining geometries. Combining three-dimensional Brownian dynamics simulations with the analytical results obtained by solving the Smoluchowski equation with different potentials of mean force and boundary conditions, we were able (i) to establish criteria validating reduction to an effective one-dimensional description, (ii) to show the role of particle-particle interactions in breaking the symmetry of the particle flux through the channel, (iii) to demonstrate entropic rectification and the non-monotonic behavior of the effective particle mobility as a function of applied force in periodic confinements.

Advancing our approach, we have proposed a theory of the channel and carrier transport efficiency. This included optimization of individual channel/carrier parameters as well as the effects of their clustering and localization within different confining geometries.

We have also used our theory to develop the thermodynamics of the efficient blockage of anthrax channels by low molecular weight compounds. The theory clarifies the role of different physical interactions in blockage efficacy.

Figure 1. The flux through the channel depends on the strength of channel-particle interactions in a non-monotonic way. For the cylindrical channel geometry and the range of the particle concentrations specified in the figure, the depth of the rectangular well that optimizes the transport is around 6 to 10 k_BT per molecule. Blockage of the channel, which is often a mechanism of channel regulation in nature, is achieved at higher well depths (A.M. Berezhkovskii and S.M. Bezrukov, On the applicability of entropy potentials in transport problems, European Physical Journal – Special Topics, 2014, 223:3063-3077).

Publications:

Skvortsov AT, Dagdug L, Berezhkovskii AM, MacGillivray IR, and Bezrukov SM (2021) Evaluating diffusion resistance of a constriction in a membrane channel by the method of boundary homogenization. Phys Rev E. 1031-1:012408. https://doi.org/10.1103/PhysRevE.103.012408 .

Misiura MM, Berezhkovskii AM, Bezrukov SM, and Kolomeisky AB (2021) Surface-facilitated trapping by active sites: From catalysts to viruses. J Chem Phys. 15518:184106. https://doi.org/10.1063/5.0069917 .

Dagdug L, Berezhkovskii AM, Zitserman VY, and Bezrukov SM (2021) Effective diffusivity of a Brownian particle in a two-dimensional periodic channel of abruptly alternating width. Phys Rev E. 1036-1:062106. https://doi.org/10.1103/PhysRevE.103.062106 .

Dagdug L, Berezhkovskii AM, Zitserman VY, and Bezrukov SM (2021) Trapping of particles diffusing in two dimensions by a hidden binding site. Phys Rev E. 1031-1:012135. https://doi.org/10.1103/PhysRevE.103.012135 .

Berezhkovskii AM, Bezrukov SM, and Makarov DE (2021) Localized potential well vs binding site: Mapping solute dynamics in a membrane channel onto one-dimensional description. J Chem Phys. 15411:111101. https://doi.org/10.1063/5.0044044 .

Berezhkovskii AM and Bezrukov SM (2021) Capturing single molecules by nanopores: measured times and thermodynamics. Phys Chem Chem Phys. 232:1610-1615. https://doi.org/10.1039/d0cp04747c .

Berezhkovskii AM, Dagdug L, and Bezrukov SM (2020) Peculiarities of the Mean Transition Path Time Dependence on the Barrier Height in Entropy Potentials. J Phys Chem B. 12412:2305-2310. https://doi.org/10.1021/acs.jpcb.9b09595 .

Berezhkovskii AM, Dagdug L, and Bezrukov SM (2019) Two-site versus continuum diffusion model of blocker dynamics in a membrane channel: Comparative analysis of escape kinetics. The Journal of Chemical Physics. 1515. https://doi.org/10.1063/1.5110489 .

Berezhkovskii AM, Dagdug L, and Bezrukov SM (2019) Exact Solutions for Distributions of First-Passage, Direct-Transit, and Looping Times in Symmetric Cusp Potential Barriers and Wells. J Phys Chem B. 12317:3786-3796. https://doi.org/10.1021/acs.jpcb.9b01616 .

Berezhkovskii AM, Dagdug L, and Bezrukov SM (2019) Trapping of diffusing particles by small absorbers localized in a spherical region. J Chem Phys. 1506:064107. https://doi.org/10.1063/1.5083808 .

Berezhkovskii AM and Bezrukov SM (2019) Blocker escape kinetics from a membrane channel analyzed by mapping blocker diffusive dynamics onto a two-site model. J Chem Phys. 15019:194103. https://doi.org/10.1063/1.5095594 .

Berezhkovskii AM and Bezrukov SM (2018) Mapping Intrachannel Diffusive Dynamics of Interacting Molecules onto a Two-Site Model: Crossover in Flux Concentration Dependence. J Phys Chem B. 12249:10996-11001. https://doi.org/10.1021/acs.jpcb.8b04371 .

Berezhkovskii AM and Bezrukov SM (2018) Effect of stochastic gating on the flux through a membrane channel: a steady-state approach. Journal of Physics-Condensed Matter. 3025. https://doi.org/10.1088/1361-648X/aac4df .

Berezhkovskii AM and Bezrukov SM (2018) Stochastic Gating as a Novel Mechanism for Channel Selectivity. Biophys J. 1145:1026-1029. https://doi.org/10.1016/j.bpj.2018.01.007 .