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 .

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. First passage, looping, and direct transition in expanding and narrowing tubes: Effects of the entropy potential. Journal of Chemical Physics, 2017, 147:134104.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. A new insight into diffusional escape from a biased cylindrical trap. Journal of Chemical Physics, 2017, 147:104103.

A.M. Berezhkovskii, L. and S.M. Bezrukov. Effect of stochastic gating on channel-facilitated transport of non-interacting and strongly repelling solutes. Journal of Chemical Physics, 2017, 147:084109.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. Bulk-mediated surface transport in the presence of bias. Journal of Chemical Physics, 2017, 147:014103.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. Mean direct-transit and looping times as functions of the potential shape. Journal of Physical Chemistry B, 2017, 121:5455−5460.

A.M. Berezhkovskii and S.M. Bezrukov. Intermittent free diffusion in the presence of sparse obstacles: Mean obstacle encounter time. Journal of Physics A: Mathematical and Theoretical, 2016, 49:434002.

R. Verdel, L. Dagdug, A.M. Berezhkovskii, and S.M. Bezrukov. Unbiased diffusion in two-dimensional channels with corrugated walls. Journal of Chemical Physics, 2016, 144:084106.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. Range of applicability of modified Fick-Jacobs equation in two dimensions. Journal of Chemical Physics, 2015, 143:164102.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. A new approach to the problem of bulk-mediated surface diffusion. Journal of Chemical Physics, 2015, 143:084103.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. Biased diffusion in three-dimensional comb-like structures. Journal of Chemical Physics, 2015, 142:134101.

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.

S.M. Bezrukov, L. Schimansky-Geier, and G. Schmid. Brownian motion in confined geometries. European Physical Journal – Special Topics, 2014, 223:3021-3025.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. From normal to anomalous diffusion in comb-like structures in three dimensions. Journal of Chemical Physics, 2014, 141:054907.

A.M. Berezhkovskii, L. Dagdug, V.A. Lizunov, J. Zimmerberg, and S.M. Bezrukov. Trapping by clusters of channels, receptors, and transporters: Quantitative description. Biophysical Journal, 2014, 106:500-509.

A.M. Berezhkovskii, L. Dagdug, and S.M. Bezrukov. Discriminating between anomalous diffusion and transient behavior in micro-heterogeneous environments. Biophysical Journal, 2014, 106:L09-L11.

A.M. Berezhkovskii, L. Dagdug, M.-V. Vazquez, V.A. Lizunov, J. Zimmerberg, and S.M. Bezrukov. Trapping of diffusing particles by clusters of absorbing disks on a reflecting wall with disk centers on sites of a square lattice. Journal of Chemical Physics, 2013, 138:064105.

L. Dagdug, A.M. Berezhkovskii, and S.M. Bezrukov. Particle lifetime in cylindrical cavity with absorbing spot on the wall. Going beyond the narrow escape problem. Journal of Chemical Physics, 2012, 137(23):234108.

E.M. Nestorovich, V.A. Karginov, A.M. Berezhkovskii, V.A. Parsegian, and S.M. Bezrukov. Kinetics and thermodynamics of binding reactions as exemplified by anthrax channel blockage with a cationic cyclodextrin derivative. Proc. Natl. Acad. Sci. USA, 2012, 109:18453-18458.

L. Dagdug, A.M. Berezhkovskii, Yu.A. Makhnovskii, V.Yu. Zitserman, and S.M. Bezrukov. Force-dependent mobility and entropic rectification in tubes of periodically varying geometry. Journal of Chemical Physics, 2012, 136:214110.

A.M. Berezhkovskii, L. Dagdug, V.A. Lizunov, J. Zimmerberg, and S.M. Bezrukov. Clusters of absorbing disks on a reflecting wall: Competition for diffusing particles. Journal of Chemical Physics, 2012, 136:211102.

L. Dagdug, M.-V. Vazquez, A.M. Berezhkovskii, V.Yu. Zitserman, and S.M. Bezrukov. Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation. Journal of Chemical Physics, 2012, 136:204106.

A.M. Berezhkovskii and S.M. Bezrukov. Surface area of the domain visited by a spherical Brownian particle. Chaos, 2011, 21:047519.

A.M. Berezhkovskii, V.A. Lizunov, J. Zimmerberg, and S.M. Bezrukov. Functional role for transporter isoforms in optimizing membrane transport. Biophysical Journal, 2011, 101:L14-L16.

L. Dagdug, A.M. Berezhkovskii, Yu.A. Makhnovskii, V.Yu. Zitserman, and S.M. Bezrukov. Turnover behavior of effective mobility in a tube with periodic entropy potential. Journal of Chemical Physics, 2011, 134:101102.

A.M. Berezhkovskii and S.M. Bezrukov. Effective drift and diffusion of a particle jumping between mobile and immobile states. Journal of Electroanalytical Chemistry, 2011, 660:352-355.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Fluxes of non-interacting and strongly repelling particles through a single conical channel: Analytical results and their numerical tests. Chemical Physics, 2010, 375:523-528.

L. Dagdug, M.-V. Vazquez, A.M. Berezhkovskii, and S.M. Bezrukov. Unbiased diffusion in tubes with corrugated walls. Journal of Chemical Physics, 2010, 133:034707.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Entropic effects in channel-facilitated transport: Inter-particle interactions break the flux symmetry. Phys Rev E Stat Nonlin Soft Matter Phys, 80(2 Pt 1):020904.

V.Yu. Zitserman, A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Relaxation and fluctuations of the number of particles in a membrane channel at arbitrary particle-channel interaction. Journal of Chemical Physics, 2008, 129:095101.

A.M. Berezhkovskii and S.M. Bezrukov. Fluctuation theorem for channel-facilitated membrane transport of interacting and non-interacting solutes. Journal of Physical Chemistry B, 2008, 112:6228-6232.

A.M. Berezhkovskii and S.M. Bezrukov. Counting translocations of strongly repelling particles through single channels: Fluctuation theorem for membrane transport. Physical Review Letters, 2008, 100:038104.

S.M. Bezrukov, A.M. Berezhkovskii, and A. Szabo. Diffusion model of solute dynamics in a membrane channel: Mapping onto the two-site model and optimizing the flux. Journal of Chemical Physics, 2007, 127:115101.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Diffusion in a tube of varying cross section: Numerical study of reduction to effective one-dimensional description. Journal of Chemical Physics, 2007, 126:134706.

A.M. Berezhkovskii and S.M. Bezrukov. Site model for channel-facilitated membrane transport: Invariance of translocation time distribution with respect to direction of passage. Journal of Physics: Condensed Matter, 2007, 19:065148.

M.A. Pustovoit, A.M. Berezhkovskii, and S.M. Bezrukov. Analytical theory of hysteresis in ion channels: Two-state model. Journal of Chemical Physics, 2006, 125:194907.

A.M. Berezhkovskii, G. Hummer, and S.M. Bezrukov. Identity of distributions of direct uphill and downhill translocation times for particles traversing membrane channels. Physical Review Letters, 2006, 97:020601.

V.Yu. Zitserman, A.M. Berezhkovskii, V.A. Parsegian, and S.M. Bezrukov. Non-ideality of polymer solutions in the pore and concentration-dependent partitioning. Journal of Chemical Physics, 2005, 123:146101.

A.M. Berezhkovskii and S.M. Bezrukov. Channel-facilitated membrane transport: Constructive role of particle attraction to the channel pore.  Chemical Physics, 2005, 319:342-349.

A.M. Berezhkovskii and S.M. Bezrukov. Optimizing transport of metabolites through large channels: Molecular sieves with and without binding. Biophysical Journal, 2005, 88:L17-L19.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Channel-facilitated membrane transport: Average lifetimes in the channel.  Journal of Chemical Physics, 2003, 119:3943-3951.

L. Dagdug, A.M. Berezhkovskii, S.M. Bezrukov, and G.H. Weiss. Diffusion-controlled reactions with a binding site hidden in the channel.  Journal of Chemical Physics, 2003, 118:2367-2373.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Channel-facilitated membrane transport: Transit probability and interaction with the channel.  Journal of Chemical Physics, 2002, 116:9952-9956.

A.M. Berezhkovskii, M.A. Pustovoit, and S.M. Bezrukov. Effect of binding on particle number fluctuations in a membrane channel.  Journal of Chemical Physics, 2002, 116:6216-6220.

S.M. Bezrukov, A.M. Berezhkovskii, M.A. Pustovoit, and A. Szabo. Particle number fluctuations in a membrane channel.  Journal of Chemical Physics, 2000, 113:8206-8211.