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Alexander M Berezhkovskii

Publications and source records attributed to Alexander M Berezhkovskii.

18 recordsLinked to original sources
PubMed2006

Diffusion-limited binding to a site on the wall of a membrane channel.

The authors develop a theory of diffusion-controlled reactions with a site located on the wall of a cylindrical membrane channel that connects two reservoirs containing diffusing particles which are trapped by the site at the first contact. An expression for the Laplace transform of the rate coefficient, kt, is derived assuming that the size of the site is small compared to the channel radius. The expression is used to find the stationary value of the rate coefficient, kinfinity, as a function of the length and radius of the channel, the radius of the site, and its position inside the channel (distances from the two ends of the channel) as well as the particle diffusion constants in the bulk and in the channel. Their derivation is based on the one-dimensional description of the particle motion in the channel, which is generalized to include binding to the site into consideration. The validity of the approximate one-dimensional description of diffusion and binding was checked by three-dimensional Brownian dynamics simulations. They found that the one-dimensional description works reasonably well when the size of the site does not exceed 0.2 of the channel radius.

Binding Sites↗
PubMed2006

Escape from a cavity through a small window: turnover of the rate as a function of friction constant.

To escape from a cavity through a small window the particle has to overcome a high entropy barrier to find the exit. As a consequence, its survival probability in the cavity decays as a single exponential and is characterized by the only parameter, the rate constant. We use simulations to study escape of Langevin particles from a cubic cavity through a small round window in the center of one of the cavity walls with the goal of analyzing the friction dependence of the escape rate. We find that the rate constant shows the turnover behavior as a function of the friction constant, zeta: The rate constant grows at very small zeta, reaches a maximum value which is given by the transition-state theory (TST), and then decreases approaching zero as zeta-->infinity. Based on the results found in simulations and some general arguments we suggest a formula for the rate constant that predicts a turnover of the escape rate for ergodic cavities in which collisions of the particle with the cavity walls are defocusing. At intermediate-to-high friction the formula describes transition between two known results for the rate constant: the TST estimation and the high friction limiting behavior that characterizes escape of diffusing particles. In this range of friction the rate constants predicted by the formula are in good agreement with those found in simulations. At very low friction the rate constants found in simulations are noticeably smaller than those predicted by the formula. This happens because the simulations were run in the cubic cavity which is not ergodic.

Biophysical Phenomena↗
PubMed2006

Identity of distributions of direct uphill and downhill translocation times for particles traversing membrane channels.

We study the distribution of direct translocation times for particles passing through membrane channels connecting two reservoirs. The direct translocation time is a conditional first-passage time defined as the residence time of the particle in the channel while passing to the other side of the membrane directly, i.e., without returning to the reservoir from which it entered. We show that the distributions of direct translocation times are identical for translocation in both directions, independent of any asymmetry in the potential across the channel and, hence, the translocation probabilities.

Biological Transport↗
PubMed2006

Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient.

A general formalism for treating lateral diffusion in a multilayer medium is developed. The formalism is based on the relation between the lateral diffusion and the distribution of the cumulative residence time, which the diffusing particle spends in different layers. We exploit this fact to derive general expressions which give the global and local time-dependent diffusion coefficients in terms of the average cumulative times spent by the particle in different layers and the probabilities of finding the particle in different layers, respectively. These expressions are used to generalize two recently obtained results: (a) A solution for the short-time behavior of the lateral diffusion coefficient in two layers separated by a permeable membrane obtained by a perturbation theory is extended to the entire range of time. (b) A solution for the time-dependent diffusion coefficient of a ligand, which repeatedly dissociates and rebinds to sites on a planar surface, obtained under the assumption that the medium above the surface is infinite, is generalized to allow for the medium layer of finite thickness. For the latter problem we derive an expression for the Fourier-Laplace transform of the propagator in terms of the double Laplace transform of the probability density of the cumulative residence time spent by the ligand in the medium layer.

Diffusion↗
PubMed2005

Time-dependent diffusion coefficients in periodic porous materials.

We derive an approximate solution for the Laplace transform of the time-dependent diffusion coefficient, D(t), of a molecule diffusing in a periodic porous material. In our model, the material is represented by a simple cubic lattice of identical cubic cavities filled with a solvent and connected by small circular apertures in otherwise reflecting cavity walls, the thickness of which can be neglected. The solution describes the decrease of D(t) from its initial value, D(0) = D, where D is the diffusion constant in the free solvent, to its asymptotic value, D(infinity) = D(eff), which is much smaller than D. A simple heuristic formula for the mean-squared displacement of the diffusing molecule is suggested. The theoretically predicted results are in good agreement with the data obtained from Brownian dynamics simulations.

Diffusion↗
PubMed2005

Ligand accumulation in autocrine cell cultures.

Cell-culture assays are routinely used to analyze autocrine signaling systems, but quantitative experiments are rarely possible. To enable the quantitative design and analysis of experiments with autocrine cells, we develop a biophysical theory of ligand accumulation in cell-culture assays. Our theory predicts the ligand concentration as a function of time and measurable parameters of autocrine cells and cell-culture experiments. The key step of our analysis is the derivation of the survival probability of a single ligand released from the surface of an autocrine cell. An expression for this probability is derived using the boundary homogenization approach and tested by stochastic simulations. We use this expression in the integral balance equations, from which we find the Laplace transform of the ligand concentration. We demonstrate how the theory works by analyzing the autocrine epidermal growth factor receptor system and discuss the extension of our methods to other experiments with cultured autocrine cells.

Autocrine Communication↗
PubMed2004

Diffusion in the presence of periodically spaced permeable membranes.

The diffusion of molecules in biological tissues and some other microheterogeneous systems is affected by the presence of permeable barriers. This leads to the slowdown of diffusion at long times as compared to barrier-free diffusion. At short times the effect of barriers is weak. In consequence, the diffusion coefficient D(t) decreases as a function of time. We derive an exact solution for the Laplace transform of D(t) for diffusion in a space separated into layers by equally spaced, parallel identical planes of arbitrary permeability. Additionally, we give an approximation to D(t) which is reasonably accurate over the whole range of the partition permeability from zero (the case of isolated layers) to infinity (the case of no barriers).

Journal Article↗
PubMed2004

Boundary homogenization for trapping by patchy surfaces.

We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations. (c) 2004 American Institute of Physics.

Journal Article↗
PubMed2004

Rate constant for diffusion-influenced ligand binding to receptors of arbitrary shape on a cell surface.

The theory of ligand binding to receptors on a cell surface suggested by Berg and Purcell and generalized by Zwanzig and Szabo uses the assumption that receptors are circular absorbing disks on an otherwise reflecting sphere. One of the key ingredients of this theory is a solution for the rate constant for ligand binding to a single circular receptor on a reflecting plane. We give an exact solution for the rate constant for binding to a single elliptic receptor and an approximate solution for binding to a single receptor of more general shape. The latter was tested by Brownian dynamics simulations. We found that the approximate formula predicted the rate constant with better than 10% accuracy for all studied receptor shapes. Using our solutions one can find the rate constant for ligand binding to a cell covered by N noncircular receptors by means of the Zwanzig-Szabo formula.

Cell Membrane↗
PubMed2004

Ligand trapping in epithelial layers and cell cultures.

We analyze a stochastic model that describes receptor-mediated ligand trapping in epithelial layers and cell culture assays. In both cases, the problem is reduced to diffusion of a Brownian particle between the partially absorbing and reflective surfaces. We derive an analytical expression for the spatial distribution of the trapping points and identify the domains of applicability of the two limiting regimes. We conclude that a thin layer approximation is applicable for ligand trapping in epithelial layers while a typical cell culture experiment is appropriately described within an infinite layer approximation.

Animals↗
PubMed2004

Kinetics of ligand equilibration between tubular and vesicular parts of the endosome.

The kinetics of ligand equilibration between the tubular and vesicular parts of the endosome are studied for ligands diffusing in the vesicle and in a narrow cylindrical tubule attached to it. The key quantity in our analysis is the fraction of ligands in the vesicle at time t, P(ves)(t). We derive an expression for the Laplace transform of P(ves)(t) as a function of the vesicle volume and the length and radius of the tubule as well as the ligand diffusion coefficients in the vesicle and in the tubule. This transform is used to find the average equilibration time as a function of the system parameters.

Biological Transport, Active↗
PubMed2004

Field-dependent effect of crown ether (18-crown-6) on ionic conductance of alpha-hemolysin channels.

Closing linear poly(ethylene glycol) (PEG) into a circular "crown" dramatically changes its dynamics in the alpha-hemolysin channel. In the electrically neutral crown ether (C2H4O)6, six ethylene oxide monomers are linked into a circle that gives the molecule ion-complexing capacity and increases its rigidity. As with linear PEG, addition of the crown to the membrane-bathing solution decreases the ionic conductance of the channel and generates additional conductance noise. However, in contrast to linear PEG, both the conductance reduction (reporting on crown partitioning into the channel pore) and the noise (reporting on crown dynamics in the pore) now depend on voltage strongly and nonmonotonically. Within the whole frequency range accessible in channel reconstitution experiments, the noise power spectrum is "white", showing that crown exchange between the channel and the bulk solution is fast. Analyzing these data in the framework of a Markovian two-state model, we are able to characterize the process quantitatively. We show that the lifetime of the crown in the channel reaches its maximum (a few microseconds) at about the same voltage (approximately 100 mV, negative from the side of protein addition) where the crown's reduction of the channel conductance is most pronounced. Our interpretation is that, because of its rigidity, the crown feels an effective steric barrier in the narrowest part of the channel pore. This barrier together with crown-ion complexing and resultant interaction with the applied field leads to behavior usually associated with voltage-dependent binding in the channel pore.

Computer Simulation↗
PubMed2003

Stochastic model of autocrine and paracrine signals in cell culture assays.

Autocrine signaling systems are commonly studied under cell culture conditions. In a typical cell culture assay, a layer of liquid medium covers a random two-dimensional dispersion of cells, which secrete ligands. In a growing number of experiments, it is important to characterize the spatial range of autocrine and paracrine cell communication. Currently, the spatial distribution of diffusing signals can be analyzed only indirectly, from their effects on the intracellular signaling or physiological responses of autocrine cells. To directly characterize the spatial range of secreted ligands, we propose a stochastic model for autocrine cell cultures and analyze it using a combination of analytical and computational tools. The two main results derived within the framework of this model are 1), an expression for the fraction of autocrine trajectories, i.e., the probability for a ligand to be trapped by the same cell from which it has been secreted; and 2), an expression for the spatial distribution of trapping points of paracrine trajectories. We test these analytical results by stochastic simulations with efficient Brownian dynamics code and apply our model to analyze the spatial operation of autocrine epidermal growth factor receptor systems.

Algorithms↗
PubMed2002

Number of distinct sites visited by a random walker trapped by an absorbing boundary.

The number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics. All previous investigations have used the assumption that the lattice is unbounded. An assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t. We show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present. A more complete analysis is possible for a random walk on a line terminated by an absorbing point.

Absorption↗