We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as a... more We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as an instanton, i.e., in one run and without dwelling anywhere on the way from the bottom of the well to the top of the barrier. For a sufficiently steep slope the instanton time equals the time it takes the particle to deterministically slide down the same slope. We show that the instanton time is also the relaxation time for the escape rate after the barrier changes shape. ͓S1063-651X͑99͒04906-5͔
Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equi... more Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.
Proceedings of the National Academy of Sciences, 1995
Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc t... more Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.
Proceedings of the National Academy of Sciences, 1994
Transport of a divalent cation (Ca2+) and three DNA indicators [ethidium bromide (EB), propidium ... more Transport of a divalent cation (Ca2+) and three DNA indicators [ethidium bromide (EB), propidium iodide (PI), and ethidium homodimer (EthD-1)] across electroporated membranes of several mammalian cell lines was found to be selective and asymmetrical. In low salt medium, Ca2+ and EB were preferentially transported across the anodefacing cell membrane while PI and EthD-1 predominately entered at the site facing the cathode. In high salt medium, the entry site for Ca2+ and EB was reversed to the cathode-facing hemisphere while it remained unchanged for PI and EthD-1. In all these experiments, the observed transport patterns remained unaffected whether the dyes (or ion) were present during or added after the electroporating pulse. The data suggest that asymmetric pores are created on both sides of the membrane facing the electrodes, with smaller pore size (but greater in number) on the anode side and larger pores (with a lower population) on the cathode side. Furthermore, the rate of re...
Protein molecular motors-perfected over the course of millions of years of evolution-play an esse... more Protein molecular motors-perfected over the course of millions of years of evolution-play an essential role in moving and assembling biological structures. Recently chemists have been able to synthesize molecules that emulate in part the remarkable capabilities of these biomolecular motors (for extensive reviews see the recent papers:
Proceedings of the National Academy of Sciences, 1986
Recently, it has been demonstrated that free energy from an alternating electric field can drive ... more Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing"...
... nonspecific binding of ligand to the surface followed by two-dimensional diffusion leading to... more ... nonspecific binding of ligand to the surface followed by two-dimensional diffusion leading to reaction. Thus, in the present work we utilize a branching method*-12 for the calculation of diffusion-controlled interfacial reaction rates. ...
Olga Sosnovtseva and Erik Mosekilde have collaborated for more than a decade in the areas of biol... more Olga Sosnovtseva and Erik Mosekilde have collaborated for more than a decade in the areas of biological physics and modeling of complex dynamical phenomena in living systems. During the spring of 2004 they formulated the application to the European Biotechnology for Health Programme that led to the establishment of BioSim, an unusually successful Network of Excellence in “Biosimulation – A New Tool in Drug Development”, described in detail at http://biosim.fysik.dtu.dk:8080/biosim/index.jsp. Erik Mosekilde is a professor of physics at The Technical University of Denmark (DTU), where he teaches courses in complex systems theory and modeling of biological systems. In 1977, he defended his second doctor’s degree in theoretical and experimental physics, but at that time he had already become interested in modeling the dynamics of economic and biological systems. The challenge was to try to establish mechanism-based models of systems that had not previously been submitted to this approac...
I give a simple analysis of the game that I previously published in Scientific American which sho... more I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only two states and is described by a first-order Markov process. In 1986–7 my colleagues and I posed the following " paradox. " [1, 2] Consider a random walk on a cycle of bases governed by one of two sets of transition constants for stepping between the bases. Using either set alone, the walk is biased to favor completion of a counterclockwise cycle. However, either periodic[1] or random[2] alternation between the two sets causes net clockwise cycling! To illustrate as simply as possible this paradoxical behavior, I published [3] a very simple game played with a checker stepping on part of a checkerboard. The stepping is decided by the roll of a pair of dice. Alternation between two sets of rules for the stepping is achieved by flipping a ...
The motion of a heavily damped Brownian particle in a periodic potential subject to a dichotomous... more The motion of a heavily damped Brownian particle in a periodic potential subject to a dichotomously fluctuating perturbation is considered. We show that even if the net force is always zero, flow is induced by a fluctuation of the energy barrier, but only at flipping times roughly in between the adiabatic adjustment times on the left and right of the barrier. Predictions of our model are consistent with recent experimental data obtained by Svoboda et al. [Nature (London) 365, 721-727 (1993)] for a single kinesin molecule moving along a biopolymer.
ABSTRACT We consider a membrane protein that can exist in two configurations, either one of which... more ABSTRACT We consider a membrane protein that can exist in two configurations, either one of which acts as a poor ion channel, allowing ions to slowly leak across the membrane from high to low elctrochemical potential. We show that random external fluctuations can provide the energy to turn this poor channel into a good pump that drives ion transport from low to high electrochemical potential. We discuss this result in terms of a gambling analogy, and point to possible implications for fields as far ranging as population biology, economics, and actuarial science.
We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as a... more We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as an instanton, i.e., in one run and without dwelling anywhere on the way from the bottom of the well to the top of the barrier. For a sufficiently steep slope the instanton time equals the time it takes the particle to deterministically slide down the same slope. We show that the instanton time is also the relaxation time for the escape rate after the barrier changes shape. ͓S1063-651X͑99͒04906-5͔
Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equi... more Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.
Proceedings of the National Academy of Sciences, 1995
Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc t... more Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.
Proceedings of the National Academy of Sciences, 1994
Transport of a divalent cation (Ca2+) and three DNA indicators [ethidium bromide (EB), propidium ... more Transport of a divalent cation (Ca2+) and three DNA indicators [ethidium bromide (EB), propidium iodide (PI), and ethidium homodimer (EthD-1)] across electroporated membranes of several mammalian cell lines was found to be selective and asymmetrical. In low salt medium, Ca2+ and EB were preferentially transported across the anodefacing cell membrane while PI and EthD-1 predominately entered at the site facing the cathode. In high salt medium, the entry site for Ca2+ and EB was reversed to the cathode-facing hemisphere while it remained unchanged for PI and EthD-1. In all these experiments, the observed transport patterns remained unaffected whether the dyes (or ion) were present during or added after the electroporating pulse. The data suggest that asymmetric pores are created on both sides of the membrane facing the electrodes, with smaller pore size (but greater in number) on the anode side and larger pores (with a lower population) on the cathode side. Furthermore, the rate of re...
Protein molecular motors-perfected over the course of millions of years of evolution-play an esse... more Protein molecular motors-perfected over the course of millions of years of evolution-play an essential role in moving and assembling biological structures. Recently chemists have been able to synthesize molecules that emulate in part the remarkable capabilities of these biomolecular motors (for extensive reviews see the recent papers:
Proceedings of the National Academy of Sciences, 1986
Recently, it has been demonstrated that free energy from an alternating electric field can drive ... more Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing"...
... nonspecific binding of ligand to the surface followed by two-dimensional diffusion leading to... more ... nonspecific binding of ligand to the surface followed by two-dimensional diffusion leading to reaction. Thus, in the present work we utilize a branching method*-12 for the calculation of diffusion-controlled interfacial reaction rates. ...
Olga Sosnovtseva and Erik Mosekilde have collaborated for more than a decade in the areas of biol... more Olga Sosnovtseva and Erik Mosekilde have collaborated for more than a decade in the areas of biological physics and modeling of complex dynamical phenomena in living systems. During the spring of 2004 they formulated the application to the European Biotechnology for Health Programme that led to the establishment of BioSim, an unusually successful Network of Excellence in “Biosimulation – A New Tool in Drug Development”, described in detail at http://biosim.fysik.dtu.dk:8080/biosim/index.jsp. Erik Mosekilde is a professor of physics at The Technical University of Denmark (DTU), where he teaches courses in complex systems theory and modeling of biological systems. In 1977, he defended his second doctor’s degree in theoretical and experimental physics, but at that time he had already become interested in modeling the dynamics of economic and biological systems. The challenge was to try to establish mechanism-based models of systems that had not previously been submitted to this approac...
I give a simple analysis of the game that I previously published in Scientific American which sho... more I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only two states and is described by a first-order Markov process. In 1986–7 my colleagues and I posed the following " paradox. " [1, 2] Consider a random walk on a cycle of bases governed by one of two sets of transition constants for stepping between the bases. Using either set alone, the walk is biased to favor completion of a counterclockwise cycle. However, either periodic[1] or random[2] alternation between the two sets causes net clockwise cycling! To illustrate as simply as possible this paradoxical behavior, I published [3] a very simple game played with a checker stepping on part of a checkerboard. The stepping is decided by the roll of a pair of dice. Alternation between two sets of rules for the stepping is achieved by flipping a ...
The motion of a heavily damped Brownian particle in a periodic potential subject to a dichotomous... more The motion of a heavily damped Brownian particle in a periodic potential subject to a dichotomously fluctuating perturbation is considered. We show that even if the net force is always zero, flow is induced by a fluctuation of the energy barrier, but only at flipping times roughly in between the adiabatic adjustment times on the left and right of the barrier. Predictions of our model are consistent with recent experimental data obtained by Svoboda et al. [Nature (London) 365, 721-727 (1993)] for a single kinesin molecule moving along a biopolymer.
ABSTRACT We consider a membrane protein that can exist in two configurations, either one of which... more ABSTRACT We consider a membrane protein that can exist in two configurations, either one of which acts as a poor ion channel, allowing ions to slowly leak across the membrane from high to low elctrochemical potential. We show that random external fluctuations can provide the energy to turn this poor channel into a good pump that drives ion transport from low to high electrochemical potential. We discuss this result in terms of a gambling analogy, and point to possible implications for fields as far ranging as population biology, economics, and actuarial science.
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Papers by Dean Astumian