Fixed-density boundary conditions in overdamped Langevin simulations of diffusion in channels

We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when considering the diffusion of ions in molecular channels, between the different concentrations at both sides of the cellular membrane. For this application the overdamped limit of Brownian motion (leading to a first order Langevin equation) is most convenient, but in previous works some difficulties associated with this limit were found for the implementation of the boundary conditions. We derive here an algorithm that, unlike previous attempts, does not require the simulation of particle reservoirs or the consideration of velocity variables or adjustable parameters. Simulations of Brownian particles in simple cases show that results agree perfectly with theory, both for the local concentration values and for the resulting particle flux in nonequilibrium situations. The algorithm is appropriate for the modeling of more complex ionic channels and, in general, for the treatment of analogous boundary conditions in other physical models using first order Langevin equations.Peer ReviewedPostprint (author's final draft

Physical properties of voltage gated pores

Experiments on single ionic channels have contributed to a large extent to our current view on the function of cell membrane. In these experiments the main observables are the physical quantities: ionic concentration, membrane electrostatic potential and ionic uxes, all of them presenting large uctuations. The classical theory of Goldman{Hodking{Katz assumes that an open channel can be well described by a physical pore where ions follow statistical physics. Nevertheless real molecular channels are active pores with open and close dynamical states. By skipping the molecular complexity of real channels, here we present the internal structure and calibration of two active pore models. These models present a minimum set of degrees of freedom, speci cally ion positions and gate states, which follow Langevin equations constructed from a unique potential energy functional and by using standard rules of statistical physics. Numerical simulations of both models are implemented and the results show that they have dynamical properties very close to those observed in experiments of Na and K molecular channels. In particular a signi cant e ect of the external ion concentration on gating dynamics is predicted, which is consistent with previous experimental observations. This approach can be extended to other channel types with more speci c phenomenology

Complex dynamics in double-diffusive convection

The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens-Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1.Comment: 8 pages, 5 figure

Physical properties of voltage gated pores

Experiments on single ionic channels have contributed to a large extent to our current view on the function of cell membrane. In these experiments the main observables are the physical quantities: ionic concentration, membrane electrostatic potential and ionic fluxes, all of them presenting large fluctuations. The classical theory of Goldman–Hodking–Katz assumes that an open channel can be well described by a physical pore where ions follow statistical physics. Nevertheless real molecular channels are active pores with open and close dynamical states. By skipping the molecular complexity of real channels, here we present the internal structure and calibration of two active pore models. These models present a minimum set of degrees of freedom, specifically ion positions and gate states, which follow Langevin equations constructed from a unique potential energy functional and by using standard rules of statistical physics. Numerical simulations of both models are implemented and the results show that they have dynamical properties very close to those observed in experiments of Na and K molecular channels. In particular a significant effect of the external ion concentration on gating dynamics is predicted, which is consistent with previous experimental observations. This approach can be extended to other channel types with more specific phenomenology.Peer ReviewedPostprint (published version

Periodic spiking by a pair of ionic channels

Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual channels. Here we use a Langevin formulation for the stochastic dynamics of a pair of Na and K ionic channels. These two channels are simple gated pore models where a minimum set of degrees of freedom follow standard statistical physics. The whole system is totally autonomous without any external energy input, except for the chemical energy of the different ionic concentrations across the membrane. As a result it is shown that a unique pair of different ionic channels can sustain membrane potential periodic spikes. The spikes are due to the interaction between the membrane potential, the ionic flows and the dynamics of the internal parts (gates) of each channel structures. The spike involves a series of dynamical steps being the more relevant one the leak of Na ions. Missing spike events are caused by the altered functioning of specific model parts. The time dependent spike structure is comparable with experimental data.This work was supported by the Ministerio de Economia y Competividad (Spain) and FEDER (European Union), under projects FIS2015-66503-C01-P2/P3 and by the Generalitat de Catalunya Projects 2009SGR14 and 2014SGR878Peer ReviewedPreprin

Oscillatory Instabilities in Directional Solidification with Solutal Convection. Transient Regime

Peer ReviewedPostprint (published version

Molecular Na-channel excitability from statistical physics

The excitable properties of the neural cell membrane is the driving mechanism of the neural pulses. Coordinated ionic fluxes across Na and K channels are the devices responsible of this function. Here we present a simple microscopic physical scenario which accounts for this phenomenology. The main elements are ions and channel doors that obey the standard formulation of statistical physics (overdamped Langevin equations) with appropriate nonlinear interacting potentials. From these equations we obtain the ionic flux and the dynamics of the membrane potential. We show that the excitable properties of the membrane are present in a single and simple Na channel. From this framework, additional microscopic information can be obtained, such as statistics of single-channels dynamics or the energetics of action potential events.Peer ReviewedPostprint (author’s final draft

Generation and control of monodisperse bubble suspensions in microgravity

A new experimental setup for the generation of homogeneous, monodisperse bubble suspensions in turbulent duct flows in microgravity has been designed and tested in drop tower experiments. The setup provides independent control of bubble size, void fraction and degree of turbulence. The device combines several slug-flow injectors that produce monodisperse bubble jets, with a turbulent co-flow that ensures homogeneous spatial spreading. Bubble separation in the scale of the most energetic eddies of the flow, and bubble size sufficiently smaller, ensure that turbulence is most efficient as a mechanism for spatial spreading of bubbles while preventing coalescence, thus optimizing the homogeneous and monodisperse character of the suspension. The setup works in a regime for which bubbles are spherical, but sufficiently large compared to the turbulent dissipative scales to allow for two-way coupling between bubbles and carrying flow. The volume fraction is kept relatively small to facilitate particle tracking techniques. To illustrate the potential uses of the method we characterize the statistics of bubble velocity fluctuations in steady regimes and we characterize the transient relaxation of the buoyancy-driven pseudo-turbulence when gravity is switched-off