Test of the nonequilibrium kinetic focusing of voltage-gated ion channels

Dynamic memory of a single voltage-gated potassium ion channel: A stochastic nonequilibrium thermodynamic analysis

In this work, we have studied the stochastic response of a single voltage-gated potassium ion channel to a periodic external voltage that keeps the system out-of-equilibrium. The system exhibits memory, resulting from time-dependent driving, that is reflected in terms of dynamic hysteresis in the current-voltage characteristics. The hysteresis loop area has a maximum at some intermediate voltage frequency and disappears in the limits of low and high frequencies. However, the (average) dissipation at long-time limit increases and finally goes to saturation with rising frequency. This raises the question: how diminishing hysteresis can be associated with growing dissipation? To answer this, we have studied the nonequilibrium thermodynamics of the system and analyzed different thermodynamic functions which also exhibit hysteresis. Interestingly, by applying a temporal symmetry analysis in the high-frequency limit, we have analytically shown that hysteresis in some of the periodic responses of the system does not vanish. On the contrary, the rates of free energy and internal energy change of the system as well as the rate of dissipative work done on the system show growing hysteresis with frequency. Hence, although the current-voltage hysteresis disappears in the high-frequency limit, the memory of the ion channel is manifested through its specific nonequilibrium thermodynamic responses.

Cellular defibrillation: interaction of micro-scale electric fields with voltage-gated ion channels

We study the effect of micro-scale electric fields on voltage-gated ion channels in mammalian cell membranes. Such micro- and nano-scale electric fields mimic the effects of multiferroic nanoparticles that were recently proposed [1] as a novel way of controlling the function of voltage-sensing biomolecules such as ion channels. This article describes experimental procedures and initial results that reveal the effect of the electric field, in close proximity of cells, on the ion transport through voltage-gated ion channels. We present two configurations of the whole-cell patch-clamping apparatus that were used to detect the effect of external stimulation on ionic currents and discuss preliminary results that indicate modulation of the ionic currents consistent with the applied stimulus.

Active polymer translocation in the three-dimensional domain

In this work we study the translocation process of a polymer through a nanochannel where a time dependent force is acting. Two conceptually different types of driving are used: a deterministic sinusoidal one and a random telegraph noise force. The mean translocation time presents interesting resonant minima as a function of the frequency of the external driving. For the computed sizes, the translocation time scales with the polymer length according to a power law with the same exponent for almost all the frequencies of the two driving forces. The dependence of the translocation time with the polymer rigidity, which accounts for the persistence length of the molecule, shows a different low frequency dependence for the two drivings.

On the estimation of cooperativity in ion channel kinetics: activation free energy and kinetic mechanism of Shaker K+ channel

In this paper, we have explored generic criteria of cooperative behavior in ion channel kinetics treating it on the same footing with multistate receptor-ligand binding in a compact theoretical framework. We have shown that the characterization of cooperativity of ion channels in terms of the Hill coefficient violates the standard Hill criteria defined for allosteric cooperativity of ligand binding. To resolve the issue, an alternative measure of cooperativity is proposed here in terms of the cooperativity index that sets a unified criteria for both the systems. More importantly, for ion channel this index can be very useful to describe the cooperative kinetics as it can be readily determined from the experimentally measured ionic current combined with theoretical modelling. We have analyzed the correlation between the voltage value and slope of the voltage-activation curve at the half-activation point and consequently determined the standard free energy of activation of the ion channel using two well-established mechanisms of cooperativity, namely, Koshland-Nemethy-Filmer (KNF) and Monod-Wyman-Changeux (MWC) models. Comparison of the theoretical results for both the models with appropriate experimental data of mutational perturbation of Shaker K(+) channel supports the experimental fact that the KNF model is more suitable to describe the cooperative behavior of this class of ion channels, whereas the performance of the MWC model is unsatisfactory. We have also estimated the mechanistic performance through standard free energy of channel activation for both the models and proposed a possible functional disadvantage in the MWC scheme.

Focusing in multiwell potentials: applications to ion channels

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

Wavelet-based protocols for ion channel electrophysiology

BACKGROUND

Fluctuation-induced phenomena caused by both random and deterministic stimuli have been previously studied in a variety of contexts. They are based on the interplay between the spectro-temporal patterns of the signal and the kinetics of the system it is applied to. The aim of this study was to develop a method for designing fluctuating inputs into nonlinear system which would elicit the most desired system output and to implement the method to studies of ion channels.

RESULTS

We describe an algorithm based on constructing the input as a superposition of wavelets and optimizing it according to a selected cost functional. The algorithm is applied to ion channel electrophysiology where the input is the fluctuating voltage delivered through a patch-clamp experimental apparatus and the output is the whole-cell ionic current. The algorithm is optimized to aid selection of Markov models of the gating kinetics of the voltage-gated Shaker K+ channel and tested by comparison of numerically obtained ionic currents predicted by different models with experimental data obtained from the Shaker K+ channels. Other applications and optimization criteria are also suggested.

CONCLUSION

The method described in this paper can be useful in development and testing of models of ion channel gating kinetics, developing voltage inputs that optimize certain nonequilibrium phenomena in ion channels, such as the kinetic focusing, and potentially has applications to other fields.

Entropy hysteresis and nonequilibrium thermodynamic efficiency of ion conduction in a voltage-gated potassium ion channel

Here we have studied the nonequilibrium thermodynamic response of a voltage-gated Shaker potassium ion channel using a stochastic master equation. For a constant external voltage, the system reaches equilibrium indicated by the vanishing total entropy production rate, whereas for oscillating voltage the current and entropy production rates show dynamic hysteretic behavior. Here we have shown quantitatively that although the hysteresis loop area vanishes in low and high frequency domains of the external voltage, they are thermodynamically distinguishable. In the very low frequency domain, the system remains close to equilibrium, whereas at high frequencies it goes to a nonequilibrium steady state (NESS) associated with a finite value of dissipation function. At NESS, the efficiency of the ion conduction can also be related with the nonlinear dependence of the dissipation function on the power of the external field. Another intriguing aspect is that, at the high frequency limit, the total entropy production rate oscillates at NESS with half of the time period of the external voltage.

Suppression of thermally activated escape by heating

The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential landscape, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level.