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1.
Phys Rev Lett ; 126(21): 218102, 2021 May 28.
Artículo en Inglés | MEDLINE | ID: mdl-34114848

RESUMEN

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.


Asunto(s)
Canales Iónicos/química , Canales Iónicos/genética , Modelos Biológicos , Modelos Químicos , Mutación Puntual , Proteínas Bacterianas/química , Proteínas Bacterianas/genética , Proteínas Bacterianas/metabolismo , Sitios de Unión , Fenómenos Biofísicos , Canales Iónicos/metabolismo , Modelos Genéticos , Modelos Moleculares , Canales de Potasio/química , Canales de Potasio/genética , Canales de Potasio/metabolismo , Termodinámica
2.
Biochim Biophys Acta Biomembr ; 1862(9): 183301, 2020 09 01.
Artículo en Inglés | MEDLINE | ID: mdl-32360369

RESUMEN

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Qf at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing ∣Qf∣ should lead to a shift in selectivity sequences toward larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Qf∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Qf∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca2+ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca2+ conduction on pH are qualitatively consistent with the predictions of the model.


Asunto(s)
Secuencia de Aminoácidos/genética , Líquidos Iónicos/química , Canales de Sodio/química , Ácido Aspártico/química , Calcio/metabolismo , Ácido Glutámico/química , Iones/química , Mutagénesis Sitio-Dirigida , Técnicas de Placa-Clamp , Canales de Sodio/genética
3.
Artículo en Inglés | MEDLINE | ID: mdl-24329301

RESUMEN

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.


Asunto(s)
Canales de Calcio/genética , Canales de Calcio/metabolismo , Modelos Biológicos , Mutación , Canales de Sodio/genética , Canales de Sodio/metabolismo , Calcio/metabolismo , Reproducibilidad de los Resultados , Sodio/metabolismo , Especificidad por Sustrato , Termodinámica
4.
Phys Biol ; 10(2): 026007, 2013 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-23481350

RESUMEN

We report self-consistent Brownian dynamics simulations of a simple electrostatic model of the selectivity filters (SF) of calcium ion channels. They reveal regular structure in the conductance and selectivity as functions of the fixed negative charge Qf at the SF. With increasing Qf, there are distinct regions of high conductance (conduction bands) M0, M1, M2 separated by regions of almost zero-conductance (stop-bands). Two of these conduction bands, M1 and M2, are related to the saturated calcium occupancies of P = 1 and P = 2, respectively and demonstrate self-sustained conductivity. Despite the model's limitations, its M1 and M2 bands show high calcium selectivity and prominent anomalous mole fraction effects and can be identified with the L-type and RyR calcium channels. The non-selective band M0 can be identified with a non-selective cation channel, or with OmpF porin.


Asunto(s)
Canales de Calcio/metabolismo , Calcio/metabolismo , Simulación por Computador , Modelos Biológicos , Canales de Calcio/química , Conductividad Eléctrica , Electricidad Estática
5.
Phys Rev E Stat Nonlin Soft Matter Phys ; 80(2 Pt 1): 021925, 2009 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-19792169

RESUMEN

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.


Asunto(s)
Conductividad Eléctrica , Activación del Canal Iónico , Canales Iónicos/metabolismo , Modelos Biológicos , Difusión , Canales Iónicos/química , Modelos Lineales , Porosidad , Electricidad Estática
6.
Phys Rev Lett ; 96(8): 083903, 2006 Mar 03.
Artículo en Inglés | MEDLINE | ID: mdl-16606182

RESUMEN

Continuous and pulsed forms of control of a multistable system are compared directly, both theoretically and numerically, taking as an example the switching of a periodically driven class-B laser between its stable and unstable pulsing regimes. It is shown that continuous control is the more energy efficient. This result is illuminated by making use of the close correspondence that exists between the problems of energy-optimal control and the stability of a steady state.


Asunto(s)
Rayos Láser , Modelos Teóricos , Dinámicas no Lineales
7.
Phys Rev E Stat Nonlin Soft Matter Phys ; 72(3 Pt 2): 036131, 2005 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-16241539

RESUMEN

Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.

8.
Phys Rev E Stat Nonlin Soft Matter Phys ; 72(2 Pt 1): 021905, 2005 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-16196602

RESUMEN

We present a Bayesian dynamical inference method for characterizing cardiorespiratory (CR) dynamics in humans by inverse modeling from blood pressure time-series data. The technique is applicable to a broad range of stochastic dynamical models and can be implemented without severe computational demands. A simple nonlinear dynamical model is found that describes a measured blood pressure time series in the primary frequency band of the CR dynamics. The accuracy of the method is investigated using model-generated data with parameters close to the parameters inferred in the experiment. The connection of the inferred model to a well-known beat-to-beat model of the baroreflex is discussed.


Asunto(s)
Determinación de la Presión Sanguínea/métodos , Presión Sanguínea/fisiología , Diagnóstico por Computador/métodos , Frecuencia Cardíaca/fisiología , Modelos Biológicos , Oscilometría/métodos , Mecánica Respiratoria/fisiología , Algoritmos , Relojes Biológicos/fisiología , Simulación por Computador , Humanos , Modelos Estadísticos , Dinámicas no Lineales , Flujo Pulsátil/fisiología
9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 72(2 Pt 2): 026202, 2005 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-16196679

RESUMEN

An algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. The strengths of the algorithm are illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. The efficiency and accuracy of the algorithm are further demonstrated by inferring a model for a system of five globally and locally coupled noisy oscillators.

10.
Phys Rev E Stat Nonlin Soft Matter Phys ; 71(4 Pt 2): 046203, 2005 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-15903766

RESUMEN

We study fluctuational transitions in discrete and continuous dynamical systems that have two coexisting attractors in phase space, separated by a fractal basin boundary which may be either locally disconnected or locally connected. Theoretical and numerical evidence is given to show that, in each case, the transition occurs via a unique accessible point on the boundary, both in discrete systems and in flows. The complicated structure of the escape paths inside the locally disconnected fractal basin boundary is determined by a hierarchy of homoclinic points. The interrelation between the mechanism of transitions and the hierarchy is illustrated by consideration of fluctuational transitions in dynamical systems demonstrating "fractal-fractal" basin boundary metamorphosis at some value of a control parameter. The most probable escape path from an attractor, which can be either regular or chaotic, is found for each type of boundary using both statistical analysis of fluctuational trajectories and the Hamiltonian theory of fluctuations.

11.
Phys Rev Lett ; 94(9): 098101, 2005 Mar 11.
Artículo en Inglés | MEDLINE | ID: mdl-15784004

RESUMEN

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.


Asunto(s)
Fenómenos Fisiológicos Cardiovasculares , Modelos Cardiovasculares , Dinámicas no Lineales , Presión Sanguínea/fisiología , Procesos Estocásticos
12.
Phys Rev Lett ; 91(17): 174104, 2003 Oct 24.
Artículo en Inglés | MEDLINE | ID: mdl-14611351

RESUMEN

Fluctuational transitions between two coexisting chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the transition mechanism is determined by a hierarchy of homoclinic points. The most probable escape path from a chaotic attractor to the fractal boundary is found using both statistical analyses of fluctuational trajectories and the Hamiltonian theory of fluctuations.

13.
Phys Rev Lett ; 90(21): 210201, 2003 May 30.
Artículo en Inglés | MEDLINE | ID: mdl-12786539

RESUMEN

A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of nonequilibrium systems. Results for the quasistationary probability distribution in two model systems are compared with the asymptotically exact theory in the limit of extremely small noise intensity. Singularities of the nonequilibrium distributions are revealed by the simulations.

14.
Phys Rev E Stat Nonlin Soft Matter Phys ; 66(2 Pt 1): 021108, 2002 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-12241151

RESUMEN

Singular behavior and the formation of plateaus in the probability distribution in a nonadiabatically driven system are investigated numerically in the weak noise limit. A simple extension of the recently introduced logarithmic susceptibility theory is proposed to construct an approximation of the nonequilibrium potential that is valid throughout whole of the phase space.

15.
Physiol Meas ; 22(3): 551-64, 2001 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-11556674

RESUMEN

A mathematical model of the cardiovascular system is simulated numerically. The basic unit in the model is an oscillator that possesses a structural stability and robustness motivated by physiological understanding and by the analysis of measured time series. Oscillators with linear couplings are found to reproduce the main characteristic features of the experimentally obtained spectra. To explain the variability of cardiac and respiratory frequencies, however, it is essential to take into account the rest of the system, i.e. to consider the effect of noise. It is found that the addition of noise also results in epochs of synchronization, as observed experimentally. Preliminary analysis suggests that there is a mixture of linear and parametric couplings, but that the linear coupling seems to dominate.


Asunto(s)
Modelos Cardiovasculares , Periodicidad , Artefactos , Presión Sanguínea/fisiología , Frecuencia Cardíaca/fisiología , Humanos , Dinámicas no Lineales , Flujo Sanguíneo Regional/fisiología , Procesos Estocásticos
16.
Chaos ; 11(3): 587-594, 2001 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-12779496

RESUMEN

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.

17.
Chaos ; 11(3): 595-604, 2001 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-12779497

RESUMEN

Noise-induced escape from the metastable part of a potential is considered on time scales preceding the formation of quasiequilibrium within that part of the potential. It is shown that, counterintuitively, the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction. (c) 2001 American Institute of Physics.

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