Non-Markovian stochastic resonance: three-state model of ion channel gating.

Stochastic resonance in single voltage-dependent ion channels is investigated within a three-state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an additional closed state for the ion channel which mimics the manifold of voltage-independent closed subconformations (inactivated "state"). The conformational transition into the open state occurs through a domain of voltage-dependent closed subconformations (closed "state"). At distinct variance with the standard two-state and also the three-state Markovian approach, the inactivated state is characterized by a broad, nonexponential probability distribution of corresponding residence times. The linear response to a periodic voltage signal is determined for arbitrary distributions of the channel's recovery times. Analytical results are obtained for the spectral amplification of the applied signal and the corresponding signal-to-noise ratio. Alternatively, these results are also derived by use of a corresponding two-state non-Markovian theory which is based on driven integral renewal equations [I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004)]. The non-Markovian features of stochastic resonance are studied for a power law distribution of the residence time intervals in the inactivated state which exhibits a large variance. A comparison with the case of biexponentially distributed residence times possessing the same mean value, i.e., the simplest non-Markovian two-state description, is also presented.

[1]  R. L. Stratonovich,et al.  Topics in the theory of random noise , 1967 .

[2]  L S Liebovitch,et al.  Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. , 1987, Biophysical journal.

[3]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[4]  Closed-time distribution of ionic channels. Analytical solution to a one-dimensional defect-diffusion model. , 1989, Biophysical journal.

[5]  B. Hille.  Ionic channels of excitable membranes , 2001 .

[6]  Bruce J. West,et al.  Fractal physiology for physicists: Lévy statistics , 1994 .

[7]  Peter Hänggi,et al.  STOCHASTIC RESONANCE AND OPTIMAL CLUSTERING FOR ASSEMBLIES OF ION CHANNELS , 2004, The Random and Fluctuating World.

[8]  Bernd Nilius,et al.  The principle of temperature-dependent gating in cold- and heat-sensitive TRP channels , 2004, Nature.

[9]  V. M. Kenkre,et al.  Generalized master equations for continuous-time random walks , 1973 .

[10]  P. Hänggi,et al.  Theory of non-Markovian stochastic resonance. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  I. Goychuk,et al.  Stochastic resonance as a collective property of ion channel assemblies , 2001, physics/0106036.

[12]  Jung,et al.  Amplification of small signals via stochastic resonance. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[13]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[14]  Peter Hänggi,et al.  Theory of frequency and phase synchronization in a rocked bistable stochastic system. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[16]  J. Sandblom,et al.  Amplification of electromagnetic signals by ion channels. , 1997, Biophysical journal.

[17]  P. M. Lee,et al.  Random Walks and Random Environments: Volume 1: Random Walks , 1995 .

[18]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[19]  A. Burshtein,et al.  Non-Markov theory of sudden modulation , 1986 .

[20]  Jung,et al.  Resonantly driven Brownian motion: Basic concepts and exact results. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[21]  I. Goychuk,et al.  Information transfer with rate-modulated Poisson processes: a simple model for nonstationary stochastic resonance. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  F Bezanilla,et al.  Gating of Shaker K+ channels: II. The components of gating currents and a model of channel activation. , 1994, Biophysical journal.

[23]  L. Schimansky-Geier,et al.  Stochastic resonance in a non-markovian discrete state model for excitable systems. , 2003, Physical review letters.

[24]  P. Hänggi,et al.  Oscillatory systems driven by noise: frequency and phase synchronization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Lukasz Machura,et al.  Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems , 2004, physics/0409065.

[26]  E. Salpeter,et al.  Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[27]  P. Hänggi,et al.  Non-Markovian stochastic resonance. , 2003, Physical review letters.

[28]  Quantum dynamics with non-Markovian fluctuating parameters. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  P. Hänggi,et al.  Fractional diffusion modeling of ion channel gating. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Peter Hänggi,et al.  Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing. , 2002, Chemphyschem : a European journal of chemical physics and physical chemistry.

[31]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[32]  Larry S. Liebovitch,et al.  Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes , 1987 .

[33]  M. Pellegrino,et al.  Periodic forcing of a K+ channel at various temperatures. , 1994, Biophysical journal.

[34]  The role of conformational di"usion in ion channel gating , 2003, physics/0601071.

[35]  Sergey M. Bezrukov,et al.  Stochastic resonance in non-dynamical systems without response thresholds , 1997, Nature.

[36]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[37]  Peter Hänggi,et al.  Stochastic Nonlinear Dynamics Modulated by External Periodic Forces , 1989 .

[38]  P. Hänggi,et al.  Frequency and phase synchronization in stochastic systems. , 2002, Chaos.

[39]  Peter Jung,et al.  Optimal sizes of ion channel clusters , 2001 .

[40]  S. Marom,et al.  Slow Changes in the Availability of Voltage-gated Ion Channels: Effects on the Dynamics of Excitable Membranes , 1998, The Journal of Membrane Biology.

[41]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[42]  Sergey M. Bezrukov,et al.  Noise-induced enhancement of signal transduction across voltage-dependent ion channels , 1995, Nature.

[43]  Peter Hänggi,et al.  Ion channel gating: A first-passage time analysis of the Kramers type , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[44]  P Hänggi,et al.  Stochastic resonance in ion channels characterized by information theory. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[45]  S. Marom,et al.  Effects of Density and Gating of Delayed-Rectifier Potassium Channels on Resting Membrane Potential and its Fluctuations , 1996, The Journal of Membrane Biology.

[46]  Frank Moss,et al.  Stochastic resonance: noise-enhanced order , 1999 .