By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomenon o... more By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomenon of Stochastic Resonance (SR) for a distribution of ion channels within a cluster of variable size. In the presence of a periodic stimulus we demonstrate intrinsic SR vs. decreasing patch size, or, put differently, {vs.} increasing internal noise strength. SR with external noise occurs only for large cluster sizes which possess sub-optimal internal noise levels. In particular, SR in biology thus seemingly is rooted in the collective properties of optimally selected ion channel assemblies. Moreover, upon investigating the signal-to-noise ratio (SNR) for sub-threshold sinusoidal driving vs. driving frequency we encounter also a stochastic resonance behavior which reflects the existence of a random internal limit cycle. The occurrence of intrinsic SR in a combination with the conventional frequency resonance may be of importance for the frequency tuning in biological signal processing.
ABSTRACT By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phe... more ABSTRACT By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomena of Stochastic Resonance (SR) and Coherence Resonance (CR) in assemblies of ion channels. If no stimulus is applied we find the existence of an optimal size of the membrane for which the internal noise alone causes a most regular spiking activity (intrinsic CR). In the presence of an applied stimulus we demonstrate SR vs. decreasing patch size (i. e., vs. increasing internal noise strength). SR with external noise occurs only for large sizes which possess sub-optimal internal noise levels. SR in biology thus seemingly is rooted in the collective properties of large ion channel assemblies. Investigating the signal-to-noise ratio (SNR) for sub-threshold sinusoidal driving vs. the frequency we find a bell-shaped behavior vs. frequency which reflects the existence of a random internal limit cycle. Finally we study the role of synchronization vs. decreasing internal noise intensity (i.e. increasing path area).
ABSTRACT Biology and physics share common ancestors. The progress of methods of statistical physi... more ABSTRACT Biology and physics share common ancestors. The progress of methods of statistical physics and the developments of new physical tools and various ingenious experimental techniques have triggered dramatic progress for the field of biophysics. Likewise, the two fields fertilized each other repeatedly over the last decades. Most import antly, the complexity of biophysics inspired new developments in physics and chemical physics. In this contribution, we focus on some recent problems that attracted the interest of many statistical physicists. Biological cells contain nanoscale machineries that exhibit a unique combination of high efficiency, high reliability and recognition features and self-assembly properties. Most importantly, these biological machines transport material and perform work in a noisy environment. Here, we will elaborate on the constructive role of noise for the amplification and enhanced detection of weak information-carrying signals (Stochastic Resonance in Biology) and directed transport of vesicles and the like (Brownian Motors in Biology). Quantum statistical physics enters the biological complexity at the interface of electronic transport processes and the interaction with light. In this context, physicists and chemists have become increasingly interested in the electronic properties of the »molecule of life«, the DNA. We will comment on the present hot debate whether
ABSTRACT We consider the statistical properties of action potentials generated by clusters of sod... more ABSTRACT We consider the statistical properties of action potentials generated by clusters of sodium and potassium channels due to channel noise and/or external stimulation. Since the fluctuations are related to the cluster size, a size-resonance effect-analog to stochastic resonance-is observed that facilitates optimal decoding of small external stimuli at optimal cluster sizes. Furthermore, in analogy to the coherence resonance effect, the channel-noise induced firing patterns exhibit a resonant-like temporal coherence as a function of the cluster size even in the absence of a periodic stimulus. In the presence of additional synaptic noise, SR occurs only for large cluster sizes which possess suboptimal internal noise levels.
We investigate the influence of gating charge effects on the channel noise-induced spontaneous sp... more We investigate the influence of gating charge effects on the channel noise-induced spontaneous spiking activity of excitable membrane patches [1] within a stochastic Hodgkin-Huxley model [2]. The random switching of the channel gates between an open and a closed configuration is always connected with movement of gating charge within the cell membrane. At the beginning of an action potential the
The in/uence of intrinsic channel noise on the spontaneous spikingactivity of poisoned ex- citabl... more The in/uence of intrinsic channel noise on the spontaneous spikingactivity of poisoned ex- citable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemmingfrom the stochastic dynamics of individual ion channels is known to a3ect the collective properties of the whole ion channel cluster. There exists an optimal size of the membrane patch for which, solely, the internal noise causes a most regular spontaneous generation of action potentials. In addition to the variation of the size of ion channel clusters, living organisms may adopt the densities of ion channels in order to optimally regulate the spontaneous spikingactivity. In our model, we selectively control via poisoningthe densities of speci4c, active ion channels. Interestingly enough, by such poisoning of some of the potas- sium, or the sodium ion channels, respectively, it is possible to either increase, or decrease the regularity of the spike train. c
By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomenon o... more By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomenon of Stochastic Resonance (SR) for a distribution of ion channels within a cluster of variable size. In the presence of a periodic stimulus we demonstrate intrinsic SR vs. decreasing patch size, or, put differently, {vs.} increasing internal noise strength. SR with external noise occurs only for large cluster sizes which possess sub-optimal internal noise levels. In particular, SR in biology thus seemingly is rooted in the collective properties of optimally selected ion channel assemblies. Moreover, upon investigating the signal-to-noise ratio (SNR) for sub-threshold sinusoidal driving vs. driving frequency we encounter also a stochastic resonance behavior which reflects the existence of a random internal limit cycle. The occurrence of intrinsic SR in a combination with the conventional frequency resonance may be of importance for the frequency tuning in biological signal processing.
ABSTRACT By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phe... more ABSTRACT By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomena of Stochastic Resonance (SR) and Coherence Resonance (CR) in assemblies of ion channels. If no stimulus is applied we find the existence of an optimal size of the membrane for which the internal noise alone causes a most regular spiking activity (intrinsic CR). In the presence of an applied stimulus we demonstrate SR vs. decreasing patch size (i. e., vs. increasing internal noise strength). SR with external noise occurs only for large sizes which possess sub-optimal internal noise levels. SR in biology thus seemingly is rooted in the collective properties of large ion channel assemblies. Investigating the signal-to-noise ratio (SNR) for sub-threshold sinusoidal driving vs. the frequency we find a bell-shaped behavior vs. frequency which reflects the existence of a random internal limit cycle. Finally we study the role of synchronization vs. decreasing internal noise intensity (i.e. increasing path area).
ABSTRACT Biology and physics share common ancestors. The progress of methods of statistical physi... more ABSTRACT Biology and physics share common ancestors. The progress of methods of statistical physics and the developments of new physical tools and various ingenious experimental techniques have triggered dramatic progress for the field of biophysics. Likewise, the two fields fertilized each other repeatedly over the last decades. Most import antly, the complexity of biophysics inspired new developments in physics and chemical physics. In this contribution, we focus on some recent problems that attracted the interest of many statistical physicists. Biological cells contain nanoscale machineries that exhibit a unique combination of high efficiency, high reliability and recognition features and self-assembly properties. Most importantly, these biological machines transport material and perform work in a noisy environment. Here, we will elaborate on the constructive role of noise for the amplification and enhanced detection of weak information-carrying signals (Stochastic Resonance in Biology) and directed transport of vesicles and the like (Brownian Motors in Biology). Quantum statistical physics enters the biological complexity at the interface of electronic transport processes and the interaction with light. In this context, physicists and chemists have become increasingly interested in the electronic properties of the »molecule of life«, the DNA. We will comment on the present hot debate whether
ABSTRACT We consider the statistical properties of action potentials generated by clusters of sod... more ABSTRACT We consider the statistical properties of action potentials generated by clusters of sodium and potassium channels due to channel noise and/or external stimulation. Since the fluctuations are related to the cluster size, a size-resonance effect-analog to stochastic resonance-is observed that facilitates optimal decoding of small external stimuli at optimal cluster sizes. Furthermore, in analogy to the coherence resonance effect, the channel-noise induced firing patterns exhibit a resonant-like temporal coherence as a function of the cluster size even in the absence of a periodic stimulus. In the presence of additional synaptic noise, SR occurs only for large cluster sizes which possess suboptimal internal noise levels.
We investigate the influence of gating charge effects on the channel noise-induced spontaneous sp... more We investigate the influence of gating charge effects on the channel noise-induced spontaneous spiking activity of excitable membrane patches [1] within a stochastic Hodgkin-Huxley model [2]. The random switching of the channel gates between an open and a closed configuration is always connected with movement of gating charge within the cell membrane. At the beginning of an action potential the
The in/uence of intrinsic channel noise on the spontaneous spikingactivity of poisoned ex- citabl... more The in/uence of intrinsic channel noise on the spontaneous spikingactivity of poisoned ex- citable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemmingfrom the stochastic dynamics of individual ion channels is known to a3ect the collective properties of the whole ion channel cluster. There exists an optimal size of the membrane patch for which, solely, the internal noise causes a most regular spontaneous generation of action potentials. In addition to the variation of the size of ion channel clusters, living organisms may adopt the densities of ion channels in order to optimally regulate the spontaneous spikingactivity. In our model, we selectively control via poisoningthe densities of speci4c, active ion channels. Interestingly enough, by such poisoning of some of the potas- sium, or the sodium ion channels, respectively, it is possible to either increase, or decrease the regularity of the spike train. c
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