Noisy saltatory spike propagation: The breakdown of signal transmission due to channel noise

Noisy saltatory spike propagation along myelinated axons is studied within a stochastic Hodgkin-Huxley model. The intrinsic noise (whose strength is inverse proportional to the nodal membrane size) arising from fluctuations of the number of open ion channels influences the dynamics of the membrane potential in a node of Ranvier where the sodium ion channels are predominantly localized. The nodes of Ranvier are linearly coupled. As the measure for the signal propagation reliability we focus on the ratio between the number of initiated spikes and the transmitted spikes. This work supplements our earlier study [A. Ochab-Marcinek, G. Schmid, I. Goychuk and P. H\"anggi, Phys. Rev E 79, 011904 (2009)] towards stronger channel noise intensity and supra-threshold coupling. For strong supra-threshold coupling the transmission reliability decreases with increasing channel noise level until the causal relationship is completely lost and a breakdown of the spike propagation due to the intrinsic noise is observed.Comment: To appear in EPJS

«The burning question of physicochemical science». Philosophical remarks about Thomas Huxley's reading of Cartesian physics

A Descartes, Thomas H. Huxley (1825-1895) riserva un posto particolare nelle sue opere. Le sue concezioni fisiche e metafisiche costituirebbero la prova che il Francese sarebbe il precursore sia dell’idealismo sia del materialismo del suo tempo e perciò Huxley rinviene nei suoi lavori sulla fisica importanti suggerimenti tanto per la filosofia quanto per la scienza ottocentesche. Le strade più significative che Descartes avrebbe percorso riguardano «la fondazione di una cosmogonia razionale e di una psicologia fisiologica». Il fatto che il mondo (fisico e organico) è subordinato alle medesime leggi della scienza proverebbe che Descartes si trovasse nel giusto. Per questo motivo riteniamo che Huxley attraverso la sua operazione intellettuale miri sostanzialmente a combattere il Positivismo difendendo il valore della New Philosophy. Sosteniamo la tesi che Huxley consideri necessaria una ripresa del razionalismo cartesiano all’interno della filosofia del XIX secolo: i) per rafforzare le asserzioni della scienza in ambito metodologico; ii) per sostenere la tesi che le leggi di natura sono solo astrazioni matematiche e non descrizioni noumeniche della realtà naturale. Riguardo al primo punto, Huxley si avvale della fisica cartesiana come se si trattasse della porzione di un nuovo meccanicismo fisiologico; la seconda tesi ci porterebbe a considerare le leggi di natura di Descartes come un tentativo di integrare le istanze di Descartes e di Hume.Descartes has a special place in the works of Thomas H. Huxley (1825-1895). Descartes’ physics and metaphysics makes him think that the French Philosopher was the ancestor as much of the idealism as of the materialism of his time. Huxley shows that Descartes’s works on physics are full of important suggestions for the philosophy and science of the 19th century. The most important paths Descartes pointed out were in his view the «foundations of rational cosmogony and of physiological psychology». The fact that the (physical and organic) world is subordinate to identical scientific laws proves that Descartes was right. I argue that Huxley’s intellectual operation strives to undermine Comtean positivism and to preserve the New Philosophy. I suppose that Huxley considers the presence of Cartesian rationalism in the 19th century as necessary: i) to strengthen the methodological assertions of science; ii) to support the argument that the laws of nature are only mathematical abstractions and not ‘noumenal’ descriptions of nature. On the first issue, Huxley introduces Cartesian physics as a portion of the new mechanism in physiology; the second hypothesis leads us to consider the Cartesian laws of nature as an attempt to integrate both Descartes’ and Hume’s points of view

An experiment with science for the nineteenth- century book trade: the International Scientific Series

The theory, method and disciplinary foundations of ‘book history’ are addressed in the context of a close examination of the International Scientific Series, a set of monographs that appeared from 1871 to 1911 in Britain, France, Germany, Italy, Russia and the United States. Working closely with entrepreneurial publishers, most authors of ISS volumes were scientific professionals (T. H. Huxley, John Tyndall, Herbert Spencer and E. L. Youmans were among the founders) aiming to educate a broad popular audience. Commercial, scholarly and other pressures made the texts less fixed than they appear: revisions, appendices and other evidences of textual instability have been overlooked by previous commentators

A Microscopic Mechanism for Muscle's Motion

The SIRM (Stochastic Inclined Rods Model) proposed by H. Matsuura and M. Nakano can explain the muscle's motion perfectly, but the intermolecular potential between myosin head and G-actin is too simple and only repulsive potential is considered. In this paper we study the SIRM with different complex potential and discuss the effect of the spring on the system. The calculation results show that the spring, the effective radius of the G-actin and the intermolecular potential play key roles in the motion. The sliding speed is about $4.7\times10^{-6}m/s$ calculated from the model which well agrees with the experimental data.Comment: 9 pages, 6 figure

Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator

The Hodgkin-Huxley model describes action potential generation in certain types of neurons and is a standard model for conductance-based, excitable cells. Following the early work of Winfree and Best, this paper explores the response of a spontaneously spiking Hodgkin-Huxley neuron model to a periodic pulsatile drive. The response as a function of drive period and amplitude is systematically characterized. A wide range of qualitatively distinct responses are found, including entrainment to the input pulse train and persistent chaos. These observations are consistent with a theory of kicked oscillators developed by Qiudong Wang and Lai-Sang Young. In addition to general features predicted by Wang-Young theory, it is found that most combinations of drive period and amplitude lead to entrainment instead of chaos. This preference for entrainment over chaos is explained by the structure of the Hodgkin-Huxley phase resetting curve.Comment: Minor revisions; modified Fig. 3; added reference

Macroscopic equations governing noisy spiking neuronal populations

At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely relied on heuristic partial (and partially justified) macroscopic models, which successfully reproduced a number of relevant phenomena. The relationship between these macroscopic models and the spiking noisy dynamics of the underlying cells has since then been a great endeavor. Based on recent mean-field reductions for such spiking neurons, we present here {a principled reduction of large biologically plausible neuronal networks to firing-rate models, providing a rigorous} relationship between the macroscopic activity of populations of spiking neurons and popular macroscopic models, under a few assumptions (mainly linearity of the synapses). {The reduced model we derive consists of simple, low-dimensional ordinary differential equations with} parameters and {nonlinearities derived from} the underlying properties of the cells, and in particular the noise level. {These simple reduced models are shown to reproduce accurately the dynamics of large networks in numerical simulations}. Appropriate parameters and functions are made available {online} for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley models