Related papers: How is information transmitted in a nerve?
Neurons are the central biological objects in understanding how the brain works. The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear…
This paper introduces a model of excitability that unifies the mechanism of an important neuronal property both in time and in space. As a starting point, we revisit both a key model of temporal excitability, proposed by Hodgkin and Huxley,…
We consider noise-assisted spike propagation in myelinated axons within a multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal…
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…
Based on numerical simulation of Hodgkin and Huxley type neuron stimulated from many synaptic inputs, an abstract concept of signal processing in individual neuron is proposed. In the concept proposed, neuron performs binding of synaptic…
Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many…
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a single local layer of visual cortex V1. Our…
Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with…
Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations,…
In a recent paper [A. Moujahid, A. d'Anjou, F. J. Torrealdea and F. Torrealdea, Phys. Rev. E {\bf 83}, 031912 (2011)], the authors have calculated the energy consumed in firing neurons by using the Hodgkin-Huxley (HH) model. The energy…
How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here we use the classic Hodgkin-Huxley formulation of…
We develop a mathematical model of information transmission across the biological neural network of the human brain. The overall function of the brain consists of the emergent processes resulting from the spread of information through the…
Hodgkin-Huxley equations as a monumental breakthrough in biological and physiological theory of the 20th century had been distilled into many simplified models to study, typically FitzHugh-Nagumo equations and Hindmarsh-Rose equations, but…
The generation and conduction of action potentials represents a fundamental means of communication in the nervous system, and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in a…
Recent studies have revealed the complex structure of nerve signals in axons. Besides the electrical signal, mechanical and thermal effects are also detected in many experimental studies. In this paper, the mathematical models of heat…
Mathematical models describing the signals propagating in nerve fibres are described. The emphasis is on the mathematical structures of governing equations while the extremely rich physiological aspects are here not analysed. Based on…
The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a constant current to the system results in a single voltage spike, it is possible to produce more…
Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information.…
A wide range of networked systems exhibit highly connected nodes (hubs) as prominent structural elements. The functional roles of hubs in the collective nonlinear dynamics of many such networks, however, are not well understood. Here we…
We suggest that the propagation of the action potential is driven by a pressure pulse propagating in the axoplasm along the axon length. The pressure pulse mechanically activates Na ion channels embedded in the axon membrane. This…