Related papers: The Nature of the Action Potential
The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual…
We study a stochastic process describing the continuous time evolution of the membrane potentials of finite system of neurons in the absence of external stimuli. The values of the membrane potentials evolve under the effect of {\it chemical…
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…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends…
Stimulated by ongoing discussions about the relevance of mechanical motion in the propagation of nerve signals capillary waves of water-based electrolytes in elastic tubular systems are considered as an essential ingredient. Their…
Serotonergic, noradrenergic and dopaminergic brainstem (including midbrain) neurons, often exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz, though dopaminergic and noradrenergic neurons only exhibit such…
The soliton wave model of action potentials, and the proposal of induced lipid pores, are potentially paradigm shifting ideas which challenge accepted views of the Hodgkin-Huxley model and of protein-based ion channels. These two proposals…
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…
Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant…
This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses. This system can be informally…
In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We do not impose on the neurons mean-field type interactions.…
We consider a system of $N$ neurons, each spiking randomly with rate depending on its membrane potential. When a neuron spikes, its potential is reset to $0$ and all other neurons receive an additional amount $h/N$ of potential, where $ h >…
Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…
We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems…
The functional significance of correlations between action potentials of neurons is still a matter of vivid debates. In particular it is presently unclear how much synchrony is caused by afferent synchronized events and how much is…
In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory…
In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…
A new stimulation paradigm is presented for the stimulation of nerve cells by extracellular electric currents. In the new paradigm stimulation is achieved with the current spike induced by a voltage step whenever the voltage step is applied…
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…