A space-fractional cable equation for the propagation of action potentials in myelinated neurons

Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells, and the extracellular space. Given the complexity of brain's structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A space-fractional cable equation for the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non-locality on the distribution of the membrane potential are investigated using numerical simulations.Comment: 20 pages, 14 figures; added reference, updated formulas, added new formulas, corrected typos, added 4 figure

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation

Modulation of neural cell membrane conductance by the herbal anxiolytic and antiepileptic drug aswal

To evaluate the effects of aswal on ionic fluxes and neuronal excitation, we performed extracellular and whole cell patch clamp recordings on CA1 pyramidal neurons of guinea pigs and Long-Evans rats. Aswal (100-250 mg/l) was administered systemically, and its effects on the rate of synchronized extracellular field potentials (EFP), membrane parameters, action potentials and postsynaptic potentials were recorded. The extracellular results obtained are consistent with calcium antagonistic properties. Intracellular recordings suggest that a direct sodium antagonistic effect as seen in many antiepileptic drugs plays no significant role. Further effects on ligand gated ion channels are discussed controversially. In summary, the cellular action of aswal appears heterogeneous with calcium antagonism playing a prominent role in counteracting excitation which may be a common feature in epilepsy and different psychiatric conditions as mood and anxiety disorder. Copyright (C) 2000 S. Karger AG, Basel

Deforming tachyon kinks and tachyon potentials

In this paper we investigate deformation of tachyon potentials and tachyon kink solutions. We consider the deformation of a DBI type action with gauge and tachyon fields living on D1-brane and D3-brane world-volume. We deform tachyon potentials to get other consistent tachyon potentials by using properly a deformation function depending on the gauge field components. Resolutions of singular tachyon kinks via deformation and applications of deformed tachyon potentials to scalar cosmology scenario are discussed.Comment: To appear in JHEP, 19 pages, 5 eps figures, minor changes and one reference adde

Similarities between action potentials and acoustic pulses in a van der Waals fluid

An action potential is typically described as a purely electrical change that propagates along the membrane of excitable cells. However, recent experiments have demonstrated that non-linear acoustic pulses that propagate along lipid interfaces and traverse the melting transition, share many similar properties with action potentials. Despite the striking experimental similarities, a comprehensive theoretical study of acoustic pulses in lipid systems is still lacking. Here we demonstrate that an idealized description of an interface near phase transition captures many properties of acoustic pulses in lipid monolayers, as well as action potentials in living cells. The possibility that action potentials may better be described as acoustic pulses in soft interfaces near phase transition is illustrated by the following similar properties: correspondence of time and velocity scales, qualitative pulse shape, sigmoidal response to stimulation amplitude (an `all-or-none' behavior), appearance in multiple observables (particularly, an adiabatic change of temperature), excitation by many types of stimulations, as well as annihilation upon collision. An implication of this work is that crucial functional information of the cell may be overlooked by focusing only on electrical measurements.Comment: 8 pages, 5 figure

Matrix Ernst Potentials and Orthogonal Symmetry for Heterotic String in Three Dimensions

A new matrix representation for low-energy limit of heterotic string theory reduced to three dimensions is considered. The pair of matrix Ernst Potentials uniquely connected with the coset matrix is derived. The action of the symmetry group on the Ernst potentials is established.Comment: 10 pages in LaTe