Spontaneous Action Potentials and Neural Coding in Unmyelinated Axons

O’Donnell, Cian; Rossum, Mark C. W. van

doi:10.1162/neco_a_00705

Cited by 4 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The impact of random ion channel fluctuations on the timing of action potentials in nerve cells provides an important example. Channel noise can have a significant effect on spike generation (Mainen & Sejnowski, 1995;Schneidman, Freedman, & Segev, 1998), propagation along axons (Faisal & Laughlin, 2007), and spontaneous (ectopic) action potential generation in the absence of stimulation (O'Donnell & van Rossum, 2015). At the network level, channel noise can drive the endogenous variability of vital rhythms such as respiratory activity (Yu, Dhingra, Dick, & Galán, 2017).…”

Section: Introductionmentioning

confidence: 99%

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Thomas

2020

Neural Computation

View full text Add to dashboard Cite

Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor [Formula: see text] and suggested a Langevin formulation with noise coefficient matrix [Formula: see text] such that SS[Formula: see text]. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this letter, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 [Formula: see text] 28 noise coefficient matrix [Formula: see text]. We show that (1) the corresponding 14D system of ordinary differential equations is consistent with the classical 4D representation of the HH system; (2) the 14D representation leads to a noise coefficient matrix [Formula: see text] that can be obtained cheaply on each time step, without requiring a matrix decomposition; (3) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, as well as trajectories of several existing Langevin models; (4) our 14D representation (and those equivalent to it) gives the most accurate interspike interval distribution, not only with respect to moments but under both the [Formula: see text] and [Formula: see text] metric-space norms; and (5) the 14D representation gives an approximation to exact Markov chain simulations that are as fast and as efficient as all equivalent models. Our approach goes beyond existing models, in that it supports a stochastic shielding decomposition that dramatically simplifies [Formula: see text] with minimal loss of accuracy under both voltage- and current-clamp conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Thomas

2020

Neural Computation

View full text Add to dashboard Cite

show abstract

“…Channel noise has been studied in the context of electrical stimulation of the auditory nerve by cochlear implants [15,16] and hippocampal neurons [17]. Noise and voltage fluctuations in excitable cells can also affect spike generation [18,19], propagation along axons [20], and spontaneously generate action potentials in the absence of external stimulation [21].…”

Section: Introductionmentioning

confidence: 99%

Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses

Sokol,

Baker,

Baker

et al. 2024

Biomed. Phys. Eng. Express

View full text Add to dashboard Cite

Noise activity is known to affect neural networks, enhance the system response to weak external signals, and lead to stochastic resonance phenomenon that can effectively amplify signals in nonlinear systems. In most treatments, channel noise has been modeled based on multi-state Markov descriptions or the use stochastic differential equation models. Here we probe a computationally simple approach based on a minor modification of the traditional Hodgkin-Huxley approach to embed noise in neural response. Results obtained from numerous simulations with different excitation frequencies and noise amplitudes for the action potential firing show very good agreement with output obtained from well-established models. Furthermore, results from the Mann-Whitney U test reveal a statistically insignificant difference. The distribution of the time interval between successive potential spikes obtained from this simple approach compared very well with the results of complicated Pu-Thomas type methods at much reduced computational cost. This present method could also possibly be applied to the analysis of spatial variations and/or differences in characteristics of random incident electromagnetic signals.

show abstract

“…Due partly to the sparsity of the experimental data required for model constraint, but also because of the mathematical complexity involved, few analytical results mapping from distributed stochastic synaptic input to the output firing rate for neurons with dendritic structure have followed the early work of Tuckwell [30][31][32]. Nevertheless there is increasing interest in the integrative and firing response of spatial neuron models [33,34], neurons subject to and generating electric fields [35][36][37], and the effect of axonal load and position of the actionpotential initiation region [34,[38][39][40][41][42]. As well the simulation-based approach using multicompartmental reconstructions, a number of recent studies have combined analytical simplifications or reductions of cables coupled to non-linear or spike generating models.…”

Section: Introductionmentioning

confidence: 99%

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

2020

View full text Add to dashboard Cite

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a nonmonotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.

show abstract

Spontaneous Action Potentials and Neural Coding in Unmyelinated Axons

Cited by 4 publications

References 14 publications

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

Contact Info

Product

Resources

About