A perturbation analysis of spontaneous action potential initiation by stochastic ion channels

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold

Spike Onset Dynamics and Response Speed in Neuronal Populations

Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency of the order of average firing rate or the inverse membrane time constant. The biophysical origin of the observed high cutoff frequencies is thus not well understood. Here we introduce a neuron model with dynamical action potential generation, in which the linear response can be analytically calculated for uncorrelated synaptic noise. We find that the cutoff frequencies increase to very large values when the time scale of action potential initiation becomes short

Action Potential Initiation in the Hodgkin-Huxley Model

A recent paper of B. Naundorf et al. described an intriguing negative correlation between variability of the onset potential at which an action potential occurs (the onset span) and the rapidity of action potential initiation (the onset rapidity). This correlation was demonstrated in numerical simulations of the Hodgkin-Huxley model. Due to this antagonism, it is argued that Hodgkin-Huxley-type models are unable to explain action potential initiation observed in cortical neurons in vivo or in vitro. Here we apply a method from theoretical physics to derive an analytical characterization of this problem. We analytically compute the probability distribution of onset potentials and analytically derive the inverse relationship between onset span and onset rapidity. We find that the relationship between onset span and onset rapidity depends on the level of synaptic background activity. Hence we are able to elucidate the regions of parameter space for which the Hodgkin-Huxley model is able to accurately describe the behavior of this system

Dispersion of cardiac action potential duration and the initiation of re-entry: A computational study

BACKGROUND: The initiation of re-entrant cardiac arrhythmias is associated with increased dispersion of repolarisation, but the details are difficult to investigate either experimentally or clinically. We used a computational model of cardiac tissue to study systematically the association between action potential duration (APD) dispersion and susceptibility to re-entry. METHODS: We simulated a 60 × 60 mm 2 D sheet of cardiac ventricular tissue using the Luo-Rudy phase 1 model, with maximal conductance of the K+ channel gKmax set to 0.004 mS mm-2. Within the central 40 × 40 mm region we introduced square regions with prolonged APD by reducing gKmax to between 0.001 and 0.003 mS mm-2. We varied (i) the spatial scale of these regions, (ii) the magnitude of gKmax in these regions, and (iii) cell-to-cell coupling. RESULTS: Changing spatial scale from 5 to 20 mm increased APD dispersion from 49 to 102 ms, and the susceptible window from 31 to 86 ms. Decreasing gKmax in regions with prolonged APD from 0.003 to 0.001 mS mm-2 increased APD dispersion from 22 to 70 ms, and the susceptible window from <1 to 56 ms. Decreasing cell-to-cell coupling by changing the diffusion coefficient from 0.2 to 0.05 mm2 ms-1 increased APD dispersion from 57 to 88 ms, and increased the susceptible window from 41 to 74 ms. CONCLUSION: We found a close association between increased APD dispersion and susceptibility to re-entrant arrhythmias, when APD dispersion is increased by larger spatial scale of heterogeneity, greater electrophysiological heterogeneity, and weaker cell-to-cell coupling

Arrhythmogenic late Ca2+sparks in failing heart cells and their control by action potential configuration

Sudden death in heart failure patients is a major clinical problem worldwide, but it is unclear how arrhythmogenic early afterdepolarizations (EADs) are triggered in failing heart cells. To examine EAD initiation, high-sensitivity intracellular Ca2+ measurements were combined with action potential voltage clamp techniques in a physiologically relevant heart failure model. In failing cells, the loss of Ca2+ release synchrony at the start of the action potential leads to an increase in number of microscopic intracellular Ca2+ release events (“late” Ca2+ sparks) during phase 2–3 of the action potential. These late Ca2+ sparks prolong the Ca2+ transient that activates contraction and can trigger propagating microscopic Ca2+ ripples, larger macroscopic Ca2+ waves, and EADs. Modification of the action potential to include steps to different potentials revealed the amount of current generated by these late Ca2+ sparks and their (subsequent) spatiotemporal summation into Ca2+ ripples/waves. Comparison of this current to the net current that causes action potential repolarization shows that late Ca2+ sparks provide a mechanism for EAD initiation. Computer simulations confirmed that this forms the basis of a strong oscillatory positive feedback system that can act in parallel with other purely voltage-dependent ionic mechanisms for EAD initiation. In failing heart cells, restoration of the action potential to a nonfailing phase 1 configuration improved the synchrony of excitation–contraction coupling, increased Ca2+ transient amplitude, and suppressed late Ca2+ sparks. Therapeutic control of late Ca2+ spark activity may provide an additional approach for treating heart failure and reduce the risk for sudden cardiac death

Neuromodulation: Action Potential Modeling

There have been many different studies performed in order to examine various properties of neurons. One of the most important properties of neurons is an ability to originate and propagate action potential. The action potential is a source of communication between different neural structures located in different anatomical regions. Many different studies use modeling to describe the action potential and its properties. These models mathematically describe physical properties of neurons and analyze and explain biological and electrochemical processes such as action potential initiation and propagation. Therefore, one of the most important functions of neurons is an ability to provide communication between different neural structures located in different anatomical regions. This is achieved by transmitting electrical signals from one part of the body to another. For example, neurons transmit signals from the brain to the motor neurons (efferent neurons) and from body tissues back to the brain (afferent neurons). This communication process is extremely important for a being to function properly. One of the most valuable studies in neuroscience was conducted by Alan Hodgkin and Andrew Huxley. In their work, Alan Hodgkin and Andrew Huxley used a giant squid axon to create a mathematical model which analyzes and explains the ionic mechanisms underlying the initiation and propagation of action potentials. They received the 1963 Nobel Prize in Physiology/Medicine for their valuable contribution to medical science. The Hodgkin and Huxley model is a mathematical model that describes how the action potential is initiated and how it propagates in a neuron. It is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiomyocytes. This work focuses on modeling the Hodgkin and Huxley model using MATLAB extension - Simulink. This tool provides a graphical editor, customizable block libraries, and solvers for modeling and simulating dynamic systems. Simulink model is used to describe the mechanisms and underlying processes involved in action potential initiation and propagation