اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnalytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation
77
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval, there is four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary dynamic state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant asymptotic value of the neuron potential. We have shown that in the vicinity of the asymptote the Morris-Lecar equations can be reduced to the standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping.
قيم البحث
اقرأ أيضاً
We show that the stochastic Morris-Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein-Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a lea
ky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris-Lecar firing statistics reproduces the Morris-Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of attention paid to the LIF models.
Simulating and imitating the neuronal network of humans or mammals is a popular topic that has been explored for many years in the fields of pattern recognition and computer vision. Inspired by neuronal conduction characteristics in the primary visua
l cortex of cats, pulse-coupled neural networks (PCNNs) can exhibit synchronous oscillation behavior, which can process digital images without training. However, according to the study of single cells in the cat primary visual cortex, when a neuron is stimulated by an external periodic signal, the interspike-interval (ISI) distributions represent a multimodal distribution. This phenomenon cannot be explained by all PCNN models. By analyzing the working mechanism of the PCNN, we present a novel neuron model of the primary visual cortex consisting of a continuous-coupled neural network (CCNN). Our model inherited the threshold exponential decay and synchronous pulse oscillation property of the original PCNN model, and it can exhibit chaotic behavior consistent with the testing results of cat primary visual cortex neurons. Therefore, our CCNN model is closer to real visual neural networks. For image segmentation tasks, the algorithm based on CCNN model has better performance than the state-of-art of visual cortex neural network model. The strength of our approach is that it helps neurophysiologists further understand how the primary visual cortex works and can be used to quantitatively predict the temporal-spatial behavior of real neural networks. CCNN may also inspire engineers to create brain-inspired deep learning networks for artificial intelligence purposes.
During wakefulness and deep sleep brain states, cortical neural networks show a different behavior, with the second characterized by transients of high network activity. To investigate their impact on neuronal behavior, we apply a pairwise Ising mode
l analysis by inferring the maximum entropy model that reproduces single and pairwise moments of the neurons spiking activity. In this work we first review the inference algorithm introduced in Ferrari,Phys. Rev. E (2016). We then succeed in applying the algorithm to infer the model from a large ensemble of neurons recorded by multi-electrode array in human temporal cortex. We compare the Ising model performance in capturing the statistical properties of the network activity during wakefulness and deep sleep. For the latter, the pairwise model misses relevant transients of high network activity, suggesting that additional constraints are necessary to accurately model the data.
One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cel
ls voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesnt, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochast
The input-output behaviour of the Wiener neuronal model subject to alternating input is studied under the assumption that the effect of such an input is to make the drift itself of an alternating type. Firing densities and related statistics are obta
ined via simulations of the sample-paths of the process in the following three cases: the drift changes occur during random periods characterized by (i) exponential distribution, (ii) Erlang distribution with a preassigned shape parameter, and (iii) deterministic distribution. The obtained results are compared with those holding for the Wiener neuronal model subject to sinusoidal input
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
