Generalisation of neuronal excitability allows for the identification of an excitability change parameter that links to an experimentally measurable value
Jantine A. C. Broek, Guillaume Drion
备注：
21 pages, 10 main figures, 3 supplementary figures
Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect information processing, such as thresholding and gain scaling. These properties can be mathematically studied using generalised phenomenological models, such as the Fitzhugh-Nagumo model and the mirrored FHN. The FHN model shows that each excitability type corresponds to one specific type of bifurcation in the phase plane: Type I underlies a saddle-node on invariant cycle bifurcation, and Type II a Hopf bifurcation. The difficulty of modelling Type I excitability is that it is not only represented by its underlying bifurcation, but also should be able to generate frequency while maintaining a small depolarising current. Using the mFHN model, we show that this situation is possible without modifying the phase portrait, due to the incorporation of a slow regenerative variable. We show that in the singular limit of the mFHN model, the time-scale separation can be chosen such that there is a configuration of a classical phase portrait that allows for SNIC bifurcation, zero-frequency onset and a depolarising current, such as observed in Type I excitability. Using the definition of slow conductance, g_s, we show that these mathematical findings for excitability change are translatable to reduced conductance based models and also relates to an experimentally measurable quantity. This not only allows for a measure of excitability change, but also relates the mathematical parameters that indicate a physiological Type I excitability to parameters that can be tuned during experiments.
The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables.
Neuronal excitability is known to be affected by transcranial electrical stimulation. However, due to the existence of both excitatory and inhibitory neurons in the cortex, the mechanism of neuronal excitability shift is still not clear. Here, we study electrical stimulation disturbance on neuronal excitability in the neuromuscular system on an acute rat model. We design a special stimulation waveform of enveloped high frequency stimulation (EHFS). With modeling and in vivo measurements, EHFS is confirmed to synchronize the neuronal recruitment at the positive and negative electrode. This uniq…
We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published c…
The influence of temperature on neuronal excitability is studied by numerical simulations on the spiking threshold characteristics of bushy cells in cochlear nucleus periodically stimulated by synaptic currents. The results reveal that there is a cut-off frequency for the spiking of bushy cell in a specific temperature environment, corresponding to the existence of a critical temperature for the neuron to respond with real spikes to the synaptic stimulus of a given frequency, due to the finiteness of spike width. An optimal temperature range for neuronal spiking is also found for a specific st…
NMDA receptors (NMDA-R) typically contribute to excitatory synaptic transmission in the central nervous system. While calcium influx through NMDA-R plays a critical role in synaptic plasticity, experimental evidence indicates that NMDAR-mediated calcium influx also modifies neuronal excitability through the activation of calcium-activated potassium channels. This mechanism has not yet been studied theoretically. Our theoretical model provides a simple description of neuronal electrical activity that takes into account the tonic activity of extrasynaptic NMDA receptors and a cytosolic calcium c…
The brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we study the joint dynamics of two cortical columns described by Jansen-Rit neural mass models, and show that coupling between the columns gives rise to stochastic initiations of sustained collective activity, which can be interpreted as epileptic events. For large enough coupling strengths, termination of these events results mainly from the emergence of synchronization between the columns, and thus is contr…
We present experimental and theoretical arguments, at the single neuron level, suggesting that neuronal response fluctuations reflect a process that positions the neuron near a transition point that separates excitable and unexcitable phases. This view is supported by the dynamical properties of the system as observed in experiments on isolated cultured cortical neurons, as well as by a theoretical mapping between the constructs of self organized criticality and membrane excitability biophysics.
Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained the core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show t…
The Hodgkin-Huxley (HH) model is the currently accepted formalism of neuronal excitability. However, the HH model does not capture a number of biophysical behaviors associated with action potentials or propagating nerve impulses. Physical mechanisms underlying these processes, such as reversible heat transfer and axonal swelling have been separately investigated and compartmentally modeled to indicate the nervous system is not purely electrical or biochemical. Rather, mechanical forces and principles of thermodynamics also govern neuronal excitability and signaling. To advance our understandin…
Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the last decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of active dendritic trees is a highly non-linear function of their afferent rate, attaining extremely large dynamic…
We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of spontaneous neuronal activity near a critical point of a phase transition is a characteristic property that can be used to identify the bifurcation mechanism of the transition. We demonstrate that bursts …
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational p…
The phase-response curve (PRC) is an important tool to determine the excitability type of single neurons which reveals consequences for their synchronizing properties. We review five methods to compute the PRC from both model data and experimental data and compare the numerically obtained results from each method. The main difference between the methods lies in the reliability which is influenced by the fluctuations in the spiking data and the number of spikes available for analysis. We discuss the significance of our results and provide guidelines to choose the best method based on the availa…
Neuronal electricality founded in murburn-thermodynamic principles: 2. Comparisons, evidenced explanations, and predictions
Amrita School of Artificial Intelligence, Coimbatore, Amrita Vishwa Vidyapeetham（阿姆利塔人工智能学院，阿姆利塔维迪亚佩塔姆大学）；Satyamjayatu: The Science & Ethics Foundation（真理至上：科学与伦理基金会）；University of Rostock（罗斯托克大学）；Wayne State University（韦恩州立大学）
