We first review the essential framework of Hodgkin-Huxley type models for action potential generation. Indeed, a range of background activity exists where the classical Hodgkin-Huxley model agrees with the experimental data reported in. We find that the parameter relating onset rapidity to onset span depends on the amount of synaptic background activity included in the model. As anticipated by, a broad class of ion channel models displays an inverse relationship between onset rapidity and onset span. The formula that we arrive at can be used to compare experimental observations with the parameter values incorporated into such models. To derive an analytical characterization of this relationship, we directly compute the probability distribution of the onset potential and demonstrate how it depends on model parameters. Our analysis applies to the classical Hodgkin-Huxley model, in addition to generalizations thereof, including those in which the channel opening probability depends on channel density. Here we use a standard technique from theoretical physics (the path integral) to derive an analytical formula relating the onset rapidity and onset span. in where it is suggested that the physiological setting of is unrealistic, and the model inadequate. This seemingly compelling reappraisal of the original data was in turn dissected by Naundorf et al. Whole-cell recordings from the soma of cortical pyramidal cells in vitro demonstrated faster onset rapidity and larger onset span then those obtained from the axon initial segment. In it was proposed that the observed combination of large onset span and swift onset rapidity could be captured using a Hodgkin-Huxley model if action potentials were initiated at one place within the cell, (the axon initial segment), and then propagated around 30 microns to the site at which they were recorded, (the soma). The result reported in was critically analyzed in a recent letter of D. To fix this discrepancy argues for a radical rethinking of the basic underpinnings of the Hodgkin and Huxley model, in which the probability of an ion channel being open depends not only on the membrane potential but also on the local density of channels. If parameters are adjusted to fit the onset rapidity of the data, the observed onset span disagrees with the model, and vice versa. In particular, within the Hodgkin-Huxley model they demonstrate through numerical simulations an antagonistic relationship between these two variables. argue that the variability or span of onset potentials observed in experiments, in conjunction with their swift onset rapidity, cannot be explained by the Hodgkin-Huxley model. the membrane potential at which an action potential fires, and the onset rapidity, or rate with which the action potential initially fires. The authors focus on two variables, the onset potential, i.e. Therein the dynamics of action potential initiation in cortical neurons in vivo and in vitro are analyzed. A key feature of their model is that the channels open independently of each other the probability that a channel is open depends only on the membrane voltage history.Ī recent paper challenged this picture. Action potentials arise from the synergistic action of sodium channels and potassium channels, each of which opens and closes in a voltage dependent fashion. In 1952, Hodgkin and Huxley explained how action potentials are generated through the electrical excitability of neuronal membranes. 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. We find that the relationship between onset span and onset rapidity depends on the level of synaptic background activity. We analytically compute the probability distribution of onset potentials and analytically derive the inverse relationship between onset span and onset rapidity. Here we apply a method from theoretical physics to derive an analytical characterization of this problem. 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. This correlation was demonstrated in numerical simulations of the Hodgkin-Huxley model. 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).
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