1,640 research outputs found
Macroscopic equations governing noisy spiking neuronal populations
At functional scales, cortical behavior results from the complex interplay of
a large number of excitable cells operating in noisy environments. Such systems
resist to mathematical analysis, and computational neurosciences have largely
relied on heuristic partial (and partially justified) macroscopic models, which
successfully reproduced a number of relevant phenomena. The relationship
between these macroscopic models and the spiking noisy dynamics of the
underlying cells has since then been a great endeavor. Based on recent
mean-field reductions for such spiking neurons, we present here {a principled
reduction of large biologically plausible neuronal networks to firing-rate
models, providing a rigorous} relationship between the macroscopic activity of
populations of spiking neurons and popular macroscopic models, under a few
assumptions (mainly linearity of the synapses). {The reduced model we derive
consists of simple, low-dimensional ordinary differential equations with}
parameters and {nonlinearities derived from} the underlying properties of the
cells, and in particular the noise level. {These simple reduced models are
shown to reproduce accurately the dynamics of large networks in numerical
simulations}. Appropriate parameters and functions are made available {online}
for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley
models
Multistable jittering in oscillators with pulsatile delayed feedback
Oscillatory systems with time-delayed pulsatile feedback appear in various
applied and theoretical research areas, and received a growing interest in the
last years. For such systems, we report a remarkable scenario of
destabilization of a periodic regular spiking regime. In the bifurcation point
numerous regimes with non-equal interspike intervals emerge simultaneously. We
show that this bifurcation is triggered by the steepness of the oscillator's
phase resetting curve and that the number of the emerging, so-called
"jittering" regimes grows exponentially with the delay value. Although this
appears as highly degenerate from a dynamical systems viewpoint, the
"multi-jitter" bifurcation occurs robustly in a large class of systems. We
observe it not only in a paradigmatic phase-reduced model, but also in a
simulated Hodgkin-Huxley neuron model and in an experiment with an electronic
circuit
Bistable dynamics underlying excitability of ion homeostasis in neuron models
When neurons fire action potentials, dissipation of free energy is usually
not directly considered, because the change in free energy is often negligible
compared to the immense reservoir stored in neural transmembrane ion gradients
and the long-term energy requirements are met through chemical energy, i.e.,
metabolism. However, these gradients can temporarily nearly vanish in
neurological diseases, such as migraine and stroke, and in traumatic brain
injury from concussions to severe injuries. We study biophysical neuron models
based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent
ion concentrations inside and outside the cell and metabolic energy-driven
pumps. We reveal the basic mechanism of a state of free energy-starvation (FES)
with bifurcation analyses showing that ion dynamics is for a large range of
pump rates bistable without contact to an ion bath. This is interpreted as a
threshold reduction of a new fundamental mechanism of 'ionic excitability' that
causes a long-lasting but transient FES as observed in pathological states. We
can in particular conclude that a coupling of extracellular ion concentrations
to a large glial-vascular bath can take a role as an inhibitory mechanism
crucial in ion homeostasis, while the Na/K pumps alone are insufficient
to recover from FES. Our results provide the missing link between the HH
formalism and activator-inhibitor models that have been successfully used for
modeling migraine phenotypes, and therefore will allow us to validate the
hypothesis that migraine symptoms are explained by disturbed function in ion
channel subunits, Na/K pumps, and other proteins that regulate ion
homeostasis.Comment: 14 pages, 8 figures, 4 table
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