1,251 research outputs found
Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons
Multistability, the coexistence of multiple attractors in a dynamical system,
is explored in bursting nerve cells. A modeling study is performed to show that
a large class of bursting systems, as defined by a shared topology when
represented as dynamical systems, is inherently suited to support
multistability. We derive the bifurcation structure and parametric trends
leading to multistability in these systems. Evidence for the existence of
multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica
that is consistent with our proposed mechanism is presented. Although these
experimental results are preliminary, they indicate that single neurons may be
capable of dynamically storing information for longer time scales than
typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure
Potential mechanisms for imperfect synchronization in parkinsonian basal ganglia
Neural activity in the brain of parkinsonian patients is characterized by the
intermittently synchronized oscillatory dynamics. This imperfect
synchronization, observed in the beta frequency band, is believed to be related
to the hypokinetic motor symptoms of the disorder. Our study explores potential
mechanisms behind this intermittent synchrony. We study the response of a
bursting pallidal neuron to different patterns of synaptic input from
subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe)
neuron is sensitive to the phase of the input from the STN cell and can exhibit
intermittent phase-locking with the input in the beta band. The temporal
properties of this intermittent phase-locking show similarities to the
intermittent synchronization observed in experiments. We also study the
synchronization of GPe cells to synaptic input from the STN cell with
dependence on the dopamine-modulated parameters. Dopamine also affects the
cellular properties of neurons. We show how the changes in firing patterns of
STN neuron due to the lack of dopamine may lead to transition from a lower to a
higher coherent state, roughly matching the synchrony levels observed in basal
ganglia in normal and parkinsonian states. The intermittent nature of the
neural beta band synchrony in Parkinson's disease is achieved in the model due
to the interplay of the timing of STN input to pallidum and pallidal neuronal
dynamics, resulting in sensitivity of pallidal output to the phase of the
arriving STN input. Thus the mechanism considered here (the change in firing
pattern of subthalamic neurons through the dopamine-induced change of membrane
properties) may be one of the potential mechanisms responsible for the
generation of the intermittent synchronization observed in Parkinson's disease.Comment: 27 pages, 9 figure
Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons
First return maps of interspike intervals for biological neurons that
generate repetitive bursts of impulses can display stereotyped structures
(neuronal signatures). Such structures have been linked to the possibility of
multicoding and multifunctionality in neural networks that produce and control
rhythmical motor patterns. In some cases, isolating the neurons from their
synaptic network revealsirregular, complex signatures that have been regarded
as evidence of intrinsic, chaotic behavior.
We show that incorporation of dynamical noise into minimal neuron models of
square-wave bursting (either conductance-based or abstract) produces signatures
akin to those observed in biological examples, without the need for fine-tuning
of parameters or ad hoc constructions for inducing chaotic activity. The form
of the stochastic term is not strongly constrained, and can approximate several
possible sources of noise, e.g. random channel gating or synaptic bombardment.
The cornerstone of this signature generation mechanism is the rich,
transient, but deterministic dynamics inherent in the square-wave
(saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes
the dynamics to populate a complex transient scaffolding or skeleton in state
space, even for models that (without added noise) generate only periodic
activity (whether in bursting or tonic spiking mode).Comment: REVTeX4-1, 18 pages, 9 figure
Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
A simple model that replicates the dynamics of spiking and spiking-bursting
activity of real biological neurons is proposed. The model is a two-dimensional
map which contains one fast and one slow variable. The mechanisms behind
generation of spikes, bursts of spikes, and restructuring of the map behavior
are explained using phase portrait analysis. The dynamics of two coupled maps
which model the behavior of two electrically coupled neurons is discussed.
Synchronization regimes for spiking and bursting activity of these maps are
studied as a function of coupling strength. It is demonstrated that the results
of this model are in agreement with the synchronization of chaotic
spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure
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