3,924 research outputs found
Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation
Transduction of graded synaptic input into trains of all-or-none action
potentials (spikes) is a crucial step in neural coding. Hodgkin identified three
classes of neurons with qualitatively different analog-to-digital transduction
properties. Despite widespread use of this classification scheme, a
generalizable explanation of its biophysical basis has not been described. We
recorded from spinal sensory neurons representing each class and reproduced
their transduction properties in a minimal model. With phase plane and
bifurcation analysis, each class of excitability was shown to derive from
distinct spike initiating dynamics. Excitability could be converted between all
three classes by varying single parameters; moreover, several parameters, when
varied one at a time, had functionally equivalent effects on excitability. From
this, we conclude that the spike-initiating dynamics associated with each of
Hodgkin's classes represent different outcomes in a nonlinear
competition between oppositely directed, kinetically mismatched currents. Class
1 excitability occurs through a saddle node on invariant circle bifurcation when
net current at perithreshold potentials is inward (depolarizing) at steady
state. Class 2 excitability occurs through a Hopf bifurcation when, despite net
current being outward (hyperpolarizing) at steady state, spike initiation occurs
because inward current activates faster than outward current. Class 3
excitability occurs through a quasi-separatrix crossing when fast-activating
inward current overpowers slow-activating outward current during a stimulus
transient, although slow-activating outward current dominates during constant
stimulation. Experiments confirmed that different classes of spinal lamina I
neurons express the subthreshold currents predicted by our simulations and,
further, that those currents are necessary for the excitability in each cell
class. Thus, our results demonstrate that all three classes of excitability
arise from a continuum in the direction and magnitude of subthreshold currents.
Through detailed analysis of the spike-initiating process, we have explained a
fundamental link between biophysical properties and qualitative differences in
how neurons encode sensory input
Identification of Molecular Pathologies Sufficient to Cause Neuropathic Excitability in Primary Somatosensory Afferents Using Dynamical Systems Theory
Pain caused by nerve injury (i.e. neuropathic pain) is associated with development of neuronal hyperexcitability at several points along the pain pathway. Within primary afferents, numerous injury-induced changes have been identified but it remains unclear which molecular changes are necessary and sufficient to explain cellular hyperexcitability. To investigate this, we built computational models that reproduce the switch from a normal spiking pattern characterized by a single spike at the onset of depolarization to a neuropathic one characterized by repetitive spiking throughout depolarization. Parameter changes that were sufficient to switch the spiking pattern also enabled membrane potential oscillations and bursting, suggesting that all three pathological changes are mechanistically linked. Dynamical analysis confirmed this prediction by showing that excitability changes co-develop when the nonlinear mechanism responsible for spike initiation switches from a quasi-separatrix-crossing to a subcritical Hopf bifurcation. This switch stems from biophysical changes that bias competition between oppositely directed fast- and slow-activating conductances operating at subthreshold potentials. Competition between activation and inactivation of a single conductance can be similarly biased with equivalent consequences for excitability. “Bias” can arise from a multitude of molecular changes occurring alone or in combination; in the latter case, changes can add or offset one another. Thus, our results identify pathological change in the nonlinear interaction between processes affecting spike initiation as the critical determinant of how simple injury-induced changes at the molecular level manifest complex excitability changes at the cellular level. We demonstrate that multiple distinct molecular changes are sufficient to produce neuropathic changes in excitability; however, given that nerve injury elicits numerous molecular changes that may be individually sufficient to alter spike initiation, our results argue that no single molecular change is necessary to produce neuropathic excitability. This deeper understanding of degenerate causal relationships has important implications for how we understand and treat neuropathic pain
A biophysical model explains the spontaneous bursting behavior in the developing retina
During early development, waves of activity propagate across the retina and
play a key role in the proper wiring of the early visual system. During the
stage II these waves are triggered by a transient network of neurons, called
Starburst Amacrine Cells (SACs), showing a bursting activity which disappears
upon further maturation. While several models have attempted to reproduce
retinal waves, none of them is able to mimic the rhythmic autonomous bursting
of individual SACs and reveal how these cells change their intrinsic properties
during development. Here, we introduce a mathematical model, grounded on
biophysics, which enables us to reproduce the bursting activity of SACs and to
propose a plausible, generic and robust, mechanism that generates it. The core
parameters controlling repetitive firing are fast depolarizing -gated
calcium channels and hyperpolarizing -gated potassium channels. The
quiescent phase of bursting is controlled by a slow after hyperpolarization
(sAHP), mediated by calcium-dependent potassium channels. Based on a
bifurcation analysis we show how biophysical parameters, regulating calcium and
potassium activity, control the spontaneously occurring fast oscillatory
activity followed by long refractory periods in individual SACs. We make a
testable experimental prediction on the role of voltage-dependent potassium
channels on the excitability properties of SACs and on the evolution of this
excitability along development. We also propose an explanation on how SACs can
exhibit a large variability in their bursting periods, as observed
experimentally within a SACs network as well as across different species, yet
based on a simple, unique, mechanism. As we discuss, these observations at the
cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Gain control with A-type potassium current: IA as a switch between divisive and subtractive inhibition
Neurons process information by transforming barrages of synaptic inputs into
spiking activity. Synaptic inhibition suppresses the output firing activity of
a neuron, and is commonly classified as having a subtractive or divisive effect
on a neuron's output firing activity. Subtractive inhibition can narrow the
range of inputs that evoke spiking activity by eliminating responses to
non-preferred inputs. Divisive inhibition is a form of gain control: it
modifies firing rates while preserving the range of inputs that evoke firing
activity. Since these two "modes" of inhibition have distinct impacts on neural
coding, it is important to understand the biophysical mechanisms that
distinguish these response profiles.
We use simulations and mathematical analysis of a neuron model to find the
specific conditions for which inhibitory inputs have subtractive or divisive
effects. We identify a novel role for the A-type Potassium current (IA). In our
model, this fast-activating, slowly- inactivating outward current acts as a
switch between subtractive and divisive inhibition. If IA is strong (large
maximal conductance) and fast (activates on a time-scale similar to spike
initiation), then inhibition has a subtractive effect on neural firing. In
contrast, if IA is weak or insufficiently fast-activating, then inhibition has
a divisive effect on neural firing. We explain these findings using dynamical
systems methods to define how a spike threshold condition depends on synaptic
inputs and IA.
Our findings suggest that neurons can "self-regulate" the gain control
effects of inhibition via combinations of synaptic plasticity and/or modulation
of the conductance and kinetics of A-type Potassium channels. This novel role
for IA would add flexibility to neurons and networks, and may relate to recent
observations of divisive inhibitory effects on neurons in the nucleus of the
solitary tract.Comment: 20 pages, 11 figure
The location of the axon initial segment affects the bandwidth of spike initiation dynamics
The dynamics and the sharp onset of action potential (AP) generation have recently been the subject of intense experimental and theoretical investigations. According to the resistive coupling theory, an electrotonic interplay between the site of AP initiation in the axon and the somato-dendritic load determines the AP waveform. This phenomenon not only alters the shape of AP recorded at the soma, but also determines the dynamics of excitability across a variety of time scales. Supporting this statement, here we generalize a previous numerical study and extend it to the quantification of the input-output gain of the neuronal dynamical response. We consider three classes of multicompartmental mathematical models, ranging from ball-and-stick simplified descriptions of neuronal excitability to 3D-reconstructed biophysical models of excitatory neurons of rodent and human cortical tissue. For each model, we demonstrate that increasing the distance between the axonal site of AP initiation and the soma markedly increases the bandwidth of neuronal response properties. We finally consider the Liquid State Machine paradigm, exploring the impact of altering the site of AP initiation at the level of a neuronal population, and demonstrate that an optimal distance exists to boost the computational performance of the network in a simple classification task. Copyright
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