34 research outputs found
Soma-Axon Coupling Configurations That Enhance Neuronal Coincidence Detection
Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, IKLT in the axon enhances coincidence detection more effectively than IKLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons
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
Gain Control With A-Type Potassium Current: IA As A Switch Between Divisive And Subtractive Inhibition
Neurons process and convey information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition typically 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. In this study, we use simulations and mathematical analysis of a neuron model to find the specific conditions (parameter sets) for which inhibitory inputs have subtractive or divisive effects. Significantly, 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. In particular, 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 (plane analysis and fast-slow dissection) 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
A point process framework for modeling electrical stimulation of the auditory nerve
Model-based studies of auditory nerve responses to electrical stimulation can
provide insight into the functioning of cochlear implants. Ideally, these
studies can identify limitations in sound processing strategies and lead to
improved methods for providing sound information to cochlear implant users. To
accomplish this, models must accurately describe auditory nerve spiking while
avoiding excessive complexity that would preclude large-scale simulations of
populations of auditory nerve fibers and obscure insight into the mechanisms
that influence neural encoding of sound information. In this spirit, we develop
a point process model of the auditory nerve that provides a compact and
accurate description of neural responses to electric stimulation. Inspired by
the framework of generalized linear models, the proposed model consists of a
cascade of linear and nonlinear stages. We show how each of these stages can be
associated with biophysical mechanisms and related to models of neuronal
dynamics. Moreover, we derive a semi-analytical procedure that uniquely
determines each parameter in the model on the basis of fundamental statistics
from recordings of single fiber responses to electric stimulation, including
threshold, relative spread, jitter, and chronaxie. The model also accounts for
refractory and summation effects that influence the responses of auditory nerve
fibers to high pulse rate stimulation. Throughout, we compare model predictions
to published physiological data and explain differences in auditory nerve
responses to high and low pulse rate stimulation. We close by performing an
ideal observer analysis of simulated spike trains in response to sinusoidally
amplitude modulated stimuli and find that carrier pulse rate does not affect
modulation detection thresholds.Comment: 1 title page, 27 manuscript pages, 14 figures, 1 table, 1 appendi
The what and where of adding channel noise to the Hodgkin-Huxley equations
One of the most celebrated successes in computational biology is the
Hodgkin-Huxley framework for modeling electrically active cells. This
framework, expressed through a set of differential equations, synthesizes the
impact of ionic currents on a cell's voltage -- and the highly nonlinear impact
of that voltage back on the currents themselves -- into the rapid push and pull
of the action potential. Latter studies confirmed that these cellular dynamics
are orchestrated by individual ion channels, whose conformational changes
regulate the conductance of each ionic current. Thus, kinetic equations
familiar from physical chemistry are the natural setting for describing
conductances; for small-to-moderate numbers of channels, these will predict
fluctuations in conductances and stochasticity in the resulting action
potentials. At first glance, the kinetic equations provide a far more complex
(and higher-dimensional) description than the original Hodgkin-Huxley
equations. This has prompted more than a decade of efforts to capture channel
fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of
these approaches, while intuitively appealing, produce quantitative errors when
compared to kinetic equations; others, as only very recently demonstrated, are
both accurate and relatively simple. We review what works, what doesn't, and
why, seeking to build a bridge to well-established results for the
deterministic Hodgkin-Huxley equations. As such, we hope that this review will
speed emerging studies of how channel noise modulates electrophysiological
dynamics and function. We supply user-friendly Matlab simulation code of these
stochastic versions of the Hodgkin-Huxley equations on the ModelDB website
(accession number 138950) and
http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl