541 research outputs found
A modified cable formalism for modeling neuronal membranes at high frequencies
Intracellular recordings of cortical neurons in vivo display intense
subthreshold membrane potential (Vm) activity. The power spectral density (PSD)
of the Vm displays a power-law structure at high frequencies (>50 Hz) with a
slope of about -2.5. This type of frequency scaling cannot be accounted for by
traditional models, as either single-compartment models or models based on
reconstructed cell morphologies display a frequency scaling with a slope close
to -4. This slope is due to the fact that the membrane resistance is
"short-circuited" by the capacitance for high frequencies, a situation which
may not be realistic. Here, we integrate non-ideal capacitors in cable
equations to reflect the fact that the capacitance cannot be charged
instantaneously. We show that the resulting "non-ideal" cable model can be
solved analytically using Fourier transforms. Numerical simulations using a
ball-and-stick model yield membrane potential activity with similar frequency
scaling as in the experiments. We also discuss the consequences of using
non-ideal capacitors on other cellular properties such as the transmission of
high frequencies, which is boosted in non-ideal cables, or voltage attenuation
in dendrites. These results suggest that cable equations based on non-ideal
capacitors should be used to capture the behavior of neuronal membranes at high
frequencies.Comment: To appear in Biophysical Journal; Submitted on May 25, 2007; accepted
on Sept 11th, 200
Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework
The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Here we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded in a simple one-dimensional cable. This system is shown to support saltatory waves as a result of the discrete distribution of spines. Moreover, we demonstrate one of the ways to incorporate noise into the spine-head whilst retaining computational tractability of the model. The SDS model sustains a variety of propagating patterns
Intrinsic gain modulation and adaptive neural coding
In many cases, the computation of a neural system can be reduced to a
receptive field, or a set of linear filters, and a thresholding function, or
gain curve, which determines the firing probability; this is known as a
linear/nonlinear model. In some forms of sensory adaptation, these linear
filters and gain curve adjust very rapidly to changes in the variance of a
randomly varying driving input. An apparently similar but previously unrelated
issue is the observation of gain control by background noise in cortical
neurons: the slope of the firing rate vs current (f-I) curve changes with the
variance of background random input. Here, we show a direct correspondence
between these two observations by relating variance-dependent changes in the
gain of f-I curves to characteristics of the changing empirical
linear/nonlinear model obtained by sampling. In the case that the underlying
system is fixed, we derive relationships relating the change of the gain with
respect to both mean and variance with the receptive fields derived from
reverse correlation on a white noise stimulus. Using two conductance-based
model neurons that display distinct gain modulation properties through a simple
change in parameters, we show that coding properties of both these models
quantitatively satisfy the predicted relationships. Our results describe how
both variance-dependent gain modulation and adaptive neural computation result
from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio
Modeling extracellular field potentials and the frequency-filtering properties of extracellular space
Extracellular local field potentials (LFP) are usually modeled as arising
from a set of current sources embedded in a homogeneous extracellular medium.
Although this formalism can successfully model several properties of LFPs, it
does not account for their frequency-dependent attenuation with distance, a
property essential to correctly model extracellular spikes. Here we derive
expressions for the extracellular potential that include this
frequency-dependent attenuation. We first show that, if the extracellular
conductivity is non-homogeneous, there is induction of non-homogeneous charge
densities which may result in a low-pass filter. We next derive a simplified
model consisting of a punctual (or spherical) current source with
spherically-symmetric conductivity/permittivity gradients around the source. We
analyze the effect of different radial profiles of conductivity and
permittivity on the frequency-filtering behavior of this model. We show that
this simple model generally displays low-pass filtering behavior, in which fast
electrical events (such as Na-mediated action potentials) attenuate very
steeply with distance, while slower (K-mediated) events propagate over
larger distances in extracellular space, in qualitative agreement with
experimental observations. This simple model can be used to obtain
frequency-dependent extracellular field potentials without taking into account
explicitly the complex folding of extracellular space.Comment: text (LaTeX), 6 figs. (ps
A rare schizophrenia risk variant of CACNA1I disrupts CaV3.3 channel activity
CACNA1I is a candidate schizophrenia risk gene. It encodes the pore-forming human CaV3.3 α1 subunit, a subtype of voltage-gated calcium channel that contributes to T-type currents. Recently, two de novo missense variations, T797M and R1346H, of hCaV3.3 were identified in individuals with schizophrenia. Here we show that R1346H, but not T797M, is associated with lower hCaV3.3 protein levels, reduced glycosylation, and lower membrane surface levels of hCaV3.3 when expressed in human cell lines compared to wild-type. Consistent with our biochemical analyses, whole-cell hCaV3.3 currents in cells expressing the R1346H variant were ~50% of those in cells expressing WT hCaV3.3, and neither R1346H nor T797M altered channel biophysical properties. Employing the NEURON simulation environment, we found that reducing hCaV3.3 current densities by 22% or more eliminates rebound bursting in model thalamic reticular nucleus (TRN) neurons. Our analyses suggest that a single copy of Chr22: 39665939G > A CACNA1I has the capacity to disrupt CaV3.3 channel-dependent functions, including rebound bursting in TRN neurons, with potential implications for schizophrenia pathophysiology
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