285 research outputs found
How adaptation currents change threshold, gain and variability of neuronal spiking
Many types of neurons exhibit spike rate adaptation, mediated by intrinsic
slow -currents, which effectively inhibit neuronal responses. How
these adaptation currents change the relationship between in-vivo like
fluctuating synaptic input, spike rate output and the spike train statistics,
however, is not well understood. In this computational study we show that an
adaptation current which primarily depends on the subthreshold membrane voltage
changes the neuronal input-output relationship (I-O curve) subtractively,
thereby increasing the response threshold. A spike-dependent adaptation current
alters the I-O curve divisively, thus reducing the response gain. Both types of
adaptation currents naturally increase the mean inter-spike interval (ISI), but
they can affect ISI variability in opposite ways. A subthreshold current always
causes an increase of variability while a spike-triggered current decreases
high variability caused by fluctuation-dominated inputs and increases low
variability when the average input is large. The effects on I-O curves match
those caused by synaptic inhibition in networks with asynchronous irregular
activity, for which we find subtractive and divisive changes caused by external
and recurrent inhibition, respectively. Synaptic inhibition, however, always
increases the ISI variability. We analytically derive expressions for the I-O
curve and ISI variability, which demonstrate the robustness of our results.
Furthermore, we show how the biophysical parameters of slow
-conductances contribute to the two different types of adaptation
currents and find that -activated -currents are
effectively captured by a simple spike-dependent description, while
muscarine-sensitive or -activated -currents show a
dominant subthreshold component.Comment: 20 pages, 8 figures; Journal of Neurophysiology (in press
Noise Suppression and Surplus Synchrony by Coincidence Detection
The functional significance of correlations between action potentials of
neurons is still a matter of vivid debates. In particular it is presently
unclear how much synchrony is caused by afferent synchronized events and how
much is intrinsic due to the connectivity structure of cortex. The available
analytical approaches based on the diffusion approximation do not allow to
model spike synchrony, preventing a thorough analysis. Here we theoretically
investigate to what extent common synaptic afferents and synchronized inputs
each contribute to closely time-locked spiking activity of pairs of neurons. We
employ direct simulation and extend earlier analytical methods based on the
diffusion approximation to pulse-coupling, allowing us to introduce precisely
timed correlations in the spiking activity of the synaptic afferents. We
investigate the transmission of correlated synaptic input currents by pairs of
integrate-and-fire model neurons, so that the same input covariance can be
realized by common inputs or by spiking synchrony. We identify two distinct
regimes: In the limit of low correlation linear perturbation theory accurately
determines the correlation transmission coefficient, which is typically smaller
than unity, but increases sensitively even for weakly synchronous inputs. In
the limit of high afferent correlation, in the presence of synchrony a
qualitatively new picture arises. As the non-linear neuronal response becomes
dominant, the output correlation becomes higher than the total correlation in
the input. This transmission coefficient larger unity is a direct consequence
of non-linear neural processing in the presence of noise, elucidating how
synchrony-coded signals benefit from these generic properties present in
cortical networks
Estimation in discretely observed diffusions killed at a threshold
Parameter estimation in diffusion processes from discrete observations up to
a first-hitting time is clearly of practical relevance, but does not seem to
have been studied so far. In neuroscience, many models for the membrane
potential evolution involve the presence of an upper threshold. Data are
modeled as discretely observed diffusions which are killed when the threshold
is reached. Statistical inference is often based on the misspecified likelihood
ignoring the presence of the threshold causing severe bias, e.g. the bias
incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological
relevant parameters can be up to 25-100%. We calculate or approximate the
likelihood function of the killed process. When estimating from a single
trajectory, considerable bias may still be present, and the distribution of the
estimates can be heavily skewed and with a huge variance. Parametric bootstrap
is effective in correcting the bias. Standard asymptotic results do not apply,
but consistency and asymptotic normality may be recovered when multiple
trajectories are observed, if the mean first-passage time through the threshold
is finite. Numerical examples illustrate the results and an experimental data
set of intracellular recordings of the membrane potential of a motoneuron is
analyzed.Comment: 29 pages, 5 figure
Balanced Synaptic Input Shapes the Correlation between Neural Spike Trains
Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states
Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process
Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential
From Spiking Neuron Models to Linear-Nonlinear Models
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates
Parameter estimation in neuronal stochastic differential equation models from intracellular recordings of membrane potentials in single neurons: a Review
International audienceDynamics of the membrane potential in a single neuron can be studied estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolution. One-dimensional models are the stochastic integrate-and-fire neuronal diffusion models. More biophysical neuronal models take into account the dynamics of ion channels or synaptic activity, leading to multidimensional diffusion models. Since only the membrane potential can be measured, this complicates the statistical inference and parameter estimation from these partially observed detailed models. This paper reviews parameter estimation techniques from intracellular recordings in these diffusion models
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