This result suggested that lateral inhibition adjusted the membrane potentials of postsynaptic neurons so that their spiking processes accurately performed sequence sampling.

If we focus on the peristimulus time histogram (PSTH) for the average membrane potential of output neurons aligned to external events, both neuron groups initially show weak responses to both correlation events, and yet the depolarization is relatively higher for source A than for source B (Fig 2C left).

yj(t) The spiking activity of output neuron j uk’(t) Membrane potential of inhibitory neuron k zk(t) The spiking activity of inhibitory neuron k wjix The synaptic weight of a feed-forward excitatory connection from ito j qifl Response probability of input neuron ito external source p 11X, 12X The correlation kernel functions used the gamma distribution With shape parameter kg = 3 in order to reproduce broad spike correlations typically observed in cortical neurons [36,37].

Output neurons are modeled with the Poisson neuron model [5,38,45] in which the membrane potential of neuron j at time tis described as where wjiX and wjkz are the EPSPs/IPSPs of input currents from input neuron x,- and lateral tory connections are clin and dij.

In the LIF model, the membrane potentials of excitatory neurons follow

Mathematically, to perform sampling from a probabilistic distribution, we first needed to calculate the occurrence probability of each state; however, in a neural model, membrane potentials of output neurons approximately represent the occurrence probability through membrane dynamics.

We further studied the response of the models for the same inputs and 1 found that the logarithm of the average membrane potential ufi = W Z well approxi-,Ll jEQP‘ mates the log-posterior estimated in Bayesian ICA, even in the absence of a stimulus (Fig 7E).

Astroglial membrane potential dynamics induced by stimulation

23), we measured astroglial membrane potential depolarization and found that it reached ~ 1.3 mV

After validating the responses of the tri-compartment model to basal stimulation, we investigated the impact of trains of stimulations on the dynamics of astroglial membrane potential .

We quantified K+ neuroglial interactions during basal and high activity, and found that Kir4.1 channels play a crucial role in K+ clearance and astroglial and neuronal membrane potential dynamics, especially during repetitive stimulations, and prominently regulate neuronal excitability for 3 to 10 Hz rhythmic activity.

The associated neuronal membrane potential is coupled with the dynamics of intracellular and extracellular Na+ and K+ levels via the dependence of the neuronal currents to the Nernst equation.

This current is the initial input of a classical Hodg-kin-Huxley model, which describes the neuronal membrane potential dynamics (entry of Na+ and exit of K+).

We obtain that K+ fluxes through Kir4.1 channels vanish around astrocytic resting membrane potential (~-80 mV) and are outward during astrocytic depolarization for a fixed [KJF]O (2.5 mM, Fig.

Where the dynamics of the membrane potential V depend on the capacitance C, leak conductance gL, resting potential EL, an adaptation variable w, DC current input IO, and fluctuating synaptic currents Isyn(t).

This causes the PSC amplitude to vary as a function of the membrane potential .

Using the same presynaptic spike times and weights delivered to the observed neurons, we then optimize the parameters of these models to match both the observed membrane potential and spike timing (Fig.

We adjusted the gain of the injected fluctuating current to produce membrane potential fluctuations with ~ 15—20 mV peak to peak amplitude and DC current to achieve postsynaptic spiking ~ 5Hz.

The average input had an amplitude of 0.15 0 (corresponding to ~ 15pA, depending on o), and membrane potential responses to injection of this current again mimicked the statistics of membrane potential fluctuations in vivo with amplitudes of 15—20mV [8,38,39].

Injected currents induced membrane potential fluctuations typical for in vivo activity [8,48,49].

However, several statistical models have been developed that explicitly aim to describe the underlying membrane potential dynamics [60,61] and tend to yield more accurate spike prediction.

However, the injected fluctuating current reproduces well the membrane potential fluctuations recorded in the soma of neocortical neurons in vivo [8,48,49].

Although the model used here does not explicitly describe the underlying fluctuations in membrane potential that result from the current injection, the contribution of the cumulative coupling terms of all inputs (N = 1024, red trace in Fig.

These results suggest that, although single trial spike prediction with the GLM is quite accurate, more precise models, with additional nonlinearities [41,42] or explicit estimates of the underlying membrane potential [43], might be necessary to provide a full account of the transformations that occur as fluctuating current input leads to spiking output.

As with other integrate-and-fire models, spikes occur when the membrane potential crosses a threshold VT, after which the potential is immediately reset to Vreset.

The change to Ih conductance accounted for the differences between dendritic sag, dendritic resting membrane potential relative to the soma, and dendritic input resistance in our experiments compared to those in rat L5 somatosensory corteX (See 82 Fig.

To estimate the width of dendritic plateau potentials in the apical dendrite with long dendritic current injection, we determine the longest depolarization sustained at 20% or more above the baseline level (defined as the most hyperpolarized membrane potential during the dendritic current injection).

(b) The difference in resting membrane potential of dendrite and soma, sag, and input resistance as a function of distance from the soma in experiments (black) and the model (blue).

(top) The somatic membrane potential with (black) and without (red) NMDA conductance, in response to increasing synaptic conductance.

(bottom) The membrane potential at the location of the synapse.

membrane capacitance, resting membrane potential and time constant) according to the values described by Gertler et al.

The leaky-integrate-and-fire (LIF) neuron model was used to simulate the neurons in the network with the subthreshold dynamics of the membrane potential Vx(t) described by:

recurrentIn the above equations, 15” "(1‘) describes the total cortical excitatory, re-current and feedforward inhibition to a neuron, C" is the membrane capacitance, Gx is the leak conductance, and Vrest is the resting membrane potential.

When the membrane potential of the neuron reached Vth, a spike was elicited and the membrane potential was reset to Vrest for a refractory duration (trefz 2 ms.)

Gaussian noise was added to the model using three methods: 1) noise added to the time-varying excitatory and inhibitory conductances to simulate random channel fluctuations, 2) noise added to the current to simulated background synaptic activity contributing to the spontaneous rate, or 3) noise added to the membrane potential based spiking threshold.

As an alternative method of generating a spontaneous rate, Gaussian noise (u = O, o = 1 mV) was added as an injected current (810 Fig) or Gaussian noise (u = O, o = 3 mV) was added to the membrane potential spiking threshold, normally set at -45 mV (811 Fig).

While our model’s ability to generate non-synchronized responses required a source of internal noise (or sufficient temporal jitter of synaptic inputs), other methods of generating internal noise also produced similar results, including injecting noise as a current into the integrate-and-fire model to simulate background synaptic activity [30] (810 Fig) and adding Gaussian noise to the membrane potential spiking threshold [31] (811 Fig).