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).

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).