The noisy threshold regime, where even a small set of presynaptic neurons can significantly affect postsynaptic spike-timing, is suggested as a key requisite for computation in neurons with high variability. It also has been proposed that signals under the noisy conditions are successfully transferred by a few strong synapses and/or by an assembly of nearly synchronous synaptic activities. We analytically investigate the impact of a transient signaling input on a leaky integrate-and-fire postsynaptic neuron that receives background noise near the threshold regime. The signaling input models a single strong synapse or a set of synchronous synapses, while the background noise represents a lot of weak synapses. We find an analytic solution that explains how the first-passage time (ISI) density is changed by transient signaling input. The analysis allows us to connect properties of the signaling input like spike timing and amplitude with postsynaptic first-passage time density in a noisy environment. Based on the analytic solution, we calculate the Fisher information with respect to the signaling input’s amplitude. For a wide range of amplitudes, we observe a non-monotonic behavior for the Fisher information as a function of background noise. Moreover, Fisher information non-trivially depends on the signaling input’s amplitude; changing the amplitude, we observe one maximum in the high level of the background noise. The single maximum splits into two maximums in the low noise regime. This finding demonstrates the benefit of the analytic solution in investigating signal transfer by neurons.
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An appealing challenge in Neuroscience is to identify network architecture from neural activity. A key requirement is the knowledge of statistical input-output relation of single neurons in vivo. Using a recent exact solution of spike-timing for leaky integrate-and-fire neurons under noisy inputs balanced near threshold, we construct a unified framework that links synaptic inputs, spiking nonlinearity, and network architecture, with statistics of population activity. The framework predicts structured higher-order interactions of neurons receiving common inputs under different architectures: It unveils two network motifs behind sparse activity reported in visual neurons. Comparing model's prediction with monkey's V1 neurons, we found excitatory inputs to pairs explain the sparse activity characterized by negative triple-wise interactions, ruling out shared inhibition. While the model predicts variation in the structured activity according to local circuitries, we show strong negative interactions are in general a signature of excitatory inputs to neuron pairs, whenever background activity is sparse.1 Keywords network architecture, sparse activity, common inputs, higher-order interactions, leaky integrateand-fire neuron model, threshold regime, input-output relation, triple-wise interactions, spontaneous activity
Identifying network architecture from observed neural activities is crucial in neuroscience studies. A key requirement is knowledge of the statistical input-output relation of single neurons in vivo. By utilizing an exact analytical solution of the spike-timing for leaky integrate-and-fire neurons under noisy inputs balanced near the threshold, we construct a framework that links synaptic type, strength, and spiking nonlinearity with the statistics of neuronal population activity. The framework explains structured pairwise and higher-order interactions of neurons receiving common inputs under different architectures. We compared the theoretical predictions with the activity of monkey and mouse V1 neurons and found that excitatory inputs given to pairs explained the observed sparse activity characterized by strong negative triple-wise interactions, thereby ruling out the alternative explanation by shared inhibition. Moreover, we showed that the strong interactions are a signature of excitatory rather than inhibitory inputs whenever the spontaneous rate is low. We present a guide map of neural interactions that help researchers to specify the hidden neuronal motifs underlying observed interactions found in empirical data.
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