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Paper   IPM / Physic / 15046
School of Physics
  Title:   Exact spike-timing distribution reveals higher-order interactions of neurons
1.  S. Rashid Shomali
2.  M. Nili Ahmadabadi
3.  H. Shimazaki
4.  S.N. Rasuli
  Status:   Submitted
  Year:  2017
  Supported by:  IPM
It has been suggested that variability in spike patterns of individual neuron is largely due to noisy fluctuations caused by asynchronous synaptic inputs balanced near the threshold regime [1-3]. In this regime, small fluctuations in synaptic inputs to a neuron do cause output spikes; because the membrane potential is maintained below but close enough to the threshold potential. To successfully transfer signals under such noisy conditions, it is proposed that a few relatively stronger synapses and/or an assembly of nearly synchronous ones form �??signaling inputs�?� [4]. Thus one fundamental question is how such relatively strong signaling input modifies the spiking activity of a post-synaptic neuron which receives noisy background inputs balanced near the threshold regime. Nonetheless, analytical studies on the effect of the signaling input under such conditions are scarce even with the popular leaky integrate-and-fire (LIF) neuron model. Here we analytically study the impact of a specified signaling input on spike timing of the postsynaptic LIF neuron which receives noisy inputs at the threshold regime. To this end, we first revisit Fokker�??Planck analysis of a first spike-timing distribution when the LIF neuron receives noisy synaptic inputs, but no signaling input, at the threshold regime. We then perform perturbation analysis to investigate how a signaling input modifies this first spike-timing distribution. Fortunately, we could solve all terms of perturbation analytically and find the exact first spike-timing distribution of the postsynaptic neuron; it is applicable to not only excitatory but also inhibitory input. This analytical solution allows us to describe the statistics of output spiking activity as a function of background noise, membrane dynamics, and signaling input�??s timing and amplitude. The proposed analysis of signaling input provides a powerful framework for studying information transmission, neural correlation, and timing-dependent synaptic plasticity. Among them, we investigate the impact of common signaling inputs on population activities of postsynaptic neurons. Using mixture models based on our analytical first spike-timing distribution, we calculate the higher-order interactions [5] of postsynaptic neurons in different network architectures. Comparing these results with higher-order interactions, measured from experimental data in monkey V1 [6], we try to answer whether one can reveal network architecture, responsible for the ubiquitously observed sparse activities.

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