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The influence of synaptic weight distribution on neuronal population dynamics.

ABSTRACT: The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.

SUBMITTER: Iyer R

PROVIDER: S-EPMC3808453 | biostudies-literature | 2013 Oct

REPOSITORIES: biostudies-literature

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The influence of synaptic weight distribution on neuronal population dynamics.

Iyer Ramakrishnan R Menon Vilas V Buice Michael M Koch Christof C Mihalas Stefan S

PLoS computational biology 20131024 10

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuron ...[more]

PMID: 24204219

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Project description:Abnormally strong neural synchronization may impair brain function, as observed in several brain disorders. We computationally study how neuronal dynamics, synaptic weights, and network structure co-emerge, in particular, during (de)synchronization processes and how they are affected by external perturbation. To investigate the impact of different types of plasticity mechanisms, we combine a network of excitatory integrate-and-fire neurons with different synaptic weight and/or structural plasticity mechanisms: (i) only spike-timing-dependent plasticity (STDP), (ii) only homeostatic structural plasticity (hSP), i.e., without weight-dependent pruning and without STDP, (iii) a combination of STDP and hSP, i.e., without weight-dependent pruning, and (iv) a combination of STDP and structural plasticity (SP) that includes hSP and weight-dependent pruning. To accommodate the diverse time scales of neuronal firing, STDP, and SP, we introduce a simple stochastic SP model, enabling detailed numerical analyses. With tools from network theory, we reveal that structural reorganization may remarkably enhance the network's level of synchrony. When weaker contacts are preferentially eliminated by weight-dependent pruning, synchrony is achieved with significantly sparser connections than in randomly structured networks in the STDP-only model. In particular, the strengthening of contacts from neurons with higher natural firing rates to those with lower rates and the weakening of contacts in the opposite direction, followed by selective removal of weak contacts, allows for strong synchrony with fewer connections. This activity-led network reorganization results in the emergence of degree-frequency, degree-degree correlations, and a mixture of degree assortativity. We compare the stimulation-induced desynchronization of synchronized states in the STDP-only model (i) with the desynchronization of models (iii) and (iv). The latter require stimuli of significantly higher intensity to achieve long-term desynchronization. These findings may inform future pre-clinical and clinical studies with invasive or non-invasive stimulus modalities aiming at inducing long-lasting relief of symptoms, e.g., in Parkinson's disease.

Project description:The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitute a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks resembling local cortical circuits and develop strategies for minimizing deviations from the dynamics of networks with high-resolution synaptic weights. We mimic the effect of a limited synaptic weight resolution by replacing normally distributed synaptic weights with weights drawn from a discrete distribution, and compare the resulting statistics characterizing firing rates, spike-train irregularity, and correlation coefficients with the reference solution. We show that a naive discretization of synaptic weights generally leads to a distortion of the spike-train statistics. If the weights are discretized such that the mean and the variance of the total synaptic input currents are preserved, the firing statistics remain unaffected for the types of networks considered in this study. For networks with sufficiently heterogeneous in-degrees, the firing statistics can be preserved even if all synaptic weights are replaced by the mean of the weight distribution. We conclude that even for simple networks with non-plastic neurons and synapses, a discretization of synaptic weights can lead to substantial deviations in the firing statistics unless the discretization is performed with care and guided by a rigorous validation process. For the network model used in this study, the synaptic weights can be replaced by low-resolution weights without affecting its macroscopic dynamical characteristics, thereby saving substantial amounts of memory.

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The influence of synaptic weight distribution on neuronal population dynamics.

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The influence of synaptic weight distribution on neuronal population dynamics.

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