CAREER: Nontrivial correlations in the neural code: a question of synchrony

University Of Texas At Austin, Austin TX

Investigators

Abstract

Neural networks process information by propagating patterns of electrical impulses, known as spikes. These spiking patterns exhibit a striking level of variability, even in neural network that are driven by identical sensory stimuli. Owing to this variability, neural networks have been thought to operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. This neglect of synchrony has been further supported by the apparent weakness of spiking pairwise correlations. However, recent experimental and theoretical works seriously challenge this view. Specifically, large-scale spiking recordings have revealed weak but nonzero spiking correlations. At the same time, the levels of voltage variability observed in single-cell recordings cannot be explained without some degree of input synchrony, compatible with weak but nonzero spiking correlation. To address the challenge posed by these recent findings, the PI will characterize how synaptic synchrony can stably emerge in networks that are otherwise plagued with biological noise. Specifically, the PI will (1) model synchrony-based input correlations via jump processes, (2) elucidate how noisy spike-generation mechanisms can propagate synchrony to output neurons, and (3) characterize how synchrony-based correlations can stably emerge in limit neural networks. The payoff of (1) will be characterizing how activity correlations can explain the high degree of observed neural variability. The payoff of (2) will be estimating the temporal information content of a spike. The payoff of (3) will be identifying the network features stabilizing synchrony-based correlations. While reaching for his research goals, the PI will design an original undergraduate flipped course mixing mathematics and neuroscience audiences. Within the research center that he animates, the PI will also kickstart a service offering for affiliates who want to acquire theoretical support in their research project. Cortical spiking patterns can exhibit exquisite time precision of behavioral relevance. This supports the prevalence of time codes for which neuronal spiking is synchronized. However, the maintenance of spiking precision is at odds with typically observed level of cortical noise. This supports the prevalence of rate codes, for which neurons spike asynchronously. That said, such a coding dichotomy is misleading as the same neuron can jointly acts as a synchronous coder and as an asynchronous coder. The PI will resolve the synchronous/asynchronous coding dilemma as a matter of degree rather than a matter of alternative, by characterizing collective dynamics in idealized neural circuits with nontrivial spiking correlations. Concretely, nontrivial correlations will arise from synaptic synchrony, whereby synapses to a neuron tend to coactivate over small timescales with respect to the neuron’s time constant. This is by contrast with most theoretical approaches which are rooted in mean-field approximations with trivial correlation structure. To resolve the synchronous/asynchronous coding dilemma, the PI will develop a novel theoretical and computational framework to model, quantify, and analyze the impact of synchrony on neural dynamics. The mathematical challenges at stake will be to perform (1) a stochastic analysis of biophysically-relevant neuronal models when driven by synchronous input, (2) an probabilistic analysis of the spike-generating mechanism viewed as a free-boundary problem, and (3) bifurcation and scaling analyses of the nonlinear partial differential equation capturing the so-called Poissonian mean-field dynamics. In all cases, the methodology will exploit modern analytical and probabilistic techniques in combination with advanced numerical methods. This award is jointly funded by the MPS/DMS Mathematical Biology program and CISE/IIS Robust Intelligence program. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.