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

神经网络通过传播被称为尖峰脉冲的电脉冲模式来处理信息。这些尖峰模式表现出惊人的可变性，即使在由相同感觉刺激驱动的神经网络中也是如此。由于这种可变性，神经网络一直被认为是在异步状态下运行。在异步状态下，神经元相互独立地放电，因此神经元经历同步突触输入的概率非常低。这种对同步性的忽视进一步得到了尖峰成对相关性的明显弱点的支持。然而，最近的实验和理论工作严重挑战了这一观点。具体地说，大规模的尖峰记录揭示了微弱但非零的尖峰相关性。同时，在没有一定程度的输入同步的情况下，无法解释在单电池记录中观察到的电压变异性水平，这与弱但非零的尖峰相关是兼容的。为了应对这些最新发现带来的挑战，PI将描述突触同步如何稳定地出现在原本受到生物噪声困扰的网络中。具体地说，PI将(1)通过跳跃过程模拟基于同步的输入相关性，(2)阐明噪声尖峰产生机制如何将同步传播到输出神经元，以及(3)表征基于同步的相关性如何稳定地出现在有限神经网络中。(1)的回报将是表征活动相关性如何解释观察到的高度神经变异性。(2)的回报将是估计峰值的时间信息量。(3)的回报将是确定稳定的基于同步的相关性的网络特征。在实现他的研究目标的同时，PI将设计一门融合数学和神经科学受众的原创本科翻转课程。在他制作的研究中心内，PI还将启动一项服务，为希望在其研究项目中获得理论支持的附属公司提供服务。皮层棘波模式可以表现出行为相关性的精确时间精度。这支持了神经元棘波同步的时间代码的流行。然而，维持刺激性精确度与通常观察到的皮质噪声水平是不一致的。这支持了速率代码的流行，神经元对这种代码不同步地产生尖峰。也就是说，这种编码二分法是误导的，因为同一个神经元可以联合充当同步编码者和异步编码者。PI将通过描述具有非平凡尖峰相关性的理想化神经电路中的集体动力学，将同步/异步编码困境作为一个程度问题而不是一个替代问题来解决。具体地说，非平凡的相关性将产生于突触同步，即与神经元的突触倾向于在相对于神经元的时间常数的小时间尺度上共同激活。这与大多数理论方法形成对比，这些理论方法植根于具有平凡关联结构的平均场近似。为了解决同步/异步编码的困境，PI将开发一种新的理论和计算框架来建模、量化和分析同步对神经动力学的影响。关键的数学挑战将是执行(1)当同步输入驱动时对与生物物理相关的神经元模型的随机分析，(2)被视为自由边界问题的尖峰产生机制的概率分析，以及(3)捕获所谓的泊松平均场动力学的非线性偏微分方程的分叉和标度分析。在所有情况下，该方法将利用现代分析和概率技术与先进的数值方法相结合。该奖项由MPS/DMS数学生物学计划和CISE/IIS稳健智能计划联合资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.