Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 178-203, March 2024.
Abstract. The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain’s learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and stimulus-encoding spatiotemporal patterns of neural activity. Neural activity bumps maintain short term memories of continuous parameter values, emerging in spatially organized models with short-range excitation and long-range inhibition. Previously, we demonstrated nonlinear Langevin equations derived using an interface method which accurately describe the dynamics of bumps in continuum neural fields with separate excitatory/inhibitory populations. Here we extend this analysis to incorporate effects of short term plasticity that dynamically modifies connectivity described by an integral kernel. Linear stability analysis adapted to these piecewise smooth models with Heaviside firing rates further indicates how plasticity shapes the bumps’ local dynamics. Facilitation (depression), which strengthens (weakens) synaptic connectivity originating from active neurons, tends to increase (decrease) stability of bumps when acting on excitatory synapses. The relationship is inverted when plasticity acts on inhibitory synapses. Multiscale approximations of the stochastic dynamics of bumps perturbed by weak noise reveal that the plasticity variables evolve to slowly diffusing and blurred versions of their stationary profiles. Nonlinear Langevin equations associated with bump positions or interfaces coupled to slowly evolving projections of plasticity variables accurately describe how these smoothed synaptic efficacy profiles can tether or repel wandering bumps.

中文翻译：

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具有动态连接的随机神经场中凸块的多尺度运动和变形

多尺度建模与仿真，第 22 卷，第 1 期，第 178-203 页，2024 年 3 月。
摘要。突触可塑性和神经活动动力学的不同时间尺度在大脑的学习和记忆系统中发挥着重要作用。活动依赖性可塑性重塑神经回路结构，确定神经活动的自发和刺激编码时空模式。神经活动颠簸维持连续参数值的短期记忆，出现在具有短程激发和长程抑制的空间组织模型中。之前，我们演示了使用界面方法导出的非线性朗之万方程，该方程准确地描述了具有单独的兴奋性/抑制性群体的连续神经场中的碰撞动力学。在这里，我们扩展了这种分析，以纳入短期可塑性的影响，动态修改积分内核描述的连接性。线性稳定性分析适用于这些具有海维赛发射率的分段平滑模型，进一步表明可塑性如何塑造凸块的局部动态。促进（抑制）会增强（削弱）源自活跃神经元的突触连接，当作用于兴奋性突触时，往往会增加（减少）颠簸的稳定性。当可塑性作用于抑制性突触时，这种关系就会逆转。受弱噪声扰动的凸块随机动力学的多尺度近似表明，塑性变量演变成其静止轮廓的缓慢扩散和模糊版本。与凹凸位置或界面相关的非线性朗之万方程与缓慢演变的可塑性变量的投影相结合，准确地描述了这些平滑的突触功效曲线如何束缚或排斥徘徊的凹凸。