[论文解读] Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity

Richard Gast|arXiv (Cornell University)|Jan 15, 2021

Neural dynamics and brain function参考文献 52被引用 27

一句话总结

本文为具有突触前短时突触可塑性（STP）的二次积分-放电（QIF）神经元网络提出了两种新颖的平均场模型，克服了先前基于随机放电时间近似的局限性。通过采用Ott-Antonsen方法，推导出精确的低维方程，能够捕捉到爆发放电与双稳态动力学，揭示了STP如何塑造网络的宏观行为。

ABSTRACT

In Parkinson's disease (PD), large parts of the brain transition into states of enhanced neural synchronization. These phase transitions have been associated with the death of dopaminergic neurons as well as with impaired motor function. In this thesis, we address the much-debated question of how parkinsonian synchronization depends on dopamine depletion in the basal ganglia (BG). To this end, we develop spiking neural network (SNN) models of BG circuits and study them via bifurcation analysis. First, we derive mean-field models that allow to account for various forms of short-term plasticity in SNNs. We show that such short-term plasticity mechanisms can lead to highly synchronous, periodic bursting dynamics and discuss the relevance of this bursting regime for PD. Second, we find that the external pallidum, an important part of the BG, cannot cause parkinsonian oscillations autonomously. However, our results suggest that the external pallidum may contribute to the emergence of cross-frequency coupling that has been reported for parkinsonian oscillations. Finally, we describe an open-source Python toolbox that we developed to implement and analyze mean-field models of neural dynamics. Together, this thesis provides insight into BG synchronization processes as well as the mathematical basis and software for future studies of neural synchronization.:1 Introduction 1.1 A complex systems perspective of the brain 1.2 Brain function and the phase transition to synchronized neural activity 1.3 Low-dimensional manifolds of synchronized neural activity 1.4 Phase transitions to synchronized neural activity in Parkinson’s disease 1.5 Thesis overview 2 Mathematical Models and Methods 2.1 A non-linear oscillator model of neural activity 2.2 Dynamical systems methods for the study of neural network models 2.3 Dynamics of a single QIF neuron 3 Low-Dimensional Dynamics in Spiking Neural Networks 3.1 Mean-field approaches in neuroscience 3.2 Dynamics of QIF networks with post-synaptic STP 3.3 Dynamics of QIF networks with spike-frequency adaptation 3.4 Mean-field dynamics of QIF networks with pre-synaptic STP 3.5 Discussion 4 Phase Transitions and Neural Synchronization in the External Pallidum 4.1 A new perspective on GPe structure and function 4.2 GPe model definition and analysis 4.3 Phase transitions in the GPe under static and periodic input 4.4 Discussion 5. Modeling of Neural Mean-Field Dynamics Via PyRates 5.1 Computational modeling in neuroscience 5.2 The Framework 5.3 Pre-implemented methods for neural modeling workflows 5.4 Results 5.5 Discussion 6. Conclusion and Outlook

研究动机与目标

• 将平均场理论扩展至具有突触前短时突触可塑性的脉冲发放神经网络，而此前的方法无法捕捉此类特性。
• 解决在具有分布参数的确定性QIF网络中，基于随机放电时间近似方法的局限性。
• 推导出数学上严谨的平均场方程，以保持具有突触特异性可塑性的网络的动力学特性。
• 研究突触前STP如何影响网络的宏观行为，如爆发放电与多稳态。
• 为未来具有动态突触的神经环路的介观与宏观建模提供基础。

提出的方法

• 应用Ott-Antonsen方法，推导所有神经元相互连接的QIF神经元网络在突触前STP下的平均场方程。
• 提出两种不同的方法来建模突触前STP：一种基于突触资源动力学，另一种基于改进的适应性形式。
• 采用分岔分析方法，研究所推导的平均场系统中不同动态行为模式之间的稳定性与转变。
• 将所提出的模型与近期的随机放电时间近似方法进行比较，证明其在确定性设定下存在不准确性。
• 采用标准的Tsodyks-Markram模型描述短时突触可塑性，整合了突触抑制与增强两种机制。
• 通过假设突触变量的适应过程相对于膜电位动力学较慢，推导出闭式平均场方程。

实验结果

研究问题

• RQ1 能否利用Ott-Antonsen方法，为具有突触前短时突触可塑性的QIF网络推导出精确的平均场方程？
• RQ2 与突触后模型相比，突触前STP机制（如囊泡耗竭）如何影响网络的宏观动力学？
• RQ3 随机放电时间近似方法是否能准确再现具有分布参数的确定性QIF网络的动力学？
• RQ4 在具有突触前STP的QIF网络中，会涌现出哪些动态行为模式（如爆发放电或双稳态）？
• RQ5 所推导的平均场模型在准确性和预测能力上与现有近似方法相比如何？

主要发现

• 所提出的平均场模型能准确再现具有分布参数的确定性QIF网络的宏观活动，而随机放电时间近似方法则失败。
• 这些模型能够捕捉由突触前短时突触可塑性引发的复杂网络动力学，包括周期性爆发放电与双稳态行为。
• 分岔分析表明，突触前STP可使QIF网络中出现持续的爆发放电与多稳态状态。
• 所推导的平均场方程在数学上比以往的近似方法更复杂，但能更精确、更完整地描述网络动力学。
• 研究结果表明，除非一个神经元的所有突触同时受到影响，否则突触前STP不能被当作全局宏观变量处理，而这一点在囊泡耗竭模型中并不成立。
• 结果验证了Ott-Antonsen方法在具有突触特异性动态变量的网络中的适用性，将其应用范围从神经元特异性适应性扩展至更广泛的场景。