Nuffield Department of Clinical Neuroscience, University of Oxford, Oxford X3 9DU, U.K.
MRC Brain Network Dynamics Unit, University of Oxford, Oxford X1 3TH, U.K.
Neural Comput. 2023 Aug 7;35(9):1481-1528. doi: 10.1162/neco_a_01601.
Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.
理解尖峰时间依赖可塑性（STDP）的影响对于阐明神经网络如何在长时间尺度上发生变化以及设计旨在调节神经障碍中此类网络的干预措施至关重要。然而，进展受到与具有 STDP 的神经网络模型进行模拟相关的巨大计算成本的限制，并且缺乏可以提供分析见解的低维描述。相位差依赖可塑性（PDDP）规则在相位振荡器网络中近似 STDP，该规则根据神经元对的相位差而不是尖峰时间的差异来规定突触变化。在这里，我们构建了具有 STDP 的相位振荡器网络的平均场近似，以描述这个非常高维系统的部分相空间。我们首先表明，单谐波 PDDP 规则可以近似简单形式的对称 STDP，而多谐波规则则需要准确地近似因果 STDP。然后，我们推导出了平均 PDDP 耦合权重随网络同步的演化的精确表达式。对于形成簇的 Kuramoto 振荡器的自适应网络，我们基于每个簇的平均场动力学和簇间和簇内的平均耦合权重来制定一组低维描述。最后，我们表明，这种两簇平均场模型可以拟合合成数据，为具有对称 STDP 的全自适应网络提供低维近似。我们的框架代表了朝着具有 STDP 的自适应网络的低维描述迈出的一步，例如，可以为旨在最大化脑刺激的持久效果的新疗法的开发提供信息。
