INFN, Sezione di Roma, 00185 Rome, Italy and Department of Integrative and Computational Neuroscience (ICN), Paris- Saclay Institute of Neuroscience (NeuroPSI), Centre National de la Recherche Scientifique (CNRS), 91198 Gif-sur-Yvette, France.
Department of Integrative and Computational Neuroscience (ICN), Paris-Saclay Institute of Neuroscience (NeuroPSI), Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modelisation, Université de Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France.
Phys Rev E. 2019 Dec;100(6-1):062413. doi: 10.1103/PhysRevE.100.062413.
More interest has been shown in recent years to large-scale spiking simulations of cerebral neuronal networks, coming both from the presence of high-performance computers and increasing details in experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, which is the question addressed by mean-field theories. Despite analytic solutions for the mean-field dynamics already being proposed for current-based neurons (CUBA), a complete analytic description has not been achieved yet for more realistic neural properties, such as conductance-based (COBA) network of adaptive exponential neurons (AdEx). Here, we propose a principled approach to map a COBA on a CUBA. Such an approach provides a state-dependent approximation capable of reliably predicting the firing-rate properties of an AdEx neuron with noninstantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular and synchronous irregular (slow oscillations). This result shows that a state-dependent approximation can be successfully introduced to take into account the subtle effects of COBA integration and to deal with a theory capable of correctly predicting the activity in regimes of alternating states like slow oscillations.
近年来，人们对大脑神经元网络的大规模尖峰模拟越来越感兴趣，这既得益于高性能计算机的出现，也得益于实验观察的细节不断增加。在这种情况下，了解群体动态是如何由网络的设计参数产生的，这是均值场理论所要解决的问题。尽管已经针对基于电流的神经元（CUBA）提出了用于均值场动力学的解析解，但对于更现实的神经特性，如基于电导的（COBA）自适应指数神经元（AdEx）网络，尚未实现完整的解析描述。在这里，我们提出了一种将 COBA 映射到 CUBA 的原则性方法。这种方法提供了一种状态相关的逼近，可以可靠地预测具有非瞬时 COBA 积分的 AdEx 神经元的发放率特性。我们还将我们的理论应用于群体动力学，预测了网络在非常不同的状态下的动力学特性，如异步不规则和同步不规则（慢波振荡）。该结果表明，可以成功地引入状态相关的逼近来考虑 COBA 积分的细微影响，并处理一种能够正确预测像慢波振荡这样的交替状态下的活动的理论。
