A New Thermodynamic Formalism for Neuronal Ensemble Dynamics

IBN 97-27739 SO，希夫，格鲁克曼。了解神经元集合内的同步活动对于神经科学研究至关重要。 理解和表征集合内的计算以及大脑内不同集合之间的信息流非常重要。 在所谓的“绑定问题”中，当空间上不同的神经元必须协调来计算感官知觉的各个方面时，同步至关重要。传统上，这些问题是使用相同同步（IS）的概念来解决的，该概念假设大脑的两个或多个整体在彼此锁定的时间步长中执行相同的活动。 然而，在具有通用非线性成分的集合中（其中肯定包括神经元集合），应该会出现更复杂的相干行为。 因此，我们必须拓宽超越相同同步的动态相干性概念。 混沌理论广泛地涵盖了此类非线性动力系统的研究。 该领域的一个主要理论进展是认识到这些非线性系统看似不稳定的行为可以通过一组特殊的不稳定平衡状态有效地表征。 在漫画家看来，这些所谓的不稳定周期轨道（UPO）是抽象动态景观的山丘和山谷。 随着系统随时间的进展，系统的状态可以通过 UPO 构建的动态景观中的轨迹来描述。 对于耦合系统（神经元），这些山丘和山谷的排列和对称性反映了系统内表现出的不同程度的动态一致性。最重要的是，类似于物理学中的统计力学，这些 UPO 形成了系统的微观状态框架，它们的结构变化为这种动态景观中的地形变化提供了描述。 然后可以基于这些 UPO 对各种可能的动态相干态构建热力学描述。 开发的理论工具将应用于我们存档的生物数据中神经元耦合的典型例子：两个耦合神经元和两个神经元集合。 该项目的结果将在理论上拓宽我们对耦合非线性振荡器（包括神经元、耦合机械和电子设备等）的理解，并将作为实验表征神经元集合之间使用的语法代码的初步尝试。

IBN 97-27739 SO, SCHIFF, GLUCKMANN. An understanding of synchronous activities within an ensemble of neurons is essential in the study of neuroscience. It is important to understand and characterize both the computation within an ensemble, as well as the information flow between different ensembles within the brain. In the so called "binding problem", when spatially disparate neurons must coordinate to compute aspects of sensory perception, synchrony is essential. Traditionally, these issues have been addressed using the concept of identical synchrony (IS) which assumes that two or more ensembles of the brain are performing the same activities in locked time step with each other. However, in ensembles with generic nonlinear components, of which neuronal ensembles are most certainly included, more complex coherent behaviors should arise. Consequently, our concept of dynamical coherence beyond identical synchrony must be broadened. Chaos theory broadly encompasses the study of such nonlinear dynamical systems. A major theoretical advance in this field was the recognition that seeming erratic behaviors from these nonlinear systems could be effectively characterized by a set of special unstable equilibrium states. In a cartoonist view, these so called unstable periodic orbits (UPOs) are hills and valleys of an abstract dynamical landscape. As the system progresses in time, the state of the systems can be described by a trajectory within this dynamical landscape constructed with the UPOs. For coupled systems (neurons), the arrangement and symmetry of these hills and valleys reflect the varying degree of dynamical coherence exhibited within the system. Most importantly, analogous to statistical mechanics in physics, these UPOs form a framework of microscopic states for the system and their structural changes afford a description for the topographical changes within this dynamical landscape. A thermodynamical description based on these UPOs for the various possible dynamical coherent states might then be constructed. Theoretical tools developed will be applied to quintessential examples of neuronal coupling from our archived biological data: two coupled neurons and two ensembles of neurons. Results from this project will both theoretically broaden our understanding of coupled nonlinear oscillators, including neurons, coupled mechanical and electronic devices, etc., and will serve as the initial attempt to experimentally characterize the grammatical code used between ensembles of neurons.