A New Thermodynamic Formalism for Neuronal Ensemble Dynamics

伊本97-27739所以，希夫，格卢克曼。在神经科学的研究中，了解神经元集合中的同步活动是必不可少的。重要的是要理解和描述集合内的计算，以及大脑中不同集合之间的信息流。在所谓的“绑定问题”中，当空间上不同的神经元必须协调以计算感觉的各个方面时，同步是必不可少的。传统上，这些问题是使用相同同步(IS)的概念来解决的，该概念假设两个或更多的大脑集合彼此以锁定的时间步长执行相同的活动。然而，在含有一般非线性成分的系综中，神经系综肯定包括在内，应该出现更复杂的相干行为。因此，我们关于动态一致性的概念必须超越完全同步。混沌理论广泛地涵盖了对这类非线性动力系统的研究。这一领域的一个主要理论进展是认识到这些非线性系统的看似不稳定的行为可以有效地用一组特殊的不稳定平衡态来表征。在漫画家看来，这些所谓的不稳定周期轨道(UPO)是抽象动态景观的丘陵和山谷。随着系统在时间上的进展，系统的状态可以用由UPO构建的动态景观中的轨迹来描述。对于耦合系统(神经元)，这些丘陵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力学相干。最重要的是，类似于物理学中的统计力学，这些UPO形成了系统微观状态的框架，它们的结构变化为这一动态景观中的地形变化提供了描述。然后，基于这些UPO对各种可能的动力学相干态的热力学描述可以被构造出来。开发的理论工具将应用于我们存档的生物学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。这个项目的结果将在理论上拓宽我们对耦合非线性振荡器的理解，包括神经元、耦合机械和电子设备等，并将作为实验上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.