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.
