9972913 The investigator continues work on the applications of nonlinear dynamics to cell biology and physiology with particular emphasis in neurophysiology. Specifically, the following problems are studied: 1. Analysis of synaptic bistability; what is the dynamic mechanism by which two (and more) mutually coupled neurons can maintain activity in absence of inputs? 2. How does adaptation enhance the synchronization of excitatorily coupled neural oscillators? 3. What determines the form and properties of ``lurching'' waves that arise in systems of neurons that are coupled with delays as well as in models of thalamic oscillations? 4. What is the effect of inhibition and slow excitatory synapses on the propagation of waves in cortical slices? 5. How are free and bound actin spatially distributed in the cell; is there any nontrivial spatial dependence on the length distribution of the polymerized molecule? The investigator studies how mathematical methods can be used to understand how biological systems work. Specifically, he is interested in how nerve cells interact with each other to produce activity that is related to behavior. For example, when a person or animal holds something in short-term memory (like a phone number) how does the relevant group of neurons stay on and what turns it off? Mathematical models are created and mathematical techniques are used to study these models in order to suggest new experiments. During normal and abnormal behavior parts of the nervous system are capable of producing waves that move across regions of the brain. The investigator is interested in what factors determine the properties of these waves, such as their speed and shape. Finally, he studies models of the components inside the cell that are responsible for the cell's shape and how it moves around.
