In this project the PI will develop a nonlinear dynamical method for the estimation of states and parameters in models of neurobiological systems using experimental data. Utilizing this method the PI will analyze models of individual neurons in the crustacean Pyloric central pattern generator (CPG) and models of sub-circuits of neurons within this CPG. The general problem of determining the parameters of mathematical models of individual neurons and networks of neurons will be addressed using a novel method called dynamical parameter estimation (DPE), which is based on the classical problem of optimal tracking of a desired trajectory. In this case the DPE is known in the control theory literature as a Luenberger observer with adaptive gain: a filter in the sense of Kalman. Using this approach the PI will apply the new technique to the analysis of experimental data from CPG neurons and CPG sub-circuits. Two graduate students will be involved in this efforts. The research group of the PI will also work each summer with Research Experience for Undergraduates (REU) undergraduate students program at UCSD.
Using methods of statisical physics we have created a tool to test models of complex systems using data taken from those systems. First the consistency of the model with the data is examined, then when the model parameters and states have been estimated, the model is validated by its response to new forcings. The path integral developed to describe these processes has been examined as a statitical physics problem as well. We have created new annealing methods to determine the loest action level, thus the best path associated with the model state passing through an observation window. This allows accurate estimation of model parameters and of the unmeasured state variables of the model. We test the model thus completed using new inoputs--currents for neurons, presssures for fluid flows, etc...--and test the response of the model to those new inputs. In the case of models of individual neurons this tells us when it reponse when placed in a network will be realistic. We have also developed methods to determine the connections among neurons in functional netowrks and we are now using them to understand, at a biophysical level, how networks in the birdsong system produce sparse sequences instructing muscles to produce learned song.
