UC San Diego

My thesis is a collection of theoretical and practical techniques for mapping functional or effective connectivity in cellular neuronal networks, at the cell scale. This is a challenging scale to work with, primarily because of the difficulty in labeling and measuring the activities of networks of cells. It is also important as it underlies behavior, function, and complex diseases. I present methods to measure and quantify the dynamic activities of cells using the optical flow technique, which can identify activity and directions of information processing using calcium fluorescence measurements. I present a unified framework for simulation and estimation of neuronal activity, tailored towards interpretation of experimental data, and implemented in a fully parallel fashion on graphics processor unit (GPU) cards. This framework permits experimenters to estimate hidden quantities in collected data, using any neuronal or astrocyte model. I introduce a technique for mapping functional connectivity in neuronal networks, using experimental data and an arbitrary state space model. The technique makes some simplifications that reduces the dimensionality of the estimation problem, and shows excellent performance for networks of up to 30 possible independent incoming connections. While the framework and mapping algorithms use a state space, parametric representation of individual cell dynamics, I've also developed a time-embedded, nonparametric technique for estimating input-output relationships, and applied it to estimating current from voltage measurements and spikes from fluorescent calcium. Without any knowledge of the underlying neuronal dynamics, this technique can reconstruct a current signal from measured voltage in mouse pyramidal neurons with an R-value of 0.9. Finally, I present my findings and theoretical perspectives acquired while developing the framework and methods. Optimization as a means of estimating functional weights is especially challenging due to the topology of the parameter space, with small perturbations in weights resulting in drastically different simulated dynamics. High-dimensional spaces are prone to the curse of dimensionality, and network states represented in such spaces are not likely to be stable or typical. Finally, the effects of the concentration of measure, as I believe I've observed when mapping large networks, makes it unlikely that real-world networks have more than about 7 independent functional inputs at any given time