Discrete- and Continuous-Time Probabilistic Models and Algorithms for Inferring Neuronal UP and DOWN States

UP and DOWN states, the periodic fluctuations between increased and decreased spiking activity of a neuronal population, are a fundamental feature of cortical circuits. Understanding UP-DOWN state dynamics is important for understanding how these circuits represent and transmit information in the brain. To date, limited work has been done on characterizing the stochastic properties of UP-DOWN state dynamics. We present a set of Markov and semi-Markov discrete- and continuous-time probability models for estimating UP and DOWN states from multiunit neural spiking activity. We model multiunit neural spiking activity as a stochastic point process, modulated by the hidden (UP and DOWN) states and the ensemble spiking history. We estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation-maximization (EM) algorithm and a Monte Carlo EM algorithm that uses reversible-jump Markov chain Monte Carlo sampling in the E-step. We apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi- unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow-wave sleep. Our approach provides a statistical characterization of UP-DOWN state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process.National Institutes of Health (U.S.) (Grant R01-DA015644)National Institutes of Health (U.S.) (Director Pioneer Award DP1- OD003646)National Institutes of Health (U.S.) (NIH/NHLBI grant R01-HL084502)National Institutes of Health (U.S.) (NIH institutional NRSA grant T32 HL07901

Hidden Markov Models

Hidden Markov Models (HMMs), although known for decades, have made a big career nowadays and are still in state of development. This book presents theoretical issues and a variety of HMMs applications in speech recognition and synthesis, medicine, neurosciences, computational biology, bioinformatics, seismology, environment protection and engineering. I hope that the reader will find this book useful and helpful for their own research

Population analysis of neural data -- developments in statistical methods and related computational models

A key goal of neuroscience is to understand how the remarkable computational abilities of our brain emerge as a result of interconnected neuronal populations. Recently, advances in technologies for recording neural activity have increased the number of simultaneously recorded neurons by orders of magnitude, and these technologies are becoming more widely adopted. At the same time, massive increases in computational power and improved algorithms have enabled advanced statistical analyses of neural population activity and promoted our understanding of population coding. Nevertheless, there are many unanswered emerging questions, when it comes to analyzing and interpreting neural recordings. There are two major parts to this study. First, we consider an issue of increasing importance: that many in vivo recordings are now made by calcium-dependent fluorescent imaging, which only indirectly reports neural activity. We compare measurements of extracellular single units with fluorescence changes extracted from single neurons (often used as a proxy for spike rates), both recorded from cortical neural populations of behaving mice. We perform identical analyses at the single cell level and population level, and compare the results, uncovering a number of differences, or biases. We propose a phenomenological model to transform spike trains into synthetic imaging data and test whether the transformation explains the biases found. We discover that the slow temporal dynamics of calcium imaging obscure rapid changes in neuronal selectivity and disperse dynamic features in time. As a result, spike rate modulation that is locked to temporally localized events can appear as a more sequence-like pattern of activity in the imaging data. In addition, calcium imaging is more sensitive to increases rather than decreases in spike rate, leading to biased estimates of neural selectivity. These biases need to be considered when interpreting calcium imaging data. The second part of this work embarks on a challenging yet fruitful study of latent variable analysis of simultaneously recorded neural activity in a decision-making task. To connect the neural dynamics in different stages of a decision-making task, we developed a time-varying latent dynamics system model that uncovers neural dynamics shared by neurons in a local decision-making circuit. The shared neural activity supports the dynamics of choice generation and memory in a fashion akin to drift diffusion models, and robustly maintains a decision signal in the post-decision period. Importantly, we find that error trials follow similar dynamics to those of correct trials, but their dynamics are separated in shared neural activity space, proving a more correct early decoding estimation of an animal's success or failure at a given trial. Overall, the shared neural activity dynamics can predict multiple measures of behavioral variability including performance, reaction time, and trial correctness, and therefore are a useful summary of the neural representation. Such an approach can be readily applied to study complex dynamics in other neural systems. In summary, this dissertation represents an important step towards developing model-based analysis of neuronal dynamics and understanding population codes in large-scale neural data