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Brain Connectomics is generating an ever-increasing deluge of data, which challenges us to develop new methods for analyzing and extracting new insights from these data. Connectomic researchers have focused on connectivity -- the pattern of connectivity between neurons. The strengths of synapses have also been studied by quantifying the sizes of synapses which can be regulated by learning. During my PhD, I have been developing computational methods for relating brain structure to function. I have developed tools and algorithms for analyzing connectomics data sets using Machine learning, statistical inference and Information Theory to find measures and biomarkers that can be used to probe mechanisms underlying leaning and memory in normal and diseased brains. We introduce here a powerful method for analyzing three-dimensional reconstruction from serial section electron microscopy (3DEM) to measure synaptic information storage capacity (SISC) and apply it to data following in vivo long-term potentiation (LTP). Quantifying precision is fundamental to understanding information storage and retrieval in neural circuits. We quantify this precision with Shannon information theory, which is a more reliable estimate than prior analyses based on signal detection theory. Spine head volumes are well correlated with other measures of synaptic weight, thus SISC can be determined by identifying the non-overlapping clusters of dendritic spine head volumes to determine the number of distinguishable synaptic weights. SISC analysis of spine head volumes in the stratum radiatum of hippocampal area CA1 revealed 24 distinguishable states (4.1 bits). In contrast, spine head volumes in the middle molecular layer of control dentate gyrus occupied only 5 distinguishable states (2 bits). Thus, synapses in different hippocampal regions had significantly different SISCs. Moreover, these were not fixed properties but increased by 30 min following induction of LTP in the dentate gyrus to occupy 10

Human memory and learning represent the most complex and miraculous of human abilities and also the most difficult and major challenges of modern medicine. While treatments for diseases from heart to lung have rapidly advanced, basic mechanisms of brain function rooted in memory and learning remain completely unknown, reflected by the dearth of targeted treatments available for neuropsychiatric disorders.This dissertation seeks to understand the neural processes of memory and learning at three interdependent levels of investigation --- systems of circuits, an individual circuit, and molecular modulation of circuits --- and how they can become disrupted in disease. To study these processes, I use artificial neural network models.I first consider a system of circuits (Chapter 2), studying how regions of the brain coordinate to produce coherent and flexible behavior and how disruptions lead to specific clinical syndromes. I focus on the prefrontal cortex where distinct subregions have been characterized, and analyze how simple architectural alterations in circuit interdependencies can give rise to powerful memory and learning features characteristic of humans. I then study how disruptions affect this circuit system, revealing striking parallels to patients who have suffered specific prefrontal lesions.To understand how an individual circuit learns and develops, I then focus on the internal process of strategy acquisition and evolution within a neural network (Chapter 3). To do this, I investigate a surprising experimental finding that humans and monkeys exhibit major behavioral discrepancies when solving a set of working memory tasks. I find that neural network models follow characteristic strategy progressions, exhibiting both monkey-like and human-like behavior at different stages. Furthermore, neural networks can mimic common problem solving heuristics while operating with unrelated underlying mechanisms. Counterintuitively, I find that some non-optimal heuristics c

Human memory and learning represent the most complex and miraculous of human abilities and also the most difficult and major challenges of modern medicine. While treatments for diseases from heart to lung have rapidly advanced, basic mechanisms of brain function rooted in memory and learning remain completely unknown, reflected by the dearth of targeted treatments available for neuropsychiatric disorders.This dissertation seeks to understand the neural processes of memory and learning at three interdependent levels of investigation --- systems of circuits, an individual circuit, and molecular modulation of circuits --- and how they can become disrupted in disease. To study these processes, I use artificial neural network models.I first consider a system of circuits (Chapter 2), studying how regions of the brain coordinate to produce coherent and flexible behavior and how disruptions lead to specific clinical syndromes. I focus on the prefrontal cortex where distinct subregions have been characterized, and analyze how simple architectural alterations in circuit interdependencies can give rise to powerful memory and learning features characteristic of humans. I then study how disruptions affect this circuit system, revealing striking parallels to patients who have suffered specific prefrontal lesions.To understand how an individual circuit learns and develops, I then focus on the internal process of strategy acquisition and evolution within a neural network (Chapter 3). To do this, I investigate a surprising experimental finding that humans and monkeys exhibit major behavioral discrepancies when solving a set of working memory tasks. I find that neural network models follow characteristic strategy progressions, exhibiting both monkey-like and human-like behavior at different stages. Furthermore, neural networks can mimic common problem solving heuristics while operating with unrelated underlying mechanisms. Counterintuitively, I find that some non-optimal heuristics c

Schizophrenia is a complex neuropsychiatric disorder characterized by a wide range of clinical manifestations. Even though the etiology of schizophrenia is not known, the heterogeneous nature of the disorder strongly suggests that multiple pathways and brain areas are affected by a combination of internal and external factors. These factors include and not limited to: psychological, genetic, social, and environmental determinants. Cognitive impairment is one of the commonly observed clinical manifestations of schizophrenia. Working memory, which is an ability to encode and hold information over a short period, is severely impaired in schizophrenia. (1) Characterizing how such deficits manifest in large-scale dynamics and (2) understanding the pathophysiology and circuit mechanisms behind working memory deficits associated with schizophrenia are the two main questions that I address in my dissertation.To answer the first question, I employed a method based on nonlinear systems theory to quantify large-scale dynamical states of time-series data and to identify dynamically distinct subgroups (Chapter 2). I demonstrate that the method, which utilizes delay differential analysis (DDA), can effectively extract features reflective of significant state changes and detect subgroups with similar features. Applying the method to brain signals obtained from a large cohort of schizophrenia patients further revealed subgroups with distinct dynamical characteristics aligned with neurophysiological and clinical parameters.To answer the second question, I first developed a biologically realistic computational model based on spiking recurrent neural networks (RNNs) capable of learning cognitive tasks that involve working memory (Chapter 3). By taking advantage of a close relationship between continuous and spike RNNs that emerges under certain conditions, the method provides an extremely simple platform that can be utilized to investigate how power-efficient network dynamics lead to

Schizophrenia is a complex neuropsychiatric disorder characterized by a wide range of clinical manifestations. Even though the etiology of schizophrenia is not known, the heterogeneous nature of the disorder strongly suggests that multiple pathways and brain areas are affected by a combination of internal and external factors. These factors include and not limited to: psychological, genetic, social, and environmental determinants. Cognitive impairment is one of the commonly observed clinical manifestations of schizophrenia. Working memory, which is an ability to encode and hold information over a short period, is severely impaired in schizophrenia. (1) Characterizing how such deficits manifest in large-scale dynamics and (2) understanding the pathophysiology and circuit mechanisms behind working memory deficits associated with schizophrenia are the two main questions that I address in my dissertation.To answer the first question, I employed a method based on nonlinear systems theory to quantify large-scale dynamical states of time-series data and to identify dynamically distinct subgroups (Chapter 2). I demonstrate that the method, which utilizes delay differential analysis (DDA), can effectively extract features reflective of significant state changes and detect subgroups with similar features. Applying the method to brain signals obtained from a large cohort of schizophrenia patients further revealed subgroups with distinct dynamical characteristics aligned with neurophysiological and clinical parameters.To answer the second question, I first developed a biologically realistic computational model based on spiking recurrent neural networks (RNNs) capable of learning cognitive tasks that involve working memory (Chapter 3). By taking advantage of a close relationship between continuous and spike RNNs that emerges under certain conditions, the method provides an extremely simple platform that can be utilized to investigate how power-efficient network dynamics lead to

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca2+. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. In this dissertation, I derive physically grounded mathematical models of the instantaneous rate of Ca2+-triggered neurotransmitter release. The Ca2+ traces that drive these dynamics come from simulations in MCell of spike-evoked Ca2+ influx and buffered diffusion through the presynaptic space, an approach that overcomes observational limitations of physiological experiments. With these Ca2+ traces, I drive a validated kinetic model of the SNARE complex, which mediates spike-triggered vesicle fusion for both synchronous and asynchronous release. The profiles of the resulting release rate histograms inform the parameters of the phenomenological release models, including the time scales and the facilitation of release probability. Based on these results, I construct an event-driven model of presynaptic dynamics, treating all Ca2+-sensitive processes, not just vesicle release, as Poisson processes with decaying rate parameters that may undergo activity-dependent facilitation. This approach provides a unified framework for modelling both spontaneous and spike-evoked presynaptic vesicle dynamics, for an arbitrary number of processes that define interaction between an arbitrary number of vesicle pools and recycling pathways. I validate the model against MCell and demonstrate a runtime complexity that bridges the gap between full molecular simulations and abstract synaptic models. Furthermore, I veri

Calmodulin is a ubiquitous calcium-sensing protein which activates many downstream cellular processes. Calmodulin cooperatively binds up to four calcium ions which can occupy the four EF-hand motif sites. As more calcium ions bind to calmodulin, this protein becomes more likely to change conformation from the Open/Inactive state to the Closed/Active state. Studying the kinetics of calcium binding to calmodulin can lead to further insight into how the conformational state of calmodulin depends on the local calcium concentration and the effect of cooperative binding due to calcium-induced conformational changes. This project investigates the kinetics of calcium binding to calmodulin binding sites by combining Brownian Dyanmics and Molecular Dynamics to analyze how the presence of calcium ions affects the subsequent binding of additional calcium. Obtaining the kinetic information for these interactions can inform the mechanism for cooperative calcium binding influencing the conformational state of calmodulin.

Calmodulin is a ubiquitous calcium-sensing protein which activates many downstream cellular processes. Calmodulin cooperatively binds up to four calcium ions which can occupy the four EF-hand motif sites. As more calcium ions bind to calmodulin, this protein becomes more likely to change conformation from the Open/Inactive state to the Closed/Active state. Studying the kinetics of calcium binding to calmodulin can lead to further insight into how the conformational state of calmodulin depends on the local calcium concentration and the effect of cooperative binding due to calcium-induced conformational changes. This project investigates the kinetics of calcium binding to calmodulin binding sites by combining Brownian Dyanmics and Molecular Dynamics to analyze how the presence of calcium ions affects the subsequent binding of additional calcium. Obtaining the kinetic information for these interactions can inform the mechanism for cooperative calcium binding influencing the conformational state of calmodulin.

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca2+. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. In this dissertation, I derive physically grounded mathematical models of the instantaneous rate of Ca2+-triggered neurotransmitter release. The Ca2+ traces that drive these dynamics come from simulations in MCell of spike-evoked Ca2+ influx and buffered diffusion through the presynaptic space, an approach that overcomes observational limitations of physiological experiments. With these Ca2+ traces, I drive a validated kinetic model of the SNARE complex, which mediates spike-triggered vesicle fusion for both synchronous and asynchronous release. The profiles of the resulting release rate histograms inform the parameters of the phenomenological release models, including the time scales and the facilitation of release probability. Based on these results, I construct an event-driven model of presynaptic dynamics, treating all Ca2+-sensitive processes, not just vesicle release, as Poisson processes with decaying rate parameters that may undergo activity-dependent facilitation. This approach provides a unified framework for modelling both spontaneous and spike-evoked presynaptic vesicle dynamics, for an arbitrary number of processes that define interaction between an arbitrary number of vesicle pools and recycling pathways. I validate the model against MCell and demonstrate a runtime complexity that bridges the gap between full molecular simulations and abstract synaptic models. Furthermore, I veri

Measuring functional connectivity from neural recordings is important in understandingprocessing in cortical networks. The covariance-based methods are the currentgolden standard for functional connectivity estimation. However, the link between thepair-wise correlations and the physiological connections inside the neural network is unclear.Therefore, the power of inferring physiological basis from functional connectivity estimationis limited. To build a stronger tie and better understand the relationship between functionalconnectivity and physiological neural network, we need (1) a realistic model to simulatedifferent types of neural recordings with known ground truth for benchmarking; (2) a newfunctional connectivity method that produce estimations closely reflecting the physiologicalbasis.In this thesis, (1) I tune a spiking neural network model to match with human sleepEEG data, (2) introduce a new class of methods for estimating connectivity from differentkinds of neural signals and provide theory proof for its superiority, (3) apply it to simulatedfMRI data as an application.

Measuring functional connectivity from neural recordings is important in understandingprocessing in cortical networks. The covariance-based methods are the currentgolden standard for functional connectivity estimation. However, the link between thepair-wise correlations and the physiological connections inside the neural network is unclear.Therefore, the power of inferring physiological basis from functional connectivity estimationis limited. To build a stronger tie and better understand the relationship between functionalconnectivity and physiological neural network, we need (1) a realistic model to simulatedifferent types of neural recordings with known ground truth for benchmarking; (2) a newfunctional connectivity method that produce estimations closely reflecting the physiologicalbasis.In this thesis, (1) I tune a spiking neural network model to match with human sleepEEG data, (2) introduce a new class of methods for estimating connectivity from differentkinds of neural signals and provide theory proof for its superiority, (3) apply it to simulatedfMRI data as an application.