The astounding capacity for learning ranks among the nervous system’s most impressive features. This thesis comprises studies employing varied approaches to improve understanding, at the level of neural circuits, of the brain’s capacity for learning. The first part of the thesis contains investigations of hippocampal circuitry – both theoretical work and experimental work in the mouse Mus musculus – as a model system for declarative memory. To begin, Chapter 2 presents a theory of hippocampal memory storage and retrieval that reflects nonlinear dendritic processing within hippocampal pyramidal neurons. As a prelude to the experimental work that comprises the remainder of this part, Chapter 3 describes an open source software platform that we have developed for analysis of data acquired with in vivo Ca2+ imaging, the main experimental technique used throughout the remainder of this part of the thesis. As a first application of this technique, Chapter 4 characterizes the content of signaling at synapses between GABAergic neurons of the medial septum and interneurons in stratum oriens of hippocampal area CA1. Chapter 5 then combines these techniques with optogenetic, pharmacogenetic, and pharmacological manipulations to uncover inhibitory circuit mechanisms underlying fear learning. The second part of this thesis focuses on the cerebellum-like electrosensory lobe in the weakly electric mormyrid fish Gnathonemus petersii, as a model system for non-declarative memory. In Chapter 6, we study how short-duration EOD motor commands are recoded into a complex temporal basis in the granule cell layer, which can be used to cancel Purkinje-like cell firing to the longer duration and temporally varying EOD-driven sensory responses. In Chapter 7, we consider not only the temporal aspects of the granule cell code, but also the encoding of body position provided from proprioceptive and efference copy sources. Together these studies clarify how the cerebellum-like circuitry of the electrosensory lobe combines information of different forms and then uses this combined information to predict the complex dependence of sensory responses on body position and timing relative to electric organ discharge.

Simple circuits perform simple tasks. Complex circuits can perform more complicated tasks. This is true for artificial circuits and for brain circuits. As is known from artificial networks, a complexity that makes circuits substantially more powerful is distributing learning across multiple layers. In fact, most brain circuits in vertebrate systems are multi-layer circuits (but for few that perform simple reflexes) in which learning is distributed across layers. Despite the crucial contribution of learning in middle layer neurons to the output of the circuits they are embedded in, there is little understanding of the principles defining this contribution. A very common feature in brain circuits is that middle layer neurons generate two types of signals, known as spikes. These middle layer neurons commonly have long dendrites where they generate dendritic spikes. As well, like most neurons, they generate axonal spikes near the cell body. Neurons exhibiting these two spike types include pyramidal cells in the neo-cortex and the hippocampus, the Purkinje cells in the cerebellum and many more. In this thesis I study another circuit that contains middle layer neurons, the electrosensory lateral lobe (ELL) of the mormyrid fish. The ELL is a tractable brain circuit in which the middle layer neurons generate dendritic and axonal spikes. In this thesis I show that these spike types are not two different expressions of the same inputs. Rather, they have a symbiotic relationship. Instead of all inputs triggering both spikes, some inputs can selectively drive dendritic spikes. The dendritic spikes in return modify the synaptic strength of another set of inputs. The modified inputs are then transmitted to downstream neurons via the axonal spikes, which contributes a desired signal to the output of the circuits. Effectively there is a separation of learning and signaling in the middle layer neurons through the two spike types. Having two types of spikes in the same neuron doing different computations enormously expands the computational power of the neuron. But, being in the same neuron means the separation of function is constrained and needs to be supported by biophysical principles. I have thus built a biophysical model to understand the biophysical principles underlying the separation of function. I show that in the middle layer neurons of the ELL, the axonal spikes are strongly reduced in amplitude as they backpropagate to the apical dendrites, yet they remain crucial in driving dendritic spikes. Critically, modulation of inhibitory inputs can selectively dial up or down the ability of the backpropagating axonal spikes to drive dendritic spikes. Thus, a set of inhibitory modulating inputs can selectively modulate dendritic spikes. Having learning in different layers contributing to the outcome of the circuit, naturally leads to asking how the work is divided across layers and neuron types within the circuit. In this thesis I answer this question in the context of the outcome of the ELL circuit. Finally, another signature of a complex circuit is the ability to integrate many different inputs, usually in middle layer neurons, to generate sophisticated outputs. A goal for scientists studying systems neuroscience is to understand how this integration works. In this thesis I provide a coherent model of a learning behavior called vestibulo occular reflex (VOR) adaptation, that depends on the integration of separate inputs to yield a learned behavior. The VOR is a simple reflex generated in the brain stem. Inputs from the brain stem are also sent to an area in the cerebellar cortex called the flocculus. The flocculus also receives another set of inputs that generate a different behavior, called smooth-pursuit. The integration of VOR inputs with smooth-pursuit inputs in the flocculus generate VOR adaptation. Understanding complex circuits is one of the greatest challenges for today's neuroscientists. In this thesis I tackle two such circuits and hope that through a better understandings of these circuits we gain principles that apply to other circuits and thereby advance our understanding of the brain.

Electroreception is a sensory modality found in some fish, which enables them to sense the environment through the detection of electric fields. Biological experimentation on this ability has built an intricate framework that has identified many of the components involved in electroreception's production, but lack the framework for bringing the details back together into a system-level model of how they operate together. This thesis builds and tests a computational model of the Electrosensory Lateral Line Lobe (ELL) in mormyrid electric fish in an attempt to bring some of electroreception's structural details together to help explain its function. The ELL is a brain region that functions as a primary processing area of electroreception. It acts as an adaptive filter that learns to predict reoccurring stimuli and removes them from its sensory stream, passing only novel inputs to other brain regions for further processing. By creating a model of the ELL, the relevant components which underlie the ELL's functional, electrophysiological patterns can be identified and scientific hypotheses regarding their behavior can be tested. Systems science's approach is adopted to identify the ELL's relevant components and bring them together into a unified conceptual framework. The methodological framework of computational neuroscience is used to create a computational model of this structure of relevant components and to simulate their interactions. Individual activation tendencies of the different included cell types are modeled with dynamical systems equations and are interconnected according to the connectivity of the real ELL. Several of the ELL's input patterns are modeled and incorporated in the model. The computational approach claims that if all of the relevant components of a system are captured and interconnected accurately in a computer program, then when provided with accurate representations of the inputs a simulation should produce functional patterns similar to those of the real system. These simulated patterns generated by the ELL model are compared to recordings from real mormyrid ELLs and their correspondences validate or nullify the model's integrity. By building a computation model that can capture the relevant components of the ELL's structure and through simulation reproduces its function, a systems-level understanding begins to emerge and leads to a description of how the ELL's structure, along with relevant inputs, generate its function. The model can be manipulated more easily than a biological ELL, and allows us to test hypotheses regarding how changes in the structures affect the function, and how different inputs propagate through the structure in a way that produces complex functional patterns.