Grid cell attractor networks: development and implications
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At the foundation of our ability to plan trajectories in complex terrain is a basic need to establish one’s positional bearings in the environment, i.e., to self-localize. How does the brain perform self-localization? How does a net- work of neurons conspire to solve this task? How does it self organize? Given that there might be multiple solutions to this problem, with what certainty can we say that any such model faithfully captures the neural structure and dynamics as it exists in the brain? This thesis presents a collection of three theoretical works aimed at addressing these problems, with a particular focus on biological plausibility and amenability to testing experimentally. I first introduce the context within which the work in the thesis is situ- ated. Chapter 1 provides a framework for understanding algorithmically how the brain might solve the problem of self-localization and how a neural circuit could be organized to perform self-localization based on the integration of self-motion cues, an operation known as path integration. We also introduce the neurobiology that underlies self-localization, with special emphasis on the cell types found in and around the hippocampus. We discuss the case that a particular class of cells – grid cells – subserve path integration, because of their peculiar spatial response properties and their anatomical positioning as the recipients of self-motion information. Continuous attractor models are introduced as the favored description of the grid cell circuit. Key open questions are introduced as motivation for the subsequently described work. I next focus on the question of how the grid cell circuit may have organized. In Chapter 2, it is demonstrated that an unstructured immature neural network, when subjected to biologically plausible inputs and learning rules, can learn to produce grid-like spatial responses and perform path integration. This model makes a number of predictions for experiment which are described at length. In Chapter 3, I describe a theoretically motivated experimental probe of the organization and dynamics of the grid cell circuit. The proposed experiment relies on sparse neural recordings of grid cells together with global perturbations of the circuit (and is thus experimentally feasible). It promises to yield special insight into the hidden structure of the grid cell circuit. Finally, in Chapter 4, I provide an analytical treatment of pattern formation dynamics in the grid cell circuit. This work focuses on nonlinear effects.