UC Davis

This dissertation consists of two parts: Neurodegenerative damage reduces firing coherence in a continuous attractor model of grid cells, and damage impact on the gird-cell population codes for animal's locations.

The work in Part I is motivated by the discovery of grid cells and their specific grid-like firing pattern: Grid cells, firstly found in the dorsolateral band of the medial entorhinal cortex(dMEC) in 2005, display strikingly regular periodic firing patterns on a lattice of positions in 2-D space. This helps animals to encode relative spatial location without reference to external cues. The dMEC is damaged in the early stages of Alzheimer's Disease, which affects navigation ability of a disease victim, reducing the synaptic density of neurons in the network. Within an established 2-dimensional continuous attractor neural network model of grid cell activity, we introduce neural sheet damage parameterized by radius and by the strength of the synaptic output for neurons in the damaged region. The mean proportionality of the grid field flow rate in the dMEC to the velocity of the model animal is maintained, but there is a broadened distribution of flow rates in the damaged case. This flow rate-to-velocity proportionality is essential to establish coherent grid firing fields for individual grid cells for a roaming animal. When we examine the coherence of the grid cell firing field by studying Bragg Peaks of the Fourier transformed lattice firing field intensity in both damaged and undamaged regions, we find that for a wide range of damage radius and reduced synaptic strength that for undamaged model grid cells there is an incoherent firing field structure with only a single central peak. In the radius-damage plane this is adjacent to narrow bands of striped lattices (two additional Bragg peaks), which about an orthorhombic pattern (four additional Bragg peaks), that abut the undamaged hexagonal region (six additional Bragg peaks). Within the damaged region, grid cells show no Bragg peaks outside the central one which shows reduced intensity with increasing damage, and outside the damaged region the central Bragg peak strength is largely unaffected. There is a re-entrant region of normal grid firing fields for very large damage area. We anticipate that the modified grid cell behavior can be observed in non-invasive fMRI imaging of the dMEC.

The work in Part II is motivated by a broad goal to explain navigation system: The brain is a remarkable information engine and it's efficiency may come from a hierarchy organization of neurons. At the same time, A unique topographical representation of space is found in the concerted activity of grid cells in the medial entorhinal cortex. Many in this region exhibit a hexagonal firing pattern with grid spacing. And grid spacing has been found to increase along the dorsoventral axis of dMEC but in discrete steps. Such a modular structure provides a new place-coding theory that explains why grid cells has hierarchy organization identified by different spacing. Compared with classical population code (CPC) theory, the hierarchy in grid population code (GPC) improves the coding efficiency and the noise robustness. We developed Sammeet Sreenivasan and Ila Fiete's network model (readout-grid cell network) to construct the GPC process from input signal, through grid cells modules, to the place cells sensory. The largely stable consistency between input location and inferred location by place cells proves the practicality of readout-grid cell network. Within the completed multiple-layers neural network model of grid coding, we introduce grid layers damage parameterized by radius and by the strength of the synaptic output for neurons in the damaged region. The self-consistence between location signal and inferred location is distributed within reduced coding range. For M layers of the N grid cells, damage within a single layer doesn't destroy the accurate place coding considering the maximum possible coding range ($R \sim N^M$) overloads the reduced coding range ($R_l < 500cm$). We construct the landscape of heat-map showing influence of damage in all situations, and noticed that the layers with bigger spacing (top layers) show more severe disruption given the same condition. This proves the hierarchy theory of GPC that the top panels dominate place coding and fluctuations on big-spacing modules bring more errors.