8.7 Mathematical modeling of hippocampal spatial memory with place  (Page 2/6)

His team set up a track that a rat traversed and monitored the place fields that corresponded to specific locations on the track. Dr. Knierim and his team set up local cues on a circular path and distal cues on surrounding curtains and trained rats to walk along the path in a clockwise direction. The place fields corresponding to specific locations on the track were monitored. See [link] .

During the learning phase, as the rat completed laps and became more familiar with the layout, the place fields shifted backward along the path opposite the rat's movement. In standard runs of the experiment, the rat ran clockwise around the path with the layout that it learned. In double rotation runs of the experiment, the local cues were rotated counterclockwise (backward) and distal cues were rotated in clockwise–hence the “double rotation".During the standard and the double rotation runs, the spatial inputs and place fields did not always match. In the double rotation runs, the spatial inputs tended to follow the distal cues, whereas the place fields tended to follow local cues.

One thing that might explain this is the backward shift seen in the learning phase. The natural backward shift of place fields that happens when a rat has become familiar with its environment appears to bias the place fields to follow the cues that shift backwards. The backward shift of place fields has been observed in other experiments as well when rats became familiar with a path [link] . It may be that the backward shift is a part of the learning process. Thus, we want to understand more about the backward shift and aim our research in this direction.

The backward shift may be dependent upon the weights of synapses, yet the dependence is not well understood. We focus on how the dynamic weights due to synaptic plasticity affect the backward shift of place fields.

We implemented a far simplified model of the DRE to try to understand this relationship better.

Modeling

Here we will describe the models used throughout the summer. A circuit model allows us to understand the mechanics of one neuron, while a 120-cell ring models the Double Rotation Experiment [link] , and a single-cell model was used for the analysis of weights and backward shift. Refer to [link] for the parameters used throughout the models and their values.

Neuron as a circuit: integrate and fire

We model a single place cell with the Integrate and Fire (IAF) model so that we can accurately calculate the subthreshold voltage and approximate spike times of a cell at little computational expense [link] .