My Project

I used Matlab to create a program that recreates Molter's neural model, and hopefully his results. My program consists of a single m-file script, as well as several function, found as separate m-files. It is built around a fairly simple model of the rat hippocampus. Below, to the left is an animated cartoon schematic of the model, which I designed. To the right is the graphic description of the model included in Molter's paper.

The model has three layers. The first are the sensory inputs. These are the cues that the rat recieves that indicate that it is at a particular location in the environment. These feed directly into the cells of the Entorhinal Cortex (ECII). There is one ECII cell for each space field. Each ECII cell feeds directly into a cell in the CA3 region of the hippocampus. Again, these connections are one-to-one. The CA3 region, however, is completely networked. Every cell in this layer is synaptically connected to every other cell. It is in this layer that LTP and learning occur. In addition to these basic inputs, when the rat is awake, it is believed that the brain is dominated by a "Theta Rhythm". This 4-8Hz cycle of neuronal activation pervades the brain, and influences our hippocampus model. The theta rhythm evidences itself as a "local field potential"; each layer has its own LFP that acts as a pattern generator. The two LFP generators are not in phase with each other, but they are phase-locked to each other. When asleep or resting, it is believed that the theta rhythm is disabled. During this phase, randomly-generated sharp waves (SPW) occur in the CA3 Layer.

The activity of each layer can be described by a series of equations. In Molter's paper, he described each cell as recieving a series of inputs, adjusting its own phase based on these inputs, and then sending an output to wherever it connects, as a function of this phase. Molter also describes an equation for the plasticity in the CA3 layer. In other words, this equation describes the Hebbian Learning and LTP that shapes the learning in the CA3 layer. I did not use precisely the same equations as Professor Molter. First, his plasticity equation seemed overly complex. I was worried that I had incorrectly coded it and that this was causing unusual results, so I rewrote the equation. My equation has less numerical significance, but I believe is more likely to do precisely what it is supposed to, and so should reveal the expected phenomena during results. Second, I altered the sign convention on his equation for cellular inputs. The published equation did not make intuitive sense to me, and caused the results to be bogus. Upon altering the sign convention to a setup that makes sense to me, the results were more logical, so I kept the changes. I do not reproduce the equations here; see the original paper or my Matlab code for their exact form.

My program runs in two phases. First is a learning phase. This phase first sets up the geometry of the environment and the solving parameters, and then simulates the awake rat traveling through the geometry. During this phase, the program displays the phases of the two LFP generators, to verify that they are in fact phase locked. It also graphs the pure outputs of the ECII and CA3 layers. Lastly, it uses a function that I wrote to create a Rastor plot of the outputs. The second phase represents the reactivation when the rat is asleep or at rest. In this phase, the LFP generators and sensory inputs are turned off, the SPW random spikes are generated and applied, and the simulation run with slightly modified parameters. Again, results are given as pure output plots as well as rastor plots.