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This report summarizes work done as part of the Modeling Spatial Memory with Place Cells PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem. This work was studied in the Rice University VIGRE program in the Summer of 2011. In this module, we mathematically model Kneirim's Double Rotation Experiment with a model given by Cox and Gabbiani and analytically discuss the relation between overlapping place fields and synaptic input weights.

Background: place cells in the hippocampus


Spatial memory is what allows us to keep track of our location in space by making mental maps of each environment. Let's consider what happens in the brain during the process of forming these internal maps.

Connections, called synapses, between certain neurons strengthen or weaken–a process known as synaptic plasticity. The strength, or weight, of a synapse controls how much one neuron can affect another. Synaptic plasticity is necessary for memory formation [link] .

While many neurons are involved with spatial memory, our focus is upon neurons in the hippocampus called place cells [link] . Place cells have a unique firing pattern. When an environment becomes familiar, each place cell becomes associated with one area of the environment. In other words, after repeated exposure to one environment, a place cell will come to spike in only one area of the environment, which is called that cell's place field [link] . See [link] .

The place field of one place cell. As a rat explored the square environment, experimenters monitored the activity of one place cell.ÊThe black line is the rat's trajectory, and each red dot represents a location that the place cell has become active. The place field of the particular place cell that was monitored is the area of the environment marked densely by red dots [link] .

Due to place cells' characteristic firing pattern where a cell has a single place field in each environment, it is easy to test if a rat recognizes the environment they have been placed in by examining place cell activity.

Motivation: double rotation experiment

Our research on place cells is based off of the Double Rotation Experiment (DRE) conducted by our collaborator Dr. Knierim [link] .

The Double Rotation Experiment (DRE). Rats were trained to walk clockwise around the track, and the place fields corresponding to specific locations on the track were monitored. During the learning phase, the place fields experienced a backward shift. During double rotation runs of the experiment, the local cues were rotated backward (counterclockwise), and the place fields shifted backward as well. Thus the place fields seemed to favor following the local cues. Perhaps the natural backward shift seen in the learning phase predisposes the place fields to wanting to follow cues that move backwards [link] .

Questions & Answers

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What is STMs full form?
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Bob Reply
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The nanotechnology is as new science, to scale nanometric
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Damian Reply
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Introduction about quantum dots in nanotechnology
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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