This is the result of the final project for a course on the Biophsyics of Neurons. My goal was to reproduce and validate the results of the following paper:
Loewenstein, Y., Yarom, Y., & Sompolinsky, H. (2001). The generation of oscillations in networks of electrically coupled cells. Proceedings of the National Academy of Sciences, 98(14), 8095-8100. http://www.pnas.org/content/98/14/8095.full
The authors present a number of dynamic models to describe the spiking oscillations of neurons in electrically coupled networks. Such cells are coupled by gap junctions that allow ions in the cytoplasm to equilibrate between cells. It is logical to think that such coupling would simply damp the spiking behavior, but simulations of the presented models reveal synchronous oscillations in networks of two or more cells with very interesting dynamics.
The models are presented as systems of coupled differential equations. Simulations were carried out in MATLAB using the appropriate ode* solver (ode45 was used for the simple models and ode15s for the stiffer problems of coupled networks). For a summary of the models and results refer to either Presentation.pdf or the Report.pdf which describe my simulations. For detailed background on the models and their relevance to studying neurons refer to the original paper.
Herein is contained the Matlab scripts and functions that I wrote to produce the simulations.
-
parameters.m -- defines the variables and functions used in the models
-
(Model).m -- these files define the systems of equations for each of the models using the variables defined in the parameters file.
-
Run.m and RunCellNetwork.m -- scripts with the commands to simulate the models and produce the graphics used in Report.pdf
-
StackedPlot.m -- utility function used to produce the plots for the network models
The MIT License (MIT)
Copyright (c) 2014 Travis Johnson
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.