Neuro-Related Technology Report and Alternating Spinal Cord Oscillator Simulation

Choose your own adventure:

1. An NIH-style research proposal, or an IEEE-style neuro-related technology report

You have read a lot a of journal articles this term that covered a range of topics broadly within the field of neuronal signaling and neural computation: from the molecular and electrochemical basis of signal transduction, to both electrical and optical strategies for monitoring and controlling neuronal activity - at both the single-cell and population levels. In addition, you have seen examples of both behavioral and computational modeling of circuit function – in everything from jellyfish and zebrafish, to mice and humans; and you have been exposed to data analysis and modeling strategies. Finally, you have come to appreciate some of the “neurotechnology gaps” in, for example, wearable devices, diagnostic algorithms, and therapeutic strategies that could be applied to health- and/or brain-related indications, such as phenotyping sleep, diagnosing depression, treating maladaptive states, or selectively modifying memories.

Now, it is your turn to propose a line of study or a new neuro-related technology. One way to approach this final project is to treat it as a formal extension of our in-class journal article discussions about future directions.

Likewise, you could treat this report as a “rough draft” of, for example, an NSF training grant or NIH predoctoral fellowship application, or of a thesis chapter. Depending on your level of training, it would be great if this final project somehow dove-tailed with your short-term career goals (i.e., two birds one stone).

In terms of choosing a neuro-related technology, it should be a device/algorithm/model that in some way relates to the CNS or PNS – something an engineer with neuroscience training might have contributed to. The technology does not have to be brand new, but aim for something that has emerged, or has been significantly advanced, in the last couple of years. Consider surfing the popular press and/or technical literature for inspiration. Topics that are dated, or are not considered to be neuro-technology, will not receive full credit.
As a word of warning, you cannot copy (or “re-word”) an idea that has already been published; this is plagiarism.

You can (and should) use a published idea as the springboard/inspiration to launch your own project. Failure to give credit to (i.e., cite) your source of inspiration is scientific misconduct and will be penalized.

 

2. A formalized implementation of either a data analysis project or simulation

For those of you more interested in neural computation and modeling, you may formulate a project around a data analysis project (akin to PS02 or PS04… I can provide a data set, or you can choose your own) or a neural simulation (e.g., a spinal cord oscillator or pattern generator; see end of this document). The project components (written report and oral presentation) and formatting guidelines still apply, except the research strategy will center around a discussion of your computational (rather than experimental) approach. Your written report will include an appendix section that contains the written code (not included in 3-page limit), and if applicable, an appendix section that briefly describes the data set. You must discuss the “STEM” implications and relevance of your results in depth – this is not a problem set, but a formal report on a computational project.

Choose your own adventure:

Final Project on alternating spinal cord oscillator

Write a simulation in Python to reproduce the behavior of the coupled alternating oscillator discussed in the Wang and Rinzel (1992) paper (see below for hints on interpreting their notation). The simulation should be done in a JupyterLab Notebook. The simulation will be very similar to a Hodgkin Huxley simulation, but without a K+ current (just a sodium-like current). There are four differential equations total - two for each of two identical interconnected neurons. Each neuron has one equation for voltage (determined by a leak current, an m3 h current, and an inhibitory synaptic current coming from the other neuron, that is sigmoidal function s of the other neuron’s voltage), and a second equation representing the inactivation gate of the Na+ -like current. The reason you don’t have a differential equation for the m variable is that it is assumed to update so quickly compared to the other variables that it updates instantaneously, so you can just represent it as an instantaneous function of voltage (which is given in the paper).

Regarding initial conditions, you can look at Figure 1B to see the phase plane (V versus h). A recommended approach is to pick an initial condition somewhere in the middle of the little enclosed (limit cycle) region. But, be careful not to set the two cells in exactly the same initial condition because they can get locked in a tie! Another approach: choose voltage values for the two cells from by picking a time in Figure 1A, and then picking the h’s for each cell accordingly (i.e. tied to the two voltage values).

To turn in:

1. A Jupyter Notebook iPYNB file as well as an appendix in the Written Report that reproduces the contents (i.e., pdf version of iPYNB inserted into appendix) of this iPYNB file - including all required figures (points 2-3 below). The iPYNB (and appendix) should include code descriptions (commented code cells, explanatory markdown cells), and detail the parameters used. Discuss what you are doing at each step in markdown cells. Broadly explain your approach in the formal Written Report, and include key traces/etc (that are generated in the associated iPYNB) as formal figures (with figure captions).

2. Reproduce the voltage traces shown in Figure 1A. Show the voltages of the two neurons on separate plots, or if you use the same plot, make sure they appear in different colors. State explicitly what the figure shows through the use of a caption (figure in Written Report) and a markdown cell (figure in iPYNB).

3. Create a plot like the one in Figure 1B showing V versus h for one of the neurons. Plot from the time of your initial condition through two full cycles of the oscillation. You do not need to plot the nullclines.

4. Finally, the Written Report must include a formal discussion about this computational/modeling endeavor – its relevance and/or implications and/or applications in STEM. The Final Project is not a problem set – you need to “go the extra mile”.