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I am taking my PhD qualifying exams on monday, and there is a seemingly simple practice problem that I can't seem to figure out, and I was hoping someone here would have some knowledge, or at least be able to point me in the right direction. My background is in electrical engineering, so apologies for my ignorance.

The question is:

Cell A is strongly phase-locked to spindle oscillations (12 Hz) at 180 degrees, and cell B has monosynaptic excitatory connection to cell A. Assume the synaptic delay is 3ms.

1- Draw the polar plot of cell A’s firing relative to spindle oscillations.

2- What is the relationship of cell B to spindle oscillations? If it is also phase locked to spindle oscillations what would be the degree of locking? Draw the polar plot. If the independently calculated polar plot of cell B does not show significant phase locking with spindle oscillations, what is a possible explanation?

I can't find a single resource that tells me how to draw these polar plots. Can anyone help me out?

EDIT:

12 Hz --> 83.33 ms period

Cell A fires at 83.33 ms * (180deg/360deg) = 41.66 ms

Cell B fires at 41.66 ms +3 ms = 44.66 ms

Phase of Cell B firing is (44.66 ms/83.33 ms) * 360 deg = ~192 deg

Is that right?

Polar plots of both cells

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  • $\begingroup$ Can you explain what you understand and don't understand? Surely you've encountered polar coordinates in engineering, no? have you tried Googling something like "polar plot" + "spindle oscillation" $\endgroup$
    – Bryan Krause
    Jan 4 at 16:33

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If you map every spike of a neuron to the phase of an oscillatory process (in your case a 12 Hz sine wave) then you can plot an histogram of that phases. It's usual to plot the histogram in polar coordinates as in the figure below.

For cell B, you will need to map the synaptic time delay in to phase delay using the oscillation period. This is assuming that a synaptic event from cell A induce cell B to spike and there's no other synapses or intrinsic properties of Cell B that perturb the entertainment.

Mansouri, Farrokh, et al. Frontiers in neuroscience 12 (2018): 877.

Mansouri, Farrokh, et al. Frontiers in neuroscience 12 (2018): 877.

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  • $\begingroup$ thank you so much! I couldn't figure out how to add images to this comment, so I added the polar plots to the original post. Does that seem right? I just dont want to misunderstand. Thanks again $\endgroup$
    – Brian
    Jan 4 at 19:34

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