I am a physicist interested in knowing how the action potential frequency in a presynaptic neuron compares with that in

a) a post-synaptic neuron and

b) membrane depolarisation of muslce cells, and

c) how the membrane depolarisation of muscle cells quantititavely relates to muscle contraction.

From the reading I have done so far, it seems that the theory of c) is standard, and goes by the name is 'excitation-contraction coupling'. I would think that the actual relationship between the frequency of muscle cell membrane depolarisation and degree of muscle contraction- however it is quantitifed- would differ for muscle type, depletion of Ca2+ stores from the sarcoplasmic reticulum, etc. In any case, some theory is covered here for instance, although I haven't seen much mathematical modelling and quanitative comparison here.

In any case, I am then still wondering regarding a) and b). I would think that there isn't a straightforward answer; the sequence of events is action potential -> neurotransmitter release into synaptic cleft -> neurotransmitter binding -> membrane depolarisation -> hopefully an action potential.

I already see some potential sources of non-linear behaviour in the final step, and the neurotransmitter binding ->depolarisation step would prbably also be dependent on the recptor kinetics. Since we are talking on the behaviour on a temporal scale, we would have to consider the degredation rate of the neurotransmitter within the synaptic cleft, and no doubt several pathologies arise because of some dysfunction in changes in neurotransmitter degredation/re-uptake rate... Come to think of it now actually, I think differences in the extent of binding (say due to differences in the number of receptors on post-synaptic neuron membrane) are the basis- or at least one factor- in neuroplasticity. So of course they would differ. But still the question remains as to what extent. I am not sure whether for some circuits, say those in the motor system, there is little deviation between responses in people.

To give some context to my question, I am interested in technologies which actively stimulate, or disrupt stimulation, of neurons in a controlled manner, so as to achieve a desired output effect. There are several technologies and lab techniques being developed with this in mind- optogenetics on the single-neuron level, DBS and epidural stimulation for stimulating large groups of neurons for some non-specific duration of time. I would think that these techniques could be much more powerful and potent, if we knew the temporal relationship between consecutive neural firing rates on stimulation.

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    $\begingroup$ To be blunt, if you are interested in technologies to do what you say, you need way more information than an answer to this question, although this question is already extremely broad. I'd suggest starting with a course or textbook in neuroscience. As is, you are drifting into this territory: xkcd.com/793 $\endgroup$
    – Bryan Krause
    Commented Dec 11, 2018 at 17:32
  • $\begingroup$ For example, the statement "hopefully an action potential" is a completely wrong way to think about it. Action potentials aren't an achievement that the nervous system has as a goal, they carry information. Not firing an action potential is also informative, and not nearly every input should cause an output. $\endgroup$
    – Bryan Krause
    Commented Dec 11, 2018 at 17:33
  • $\begingroup$ @BryanKrause Hi. I am aware of this; i presume my sloppy and half-hearted phrase 'hopefully an action potential', in the context of my being a physicist, gives the impression that I have absolutely no idea about neueoscience principles. I think your comment was a bit sharp. And, if context is of any importance, I am a physicist in training- still an undergraduate- so I think my knowledge of neuroscience considering my present educational status isn't half bad. Plus, when I said 'interested in [these] technologies', I meant that literally. Not that I am trying to revolutionaluse these $\endgroup$
    – Meep
    Commented Dec 11, 2018 at 19:12
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    $\begingroup$ Technologies now. I have read quite a bit on the fojndatiknal principles of neuroscience, but am yet to find a reference and quantitative comparison of rate of action potential firing from experiment. And besides, even if my background on this site seems pathetic, at least I am trying to find out. No point sitting like a lemon. And btw I have consulted Bear,Paradiso et al and Connors, White et al. $\endgroup$
    – Meep
    Commented Dec 11, 2018 at 19:16
  • $\begingroup$ I only mean to suggest you should start with the biology rather than trying to figure it out from the physics. That approach might make sense if this stuff wasn't already studied, but it has been, and if you want to understand the technologies you will need to be practiced in understanding the biology. The reason that cartoon exists is because this approach is for whatever reason really common with people with a physics background, and it can be very frustrating for the biologists in the room. $\endgroup$
    – Bryan Krause
    Commented Dec 11, 2018 at 19:40


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