Unexpected additive phase delay

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Unexpected additive phase delay

Post by CVerbist » Tue May 09, 2017 4:39 am

We have a simple Ball-And-Stick model, soma and axon, in which we inject a noisy sinusoidal input to look at the output response of the soma. In doing this we want to explore the transfer function of the neuron. We look at the magnitude and phase of the output, where the magnitude is determined by the ability of the neuron to phase lock their firing rate to that of the input. To get both of these curves we use the circular statistics framework on spike timings, described by Ilin in 2013.

We notice that the phase of the output is non stationary, while in reality the phase, for any given input frequency, should be stationary in time. The effect of this non stationary behavior is that the magnitude displays a way smaller bandwidth than expected because of destructive interference between the first half of a simulation and the second half due to this non stationary phase. This will happen only for very specific input frequencies, while it is non dependent on the firing rate of the neuron.

We've already made sure that the neuron receives the correct input signal, both by a self written mod-file and creating the stimulus offline and playing it back with Vector.play(). The issue is also not model dependent since beside this Ball-and-Stick model we also have looked at a detailed model, obtained from a third party, which gives the same results. We use standard HH-equations which result in the expected shape of the spikes, FI-curve and dv/dt curve.

Our conclusion is that there is some kind of time delay, which increases with simulation length, on the level of spike timings which in turn causes the problems described above, though we have not implemented such a time delay since it is basic HH. We are using python NEURON. A simulation characteristically runs for 100 seconds simulation time. This delay presents itself on a timescale larger than 10 seconds.

ted
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Re: Unexpected additive phase delay

Post by ted » Tue May 09, 2017 12:55 pm

Your question?

I have three.
1. Is the extended geometry necessary for the phenomenon to occur?
2. Is there a systematic difference between models with type 1, 2, or 3 excitability?
3. Is this phenomenon similar to what can happen in a linear system with periodically varying coefficients, e.g. Mathieu equation?

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Re: Unexpected additive phase delay

Post by CVerbist » Wed May 10, 2017 4:42 am

ted wrote:Your question?
Our question would be where this effect could come from, since it is unexpected and we didn't see it in a simple two-compartmental, non-neuron, model.
ted wrote:1. Is the extended geometry necessary for the phenomenon to occur?
No since we also see it in the relatively simple ball and stick model. In the ball and stick model we have investigated the influence of the number of segments in both soma- and axon-compartment, whatever configuration we took, be it 1 segments in soma and axon or more segments in axon or multiple segments in soma and axon but all gave the same results.
ted wrote:2. Is there a systematic difference between models with type 1, 2, or 3 excitability?
We have seen the effect on both type 1 and type 2 excitability, both giving the exact same results.
ted wrote:3. Is this phenomenon similar to what can happen in a linear system with periodically varying coefficients, e.g. Mathieu equation?
I'm not really familiar with the Mathieu equation but after having a cursory glance I would say it is not related. From the way I analyse our problem it is not necessarily a periodic problem but more of an additive phase/time that is introduced into the system somewhere. Since the phase by definition is periodic you could of course say that the effect is periodic. Since our system coefficient shouldn't change, since it's basic HH, they shouldn't change according to my understanding. If they can for some reason I would be more than happy to investigate the causes of this.

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Re: Unexpected additive phase delay

Post by ted » Wed May 10, 2017 8:31 am

Is the extended geometry necessary for the phenomenon to occur?
No since we also see it in the relatively simple ball and stick model.
Ah, the imprecision of human language--to me, "extended geometry" means anything more complicated than what can be represented by a single compartment. So let me ask: does the phenomenon occur in a single compartment model?
ted wrote:3. Is this phenomenon similar to what can happen in a linear system with periodically varying coefficients, e.g. Mathieu equation?
I'm not really familiar with the Mathieu equation
Not surprising. The number of eponymic equations is probably larger than the number of known mathematicians.
but after having a cursory glance I would say it is not related.
. . .
Since our system coefficient shouldn't change
Ah, but they must. m and h are governed by ODEs whose coefficients (rate constants or time constants and steady-state values) are functions of membrane potential. It is the changing of those coefficients that accounts for the operation of the HH model. Drive membrane potential with a periodically varying current, and one would expect the result to be periodic fluctuation of membrane potential. It follows that the voltage-dependent coefficients will also fluctuate periodically. Except, of course, for the possibility that under certain conditions membrane potential might show interesting unexpected phenomena, including unexpected phase shifts, or even prominent disturbances of amplitude and frequency similar to those that arise in the Mathieu equation.

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Re: Unexpected additive phase delay

Post by CVerbist » Thu May 11, 2017 4:41 am

ted wrote: So let me ask: does the phenomenon occur in a single compartment model?
We haven't tried a single compartmental model since the effect we are interested in can only be seen in multi-compartmental models, we need a soma and axon of at least one compartment. However we started with a simple two compartmental model, which was build and analysed completely outside of neuron. Here we are using the same basic HH equations, be it slightly different parameters, as we are using in the ball and stick neuron model. In this model the results were as expected and as predicted by experiments. So I think it is safe to say that this simple model works as intended and as it should. It was only when switching to neuron that these problems started manifesting itself. But we will try it anyway to see what it would give.
ted wrote: Ah, but they must. m and h are governed by ODEs whose coefficients (rate constants or time constants and steady-state values) are functions of membrane potential. It is the changing of those coefficients that accounts for the operation of the HH model. Drive membrane potential with a periodically varying current, and one would expect the result to be periodic fluctuation of membrane potential. It follows that the voltage-dependent coefficients will also fluctuate periodically. Except, of course, for the possibility that under certain conditions membrane potential might show interesting unexpected phenomena, including unexpected phase shifts, or even prominent disturbances of amplitude and frequency similar to those that arise in the Mathieu equation.
Of course, I didn't express myself too well there. Indeed all state variables will change periodically, which is not a problem, the problem however is that it seems that on this periodic change, that we impose, is another varying variable that we have not imposed on the system. This change, which to me it seems is constant in time but just builds up over time and hence influences spike times which consequently shift the phase more and more with respect to the input signal. While the phase of the output with respect to the input should remain constant as seen from the two compartmental, non neuron, model and experiments.

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