I'd be interested to know how subthreshold oscillations and noise of the inputs of a neuron are related. In particular, I would like to understand if there is some compensatory mechanism that may lead to neglect subthreshold oscillations with respect to the noise affecting synaptic inputs. This seems to me relevant to know in view of a simplified neuron model implementation for applications using very large spiking neural networks.
Hi,
Subtreshold oscillations may represent incoming synaptic input which is not synchronized enough to depolarize the cell membrane into spiking activity. Then these oscillations, which may be in the range of fast beta-gamma frequencies (20-90 Hz), could be understood as noise occuring where the synapses are.
I guess there might be several mechanisms compensating this noise, such as recurrent inhibitiory connectivity and autorreceptors or even the existence of local electical fields or intrinsic refractory periods, which may prevent the cell to be over-excited in terms of excess of incoming input and might be acting to deam this kind of oscillatory activity.
I don't know it that helped...
Hi Marcel, thanks for the attention.
With the term "subthreshold oscillations" I meant the oscillations observed in the relative refractory period of the neuron. Is the same phenomenon you are referring to?
I´ve reading a bit about the phenomenon you describe. I was referring to oscillations comming from spontaneous synaptic input. I guess that is not your case...I think your phenomenon is more related to internal resonance and intrinsic neuronal properties, isn´t it? In this case I may not be able to help you as this is a field far from my knowledge.
Alessandro,
I believe you are referring to phenomena described in the squid giant axon by Hodgkin and Huxley many years ago. My interpretation of these damped oscillations is that they reflect subthreshold kinetics of voltage-gated sodium and potassium channels and depend especially upon the constant, h, which describes the fraction of voltage gated sodium channels normally in an inactivated state at the resting potential level. At the termination of the falling phase of the AP the axonal membrane is slightly hyperpolarized at a level near the potassium equilibrium potential, leading to an increased readiness of a fraction of the voltage-gated sodium channels to become activated when the membrane returns toward the resting level. This may actually lead to a small depolarization due to net sodium influx (depolarization) and, after a delay, to an increased potassium conductance that repolarizes the membrane toward the potassium equilibrium potential, and so forth.Both effects (ion fluxes) diminish with time as the oscillations become damped out.
Intrinsic resonance can be driven by many conductances. Here is a paper you might be interested in:
Temporal synchrony and gamma-to-theta power conversion in the dendrites of CA1 pyramidal neurons. Sachin P Vaidya & Daniel Johnston
Nature Neuroscience (2013)., 16(12), 1812–1820. doi:10.1038/nn.3562
@Deforest: yes, it is exactly the phenomenon I was referring to. Thanks for the description!
@Raymond: very interesting paper! Thanks a lot!
These resonances in the neuron tend to sensitize the neuron to input at specific frequencies, i.e. filter the incoming noise. Also, the oscillations following an action potential (AP) lead not only to periods of partial refractoriness, but also to periods where the neuron is more likely to fire a next action potential. There is very nice theoretical work done, also having large networks of spiking neurons in mind, on the chances of a neuron that receives noisy input to fire after a first action potential:
Chizhov, A., & Graham, L. (2007). Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons. Physical Review E, 75(1)(011), 924. doi:10.1103/PhysRevE.75.011924.
I put a small (and far from complete) discussion of similar work in a recent paper, (sections 6.4 and 6.5, in the rest of the paper I neglect this effect):
http://link.springer.com/article/10.1007%2Fs10827-014-0517-5
I hope this was the kind of thing you were looking for.
@Bas-Jan; thanks for the tip!
From the aforesaid, it seems to me that the internal resonances of the neuron is a beneficial characteristic for the neuron selectivity to certain inputs, filtering the noise. It is not clear to me how noisy synapses and neurons could provide a "reliable system" for the transmission of neural activity.
That is, assuming that the information lies in the precise spike timing, and a temporal spike sequence is affected by synaptic noise, how a single target neuron can detect the "correct" sequence? I mean, is the internal resonance enough to perform that?
I assume with noisy synapses, you have unreliability of synapses in mind, i.e. the failure to release neurotransmitter following an action potential? (Often neglected, but failure rates are typically > 50%, and synapses with less then 20% are considered "highly reliable", http://www.sciencedirect.com/science/article/pii/S0960982296006999 ). In contrast, sometimes the term noisy synaptic input is used to describe the total of all synaptic input to a neuron, which in a large network of neurons is seemingly random noise.
Indeed, intrinsic resonance of a neuron does not help in restoring "lost" input, but rather selecting input at preferred frequencies (but this I don't know much about). The trick to prevent loss of information is that there is large redundancy in many systems. Neurons make multiple synaptic connections between each other. Several neurons receive the same input. There is a lot of work done by e.g. Laughlin on energy effectiveness, synaptic failure and redundancy in neural networks, as well as by Zador: http://jn.physiology.org/content/79/3/1219.short
Dear Alessandro, some of our articles about stochastic resonance could be useful for your interesting question. https://www.researchgate.net/profile/Elias_Manjarrez
@Elias: your studies seem to me to be oriented on the statistic resonace arising from EEG mesuraments of ensamble of neurons. But, I'm currently interested on low-level representations of single neuron behaviors.
However, thanks for your suggestion.
Other systems you may wish to investigate are the P-type electroreceptors of various weakly electric fish, that seemed tot be tuned to the frequency of the fishes' electric organ frequency. Ted Bullock and Walter Heiligenberg pointed this out many years ago, although the specific journal article escapes me now.
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