Monday, November 19, 2012

Direct control of firing rate gain by dendritic shunting inhibition.

Capaday, C. Van Vreeswijk, C. (2006) Direct control of firing rate gain by dendritic shunting inhibition. Journal of Integrative Neuroscience 5(2): 199-222.

Ok, crap. Just skimming over this paper he basically gets to the same model that I have in the local-bend system. Ugh, I knew someone must have done this. We shall see what he came up with. He makes his compartments dendrite and soma - which are equivalent to my soma and axon respectively. I've never heard of this journal, and this paper is only cited by one other paper in pubmed, and that paper is something completely different.

Intro has a nice review of all the noise papers. Holt & Koch, Chance et al, Mitchel & Silver, Prescott and De Koninck. There are slight differences in the noise mechanism across these papers.

"soma acts as an IF neuron attached, by a coupling conductance, to a passive dendritic compartment."

He is taking into account the current from the action-potential, which is normally neglected. He makes Ispike like a delta function with some integral S. Then he derives a way of incorporating the spike current as a value for the reset. So then he just jumps to his alpha-motor neuron model, where he adds in some more conductances - an AHP, and a K.

He then analytically derives the IFR in the two-compartment model. Its quite complicated. But then he gets to the firing rate being:
R=1/C_S(V_T-V_r) * (I_S + g_C/(g_C+g_D)I_D)
R is firing rate, C_S soma capacitance, V_T threshold, V_r reset, I_S current injected into soma (axon, for mine), I_D is current injected into dendrite (soma, for mine). g_C is coupling conductance, g_D is the approximate conductance of the dendrite. He then derives, similarly to mine, how Holt & Koch works, and how you can get division if current is injected in dendrite and shunting is in dendrite.


So, A is just like Holt & Koch (with a passive dendrite attached). B is just an IF and you slightly increase the conductance through the dendrite to ground. C is equivalent to A, just the current is going through an extra resistor. D is the gain-control type.

He next is considering synaptic conductances instead of currents. He talks about the upper-limit when soma shunting prevents the neuron from firing at all - due to the Voltage saturation and the excitatory reversal potential. 

"The observation emphasizes that it is the net current reaching the SIZ at the soma which determines firing rate." ala my figure 5B. 

So, yes, basically the same. He doesn't catch the trick of changing the reset potential such that the zero-crossing is the same and thus you get pure scaling. And in general I think the seperation of soma and axon is better than like dendrite and soma. All the conductance stuff he talks about is the same as what happened with my model, I just ignored it because of the complicated properties of the conductance curves - it was hard to make something work based on those functions. And acting like the dendrite is one-compartment and can actually saturate seems unlikely anyway, and currents summing from dendrites is more appropriate.