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Modeling synchronous theta activity in the medial septum: key role of local communications between different cell populations

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Abstract

It is widely believed that the theta rhythm in the hippocampus is caused by the rhythmic input from the medial septum-diagonal band of Broca (MSDB). The main MSDB output is formed by GABAergic projection neurons which are divided into two subpopulations and fire at different phases of the hippocampal theta rhythm. The MSDB also contains projection cholinergic, glutamatergic, and non-projection GABAergic neurons. These cell populations innervate each other and also GABAergic projection neurons and participate in the formation of the synchronous rhythmic output to the hippocampus. The purpose of this study is to work out a model of interactions between all neural populations of the MSDB that underlie the formation of the synchronous septal theta signal. The model is built from biologically plausible neurons of the Hodgkin-Huxley type and its architecture reflects modern data on the morphology of neural connections in the MSDB. The model satisfies the following requirements: (1) a large portion of neurons is fast-spiking; (2) the subpopulations of GABAergic projection neurons contain endogenous pacemaker neurons; (3) the phase shift of activity between subpopulations of GABAergic projection neurons is equal to about 150°; and (4) the strengths of bidirectional connections between the subpopulations of GABAergic projection cells are different. It is shown that the theta rhythm generation can be performed by a system of glutamatergic and GABAergic non-projection neurons. We also show that bursting pacemaker neurons in the subpopulation of projection GABAergic neurons play a significant role in the formation of stable antiphase outputs from the MSDB to the hippocampus.

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Acknowledgments

This work was supported by a grant from the Russian Foundation for Basic Research № 12-04-00776 and a regional grant from the Russian Foundation for Basic Research № 14-44-03607.

Conflict of interest

This study was supported by the grants of the Russian Foundation for Basic Research (№№12-04-00776-a, 14-44-03607-a, 15-04-05463-a), and grant of President of RF “Scientific schools”, НШ-850.2012.4).

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Authors and Affiliations

  1. Laboratory of System Organization of Neurons, Russian Academy of Sciences, Institute of Theoretical and Experimental Biophysics, 142290, Pushchino, Moscow Region, Russia

    Ivan E. Mysin & Valentina F. Kitchigina

  2. Laboratory of Neural Networks, Russian Academy of Sciences, Institute of Mathematical Problems of Biology, 142290, Pushchino, Moscow Region, Russia

    Yakov Kazanovich

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  1. Ivan E. Mysin
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  2. Valentina F. Kitchigina
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Correspondence to Ivan E. Mysin.

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Appendix

Appendix

1.1 A1. Description of currents

The dynamics of the gate variables of the channels are described by the equations (Wang 2002)

$$ \frac{dx}{dt}=\frac{\left({x}_{\infty }-x\right)}{\tau_x},{x}_{\infty }=\frac{\alpha_x}{\alpha_x+{\beta}_x},\kern1em {\tau}_x=\frac{1}{\alpha_x+{\beta}_x},x\in \left\{m,\;n,\;h\right\} $$
(4)

where α and β are the functions of the potential:

$$ {\alpha}_{\mathrm{m}}=-0.1\frac{V+33}{ \exp \left(-0.1\;\left(V+33\right)\right)-1},\kern1em {\beta}_m=4 \exp \left(-\frac{V+58}{18}\right),{\alpha}_h=\phi \exp \left(-\frac{V+51}{10}\right),\kern1em {\beta}_h=\frac{\phi }{ \exp \left(-0.1\;\left(V+21\right)\right)+1},{\alpha}_n=-0.01\kern0.5em \frac{\phi \left(V+38\right)}{ \exp \left(-0.1\;\left(V+38\right)\right)-1},\kern1em {\beta}_n=0.125\kern0.5em \phi \exp \left(-\frac{V+48}{80}\right). $$
(5)

For the computation of other gate variables we use the expressions

$$ {p}_{\infty }=-\frac{1}{1+ \exp \left(-\frac{V+34}{6.5}\right)},\kern1em {\tau}_p=6\kern0.5em ms,\kern1em {q}_{\infty }=\frac{1}{1+ \exp \left(\frac{V+65}{6.6}\right)},\kern1em {\tau}_q=100\left(1+\frac{1}{1+ \exp \left(-\frac{V+50}{6.8}\right)}\right),{H}_{\infty }=\frac{1}{1+ \exp \left(\frac{V+80}{10}\right)},\kern1em {\tau}_H=5+\frac{200}{ \exp \left(\frac{V+70}{20}\right)+ \exp \left(-\frac{V+70}{20}\right)}. $$
(6)

Initial values of all gate variables are x ∞ computed at the initial moment of time. The parameters of the equations are given in Table 1.

Table 1 Parameters of the model
Full size table

The value of I ext is chosen randomly from the Gaussian distribution at each moment of time with the variance equal to 0.1. In the basic model, the mean of the value I ext for Glu, GABA(PV1), GABA(PV1 burst), GABA(PV2 burst) is 0.3 nA, for GABA(CR) it is 0 nA, and for GABA(PV2) it is 0.7 nA.

1.2 A2. Parameters of synaptic currents

The gate variable s is described by the equation (Ujfalussy and Kiss, 2006)

$$ \frac{ds}{dt}=\alpha\;F\left(1-s\right)-\beta\;s, $$
(7)

where

$$ F=\frac{1}{1+ \exp \left(-\frac{V_{pre}-\theta }{K}\right)}, $$
(8)

V pre is the potential of the presynaptic neuron. The initial value of s is 0. The parameters for the equations of synaptic currents are given in Table 2.

Table 2 Parameters of the equation for currents
Full size table

In the basic model the weights of connections from the GABA(PV1) population to the GABA(PV2) population and from the glutamatergic population to GABA(CR) population are set to 0.2, the weights of connections from GABA(PV2) to GABA(PV1) are set to 0.1. Other weights are equal to 1.

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Mysin, I.E., Kitchigina, V.F. & Kazanovich, Y. Modeling synchronous theta activity in the medial septum: key role of local communications between different cell populations. J Comput Neurosci 39, 1–16 (2015). https://doi.org/10.1007/s10827-015-0564-6

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