Volume 16 Supplement 1

24th Annual Computational Neuroscience Meeting: CNS*2015

Open Access

Estimation of the synaptic conductance in a McKean-model neuron

  • Antoni Guillamon1,
  • Rafel Prohens2,
  • Antonio E Teruel2 and
  • Catalina Vich2
BMC Neuroscience201516(Suppl 1):P251

https://doi.org/10.1186/1471-2202-16-S1-P251

Published: 18 December 2015

Estimating the synaptic conductances impinging on a single neuron directly from its membrane potential is one of the open problems to be solved in order to understand the flow of information in the brain. Despite the existence of some computational strategies that give circumstantial solutions ([13] for instance), they all present the inconvenience that the estimation can only be done in subthreshold activity regimes. The main constraint to provide strategies for the oscillatory regimes is related to the nonlinearity of the input-output curve and the difficulty to compute it. In experimental studies it is hard to obtain these strategies and, moreover, there are no theoretical indications of how to deal with this inverse non-linear problem. In this work, we aim at giving a first proof of concept to address the estimation of synaptic conductances when the neuron is spiking. For this purpose, we use a simplified model of neuronal activity, namely a piecewise linear version of the Fitzhugh-Nagumo model, the McKean model ([4], among others), which allows an exact knowledge of the nonlinear f-I curve by means of standard techniques of non-smooth dynamical systems. As a first step, we are able to infer a steady synaptic conductance from the cell's oscillatory activity. As shown in Figure 1, the model shows the relative errors of the conductances of order C, where C is the membrane capacitance (C<<1), notably improving the errors obtained using filtering techniques on the membrane potential plus linear estimations, see numerical tests performed in [5].
Figure 1

Goodness of fit of the synaptic conductance parameter. Panel A represents the relative error versus the applied current for a fixed value of C = 10-4. Red points represent the values of I1 (left points) and I2 (right points) for each gsyn. Panel B represents the relative error versus the membrane capacitance for a fixed value of I=I1+10-3. In both panels, the different color traces correspond to different values of gsyn equally spaced from 0.1 to 0.3. The rest of parameters are fixed as a=0.25, v0=0, w0=0, γ=0.5, vsyn=0.25+a/2.

Authors’ Affiliations

(1)
Dept. of Applied Mathematics I, EPSEB, Universitat Politècnica de Catalunya
(2)
Dept. of Mathematics and Computer Science, Universitat de les Illes Balears

References

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Copyright

© Guillamon et al. 2015

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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