Frontiers in Computational Neuroscience (Jul 2015)

Modeling the calcium spike as a threshold triggered fixed waveform for synchronous inputs in the fluctuation regime

  • Yansong eChua,
  • Yansong eChua,
  • Yansong eChua,
  • Moritz eHelias,
  • Abigail eMorrison,
  • Abigail eMorrison,
  • Abigail eMorrison

DOI
https://doi.org/10.3389/fncom.2015.00091
Journal volume & issue
Vol. 9

Abstract

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Modeling the layer 5 pyramidal neuron as a system of three connected isopotential compartments, the soma, proximal and distal compartment, with calcium spike dynamics in the distal compartment following first order kinetics, we are able to reproduce in-vitro experimental results which demonstrate the involvement of calcium spikes in action potentials generation. To explore how calcium spikes affect the neuronal output in-vivo, we emulate in-vivo like conditions by embedding the neuron model in a regime of low background fluctuations with occasional large synchronous inputs. In such a regime, a full calcium spike is only triggered by the synchronous events in a threshold like manner and has a stereotypical waveform. Hence, in such a regime, we are able to replace the calcium dynamics with a simpler threshold triggered current of fixed waveform, which is amenable to analytical treatment. We obtain analytically the mean somatic membrane potential excursion due to a calcium spike being triggered while in the fluctuating regime. Our analytical form that accounts for the covariance between conductances and the membrane potential shows a better agreement with simulation results than a naive first order approximation.

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