Computer-aided Formal Proofs about Dendritic Integration within a Neuron

Ophélie Guinaudeau, Gilles Bernot, Alexandre Muzy, Daniel Gaffé, Franck Grammont

2018

Abstract

This article is threefold: (i) we define the first formal framework able to model dendritic integration within biological neurons, (ii) we show how we can turn continuous time into discrete time consistently and (iii) we show how a Lustre model checker can automatically perform proofs about neuron input/output behaviours owing to our framework. Our innovative formal framework is a carefully defined trade-off between abstraction and biological relevance in order to facilitate proofs. This framework is hybrid: inputs entering the synapses as well as the soma output are discrete signals made of spikes but, inside the dendrites, we combine signals quantitatively using real numbers. The soma potential is inevitably specified as a differential equation to keep a biologically accurate modelling of signal accumulation. This prevents from performing simple formal proofs. This has been our motivation to discretize time. Owing to this discretization, we are able to encode our neuron models in Lustre. Lustre is a particularly well suited flow-based language for our purpose. We also encode in Lustre a property of input/output equivalence between neurons in such a way that the model checker Kind2 is able to automatically handle the proof.

Paper Citation

in Harvard Style

Guinaudeau O., Bernot G., Muzy A., Gaffé D. and Grammont F. (2018). Computer-aided Formal Proofs about Dendritic Integration within a Neuron. In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 3: BIOINFORMATICS; ISBN 978-989-758-280-6, SciTePress, pages 49-60. DOI: 10.5220/0006680500490060

in Bibtex Style

@conference{bioinformatics18,
author={Ophélie Guinaudeau and Gilles Bernot and Alexandre Muzy and Daniel Gaffé and Franck Grammont},
title={Computer-aided Formal Proofs about Dendritic Integration within a Neuron},
booktitle={Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 3: BIOINFORMATICS},
year={2018},
pages={49-60},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006680500490060},
isbn={978-989-758-280-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 3: BIOINFORMATICS
TI - Computer-aided Formal Proofs about Dendritic Integration within a Neuron
SN - 978-989-758-280-6
AU - Guinaudeau O.
AU - Bernot G.
AU - Muzy A.
AU - Gaffé D.
AU - Grammont F.
PY - 2018
SP - 49
EP - 60
DO - 10.5220/0006680500490060
PB - SciTePress