Electrodiffusion models of synaptic potentials in dendritic spines

  • Thibault LagacheEmail author
  • Krishna Jayant
  • Rafael Yuste


The biophysical properties of dendritic spines play a critical role in neuronal integration but are still poorly understood, due to experimental difficulties in accessing them. Spine biophysics has been traditionally explored using theoretical models based on cable theory. However, cable theory generally assumes that concentration changes associated with ionic currents are negligible and, therefore, ignores electrodiffusion, i.e. the interaction between electric fields and ionic diffusion. This assumption, while true for large neuronal compartments, could be incorrect when applied to femto-liter size structures such as dendritic spines. To extend cable theory and explore electrodiffusion effects, we use here the Poisson (P) and Nernst-Planck (NP) equations, which relate electric field to charge and Fick’s law of diffusion, to model ion concentration dynamics in spines receiving excitatory synaptic potentials (EPSPs). We use experimentally measured voltage transients from spines with nanoelectrodes to explore these dynamics with realistic parameters. We find that (i) passive diffusion and electrodiffusion jointly affect the dynamics of spine EPSPs; (ii) spine geometry plays a key role in shaping EPSPs; and, (iii) the spine-neck resistance dynamically decreases during EPSPs, leading to short-term synaptic facilitation. Our formulation, which complements and extends cable theory, can be easily adapted to model ionic biophysics in other nanoscale bio-compartments.


Synaptic transmission Dendritic spines Electrodiffusion Asymptotic analysis Coarse-grained model Electrophysiology Simulations 



This work was supported by the NIMH (R01MH101218, R01MH100561) and the NINDS (R01NS110422). This material is also based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract number W911NF-12-1-0594 (MURI). T.L. was partly supported by the Fondation pour la Recherche Médicale and the Philippe foundation. K.J was supported by the Kavli Institute of Brain Science at Columbia.

Author contributions

T.L. and R.Y. conceived the project. T.L performed the modeling and analysis. K.J assisted with model development and analysis. T.L and K.J wrote the manuscript. R.Y assembled and directed the team, provided guidance, funding, and edited the manuscript.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

10827_2019_725_MOESM1_ESM.pdf (941 kb)
ESM 1 (PDF 940 kb)


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Biological SciencesColumbia UniversityNew YorkUSA
  2. 2.Neurotechnology CenterColumbia UniversityNew YorkUSA
  3. 3.Kavli institute of Brain ScienceColumbia UniversityNew YorkUSA
  4. 4.BioImage Analysis UnitInstitut PasteurParisFrance
  5. 5.Department of Electrical EngineeringColumbia UniversityNew YorkUSA

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