Electrodiffusion models of synaptic potentials in dendritic spines
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.
KeywordsSynaptic 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.
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.
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Conflict of interests
The authors declare that they have no conflict of interest.
- Jayant, K., Hirtz, J. J., Plante, I. J. L., Tsai, D. M., de Boer, W. D. A. M., Semonche, A., Peterka, D. S., Owen, J. S., Sahin, O., Shepard, K. L., & Yuste, R. (2017). Targeted intracellular voltage recordings from dendritic spines using quantum-dot-coated nanopipettes. Nature Nanotechnology, 12(4), 335–342.CrossRefGoogle Scholar
- Acker, C. D., Hoyos, E., & Loew, L. M. (2016). EPSPs Measured in Proximal Dendritic Spines of Cortical Pyramidal Neurons. eNeuro, 3(2). https://doi.org/10.1523/ENEURO.0050-15.2016.
- Cartailler, J., et al.. (2017a). Deconvolution of voltage sensor time series and electro-diffusion modeling of synaptic input in dendritic spines. Neuron, . (in press).Google Scholar
- Beaulieu-Laroche, L., Harnett, M.T. (2017). Dendritic Spines prevent synaptic voltage clamp. Neuron.Google Scholar
- Koch, C., & Poggio, T. (1983). Electrical properties of dendritic spines. TINS, 6, 80–83.Google Scholar
- Koch, C., Segev, I. (1998). Methods in neuronal modeling: from ions to networks. MIT press.Google Scholar
- Jack, J. J. B., Noble, D., & Tsien, R. W. (1975). Electric current flow in excitable cells. London: Oxford University Press.Google Scholar
- Miyazaki, K., Ross, W. N.. (2017). Sodium dynamics in pyramidal neuron dendritic spines: synaptically evoked entry predominantly through AMPA receptors and removal by diffusion. Journal of Neuroscience, p. 1758–17.Google Scholar
- Tovar, R.K., Westbrook, G. L. (2012). Ligand-Gated Ion Channels, in Cell Physiology Source Book (Fourth Edition).Google Scholar