P121 Effects of the nonlinearity, kinetics and size of the gap junction connections on the transient dynamics of coupled glial cells
Predrag Janjic*1, Dimitar Solev1, Ljupco Kocarev 1
1Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, North Macedonia
*Email: predrag.a.janjic@gmail.com
Introduction- The complex structure of massive couplings among the glial cells is not fully neurobiologically resolved, preventing realistic quantitative models. Despite the ongoing ultrastructural studies and elucidating published research focusing on glia[1] we can't extract statistical data on the number of gap junction (GJ) connections and their size. The nonlinear dependence of GJ conductance on the transjunctional voltage Vj, slow kinetics, and the GJ size-effect[2] on junction polarization suggest a rich repertoire of transient dynamic instabilities of resting glia when invaded by spreading depolarizations. Known limitations of the glial electrophysiology in-situ to measure GJ-coupled cells warrant qualifying suitable models.
Methods- We introduce a detailed point model of a coupled astrocytic cell - including several currents in the membrane kinetics and the nonlinear coupling with inactivation kinetics. Using the paradigm of a single active site in 1-d array of coupled astrocytes the main focus was on describing the bifurcations of the resting voltage Vr in the inner cell. Timescale separation allowed simplifying assumptions that enable formulating an ODE model of a "self-coupled cell", SCC. For stability analysis of such a model the 2nd cell is connected to a depolarized immediate neighbor on one-side, and a still quiet cell on the other side, both represented as fixed voltages Vdr and Vr. The numerical simulations were done on connected 1-d array.
Results- We explored the stability of the SCC in case of altered steady-state I-V curve, displaying N-shaped nonlinearity and generically present saddle-node (S-N) structure[3]. Newly introduced RMP is markedly more depolarized. The separate N-shaped nonlinearity introduced by the coupling enriched the S-N structure in all parameter perturbations. Typical cases were appearances of (a) fold limit cycle window within the range of fold curve, accompanied by a noise-induced bistability switching, or (b) a stable limit-cycle in the moderate coupling strength range. Not all of the observed dynamical regimes in the SCC survive in numerical simulation of an 1-d array, but in all cases we observed traveling front for the corresponding parameters.
Discussion- Emerging evidence from voltage imaging suggests that astrocytes do not respond dynamically as a homogeneous compartment, displaying strong variations in their depolarization between the collateral processes, or when compared to the cell body. In case of altered I-V curves they are generically prone to multistability. We observed enriched multistability scenarios in the passive response of GJ-coupled astrocytes under very basic conditions. We believe it motivates adding additional level of biophysical detail to the GJ connections and the topology of glial networks. Such groundwork is needed to extend the glial models with the advanced dynamical features of neuromodulation of their glutamate and GABA transporters and receptors.
Acknowledgements
The authors are grateful for the experimental recordings from isolated astrocytes shared by Prof. Christian Steinheauser, form the Institute of Cellular Sciences (IZN), School of Medicine, University of Bonn, Germany. PJ and DS were partially funded by R01MH125030 from the National Institute of Mental Health in US.
References
1. Aten,S., et al,(2022) Ultrastructural view of astrocyte arborization, astrocyte-astrocyte and astrocyte-synapse contacts, intracellular vesicle-like structures, and mitochondrial network, Prog Neurobiol, (213), 102264.
2. Wilders,R., and Jongsma,H.J.,(1992) Limitations of the dual voltage clamp method in assaying conductance and kinetics of gap junction channels, Biophys J 63(4), 942-953.
3. Janjic,P., Solev,D., and Kocarev,L.,(2023) Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores, Biophys J 122(8), 1470-1490.
