P332 Relating Input Resistance and Sodium Conductance
Laura Zittlow*1, Erin Munro Krull1, Lucas Swanson1 1Mathematical Sciences, Ripon College, Ripon, WI, US*E-mail: laurazittlow@gmail.com Introduction
The sodium conductance density (gNa) determines an axon’s ability to propagate APs. APs do not propagate if the gNa is too low, while they easily do if the gNa is high. Therefore, there is a sodium conductance density threshold (gNaT) [1]. Preliminary results suggest the gNaT for axons with simple morphologies linearly predicts gNaT for axons with more complex morphologies [2, 3]. To address axons with very complex morphologies, we decided to compare gNaT to input resistance (Rin). Rin, defined as the steady-state voltage to injected current ratio, inherently accounts for the axon’s morphology and electrical properties [4].
Methods We use NEURON simulations [5] to model Rin and AP propagation from an axon collateral to the end of the main axon. We varied the morphology of an extra side branch to see the effect of axon morphology on Rin and gNaT. For each simulation, we find the Rin and gNaT. We evaluate the impact of location for lengths of 0-6𝜆, several side branch morphologies and lengths from 0-6𝜆, and the location and length of sub-branches. Results Our simulations show a 1-1 correspondence between Rin and gNaT under specific morphological changes, modeled as a smooth function. Branch location and length affect Rin and gNaT inversely, with their effects stabilizing as the distances and lengths increase. However, when a short side branch connects at the same point as the simulated branch, an abnormality–“bouncing”–occurs. Because shorter side branches are easier to stimulate, the AP can temporarily move into the said branch and thenbounceout. If only one variable (distance or morphology) changes, the error difference is 10-4in gNaT for a given Rin. However, if “bouncing” occurs, then the error difference is on the scale of 10-2. Discussion Our results indicate Rinand gNaTrespond monotonically to changes in axonal morphology unless “bouncing” occurs. This suggests Rincould serve as an alternative measure for axonal morphology when predicting gNaT. It offers a computationally efficient method for estimating gNaT. However, “bouncing” disrupts the smooth relationship between Rinand gNaTby making AP propagation more likely. Moving forward, we aim to compare Rin across more complex morphologies. Additionally, we plan to curve-fit the Rin-gNaT relationship and test it against the linear estimation method and realistic axonal morphologies.
Acknowledgements Thank you to my mentor Dr. Erin Munro Krull and the rest of the Ripon College Mathematical Sciences department for the advice and guidance. Also, thank you to Ripon College's Summer Opportunities for Advanced Research (SOAR) program and the many donors who help fund the program. References [1]https://doi.org/10.1152/jn.00933.2011 [2]https://doi.org/10.1186/s12868-018-0467-3 [3]https://doi.org/10.1186/s12868-018-0467-3 [4] Carnevale, N. T., & Hines, M. L. (2006).The NEURON book.Cambridge University Press. [5] Tuckwell, H. C. (1988).Introduction to theoretical neurobiology: Volume 1. Linear cable theory and dendritic structure.Cambridge University Press.
