P289 When Can Activity-Dependent Homeostatic Plasticity Maintain Circuit-Level Dynamic Properties with Local Activity Information?

Lindsay Stolting*1, Randall D. Beer1

1Cognitive Science Department, Indiana University, Bloomington, IN, USA

*Email: lstoltin@iu.edu

Introduction

Neural circuits are remarkably robust to perturbations that threaten their function. One mechanism behind this robustness is activity-dependent homeostatic plasticity (ADHP), which tunes neural membrane and synaptic properties to ensure moderate and sustainable average activity levels [1]. The dynamics of behaving neural circuits, however, must often satisfy stricter requirements than just reasonable activity levels. For instance, successful behavior may require a specific temporal structure or phasing relationships between neurons–properties which cannot be specified by time-averaged activity information at the single-neuron level. How, then, does ADHP maintain such properties?

Methods
We explored this question in a computational model of the crustacean pyloric pattern generator, which exhibits a triphasic burst rhythm [2]. We stochastically optimize 100 continuous time recurrent neural networks to match pyloric burst ordering, then add ADHP to these models by placing two network parameters under homeostatic control. These parameters are tuned according to the temporally averaged activity of the corresponding neuron, relative to some target range [3]. The averaging window and target range are stochastically optimized 10 times for each pyloric network, with the goal of parameterizing an ADHP mechanism that recovers pyloricness after perturbation of controlled parameters.
Results
This results in a data set of ADHP mechanisms which maintain pyloricness in a degenerate set of pyloric network models to varying degrees of success. Though there are typically no true fixed points in these models, we find we can leverage timescale separation assumptions to predict asymptotic parameter configurations. We can then derive general conditions for ADHP’s success, according to whether homeostatic endpoints are also pyloric (Figure 1). More generally, we can predict for any individual pyloric network the range of homeostatic mechanisms that successfully maintain it, and validate these predictions with numerical simulation.
Discussion
Even though temporally defined properties like pyloricness cannot be directly specified by average activity levels, they can be maintained by activity-dependent homeostatic plasticity under specific conditions. To define these conditions, one must consider the set of perturbations with which the circuit may contend, in conjunction with the dynamic properties of the homeostatic mechanism itself. This work therefore suggests several avenues for experimental investigation, where responses to perturbation provide clues about homeostatic mechanisms, and knowledge of homeostatic mechanisms predicts responses to perturbation.




Figure 1. Differently parameterized ADHP mechanisms differentially recover pyloricness in a model circuit. ADHP endpoints are predicted by the overlap between target activity levels and average activity of regulated neurons. The intersection of these pseudo-nullclines may lie in or outside the pyloric region (black), resulting in successful (green), conditionally successful (yellow), or failing (red) ADHP.
Acknowledgements

This research was supported in part by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute.
References
[1] Turrigiano, G. (1999). Homeostatic plasticity in neuronal networks: The more things change, the more they stay the same.Trends in Neurosciences,22(5), 221–227.https://doi.org/10/frf24n
[2] Harris-Warrick, R. M. (Ed.). (1992). Dynamic biological networks: the stomatogastric nervous system. MIT press.
[3] Williams, H. (2005). Homeostatic plasticity improves continuous-time recurrent neural networks as a behavioural substrate. Proceedings of the International Symposium on Adaptive Motion in Animals and Machines, AMAM2005. Ilmenau, Germany: Technische Universität