Closing the Loop: Optimal Stimulation of Neuronal Networks via Adaptive Control Algorithms
Santos, Julia Ann
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The Caenorhabditis elegans (C. elegans) worm is a well-studied biological organism model. The nervous system of C. elegans is particularly appealing to study, since it is a tractable fully functional neuronal network for which electro-physical connectivity map (connectome) is fully resolved [1,2]. In this work, we use a recently established computational dynamical model of the C. elegans nervous system, which incorporated the static connectome data with intrinsic properties of neurons and their interactions. With this model, it has been demonstrated that robust oscillatory movements in motor neurons along the body can be invoked by constant current excitation of command sensory neurons (e.g., PLM neurons associated with forward crawling), and that their activation corresponds to low-dimensional Hopf bifurcation . While these first results validated the model, it is exciting to learn and visualize how the nervous system transforms its oscillatory dynamics to the muscles to support robust full body movements (e.g., forward crawling) . Moreover, it is intriguing to understand the optimal sensory stimulations that cause these movements to persist. We explore these questions by developing methods to visualize network activity in a physical space and creating a model for C. elegans musculature as a viscoelastic rod with discrete rigid segments . We map the neuronal dynamics such that they activate the muscles and deform the rod. When motor neuron activity stimulates muscles , this activation is translated into force applied to the rod, which moves in accordance with the physical properties of C. elegans. By stimulating the command PLM neurons, we establish for the first time that motor neuron dynamics are indeed producing coherent oscillatory full body movements that resemble forward crawling. We utilize our computational full body model to determine the appropriate sensory input for behavior, such as crawling, to persist after explicit external stimulation (touch) has ceased, as observed in experiments . Since such persistence could be explained by a feedback loop between the environment and sensory neurons, we propose an adaptive control algorithm that extends existing recursive least squares-based algorithms (e.g., FORCE ). The RLS algorithm is divided into training and operational phases. In the training phase, we reduce the error between desired and actual outputs by making small, rapid modifications to the weights which are applied to the network input (feedback). When the weighted feedback into sensory neurons prompts the system to produce the desired output without significant weight modification between iterations, a correct set of weights has been found . We use a low-dimensional projection of motor neuron dynamics to calculate expected and actual output, and our algorithm is capable of finding sensory input patterns that will lead to the desired movement.
- Applied mathematics