Rhythmogenesis and Bifurcation Analysis of 3-Node Neural Network Kernels

Central pattern generators (CPGs) are small neural circuits of coupled cells stably producing a range of multiphasic coordinated rhythmic activities like locomotion, heartbeat, and respiration. Rhythm generation resulting from synergistic interaction of CPG circuitry and intrinsic cellular properties remains deficiently understood and characterized. Pairing of experimental and computational studies has proven key in unlocking practical insights into operational and dynamical principles of CPGs, underlining growing consensus that the same fundamental circuitry may be shared by invertebrates and vertebrates. We explore the robustness of synchronized oscillatory patterns in small local networks, revealing universal principles of rhythmogenesis and multi-functionality in systems capable of facilitating stability in rhythm formation. Understanding principles leading to functional neural network behavior benefits future study of abnormal neurological diseases that result from perturbations of mechanisms governing normal rhythmic states. Qualitative and quantitative stability analysis of a family of reciprocally coupled neural circuits, constituted of generalized Fitzhugh–Nagumo neurons, explores symmetric and asymmetric connectivity within three-cell motifs, often forming constituent kernels within larger networks. Intrinsic mechanisms of synaptic release, escape, and post-inhibitory rebound lead to differing polyrhythmicity, where a single parameter or perturbation may trigger rhythm switching in otherwise robust networks. Bifurcation analysis and phase reduction methods elucidate qualitative changes in rhythm stability, permitting rapid identification and exploration of pivotal parameters describing biologically plausible network connectivity. Additional rhythm outcomes are elucidated, including phase-varying lags and broader cyclical behaviors, helping to characterize system capability and robustness reproducing experimentally observed outcomes. This work further develops a suite of visualization approaches and computational tools, describing robustness of network rhythmogenesis and disclosing principles for neuroscience applicable to other systems beyond motor-control. A framework for modular organization is introduced, using inhibitory and electrical synapses to couple well-characterized 3-node motifs described in this research as building blocks within larger networks to describe underlying cooperative mechanisms

Biological Neuron Voltage Recordings, Driving and Fitting Mathematical Neuronal Models

The manual process of comparing biological recordings from electrophysiological experiments to their mathematical models is time-consuming and subjective. To address this problem, we have created a blended system that allows for objective, high-throughput, and computationally inexpensive comparisons of biological and mathematical models by developing a quantitative measure of likeness (error function). Voltage recordings from biological neurons, mathematically simulated voltage times series, and their transformations are inputted into the error function. These transformations and measurements are the action potential (AP) frequency, voltage moving average, voltage envelopes, and the probability of post-synaptic channels being open. The previously recorded biological voltage times series are first, translated into mathematical data to input into mathematical neurons, creating what we call a blended system. Using the sea slug Melibe Leonina\u27s swimming central pattern generator (CPG) as our circuit to compare and the source of our biological recordings, we performed a grid search of the conductance of the inhibitory and excitatory synapse found that a weighted sum of simple functions is required for a comprehensive view of a neuron\u27s rhythmic behavior. The blended system was also shown to be able to act as rhythm directors like pacemakers and drivers of Dendronotus Iris swimming interneuron (Si) cells and was able to replicate the perturbations of biological recordings. After verification steps using different configurations, calculated mean and variance of rhythmic characteristics, as well as recordings created from data augmentation. The form of data augmentation introduced can be generalized to other biological recordings or any time series. With all these tools developed and expanding the parameter dimensions a hypothesis was posited that there is a contralateral electric synapse not previously included in the Melibe CPG model