Predicting neuronal firing from calcium imaging using a control theoretic approach

Abstract

Two-photon calcium imaging has become a powerful tool to explore the functions of neurons and the connectivity of their circuitry. Frequently, fluorescent calcium indicators are taken as a direct measure of neuronal activity. These indicators, however, are slow relative to behavior, obscuring functional relationships between an animals movements and the true neuronal activity. As a consequence, the firing rate of a neuron is a more meaningful metric. Converting calcium imaging data to the firing of a neuron is nontrivial. State of the art methods depend largely on neural networks or non-mechanistic processes, which may yield acceptable correlations between calcium dynamics and the frequency at which a neuron fires, but do not illuminate the underlying chemical exchanges within the neuron or require significant data to be trained on. Leveraging modeling frameworks from chemical reaction networks (CRN) coupled with modern control architectures, a new algorithm is presented based off of fully deterministic ordinary differential equations (ODEs). This framework utilizes model predictive control to challenge state of the art correlation scores while retaining the interpretability that comes inherent with a model. Moreover, these computations can be done in real time, thus enabling online experimentation informed by neuronal firing rates. To demonstrate the use cases of this architecture, it is tested on a ground truth dataset courtesy of the spikefinder challenge. Finally, the predictive power of the methodology put forward here is underscored by demonstrating its ability to aid in the creation of novel indicators utilized in two-photon imaging. Author summaryWe put forward a novel approach to infer when neurons fire as a function of calcium concentration. These calcium recordings are useful for imaging whole populations of neurons, such as those found in the brain, but act only as a proxy for the true underlying spiking occurrences. Moreover, these calcium traces are unfortunately noisy. To uncover the actual firing times we apply modern control architectures to a framework built from chemical reaction equations. The result is accurate, fast enough to provide information in real time, and highly interpretable. More broadly this analysis process aids understanding in contexts where methods of measurement obfuscate the desired ground truth information. Not just capable of inference, prediction is possible thanks to the fully mechanistic formulation provided here. Specifically, we may quantify how indicators, which allow the tracking of calcium, behave in the presence of differing conditions. In more general terms, this framework also enables understanding of the tools used to measure the desired underlying signals.