Predicting neuronal firing from calcium imaging using a control theoretic approach

Calcium imaging techniques, such as two-photon imaging, have 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 animal’s 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. Most state-of-the-art methods depend largely on non-mechanistic modeling frameworks such as neural networks, which do not illuminate the underlying chemical exchanges within the neuron, require significant data to be trained on, and cannot be implemented in real-time. Leveraging modeling frameworks from chemical reaction networks (CRN) coupled with a control theoretic approach, a new algorithm is presented leveraging a fully deterministic ordinary differential equation (ODE) model. This framework utilizes model predictive control (MPC) to challenge state-of-the-art correlation scores while retaining interpretability. Furthermore, 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 ground truth datasets courtesy of the spikefinder challenge. Finally, we propose potential applications of the model for guiding experimental design.Author summary: We 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 a control theoretic approach to a model derived from chemical reaction equations. The result is competitive with the state of the art, 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. To demonstrate potential applications of the model we quantify how biochemical properties of the indicators, which allow the tracking of calcium, impact prediction accuracies. In more general terms, this framework has the potential to enable understanding of the tools used to measure the desired underlying signals.