Dynamic mode decomposition for analysis and prediction of metabolic oscillations from time-lapse imaging of cellular autofluorescence

Oscillations are a common phenomenon in cell biology. They are based on non-linear coupling of biochemical reactions and can show rich dynamic behavior as found in, for example, glycolysis of yeast cells. Here, we show that dynamic mode decomposition (DMD), a numerical algorithm for linear approximation of non-linear dynamics, can be combined with time-delay embedding (TDE) to dissect damped and sustained glycolytic oscillations in simulations and experiments in a fully data-driven manner. Together with an assessment of spurious eigenvalues via residual DMD, this provides a unique spectrum for each scenario, allowing for high-fidelity time-series and image reconstruction. By machine-learning-based clustering of identified DMD modes, we are able to classify NADH oscillations, thereby discovering subtle phenotypes and accounting for cell-to-cell heterogeneity in metabolic activity. This is demonstrated for varying glucose influx and for yeast cells lacking the sterol transporters Ncr1 and Npc2, a model for Niemann Pick type C disease in humans. DMD with TDE can also discern other types of oscillations, as demonstrated for simulated calcium traces, and its forecasting ability is on par with that of Long Short-Term Memory (LSTM) neural networks. Our results demonstrate the potential of DMD for analysis of oscillatory dynamics at the single-cell level.