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

Metabolic oscillations are a common phenomenon in cell biology. They are based on non-linear coupling of biochemical reactions and can show rich dynamic behavior including sustained and damped oscillations, as found, for example, in glycolysis of yeast and other eukaryotic cells. Metabolic oscillations are often studied by time-lapse imaging of cellular autofluorescence based on the changing abundance of NAD(P)H, but the analysis of such experimental data is challenging. Here, we show that dynamic mode decomposition (DMD), a numerical algorithm for linear approximation and spectral analysis of non-linear dynamics, allows for dissecting glycolytic oscillations in simulations and experiments in a fully data-driven manner. By combining DMD with time-delay embedding the spatiotemporal dynamics of sustained and damped glycolytic oscillations can be learned. Together with a rigorous assessment of spurious eigenvalues, via residual DMD, this provides a unique spectrum for each scenario, allowing for high-fidelity time-series and image reconstruction as well as for phenotyping different starvation conditions. The ability of DMD to predict future time points depends on the delay embedding dimension and is comparable to that of long short-term memory (LSTM) neural networks. Together, our results demonstrate the potential of DMD for analysis of time-lapse microscopy of metabolic oscillations in living cells.