Spectral Operator Methods for Learning Coherent Temporal Representations in Cellular Signaling Dynamics
Keywords: Operator theory, temporal representations, delay-coordinate embeddings, Markov operator, single-cell analysis, machine learning for dynamical systems
TL;DR: A spectral operator-based learning that extracts predictable patterns from live-cell imaging data, as mechanisms of cellular dynamics across different experimental conditions.
Abstract: We present a novel operator-based framework for learning coherent temporal representations of cellular dynamics from live-cell imaging data. Recognizing the inherent stochasticity and measurement limitations in biological systems, our approach shifts the focus from predicting exact trajectories to characterizing key dynamical properties that shape cellular behaviors at the population level. By leveraging spectral analysis of the Koopman operator and smoothing via Markov semigroups of kernel integral operators, we identify near-resonant patterns and transient coherent structures that persist across different experimental conditions. This methodology effectively captures fundamental dynamics, providing insights into mechanisms of heterogeneous cell responses without the need to model precise transformation laws. We demonstrate the efficacy of our framework on a dataset of retinal pigment epithelial cells with an inducible oncogene, revealing conserved dynamical patterns across varying levels of ERK inhibition. Our work offers interpretable learned representations, even with limited and noisy single-cell-resolved recordings, advancing machine learning for dynamical systems and opening new avenues for understanding and predicting cellular behavior in response to external stimuli.
Primary Area: learning on time series and dynamical systems
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Submission Number: 12904
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