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Cancers are complex adaptive diseases regulated by the nonlinear feedbacksystems between genetic instabilities, environmental signals, cellular proteinflows, and gene regulatory networks. Understanding the cybernetics of cancerrequires the integration of information dynamics across multidimensionalspatiotemporal scales, including genetic, transcriptional, metabolic,proteomic, epigenetic, and multi-cellular networks. However, the time-seriesanalysis of these complex networks remains vastly absent in cancer research.With longitudinal screening and time-series analysis of cellular dynamics,universally observed causal patterns pertaining to dynamical systems, mayself-organize in the signaling or gene expression state-space of cancertriggering processes. A class of these patterns, strange attractors, may bemathematical biomarkers of cancer progression. The emergence of intracellularchaos and chaotic cell population dynamics remains a new paradigm in systemsoncology. As such, chaotic and complex dynamics are discussed as mathematicalhallmarks of cancer cell fate dynamics herein. Given the assumption thattime-resolved single-cell datasets are made available, a survey ofinterdisciplinary tools and algorithms from complexity theory, are herebyreviewed to investigate critical phenomena and chaotic dynamics in cancerecosystems. To conclude, the perspective cultivates an intuition forcomputational systems oncology in terms of nonlinear dynamics, informationtheory, inverse problems and complexity. We highlight the limitations we see inthe area of statistical machine learning but the opportunity at combining itwith the symbolic computational power offered by the mathematical toolsexplored.

A Review of Mathematical and Computational Methods in Cancer Dynamics