A Review of Mathematical and Computational Methods in Cancer Dynamics

TL;DR

This paper reviews mathematical and computational methods, especially nonlinear dynamics and chaos theory, to understand complex cancer systems across multiple biological scales, highlighting potential biomarkers and the need for advanced analysis tools.

Contribution

It provides a comprehensive survey of interdisciplinary mathematical tools for analyzing cancer dynamics, emphasizing chaos theory and complexity science in systems oncology.

Findings

Chaotic dynamics may serve as biomarkers for cancer progression.

Intracellular chaos and complex cell population dynamics are emerging paradigms.

Limitations exist in current statistical machine learning approaches for cancer analysis.

Abstract

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis 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, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems oncology. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.