A Review of Complex Systems Approaches to Cancer Networks

Abstract

Cancers remain the leading cause of disease-related pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple strange attractors. Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction. Deep learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

“…Cancers are complex systems, consisting of groups of adaptive malignant cells that self-organize in time and space, far from thermodynamic equilibrium. 1,21,22 In traditional (analytical) physics, natural systems are dealt with using statistical mechanics to describe systems with large degrees of freedom, and dynamical systems theory to describe the changes in time of systems constrained to phase space. However, these tools by themselves are inadequate to describe the emergent scaling behaviors observed in complex systems.…”

“…The general workflow for chaos detection, is first to obtain time series measurements, convert the data into a geometric object via time-embedding, and assess the topological properties of this object/attractor (i.e., Lyapunov exponents, entropies, fractal dimensions, and multifractality). 1 Generally, dynamical systems depend on certain control parameters, which, when changed, the stability of the fixed point can change, appear, or disappear, or give rise to a new object in its vicinity. An example would be to consider a limit cycle undergoing a Hopf bifurcation toward an unstable chaotic oscillator.…”

“…Such potential energy (attractor) landscapes can be used to study complex dynamical systems, such as the multidimensional epigenetic landscape of a population of cancer (stem) cells. 1 As mentioned, the heterogeneity and phenotypic plasticity of tumors are vastly attributed to a dynamic subset of cells within the cancer population known as CSCs. CSCs possess the capacity to both self-renew and generate all cells within a tumor, and are believed to drive tumor recurrence, therapy resistance, phenotypic plasticity, and the emergence of aggressive phenotypes.…”

“…Many network inference, clustering, and visualization algorithms useful in the dissection of cancer networks have been discussed in detail in Uthamacumaran. 1 However, the intuition for nonlinear dynamics and chaos were absent therein. This paper was written to serve that purpose, to steer the readers to develop an insight for pattern science and complex systems approaches (algorithms, simulations, and mathematical models) when investigating the state-space dynamics of cancer networks, given their time series datasets are made available.…”

“…Cancers are complex systems with multi-scale processes. 1 In principle, attractors can emerge in any cancer process at any scale when treated as a dynamical system (i.e., time series quantification). However, two main categories of cancer processes will be discussed here in the context of attractor dynamics: (1) cell state transitions and (2) pattern formation.…”