Landscape perspectives of tumor, EMT, and development

Metastasis Models: Thermodynamics and Complexity

The thermodynamic formalism of nonequilibrium systems together with the theory of complex systems and systems biology offer an appropriate theoretical framework to explain the complexity observed at the macroscopic level in physiological phenomena. In turn, they allow the establishment of an appropriate conceptual and operational framework to address the study of phenomena such as the emergence and evolution of cancer.This chapter is organized as follows: In Subheading 1, an integrated vision of these disciplines is offered for the characterization of the emergence and evolution of cancer, seen as a nonlinear dynamic system, temporally and spatially self-organized out of thermodynamic equilibrium. The development of the various mathematical models and different techniques and approaches used in the characterization of cancer metastasis is presented in Subheading 2. Subheading 3 is devoted to the time course of cancer metastasis, with particular emphasis on the epithelial-mesenchymal transition (EMT henceforth) as well as chronotherapeutic treatments. In Subheading 4, models of the spatial evolution of cancer metastasis are presented. Finally, in Subheading 5, some conclusions and remarks are presented.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Epithelial to Mesenchymal Transition: A Challenging Playground for Translational Research. Current Models and Focus on TWIST1 Relevance and Gastrointestinal Cancers

Resembling the development of cancer by multistep carcinogenesis, the evolution towards metastasis involves several passages, from local invasion and intravasation, encompassing surviving anoikis into the circulation, landing at distant sites and therein establishing colonization, possibly followed by the outgrowth of macroscopic lesions. Within this cascade, epithelial to mesenchymal transition (EMT) works as a pleiotropic program enabling cancer cells to overcome local, systemic, and distant barriers against diffusion by replacing traits and functions of the epithelial signature with mesenchymal-like ones. Along the transition, a full-blown mesenchymal phenotype may not be accomplished. Rather, the plasticity of the program and its dependency on heterotopic signals implies a pendulum with oscillations towards its reversal, that is mesenchymal to epithelial transition. Cells in intermixed E⇔M states can also display stemness, enabling their replication together with the epithelial reversion next to successful distant colonization. If we aim to include the EMT among the hallmarks of cancer that could modify clinical practice, the gap between the results pursued in basic research by animal models and those achieved in translational research by surrogate biomarkers needs to be filled. We review the knowledge on EMT, derived from models and mechanistic studies as well as from translational studies, with an emphasis on gastrointestinal cancers (GI).

Stochastic epigenetic dynamics of gene switching

Epigenetic modifications of histones crucially affect eukaryotic gene activity, while the epigenetic histone state is largely determined by the binding of specific factors such as the transcription factors (TFs) to DNA. Here, the way in which the TFs and the histone state are dynamically correlated is not obvious when the TF synthesis is regulated by the histone state. This type of feedback regulatory relation is ubiquitous in gene networks to determine cell fate in differentiation and other cell transformations. To gain insights into such dynamical feedback regulations, we theoretically analyze a model of epigenetic gene switching by extending the Doi-Peliti operator formalism of reaction kinetics to the problem of coupled molecular processes. Spin-1 and spin-1/2 coherent-state representations are introduced to describe stochastic reactions of histones and binding or unbinding of TFs in a unified way, which provides a concise view of the effects of timescale difference among these molecular processes; even in the case that binding or unbinding of TFs to or from DNA is adiabatically fast, the slow nonadiabatic histone dynamics gives rise to a distinct circular flow of the probability flux around basins in the landscape of the gene state distribution, which leads to hysteresis in gene switching. In contrast to the general belief that the change in the amount of TF precedes the histone state change, flux drives histones to be modified prior to the change in the amount of TF in self-regulating circuits. Flux-landscape analyses shed light on the nonlinear nonadiabatic mechanism of epigenetic cell fate decision making.

Bidirectional interplay between physical and biological approaches on studying the epithelial-to-mesenchymal transition

Physical approaches have made notable contributions to the study of epithelial-to-mesenchymal transition (EMT), and EMT serves as a model system for advancing physics theories. A collection of reviews and original research papers are included in this special issue.