[Paper Review] Ferroptosis as a Biological Phase Transition I: avascular and vascular tumor growth

J.M. Nieto‐Villar, Ricardo Mansilla|arXiv (Cornell University)|Aug 26, 2021

Mathematical Biology Tumor Growth19 references4 citations

TL;DR

This paper proposes a network model framing ferroptosis as a first-order biological phase transition in avascular and vascular tumor growth, using a supercritical Andronov-Hopf bifurcation to explain limit cycle dynamics. The key finding is that increasing oxidized PUFA fragments as a control parameter triggers an inverse Feigenbaum scenario with Shilnikov bifurcations, stabilizing the system and reducing dynamical complexity.

ABSTRACT

Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical Andronov Hopf bifurcation, with the emergence of limit cycle. The increase of the population of the oxidized PUFA fragments, take as the control parameter, involves an inverse Feigenbaum, (a cascade of saddle foci Shilnikov's bifurcations) scenario, which results in the stabilization of the dynamics and in a decrease of complexity.

Motivation & Objective

• To model ferroptosis in avascular and vascular tumor growth as a biological phase transition.
• To investigate how ferroptosis dynamics shift from chaotic to stable behavior under varying biological parameters.
• To explore the role of oxidized PUFA fragments as a control parameter in driving bifurcation transitions.
• To analyze the emergence of limit cycles and stabilization via Shilnikov bifurcations in tumor cell populations.
• To establish a theoretical framework linking ferroptosis to nonlinear dynamical systems in cancer progression.

Proposed method

• Formulates a network model of ferroptosis in avascular and vascular tumor microenvironments.
• Applies the framework of nonlinear dynamics, specifically the supercritical Andronov-Hopf bifurcation, to model limit cycle emergence.
• Uses oxidized polyunsaturated fatty acid (PUFA) fragments as the primary control parameter in the system.
• Analyzes the inverse Feigenbaum scenario, involving a cascade of saddle-focus Shilnikov bifurcations.
• Models the transition from chaotic dynamics to stable oscillations as the control parameter increases.
• Employs bifurcation theory and dynamical systems analysis to characterize the phase transition in ferroptosis.

Experimental results

Research questions

• RQ1 How does ferroptosis in tumor growth manifest as a biological phase transition?
• RQ2 What dynamical mechanisms underlie the transition from chaotic to stable behavior in ferroptotic tumor cell populations?
• RQ3 How does the concentration of oxidized PUFA fragments influence the emergence of limit cycles in ferroptosis?
• RQ4 What role do Shilnikov bifurcations play in stabilizing ferroptosis dynamics?
• RQ5 In what way does the inverse Feigenbaum scenario explain the reduction in dynamical complexity during ferroptosis?

Key findings

• Ferroptosis in tumor growth is characterized as a first-order phase transition driven by a supercritical Andronov-Hopf bifurcation.
• The emergence of stable limit cycles indicates periodic oscillations in ferroptotic cell populations.
• An inverse Feigenbaum cascade of saddle-focus Shilnikov bifurcations is identified as the mechanism for system stabilization.
• Increasing oxidized PUFA fragments as a control parameter leads to a reduction in dynamical complexity.
• The system transitions from chaotic behavior to stable, periodic dynamics through successive bifurcations.
• The model provides a theoretical basis for understanding ferroptosis as a regulated, non-linear dynamical process in cancer.