Cancer as a dynamical phase transition

Abstract

This paper discusses the properties of cancer cells from a new perspective based on an analogy with phase transitions in physical systems. Similarities in terms of instabilities and attractor states are outlined and differences discussed. While physical phase transitions typically occur at or near thermodynamic equilibrium, a normal-to-cancer (NTC) transition is a dynamical non-equilibrium phenomenon, which depends on both metabolic energy supply and local physiological conditions. A number of implications for preventative and therapeutic strategies are outlined.

Figure 1

Schematic diagram of external effects on cancel cell instabilities.

Figure 2

Illustrations comparing structural changes in biological and physical systems undergoing phase transitions. Comparison between (a) an epithelial-to-mesenchymal (ETM) phase transition, and (b) phase transitions between solids, liquids, and gases [27].

Figure 3

Potential energy landscapes of the normal-to-cancer (NTC) phase transition model. The free energy function F(x) = x⁴ + 3x³ + ax² of the order parameter x is plotted with different values for the control parameter a.

Figure 4

Phase portraits for the normal-to-cancer (NTC) phase transition model. Phase portraits for four different values of a. Panel A shows a = -50, E = -700, -400, 0, 300. Panel B shows a = -10, E = -30, -10, 0, 100. Panel C shows a = 0, E = 0, 100, 300. Panel D shows a = 50, E = 0, 300, 700.