Systems Biology (Methods in Molecular Biology)

Modeling may ultimately help recognizing critical factors and steps
in promoting tumor reversal.
Two methodological directions are conceivable. Firstly, applied
mathematics for identifying and measuring theattractor manifolds
for different equilibria by extrapolating information from experi-
mental data. In that respect, the mathematical formulation of the
biological problem helps in facilitating measurement quantifica-
tions rather than its qualification. Secondly, real-time multi-scale
modeling to give evidence of phenomena with cumulative effects,
for example models withmemory termsand search forprecursive
factorsto phase-space transitions. That approach can be performed
at all description levels, from cells to organs passing through tissues,
in order to induce medical actions starting from the theoretical
analysis of precursive factors before the system moves too far from

stable state B

(pre-cancer)

stable state A

(normal)

metastable stage

MET

EMT

a

b

Fig. 1The EMT-MET schema. (a) Inflammatory stimulus and myo-Ins treatment
effects on the EMT-MET process. (b) An intermediate metastable state is
necessary to accomplish a phase transition

Mathematical Modeling of Phase Transitions in Biology 101