Chapter 10
Systems Biology Modeling of Nonlinear Cancer Dynamics
Christian Cherubini, Simonetta Filippi, and Alessandro Loppini
Abstract
Systems Biology represents nowadays a promising standard framework for natural and human sciences to
attack complicated problems involving Life. Here a particular application of such a program is discussed in
the case of Cancer, by using a basic toy model for solid tumor spread for framing together two apparently
different conceptual leading paradigms of Oncogenesis.
KeywordsCancer, Systems biology, Computational biology, Mathematical modeling1 Introduction
A quantitative description of Morphogenesis, i.e., the dynamical
process realizing development in living beings, is nowadays becom-
ing a central target not only for areas as Biology, Medicine, and
Chemistry but also for Biophysics, Biomathematics, and
Bioengineering.
Dating back from Darcy Thompson’s 1917 classic monograph
“On Growth and Form” [1] in fact a description of living beings in
geometrical (or in wider sense mathematical) terms has appeared to
be not only physically sound but also unavoidable. More recently,
systemic studies on plant morphogenesis (phyllotaxis) (seeref. 2 for
a review) have shown elegant cross bridges of group theory, geom-
etry, and number theory used to explain the elegant structures of
plants, in particular about seeds disposition and flower patterns.
Also, some populations of simple living systems as fungi and amoe-
bae form colonies whose aggregation shows complicated structures
with very high levels of complexity both in time and in space.
Similar patterns, often associated with spiral geometries, also appear
in many biological contexts as cardiac and neural dynamics for
instance [3, 4]. Strikingly, many of the phenomenologies above
depicted do not belong to the realm of Life only but are also
manifested by unanimated natural systems as oscillating chemical
reactions, atmospheric eddies, or growing crystals for instanceMariano Bizzarri (ed.),Systems Biology, Methods in Molecular Biology, vol. 1702,
https://doi.org/10.1007/978-1-4939-7456-6_10,©Springer Science+Business Media LLC 2018
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