The physics of heterogeneity and cancer initiation.
Physicists and mathematicians view cells as high dimensional complex
systems94,95 with thousands of genes involved in gene
regulatory networks. According to the framework of high dimensional
complex systems, interactions of gene regulatory networks in cells could
result in multiple possible states. Out of the multiple possible
configurations, the stable states are called ‘Attractors’, and
multipotent cells differentiate into one of these stable
states95–97. Cancer may be viewed as the change in
cell state from a normal state to an aberrant state98.
Stochastic variations may provide cells with the impetus needed to
overcome the potential barrier required for a state-change. For
instance, heterogeneity is high at tissue boundaries, and tissues
boundaries are also tumour hotspots in Squamous cell
carcinoma61.
In the framework of chaotic systems, cancer progression is seen as a
change in the type of attractor, from the Torus attractor (see box 1) in
premalignant lesions to the strange attractor (See box 1) in advanced
stages of cancer, resulting in chaos98,99 (see box).
The change in the type of attractor is accompanied by
period-doubling(see box) and sequential bifurcations(see box), and cells
are able to adopt multiple aberrant metastable states as a result, which
is proposed as Box 1: Glossary explaining the common
vocabulary associated with nonlinear dynamic systems and chaotic theory
an alternative explanation for Intra tumor
heterogeneity98,99. The transition due to these
bifurcations is seen as an abrupt change in the state of the complex
system, which may be predicted by Early Warning Signals(EWS). EWS (see
box 1)have been detected in cell-fate determination of multipotent blood
progenitor cells96, and studies have suggested the use
EWS for the early detection of colorectal Cancer100and breast cancer101.
Another characteristic of complex non-linear dynamic systems is
self-repeating fractal patterns. They are fractional dimensional
structures that appear similar at different magnification levels and are
a common theme in nature, observed in snowflakes, coastlines, and
branching neurons. Fractal patterns have also been reported in tumour
growth patterns, and studies have used fractal dimension as an indicator
of tumour malignancy and carcinogenesis98,102,103.