Collective effects in cellular structure formation mediated by
compliant environments: a Monte Carlo study

I. B. Bischofs and U. S. Schwarz 

Acta Biomaterialia 2: 253-265 (2006)

Compliant environments can mediate interactions between mechanically
active cells like fibroblasts. Starting with a phenomenological model
for the behaviour of single cells, we use extensive Monte Carlo
simulations to predict non-trivial structure formation for cell
communities on soft elastic substrates as a function of elastic
moduli, cell density, noise and cell position geometry. In general, we
find a disordered structure as well as ordered string-like and
ring-like structures. The transition between ordered and disordered
structures is controlled both by cell density and noise level, while
the transition between string- and ring-like ordered structures is
controlled by the Poisson ratio. Similar effects are observed in three
dimensions. Our results suggest that in regard to elastic effects,
healthy connective tissue usually is in a macroscopically disordered
state, but can be switched to a macroscopically ordered state by
appropriate parameter variations, in a way that is reminiscent of
wound contraction or diseased states like contracture.