  Spatial self-organization emerges in distributed systems exhibiting local
interactions when nonlinearities and the appropriate propagation of signals are
at work. These kinds of phenomena can be modeled with different frameworks,
typically cellular automata or reaction-diffusion systems. A different class of
dynamical processes involves the correlated movement of agents over space,
which can be mediated through chemotactic movement or minimization of cell-cell
interaction energy. A classic example of the latter is given by the formation
of spatially segregated assemblies when cells display differential adhesion.
Here we consider a new class of dynamical models, involving cell adhesion among
two stochastically exchangeable cell states as a minimal model capable of
exhibiting well-defined, ordered spatial patterns. Our results suggest that a
whole space of pattern-forming rules is hosted by the combination of physical
differential adhesion and the value of probabilities modulating cell phenotypic
switching, showing that Turing-like patterns can be obtained without resorting
to reaction-diffusion processes. If the model is expanded allowing cells to
proliferate and die in an environment where diffusible nutrient and toxic waste
are at play, different phases are observed, characterized by regularly spaced
patterns. The analysis of the parameter space reveals that certain phases reach
higher population levels than other modes of organization. A detailed
exploration of the mean-field theory is also presented. Finally we let
populations of cells with different adhesion matrices compete for reproduction,
showing that, in our model, structural organization can improve the fitness of
a given cell population. The implications of these results for ecological and
evolutionary models of pattern formation and the emergence of multicellularity
are outlined.
