  Gene expression patterns (GEPs) are established by cross-regulating target
genes that interpret morphogen gradients. However, as development progresses,
morphogen activity is reduced, leaving the emergent GEP without stabilizing
positional cues. The GEP then can be deteriorated by the intrinsically noisy
biochemical processes acting at the cellular level. However, the established
GEPs remain spatio-temporally stable in many biological systems. Here we
combine spatial-stochastic simulations with an enhanced sampling method
(Non-Stationary Forward Flux Sampling) and a recently developed stability
theory to address how spatiotemporal integrity of a GEP is maintained without
morphogen gradients. Using a minimal embryo model consisting of spatially
coupled biochemical reactor volumes, we study a stripe pattern in which weak
cross-repression between nearest neighbor domians alternates with strong
repression between next-nearest neighbor domains, inspired by the gap gene
system in the Drosophila embryo. We find that fine-tuning of the weak
repressive interactions to an optimal level increases temporal stability of
GEPs by orders of magnitude, providing stability over developmentally relevant
times, without morphogen gradients. The numerically determined optimal
parameter regime closely agrees with the predictions of the stability theory.
By analizing the dynamics of GEP asymmetry factors, we trace back the pattern
stability enhancement to the emergence of a metastable basin and restoring
forces that counteract pattern perturbations. The origin of these forces is
further explained by the effective model, describing the emergent deterministic
dynamics of the system. Altogether, we show that metastable attractors can
emerge as a property of stochastic GEPs even without system-wide positional
cues, provided that the gene regulatory interactions shaping the pattern are
optimally tuned.
