1. Stable developmental patterns of gene expression without morphogen gradients.
- Author
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Majka, Maciej, Becker, Nils B., ten Wolde, Pieter Rein, Zagorski, Marcin, and Sokolowski, Thomas R.
- Abstract
Gene expression patterns in developing organisms are established by groups of cross-regulating target genes that are driven by morphogen gradients. As development progresses, morphogen activity is reduced, leaving the emergent pattern without stabilizing positional cues and at risk of rapid deterioration due to the inherently noisy biochemical processes at the cellular level. But remarkably, gene expression patterns remain spatially stable and reproducible over long developmental time spans 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 gene expression pattern is maintained in developing tissue lacking morphogen gradients. Using a minimal embryo model consisting of spatially coupled biochemical reactor volumes, we study a prototypical stripe pattern in which weak cross-repression between nearest neighbor expression domains alternates with strong repression between next-nearest neighbor domains, inspired by the gap gene system in the Drosophila embryo. We find that tuning of the weak repressive interactions to an optimal level can prolong stability of the expression patterns by orders of magnitude, enabling stable patterns over developmentally relevant times in the absence of morphogen gradients. The optimal parameter regime found in simulations of the embryo model closely agrees with the predictions of our coarse-grained stability theory. To elucidate the origin of stability, we analyze a reduced phase space defined by two measures of pattern asymmetry. We find that in the optimal regime, intact patterns are protected via restoring forces that counteract random perturbations and give rise to a metastable basin. Together, our results demonstrate that metastable attractors can emerge as a property of stochastic gene expression patterns even without system-wide positional cues, provided that the gene regulatory interactions shaping the pattern are optimally tuned. Author summary: Embryonic development requires the formation of gene expression patterns that locally specify distinct cell fates. In order to provide positional information reliably to the developing cells, these patterns have to remain stable for required time periods. However, gene-expression patterns are created by intrinsically noisy biochemical processes, and moreover employ mutually repressive interactions for generating their shapes. It is therefore a priori unclear if they can remain stable autonomously, without control by external cues to prevent their gradual disintegration in time. In this work, we combine mathematical theory and spatial-stochastic simulations to assess for how long initially well-formed multi-gene expression patterns can persist in the absence of external control inputs. We find that pattern persistence times can be dramatically increased when the repressive mutual interactions between the genes are optimally tuned. We trace this stability enhancement back to the emergence of effective restoring forces that create a metastable basin in the state space of the system. The optimal regime found via simulations is confirmed by our mathematical theory of stability of expression boundaries. Our work demonstrates that when properly tuned, alternating cross-repression suffices to stabilize positional gene expression patterns to ensure accurate development. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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