Control of patterning in human pluripotent stem cell colonies via a Turing system with reactive boundaries

During early stages of gastrulation, cells differentiate and organize into well-defined structures that lead to the emergence of the 3-germ layers, which represent early progenitors of precursor tissues for all the body organs.
Recently, in-vitro studies using human pluripotent stem cells (hPSC) in confined environments have shown the emergence of spatially organized markers of an early gastrulation-like state following induction by the bone morphogenetic protein 4 (BMP4), thus providing a framework to understand, and ultimately control, collective self-organization and pattern formation in hPSC.
We present minimal Turing system that is consistent with hPSC patterns observed in 2- and 3-D structures. Our approach considers that the morphogen flux at the colony boundaries is morphogen-concentration dependent (a so-called reactive boundary). Using this framework, we have quantified the effective transport dynamics of the morphogen BMP4 in hPSC colonies, and defined conditions that predict pattern properties such as marker spatial order, domain size and thresholds for symmetry-breaking events. This work presents a general framework for self-organized pattern formation that explain observed patterns in hPSC colonies, leading to a design-based specification of collective cell behavior.