The emergence of spatial patterns and organized growth is a hallmark of developing tissues. While symmetry-breaking and scaling laws govern these processes, how cells coordinate spatial patterning with size regulation remains unclear. Here, we combine quantitative imaging, a Turing activator-repressor model with self-organized reactive boundaries, and in vitro models of early mouse development to study mesodermal pattern formation in two-dimensional (2D) gastruloids. We show that colony size dictates symmetry: small colonies (radius approximately 100 micrometers) spontaneously break symmetry, while larger ones remain centro-symmetric, consistent with size-dependent positional information and model predictions. The mesodermal domain area scales robustly with colony size following a power law, independent of cell density, indicating that cells sense and respond to gastruloid size. Time-lapse imaging reveals a biphasic growth law: an early power-law expansion followed by exponential arrest, marking a dynamical phase transition. These dynamics, conserved across sizes, reflect features of criticality seen in physical systems, where self-organization, scaling, and boundary feedback converge. Our findings uncover a minimal mechanism for size-dependent pattern formation and growth control. This framework enables quantitative investigation of symmetry-breaking and scaling in self-organizing tissues, offering insights into the physical principles underlying multicellular organization.

Protein sidechain conformation prediction, or packing, is a key step in many in silico protein modeling and design tasks. Popular protein packing methods typically rely on approximated energy functions and complex algorithms to search dense rotamer libraries. Inspired by the recent success of deep learning in protein modeling tasks, we present ZymePackNet, a graph neural network based protein packing tool that does not require a rotamer library, scoring functions or a search algorithm. We train regression models using protein crystal structures represented as graphs, which are employed sequentially to “germinate” the sidechain starting from atoms anchoring the protein backbone to the sidechains’ termini, followed by an iterative refinement stage. ZymePackNet is fast and accurate compared to state-of-the-art protein packing methods. We validate our model on three native backbone datasets achieving a mean average error of 16.6°, 24.1°, 42.1°, and 53.0° for sidechain dihedral angles ( χ 1 to χ 4 ). ZymePackNet captures complex physical interactions such as π stacking without explicitly accounting for it in the model; such effects are currently lacking in the energy terms used in traditional packing tools. Contact abmukho@vt.edu Supplementary information Supplementary data are available at Bioinformatics online.

The emergence of the anterior-posterior body axis during early gastrulation constitutes a symmetry-breaking event, which is key to the development of bilateral organisms, and its mechanism remains poorly understood. Two-dimensional gastruloids constitute a simple and robust framework to study early developmental events in vitro. Although spontaneous symmetry breaking has been observed in three dimensional (3D) gastruloids, the mechanisms behind this phenomenon are poorly understood. We thus set out to explore whether a controllable 2D system could be used to reveal the mechanisms behind the emergence of asymmetry in patterned cellular structures. We first computationally simulated the emergence of organization in micro-patterned mouse pluripotent stem cell (mPSC) colonies using a Turing-like activator-repressor model with activator-concentration-dependent flux boundary condition at the colony edge. This approach allows the self-organization of the boundary conditions, which results in a larger variety of patterns than previously observed. We found that this model recapitulated previous results of centro-symmetric patterns in large colonies, and also that in simulated small colony sizes, patterns with spontaneous asymmetries emerged. Model analysis revealed reciprocal effects between diffusion and size of the colony, with model-predicted asymmetries in small pattern sizes being dominated by diffusion, and centro-symmetric patterns being size-dominated. To test these predictions, we performed experiments on micro-patterned mPSC colonies of different sizes stimulated with Bone Morphogenetic Protein 4 (BMP4), and used Brachyury (BRA)-GFP expressing cells as pattern readout. We found that while large colonies showed centro-symmetric BRA patterns, the probability of colony polarization increased with decreasing sizes, with a maximum polarization frequency of 35% at ∼200μm. These results indicate that a simple molecular activator-repressor system can provide cells with collective features capable of initiating a body-axes plan, and constitute a theoretical foundation for the engineering of asymmetry in developmental systems.