Directing multicellular organization by varying the aspect ratio of soft hydrogel microwells

Multicellular organization with precise spatial definition is an essential step in a wide range of biological processes, including morphogenesis, development, and healing. Gradients and patterns of chemoattractants are well-described guides of multicellular organization, but the influences of three-dimensional geometry of soft hydrogels on multicellular organization are less well defined. Here, we report the discovery of a new mode of self-organization of endothelial cells in ring-like patterns on the perimeters of hydrogel microwells that is independent of protein or chemical patterning and is driven only by geometry and substrate stiffness. We observe quantitatively striking influences of both the microwell aspect ratio (ε = perimeter/depth) and the hydrogel modulus. We systematically investigate the physical factors of cells and substrates that drive this multicellular behavior and present a mathematical model that explains the multicellular organization based upon balancing extracellular and cytoskeletal forces. These forces are determined in part by substrate stiffness, geometry, and cell density. The force balance model predicts the direction and distance of translational cell migration based on the dynamic interaction between tangential cytoskeletal tension and cell-cell and cell-substrate adhesion. We further show that the experimental observations can be leveraged to drive customized multicellular self-organization. Our observation of this multicellular behavior demonstrates the importance of the combinatorial effects of geometry and stiffness in complex biological processes. It also provides a new methodology for direction of cell organization that may facilitate the engineering of bionics and integrated model organoid systems.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute–surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute–surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil–water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute–surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity—suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute–surface interactions.

Theory of mechano-chemical patterning and optimal migration in cell monolayers

Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics [1], pattern formation [2] and active turbulence [3]. However, how mechanical and chemical signaling are integrated at the cellular level to give rise to such collective behaviors remains unclear. We address this by focusing on the highly conserved phenomenon of spatio-temporal waves of density [2, 4–8] and ERK/MAPK activation [9–11], which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechano-chemical coupling between three-dimensional active cellular tensions and the mechano-sensitive ERK/MAPK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce migration in a desired orientation, and we determine a theoretically optimal pattern for inducing efficient collective migration fitting well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatio-temporal instabilities and the design principles of robust and efficient long-ranged migration.