Interfacial energy constraints are sufficient to align cells over large distances

During development and wound healing, cells need to form long-ranged ordered structures to ensure precise formation of organs and repair damage. This requires cells to locate specific partner cells to which to adhere. How such cell matching reliably happens is an open problem, particularly in the presence of biological variability. Here, we use an equilibrium energy model to simulate how cell matching can occur with subcellular precision. A single parameter - encapsulating the competition between selective cell adhesion and cell compressibility - can reproduce experimental observations of cell alignment in the Drosophila embryonic heart. This demonstrates that adhesive differences between cells (in the case of the heart, mediated by filopodia interactions) are sufficient to drive cell matching without requiring cell rearrangements. The biophysical model can explain observed matching defects in mutant conditions and when there is significant biological variability. We also demonstrate that a dynamic vertex model gives results consistent with the equilibrium energy model. Overall, this work shows that equilibrium energy considerations are consistent with observed cell matching in cardioblasts, and has potential application to other systems, such as neuron connections and wound repair. Statement of SignificanceCells often need to identify specific neighboring cells, such as during wound repair and forming neural connections. Here, we develop a biophysical model of such cell-cell interactions within the context of the developing heart. We demonstrate that precise cell matching can occur by minimizing the energy costs of interfacial interactions. This model can explain a breadth of experimental observations despite it being a steady-state approximation of a dynamic system. This opens the possibility that such approaches may be applicable to other systems, providing a powerful yet simple framework for understanding cell matching.