DOI: 10.5061/dryad.kd51c5bcv
title: Optimal mechanical interactions direct multicellular network formation on elastic substrates

description: Cells self-organize into functional, ordered structures during tissue
 morphogenesis, a process that is evocative of colloidal self-assembly into
 engineered soft materials. Understanding how intercellular mechanical
 interactions may drive the formation of ordered and functional
 multicellular structures is important in developmental biology and tissue
 engineering. Here, by combining an agent-based model for contractile cells
 on elastic substrates with endothelial cell culture experiments, we show
 that substrate deformation–mediated mechanical interactions between cells
 can cluster and align them into branched networks. Motivated by the
 structure and function of vasculogenic networks, we predict how measures
 of network connectivity like percolation probability and fractal dimension
 as well as local morphological features including junctions, branches, and
 rings depend on cell contractility and density and on substrate elastic
 properties including stiffness and compressibility. We predict and confirm
 with experiments that cell network formation is substrate stiffness
 dependent, being optimal at intermediate stiffness. We also show the
 agreement between experimental data and predicted cell cluster types by
 mapping a combined phase diagram in cell density substrate stiffness.
 Overall, we show that long-range, mechanical interactions provide an
 optimal and general strategy for multicellular self-organization, leading
 to more robust and efficient realizations of space-spanning networks than
 through just local intercellular interactions.
description: # Optimal mechanical interactions direct multicellular network formation
 on elastic substrates
 [https://doi.org/10.5061/dryad.kd51c5bcv](https://doi.org/10.5061/dryad.kd51c5bcv) This data set contains the data supporting the claims related to the title article. They are those, specifically, used to construct the figures seen throughout the main text. ## Description of the data and file structure The data will be parsed according to the figure in the main text to which they correspond. Figure 2 - Final configurations of the snapshots shown in figure 2. Columns from left to right indicate the x-position, y-position, and dipole angle for the nine stated parameter values as separate labeled sheets. Figure 3 - Percolation values in A - Packing Fraction (\phi) space for \nu = 0.1, \nu = 0.5, and sticky disks. Figure 4_b - Binary pixel intensity map for stiffness values 200Pa, 4.5kPa, and 10kPa. Figure 4_c - Experimental percolation values for sub-boxed images. Figure 5_Percolation_Exp - Experimental percolation distributions. Figure 5_ShapeFactor_Exp - Experimental shape factor distributions. Column 1 indicates size of cluster in pixels, column two is the corresponding SF value. Figure 5_ShapeFactorAvg_Sim - Average shape factor values from simulations in N-E space where A<sub>0</sub> = 18.1 and E* = 4.5kPa. Figure 6_ab - Branch length distributions in pixels for three runs of each parameter value. To obtain the corresponding plots in the paper, we first divide by 40 as this roughly corresponds to the size of a simulation cell. For distributions, we do not consider branches less than 40. Figure 6_c - Ring size distribution for characteristic configurations of four parameter values corresponding to systems on the shoulder of the percolation transition and those well past the transition for two different values of \nu. To obtain the corresponding plots in the paper, we first divide by 40<sup>2</sup> as 40 roughly corresponds to the size of a simulation cell. First column indicates ring label. Second column indicates enclosed area in pixels. Figure 6_d - Connectivity map for all nodes in the post skeletonized simulation images for the four parameters corresponding to systems on the shoulder of the percolation transition and those well past the transition for two different values of \nu. First and second column represent the x and y positions of a node, respectively. Third and fourth column represent the x and y positions, respectively, of a connected node. The fifth and sixth columns indicate the corresponding arc length and Euclidean length, respectively, of the branch connecting those nodes.