Structural characterization and statistical-mechanical model of epidermal patterns

Abstract

In proliferating epithelia of mammalian skin, cells of irregular polygonal-like shapes pack into complex nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct and Fourier spaces of the cell centroids in the early stages of embryonic development show structural directional dependence, while in the late stages the patterns tend towards statistically isotropic states. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-ranged soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. Our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. We discuss ways in which our model might be extended so as to better understand morphogenesis (in particular the emergence of planar cell polarity), wound-healing, and disease progression processes in skin, and how it could be applied to the design of synthetic tissues.

References in corpus (28)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Motility-driven glass and jamming transitions in biological tissues
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Mean field theory of hard sphere glasses and jamming
• Phase transition in the collective migration of tissue cells: experiment and model
• Self-organization in systems of self-propelled particles
• Active Jamming: Self-propelled soft particles at high density
• New upper bounds on sphere packings I
• A Superior Descriptor of Random Textures and Its Predictive Capacity
• Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb Lattice
• Designed Interaction Potentials via Inverse Methods for Self-Assembly
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Inverse design of simple pairwise interactions with low-coordinated 3D lattice ground states
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Self-assembly of the simple cubic lattice with an isotropic potential
• Improved reconstructions of random media using dilation and erosion processes
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Designed Diamond Ground State via Optimized Isotropic Monotonic Pair Potentials
• Inverse Statistical Mechanics: Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes
• Topological and geometrical disorder correlate robustly in two-dimensional foams
• Random close packing in protein cores
• A Cellular Automaton Model for Tumor Dormancy: Emergence of a Proliferative Switch
• Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings

Cited by in corpus (4)

• Hyperuniform States of Matter
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Multicellular actomyosin cables in epithelia under external anisotropic stress