Epithelial Reticulum: Multiscale Tissue Dynamics

• Epithelial reticulum is a supracellular organization where interpenetrating networks of contracting (cycling/tensed) and expanding (non-cycling/compressed) cells create dynamic tissue heterogeneity.
• Mechanical models show that local rules—selective cell division, stiffness contrasts, and friction—are sufficient to generate the network morphologies seen in mature epithelia.
• Scale-free island statistics and topological defect dynamics reveal that tissue homeostasis is maintained through a balanced interplay of mechanical forces, adhesion, and proliferation.

Epithelial reticulum denotes a reticulated, supracellular organization of epithelial tissue in which network-scale structure emerges from coupled variations in proliferation, mechanics, adhesion, topology, and geometry. In recent work, the term has been used in a strict sense for a mature homeostatic architecture comprising two interpenetrating networks—regions of cycling and mechanically tensed cells, and islands of non-cycling and mechanically compressed cells—while related studies use reticulum-like or reticular morphologies to describe network structures generated by selective division rules, stiffness contrast, orientational order, and topological defects (Daraf et al., 20 Sep 2025, Madhikar et al., 2018). Across these usages, the common feature is that epithelial organization is not spatially uniform: it is a multiscale arrangement in which local cellular rules produce tissue-spanning network patterns.

1. Definition and core phenomenology

The most explicit contemporary formulation identifies an epithelial reticulum in mature, homeostatic epithelia as a supracellular structure that spans multiple scales of length and evolves dynamically during late maturation (Daraf et al., 20 Sep 2025). This reticulum consists of two interpenetrating networks: large regions of cycling and mechanically tensed cells, termed contracting cells, and islands of non-cycling and mechanically compressed cells, termed expanding cells. As the tissue matures and becomes more jammed, islands of expanding cells emerge and enlarge within a continuous ocean of contracting cells. The compressed islands grow in cell number but remain constrained in spatial spread, so the tissue develops regional heterogeneity without complete merger of the islands.

The two components of this reticulum are mechanically and proliferatively distinct. Contracting or tensed cells are larger in area, contract upon deadhesion, display a cortex-based actin cytoskeleton, and are more likely to be in S/G2/M phases. Expanding or compressed cells are smaller in pre-deadhesion area, expand upon deadhesion, possess an interior-based actin distribution, exhibit a higher nucleus-to-cell area ratio, and are typically cell-cycle inactive (Daraf et al., 20 Sep 2025). In this formulation, the reticulum is therefore not merely a geometric meshwork but a spatial partition of cell-cycle re-entry, cytoskeletal state, and mechanical load.

A recurrent misconception is that epithelial homeostasis is a uniform and static endpoint with minimal proliferation and motion. The quasi-critical reticulum contradicts that view by presenting homeostasis as a dynamic regional balance of compressive and tensile forces coupled to local proliferation dynamics (Daraf et al., 20 Sep 2025). A related, broader usage appears in mechanical modeling studies, where network-like epithelial architectures are produced without biochemical patterning, indicating that reticular morphology can emerge from biophysical rules alone (Madhikar et al., 2018).

2. Mechanical generation of reticular morphology

A direct mechanical route to reticulum-like epithelial organization is provided by the Cellular Discrete Element Model (CeDEM), which represents cells as polygons whose membranes are discretized into beads connected by springs of stiffness $K^\mathrm{spr}_i$ (Madhikar et al., 2018). Growth is governed by a growth pressure and a division threshold $A^{\mathrm{div}}$, and a cell divides when its area exceeds that threshold. Inter-cell forces are attractive and repulsive, determined by cell geometry and membrane stiffness, while membrane friction is modeled as

$\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$

Within CeDEM, division rules strongly affect tissue architecture. Division can be selective, for example by allowing only the most recently formed cells to divide, and the division plane can be random, parallel through generations, or systematically rotated (Madhikar et al., 2018). Parallel division planes generate linear or filamentous morphologies, whereas systematic rotation produces spiral or branched filament structures. The same framework therefore connects local geometric rules to large-scale epithelial patterning.

The model becomes explicitly reticular in bimodal mixtures of stiff and soft cells. Stiff cells are assigned membrane or cortex stiffness $K^\mathrm{spr}_1$ and a low growth potential, whereas soft cells have $K^\mathrm{spr}_2$ and a high growth potential. In an even mixture, soft cells proliferate rapidly and form the tissue matrix, while stiff cells are compressed into vein- or dendrite-like networks embedded in that matrix (Madhikar et al., 2018). For soft-cell inclusions in a stiff matrix, the soft population behaves like a tumor, outgrowing and compressing the surrounding stiff cells and gradually evacuating the matrix. Low friction accelerates this invasive growth; high friction slows growth, yields a more jammed and porous tissue, and can drive parts of the tumor to self-inflicted cell death under mechanical stress.

These results are significant because they show that mechanical properties alone—stiffness contrast, friction, growth potential, and division-plane orientation—are sufficient to produce matrix/network morphologies attributed to epithelial reticulum (Madhikar et al., 2018). The same study further reports that inter-cellular contact forces have an exponential tail in their statistical distribution, resembling force distributions in jammed soft matter systems, thereby placing reticular epithelial morphogenesis within a broader active-matter and jamming context.

3. Quasi-critical homeostasis and scale-free island statistics

In mature epithelial tissues, the reticulum assumes a specifically quasi-critical form. The size distribution $P(S)$ of compressed-cell islands follows a scale-free power law,

$P(S) \sim S^{-\alpha},$

with $\alpha \sim 1.5$ as the tissue matures (Daraf et al., 20 Sep 2025). This observation motivated the use of a computational model of percolating critical networks with preferential attachment, in which new expanding cells join existing islands in a biased manner. The model reproduces the observed power-law distributions and identifies a critical occupation fraction $P_c \sim 45\%$ of expanding cells, above which large islands would begin to merge.

Near this threshold, the average island size is analyzed with the finite-size scaling ansatz

$$S L^{-Y/v} = (P - P_c)^Y f\left( L^{-Y/v}/(P-P_c) \right),$$

where $A^{\mathrm{div}}$0 is the system length scale and $A^{\mathrm{div}}$1 and $A^{\mathrm{div}}$2 are critical exponents (Daraf et al., 20 Sep 2025). Experimentally, tissues remain just below $A^{\mathrm{div}}$3, which implies a quasi-critical regime close to but not crossing the percolation transition. In this regime, the reticulum achieves scale-free heterogeneity while avoiding merger of compressed-cell islands.

The dynamics of the reticulum are not fixed. Island growth is reversible under unjamming cues such as wounding, where compressed-cell islands diminish as the tissue relaxes and migratory contracting phenotypes predominate. Island growth is also detainable by cell cycle arrest treatment, including Thymidine treatment, which causes the fraction of compressed cells to stagnate (Daraf et al., 20 Sep 2025). These observations make the reticulum a dynamic state variable of epithelial maturation rather than a terminal static pattern.

A plausible implication is that quasi-criticality provides a mechanistic compromise between heterogeneity and integrity. The reported interpretation is that epithelial homeostasis is reframed as a dynamic regional balance of forces and proliferation, rather than as an equilibrium devoid of large-scale variation (Daraf et al., 20 Sep 2025).

4. Orientational order, p-atic structure, and topological defects

Reticular epithelial organization is also illuminated by liquid-crystalline descriptions of confluent epithelia. Experimental, analytical, and computational work on MDCK monolayers demonstrates that both nematic and hexatic order are present in epithelial layers, with hexatic order dominant at small length scales and nematic order dominant at larger scales (Armengol-Collado et al., 2022). The local $A^{\mathrm{div}}$4-fold symmetry of a cell shape is captured by the generalized shape function

$A^{\mathrm{div}}$5

and its coarse-grained counterpart

$A^{\mathrm{div}}$6

where averaging is performed over cells within a disk of radius $A^{\mathrm{div}}$7 (Armengol-Collado et al., 2022).

In MDCK GII cells on uncoated glass, the crossover between the two symmetries occurs at $A^{\mathrm{div}}$8 cell radii, of the order of ten cell sizes (Armengol-Collado et al., 2022). Short-scale organization resembles polycrystalline patchworks of sixfold orientation separated by chains of hexatic defects, whereas longer-scale organization forms chain-like cellular structures with smoothly varying 2-fold orientation and nematic disclinations. The corresponding decay of order parameter amplitudes obeys

$A^{\mathrm{div}}$9

with $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$0 and $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$1 in experiments (Armengol-Collado et al., 2022).

Topological defects provide a common language for these patterns. For a $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$2-fold field, defect strength is defined by

$\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$3

with charges quantized in units of $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$4 (Armengol-Collado et al., 2022). A later framework extends defect extraction directly from experimental images to a spectrum of p-atic symmetries using Minkowski tensors, with per-cell order described by $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$5, director orientation by $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$6, and order strength by $\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$7 (Happel et al., 2 Oct 2025). Defects are identified as intersections of the zero-level contours of

$\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$8

and their topological charge is measured by

$\vec{F}^\mathrm{ext}_i = -\mu \vec{v}_{ij}.$9

The principal consequence is that epithelia are not described by nematic order alone. All symmetries up to at least $K^\mathrm{spr}_1$0 generate defects in MDCK monolayers, and no strong positional or orientational correlations are found between nematic and hexatic defects (Happel et al., 2 Oct 2025). This resolves the earlier dilemma between nematic and hexatic interpretations by showing that multiple orders coexist, and suggests that reticular epithelial organization occupies a multiscale p-atic landscape rather than a single-symmetry phase (Armengol-Collado et al., 2022, Happel et al., 2 Oct 2025).

5. Adhesion-mediated force organization and topological remodeling

The mechanical coherence of epithelial reticulum depends strongly on cadherin-based intercellular adhesion. In primary mouse keratinocyte colonies, traction force microscopy shows that in the absence of cadherin-based adhesions, cells behave largely independently and traction forces extend throughout the colony, with high strain energy in both interior and peripheral regions (Mertz et al., 2012). When cadherin-based adhesions are strong, traction forces localize to the colony periphery, point radially inward, and the colony behaves as a cohesive contractile unit with little internal traction stress. Quantitatively, the distance from the colony edge required to capture 75% of the total strain energy, $K^\mathrm{spr}_1$1, is smaller in high-calcium colonies than in low-calcium colonies.

A minimal physical model accounts for this reorganization by treating each cell as a contractile elastic object coupled to its neighbors by springs of stiffness $K^\mathrm{spr}_1$2, representing cadherin junctions, and attached to a compliant substrate (Mertz et al., 2012). In the planar formulation,

$K^\mathrm{spr}_1$3

with constitutive stress

$K^\mathrm{spr}_1$4

and penetration length

$K^\mathrm{spr}_1$5

As $K^\mathrm{spr}_1$6 increases, traction and strain energy shift from internal junctions to the colony periphery. This establishes cadherin-based adhesion as a determinant of whether epithelial tissue behaves as a collection of mechanically independent units or as a unified reticular sheet.

Reticular organization is also topological in the sense of neighbor exchange and higher-order vertices. A dynamic vertex model with strain-dependent tension remodeling and mechanical memory dissipation shows how four-fold vertices and multicellular rosettes can be stabilized or resolved in epithelial tissues (Pérez-Verdugo et al., 2022). Vertex motion follows

$K^\mathrm{spr}_1$7

junction strain is

$K^\mathrm{spr}_1$8

and tension remodeling obeys

$K^\mathrm{spr}_1$9

with rest-length remodeling

$K^\mathrm{spr}_2$0

In this model, contraction-driven increases and extension-driven decreases in junction tension can transiently stabilize higher-order vertices, stalling T1 transitions, whereas memory dissipation through tension relaxation, strain relaxation, and stochastic fluctuations promotes their eventual resolution (Pérez-Verdugo et al., 2022). Tissue material state depends on remodeling rates and dissipation, with fluid-solid transitions controlled by $K^\mathrm{spr}_2$1 and cell shape index $K^\mathrm{spr}_2$2 increasing past the critical value $K^\mathrm{spr}_2$3 as $K^\mathrm{spr}_2$4 and $K^\mathrm{spr}_2$5 increase. These results are relevant to epithelial reticulum because they show how mechanical cohesion and topological lability can coexist: a tissue may be globally integrated by adhesion while remaining locally capable of rosette formation, delayed rearrangement, and controlled remodeling.

6. Curvature, defect-localized extrusion, and reticulum maintenance

In curved epithelial sheets, reticular maintenance is coupled to extrusion. A three-dimensional bubbly vertex model extends standard vertex models by allowing apical, basal, and lateral cell interfaces to be curved rather than flat (Drozdowski et al., 2024). The tissue energy is

$K^\mathrm{spr}_2$6

where $K^\mathrm{spr}_2$7, $K^\mathrm{spr}_2$8, and $K^\mathrm{spr}_2$9 are apical, basal, and lateral surface tensions, and $P(S)$0, $P(S)$1, and $P(S)$2 are the corresponding cell-surface areas. With fixed cell volume and curved interfaces, the model captures energetic effects absent from flat-face vertex descriptions.

The principal finding is a generic bulging instability at topological defects that is much stronger than in standard vertex models (Drozdowski et al., 2024). Pentagonal and heptagonal defects localize Gaussian curvature, making these sites especially susceptible to bulging and extrusion. Analytical energy calculations show that extrusion is energetically preferred at topological defects because Gaussian curvature is redistributed into the defect. This preference can be driven by a decrease in apico-basal tension or by contractile line tensions, while luminal pressure and interfacial bending rigidity suppress bulging and extrusion.

The mean-field theory includes a Gaussian-curvature contribution

$P(S)$3

and a contractile line-tension term $P(S)$4 for a ring-like actomyosin cable at the basal circumference (Drozdowski et al., 2024). Pentagonal defects extrude at higher $P(S)$5 than hexagons, indicating that less reduction in surface energy is needed to stabilize bulged or extruded states at defects. Simulation results further show that increased luminal pressure unfolds bulged pentagonal defects and reduces the opening-angle distinction between defect and non-defect cells.

For epithelial reticulum, the significance of these results is that curved, defect-bearing sheets possess built-in sites for controlled cell loss. In reticular or network-like epithelia, curvature and topology can therefore contribute directly to homeostasis by coupling geometric weak spots to extrusion, density regulation, and shape maintenance (Drozdowski et al., 2024).

7. Conceptual synthesis and open directions

Taken together, current work suggests that epithelial reticulum is best understood as a multiscale organizational state rather than a single morphological motif. At one level, it is a supracellular pattern of interpenetrating cycling/tensed and non-cycling/compressed domains poised just shy of percolation criticality (Daraf et al., 20 Sep 2025). At another, it is a mechanically generated network morphology arising from stiffness contrasts, division rules, and friction in proliferating tissues (Madhikar et al., 2018). Additional layers of description come from p-atic order and defect structure, cadherin-mediated force localization, rosette dynamics, and curvature-driven extrusion (Armengol-Collado et al., 2022, Happel et al., 2 Oct 2025, Mertz et al., 2012, Pérez-Verdugo et al., 2022, Drozdowski et al., 2024).

Several common themes recur across these frameworks. First, epithelial tissues are regionally heterogeneous even in states traditionally labeled homeostatic. Second, mechanical variables—tension, compression, adhesion, friction, and curvature—are not secondary constraints but primary organizers of tissue architecture. Third, defects and higher-order topologies are constructive elements of epithelial organization rather than mere irregularities. Fourth, the reticulum remains dynamically reversible under perturbations such as unjamming or cell-cycle arrest, indicating that it is maintained by ongoing balance rather than fixed patterning (Daraf et al., 20 Sep 2025).

A frequent oversimplification is to reduce epithelial organization to nematic order, to uniform homeostasis, or to a static honeycomb topology. The accumulated evidence instead supports a richer picture: mature epithelia host a spectrum of p-atic symmetries, quasi-critical island statistics, tunable higher-order vertices, and defect-localized extrusion, all within mechanically cohesive sheets (Armengol-Collado et al., 2022, Happel et al., 2 Oct 2025, Pérez-Verdugo et al., 2022, Drozdowski et al., 2024). This suggests that epithelial reticulum is a general descriptor for network-scale epithelial self-organization in which proliferation, active stress, orientational order, and topology are jointly regulated across scales.