Theoretical tool bridging cell polarities with development of robust morphologies

Abstract

Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development – gastrulation and the origins of folds and tubes – our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.

Model to link cell shape and polarity with organogenesis

“…To close this 37 gap we introduce a model of polarized cell-cell interactions where cells are treated as 38 point particles. As a starting point for our model, we consider the model suggested 39 in [20] which was used to study directional adhesion mediated by apical-basal (AB) 40 polarity and PCP. The model in [20], however, could not explicitly account for changes 41 in cell shapes.…”

“…As a starting point for our model, we consider the model suggested 39 in [20] which was used to study directional adhesion mediated by apical-basal (AB) 40 polarity and PCP. The model in [20], however, could not explicitly account for changes 41 in cell shapes. Here, we show that the effect of cell wedging can be modeled within a 42 point-particle representation by modifying cell-cell forces to favor a tilt in AB polarities.…”

“…Apical constriction leads to cell wedging and as a consequence the AB axes of neighboring cells become tilted towards the wedged cell ( Fig 1B-C). In [20] a flat epithelial sheet was modelled by a cell-cell interaction force favouring parallel AB polarities in neighboring cells ( Fig 1A, Eq 4). To model the effect of wedging we modify the force to favor AB polarity vectors p i in neighbor cells to tilt towards the wedged cell ( Fig 1B and 1C).…”

“…lungs and vascularization, where cells forming 241 the tubes also are the ones that secrete organizing signals that locally re-orient PCP 242 polarities and may induce anisotropic changes in cell shapes. Following [20], cells are treated as point particles interacting with neighboring cells through a pair-potential V ij . The potential has a rotationally symmetric repulsive term and a polarity-dependent attractive term.…”

“…The parameters λ i are coupling constants which define the strength of polar interactions 246 in the model. S ij (A) quantifies the coupling between AB polarity and position, whereas 247 S ij (AP ) and S(P ) ij quantify the coupling of PCP with AB and position, respectively, 248 as described in [20]. These couplings are formulated in in terms of AB vectors p i , PCP 249 vectors q i and a unit vectorr ij from cell i to j.…”