A multiscale hybrid mathematical model of epidermal-dermal interactions during skin wound healing.

Following injury, skin activates a complex wound healing programme. While cellular and signalling mechanisms of wound repair have been extensively studied, the principles of epidermal-dermal interactions and their effects on wound healing outcomes are only partially understood. To gain new insight into the effects of epidermal-dermal interactions, we developed a multiscale, hybrid mathematical model of skin wound healing. The model takes into consideration interactions between epidermis and dermis across the basement membrane via diffusible signals, defined as activator and inhibitor. Simulations revealed that epidermal-dermal interactions are critical for proper extracellular matrix deposition in the dermis, suggesting these signals may influence how wound scars form. Our model makes several theoretical predictions. First, basal levels of epidermal activator and inhibitor help to maintain dermis in a steady state, whereas their absence results in a raised, scar-like dermal phenotype. Second, wound-triggered increase in activator and inhibitor production by basal epidermal cells, coupled with fast re-epithelialization kinetics, reduces dermal scar size. Third, high-density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low-density fibrin clot leads to a hypotrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring. Taken together, our model predicts the important role of signalling across dermal-epidermal interface and the effect of fibrin clot density and wound geometry on scar formation. This hybrid modelling approach may be also applicable to other complex tissue systems, enabling the simulation of dynamic processes, otherwise computationally prohibitive with fully discrete models due to a large number of variables.

Diverse feather shape evolution enabled by coupling anisotropic signalling modules with self-organizing branching programme.

Adaptation of feathered dinosaurs and Mesozoic birds to new ecological niches was potentiated by rapid diversification of feather vane shapes. The molecular mechanism driving this spectacular process remains unclear. Here, through morphology analysis, transcriptome profiling, functional perturbations and mathematical simulations, we find that mesenchyme-derived GDF10 and GREM1 are major controllers for the topologies of rachidial and barb generative zones (setting vane boundaries), respectively, by tuning the periodic-branching programme of epithelial progenitors. Their interactions with the anterior-posterior WNT gradient establish the bilateral-symmetric vane configuration. Additionally, combinatory effects of CYP26B1, CRABP1 and RALDH3 establish dynamic retinoic acid (RA) landscapes in feather mesenchyme, which modulate GREM1 expression and epithelial cell shapes. Incremental changes of RA gradient slopes establish a continuum of asymmetric flight feathers along the wing, while switch-like modulation of RA signalling confers distinct vane shapes between feather tracts. Therefore, the co-option of anisotropic signalling modules introduced new dimensions of feather shape diversification.

Deciphering principles of morphogenesis from temporal and spatial patterns on the integument.

BACKGROUND: How tissue patterns form in development and regeneration is a fundamental issue remaining to be fully understood. The integument often forms repetitive units in space (periodic patterning) and time (cyclic renewal), such as feathers and hairs. Integument patterns are visible and experimentally manipulatable, helping us reveal pattern formative processes. Variability is seen in regional phenotypic specificities and temporal cycling at different physiological stages. RESULTS: Here we show some cellular/molecular bases revealed by analyzing integument patterns. (1) Localized cellular activity (proliferation, rearrangement, apoptosis, differentiation) transforms prototypic organ primordia into specific shapes. Combinatorial positioning of different localized activity zones generates diverse and complex organ forms. (2) Competitive equilibrium between activators and inhibitors regulates stem cells through cyclic quiescence and activation. CONCLUSIONS: Dynamic interactions between stem cells and their adjacent niche regulate regenerative behavior, modulated by multi-layers of macro-environmental factors (dermis, body hormone status, and external environment). Genomics studies may reveal how positional information of localized cellular activity is stored. In vivo skin imaging and lineage tracing unveils new insights into stem cell plasticity. Principles of self-assembly obtained from the integumentary organ model can be applied to help restore damaged patterns during regenerative wound healing and for tissue engineering to rebuild tissues. Developmental Dynamics 244:905-920, 2015. © 2015 Wiley Periodicals, Inc.