Epidermal equivalents prepared with passaged keratinocytes are typically 10–20 μm thick, whereas intact human epidermis is up to 100 μm thick. Our established mathematical model of epidermal homeostasis predicted that the undulatory pattern of the papillary layer beneath the epidermis is a key determinant of epidermal thickness. Here, we tested this prediction by seeding human keratinocytes on polyester textiles with various fiber-structural patterns in culture dishes exposed to air, aiming to develop a more physiologically realistic epidermal model using passaged keratinocytes. Textile substrate with fiber thickness and inter-fiber distance matching the computer predictions afforded a three-dimensional epidermal-equivalent model with thick stratum corneum and intercellular lamellar lipid structure. The basal layer structure was similar to that of human papillary layer. Cells located around the textile fibers were proliferating, as indicated by BrdU and YAP (Yes-associated protein) staining and expression of melanoma-associated chondroitin sulfate proteoglycan. Filaggrin, loricrin, claudin 1 and ZO-1 were all appropriately expressed. Silencing of transcriptional coactivator YAP with siRNA disturbed construction of the three-dimensional structure. Measurement of trans-epidermal water loss (TEWL) indicated that the model has excellent barrier function. Our results support the idea that mathematical modeling of complex biological processes can have predictive ability and practical value.

We give an algebraic description of screw dislocations in a crystal, especially simple cubic (SC) and body centered cubic (BCC) crystals, using free abelian groups and fibering structures. We also show that the strain energy of a screw dislocation based on the spring model is expressed by the Epstein-Hurwitz zeta function approximately. Crystal lattice and screw dislocation and topological defect and monodromy and group ring of abelian group and dislocation energy and Epstein-Hurwitz zeta function 1.1. Notations and Conventions. Throughout the article, we distinguish the euclidean space E from the real vector space R: in particular, R is endowed with an algebraic structure, while E is not. We often identify the 2-dimensional euclidean space E 2 with the complex plane C. The group U(1) acts on the set S 1 simply transitively. Given a fiber bundle F → M over a base space M, we denote the set of all continuous sections f : M → F by Γ(M, F ). Screw Dislocations in Continuum PictureLet us consider the exact sequence of groups (see [B]) (2.1) 0

The skin barrier is provided by the organized multi-layer structure of epidermal cells, which is dynamically maintained by a continuous supply of cells from the basal layer. The epidermal homeostasis can be disrupted by various skin diseases, which often cause morphological changes not only in the epidermis but in the dermis. We present a three-dimensional agent-based computational model of the epidermis that takes into account the deformability of the dermis. Our model can produce a stable epidermal structure with well-organized layers. We show that its stability depends on the cell supply rate from the basal layer. Modeling the morphological change of the dermis also enables us to investigate how the stiffness of the dermis affects the structure and barrier functions of the epidermis. Besides, we show that our model can simulate the formation of a corn (clavus) by assuming hyperproliferation and rapid differentiation. We also provide experimental data for human corn, which supports the model assumptions and the simulation result.

The skin barrier is provided by the organized multi-layer structure of epidermal cells, which is dynamically maintained by a continuous supply of cells from the basal layer. The epidermal homeostasis can be disrupted by various skin diseases, which often cause morphological changes not only in the epidermis but in the dermis. We present a three-dimensional agent-based computational model of the epidermis that takes into account the deformability of the dermis. Our model can produce a stable epidermal structure with well-organized layers. We show that its stability depends on the cell supply rate from the basal layer. Modeling the morphological change of the dermis also enables us to investigate how the stiffness of the dermis affects the structure and barrier functions of the epidermis. Besides, we show that our model can simulate the formation of a corn (clavus) by assuming hyperproliferation and rapid differentiation. We also provide experimental data for human corn, which supports the model assumptions and the simulation result.