Abstract Background Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models. Results We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture. Conclusions We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

Background: Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models. Results: We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture. Conclusions: We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

The mammalian skin epidermis is a stratified epithelium composed of multiple layers of epithelial cells that exist in appropriate sizes and proportions, and with distinct boundaries separating each other. How the epidermis develops from a single layer of committed precursor cells to form a complex multilayered structure of multiple cell types remains elusive. Here, we construct stochastic, three-dimensional, and multiscale models consisting of a lineage of multiple cell types to study the control of epidermal development. Symmetric and asymmetric cell divisions, stochastic cell fate transitions within the lineage, extracellular morphogens, cell-to-cell adhesion forces, and cell signaling are included in model. A GPU algorithm was developed and implemented to accelerate the simulations. These simulations show that a balance between cell proliferation and differentiation during lineage progression is crucial for the development and maintenance of the epidermal tissue. We also find that selective intercellular adhesion is critical to sharpening the boundary between layers and to the formation of a highly ordered structure. The long-range action of a morphogen provides additional feedback regulations, enhancing the robustness of overall layer formation. Our model is built upon previous experimental findings revealing the role of Ovol transcription factors in regulating epidermal development. Direct comparisons of experimental and simulation perturbations show remarkable consistency. Taken together, our results highlight the major determinants of a well-stratified epidermis: balanced proliferation and differentiation, and a combination of both short- (symmetric/asymmetric division and selective cell adhesion) and long-range (morphogen) regulations. These underlying principles have broad implications for other developmental or regenerative processes leading to the formation of multilayered tissue structures, as well as for pathological processes such as epidermal wound healing.

Understanding the epigenetic mechanisms that control the activation of adult stem cells holds the promise of tissue and organ regeneration. Hair follicle stem cells have emerged as a prime model to study stem cell activation. Wnt/β-catenin signaling controls multiple aspects of skin epithelial regeneration, with its excessive activity promoting the hyperactivation of hair follicle stem/progenitor cells and tumorigenesis. The contribution of chromatin factors in regulating Wnt/β-catenin pathway function in these processes is unknown. Here, we show that chromatin effector Pygopus homolog 2 (Pygo2) produced by the epithelial cells facilitates depilation-induced hair regeneration, as well as β-catenin-induced activation of hair follicle stem/early progenitor cells and trichofolliculoma-like skin hyperplasia. Pygo2 maximizes the expression of Wnt/β-catenin targets, but is dispensable for β-catenin-mediated expansion of LIM/homeobox protein Lhx2(+) cells, in the stem/early progenitor cell compartment of the hair follicle. Moreover, β-catenin and Pygo2 converge to induce the accumulation and acetylation of tumor suppressor protein p53 upon the cell cycle entry of hair follicle early progenitor cells and in cultured keratinocytes. These findings identify Pygo2 as an important regulator of Wnt/β-catenin function in skin epithelia and p53 activation as a prominent downstream event of β-catenin/Pygo2 action in stem cell activation.

During epithelial tissue morphogenesis, developmental progenitor cells undergo dynamic adhesive and cytoskeletal remodeling to trigger proliferation and migration. Transcriptional mechanisms that restrict such a mild form of epithelial plasticity to maintain lineage-restricted differentiation in committed epithelial tissues are poorly understood. Here, we report that simultaneous ablation of transcriptional repressor-encoding Ovol1 and Ovol2 results in expansion and blocked terminal differentiation of embryonic epidermal progenitor cells. Conversely, mice overexpressing Ovol2 in their skin epithelia exhibit precocious differentiation accompanied by smaller progenitor cell compartments. We show that Ovol1/Ovol2-deficient epidermal cells fail to undertake α-catenin-driven actin cytoskeletal reorganization and adhesive maturation and exhibit changes that resemble epithelial-to-mesenchymal transition (EMT). Remarkably, these alterations and defective terminal differentiation are reversed upon depletion of EMT-promoting transcriptional factor Zeb1. Collectively, our findings reveal Ovol-Zeb1-α-catenin sequential repression and highlight Ovol1 and Ovol2 as gatekeepers of epithelial adhesion and differentiation by inhibiting progenitor-like traits and epithelial plasticity.