Tissue regeneration and development involves activities in multiple scales: gene, growth factor, cell, and tissue. As an example for regeneration, in wound healing process, the tissue recovery is achieved by cell hyper-proliferation and cell movement through regulations of growth factors. Early embryo development, as an example for development, the overall embryo spatial organization depends on cell movement regulated by cell-cell adhesion genes while cell differentiation is controlled by cell fate genes. In order to study interplay among those scales, multi-scale hybrid models are developed to incorporate gene and cell information, and their emergent dynamics in tissue development and regeneration.
In chapter 2, I established a model to study skin wound healing, which focuses on mechanisms to reduce scar after wound, especially the epidermis-dermis interaction. Each individual cell in epidermis is modeled discretely using Subcellular Element Method (SEM) to study the heterogeneous cell activities, whereas the cells and extracellular matrix (ECM) in dermis are modeled by partial differential equations (PDE) in continuum. To systematically study the role of signaling factors produced by cells, the model incorporate the signaling factors in continuum as well. In further, to study the interface between discrete epidermis and continuum dermis and their interaction, the interface is modeled using Level Set Method (LSM). The model makes several predictions: First, the signaling factors in both epidermis and dermis are essential to maintain dermal stability; Second, wound-triggered increase production of signaling factors in epidermis and fast re-epithelialization kinetics reduce wound size; Third, high density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low density fibrin clot leads to a hypertrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring.
In Chapter 3, to study pattern formation of early embryo development, I created a data-informed multi-scale model to reveal the time evolution of gene expression and spatial arrangement in single cell level, allowing us to study both the mechanisms and the effective times of the mechanisms. The cells are modeled in SEM to study the heterogeneity, and the gene expressions of each cell are modeled by stochastic differential equations (SDE). Analysis on single cell RNA sequencing data both validates modeled gene expression and calibrates coefficients for physical cellular interactions in the model. The model discovered that an Epha4/Ephrinb2 gene driven cell adhesion between epiblast (EPI) and primitive endoderm (PE) ensures spatial embryo organization; a good time window for gene regulation involving fibroblast growth factor (FGF) is essential for cell to change cell fate into EPI and PE successfully.