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Cell-cell adhesion is essential for tissue growth and multicellular pattern formation, and crucial for the cellular dynamics during embryogenesis and cancer progression. Understanding the dynamical gene regulation of cell adhesion molecules (CAMs) responsible for the emerging spatial tissue behaviors is a current challenge due to the complexity of these non-linear interactions and feedback loops at different levels of abstraction-from genetic regulation to whole-organism shape formation. Continuous mathematical models of cell adhesion are ideal for the modeling of the spatial dynamics of large cell populations, where different cell types define inherent adhesion strengths. However, biologically the adhesive properties of the cell arise dynamically from differential expression of CAMs, which are precisely regulated during development and cancer progression. To extend our understanding of cell and tissue behaviors due to the regulation of adhesion molecules, here we present a novel model for the spatial dynamics of cellular patterning, growth, and shape formation due to the differential expression of CAMs and their regulation.Capturing the dynamic interplay between genetic regulation, CAM expression, and differential cell adhesion, the proposed continuous model can recapitulate the complex and emergent spatial behaviors of cell populations that change their adhesion properties dynamically due to inter-and intracellular genetic regulation. This approach can demonstrate the mechanisms responsible for classical cell sorting behaviors, cell intercalation in proliferating populations, and the involution of germ layer cells induced by a diffusing morphogen during gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way towards understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.

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