The Mechanistic Regulation of Pattern and Shape: A Systems Biology Approach

Abstract

During the development of a multicellular organism, cells must adopt both the proper fates and the correct spatial locations to form the various tissues and organs required for embryogenesis. However, understanding the dynamic mechanochemical feedback between patterning signals and morphological shape remains an open challenge. This dissertation developed mathematical models and machine learning techniques to investigate the interplay between pattern and shape in a variety of multicellular organisms. First, we developed and studied a continuous mathematical model of regulated differential cell-cell adhesion that can explain how changes in adhesion at the cellular level produce broad changes at the tissue level. This model 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. We then employed this modeling approach to explain the regulation of whole-body shape in the planarian flatworms via the feedback interaction between morphogen signals and tissue shapes during growth and degrowth. For this, we developed a machine learning pipeline to train this model of pattern and shape using standardized experimental data of planarian shape over time. We demonstrated that the trained model can recapitulate the precise dynamics of planarian whole-body proportions during growth. Furthermore, by varying only two constants controlling the signaling at the poles and the overall rate of cell apoptosis, the model dynamics can transition from growth to degrowth. Finally, we applied this model of regulated pattern and shape to understanding planarian regeneration. Using the same parameter scan technique that produced the correct parameters for degrowth simulation, we were able to find a parameter set that exhibits the general shape dynamics seen during the reshaping phase of planarian regeneration. Overall, we were able to produce the first dynamic mathematical model that includes the mechanochemical feedback between pattern and shape in planarians. This mathematical and computational approach can enable further advancements in understanding complex phenomena in biology where pattern and shape are intertwined, spanning the fields of regenerative, developmental, and cancer biology.