Zhihui Wang - US grants

The structure of the developing mammary gland is regulated by stimulatory and inhibitory epithelial-epithelial and epithelial-stromal cell interactions (e.g., signaling, adhesion). While mammary developmental biologists have gathered a wealth of molecular and cellular data, fundamental questions remain. For example, it is still unknown how cells of various types become organized into a duct. How is the organization affected by system perturbations such as altered signaling processes? The answers to these questions rely on an understanding of signaling and behavioral "rules" governing normal ductal morphogenesis and maintenance. Experimental investigations of these interactions, complemented by mathematical models, can help facilitate the understanding and definition of these rules. In this project, the investigators employ a joint experimental and mathematical modeling approach to study mammary gland development with a focus on ductal morphogenesis. With respect to cellular and tissue level parameters, the investigators design specific experiments to measure model parameters and validate model results. Particular emphasis will be placed on the nature of the signaling vs. receiving cell type(s). In parallel, the complementary expertise will be leveraged and used to develop a multiscale mathematical and computational framework to bridge the gap between tissue scale models of ductal morphogenesis and cellular scale models with detailed cell arrangements. This integrative project will allow for predicting what occurs in response to system perturbations such as loss-of-function due to mutations or epigenetic events. This can provide insight on the emergence of abnormal development programs and the initiation of tumors. The methods developed here will be applicable to modeling other organs with branching architectures such as lung, salivary, olfactory epithelium and prostate glands. Beyond these applications, the new tools developed here will also impact other problems in the biological sciences including development of other tissues and organs, wound healing, and tissue regeneration that are characterized by processes occurring in concert over a wide range of space and time scales.

One of the fundamental questions in biology is how tissues and organs develop and become organized. Developmental processes are the result of complex mechanical and signaling processes occurring inside and outside cells, and between cells and the environment. Such complex processes are very difficult to understand by using conventional experiment-based approaches alone. Recently, it has been recognized that mathematical modeling can provide a unique and complementary tool to experimental investigations by generating experimentally testable hypotheses, and that an integrated experimental and computational approach can potentially be more powerful than solely using experimental investigation, in identifying mechanisms responsible for non-intuitive developmental behavior frequently observed in experiments. However, the developmental processes involve interactions across a wide range of spatial and temporal biological scales. Thus, new mathematical models describing biological behavior at different scales, and at different levels of complexity, should be developed, linked together, and experimentally validated to provide a theoretical predictive framework to complement current developmental biology research. This is precisely what this project will address in the context of the mammary gland, for which it is still unknown how the cells of various types become organized and how this organization is affected by perturbations to the system such as from mutations. Specifically, these questions will be addressed by drawing on the complementary expertise of the researchers in mathematical and computational modeling and in experimental techniques to create and analyze a multiscale modeling framework for mammary gland development. The parameters in the models will be measured, and the models will be validated, using specifically designed experiments. The integrative work presents a necessary first step towards further development of a comprehensive, multiscale computational framework capable of accurately predicting the development of normal and abnormal mammary gland morphologies.

The complexity of tumor growth, which involves interactions within cells, among cells, and between cells and their environment, calls for development of mathematical and computational models that can connect processes from the cell, and sub-cell scales, to tissue level scales. These methods are needed to help tumor biologists gain further insight into the underlying mechanisms of the processes (e.g., proliferation, differentiation, and migration) involved in tumor development, at the scales which influence their behavior. Because of this complexity, it has been challenging to functionally link cell and tissue scale processes, the knowledge of which is key to development of predictive multiscale tumor models. However, current models typically use ad-hoc rules to bridge between scales, which limits their predictive capability. This project will address this challenge by developing a new multiscale method where directly measurable quantities at the cell-scale inform the model parameters at the continuum tissue scale through rigorous, mathematical upscaling techniques. The multiscale model will be tested and validated by comparing simulation results against experimentally obtained information about the overall growth rates and spatiotemporal behaviors of the different cells and tumors. The new multiscale method will be used to study pancreatic tumors to elucidate the transition of pancreatic lesions into invasive pancreatic ductal adenocarcinoma (PDAC). By integrating patient data analysis with quantitative tumor modeling, the project will develop reliable methods that can predict the likelihood of pancreatic cyst progression to PDAC using relatively non-invasive approaches.

The project team will develop a new class of multiscale models that bridge these scales non-phenomenologically through application of rigorous upscaling techniques in order to close the continuum equations at the tissue scale and provide an accurate description of the processes across both cell and tissue scales. Specifically, stochastic agent-based models at the cell-scale and continuum partial differential equation models at the tissue-scale will be developed. Consistent functional relationships between the variables at the tissue-scale and measurements at the cell-scale will be found by upscaling the discrete models by using and extending the framework of dynamic density functional theory (DDFT) to obtain multi-cell scale continuum equations that account for correlations among cells as well as biological processes such cell birth and death. Further upscaling to the tissue scale will be done by identifying and deriving equations for slowly varying variables. The consistency of the different models in domains where the scales overlap will be tested and validated. The new multiscale method will be applied to model the progression of pancreatic neoplasms into invasive carcinomas in order to estimate the probability of this progression. Large-scale human patient datasets of pancreatic lesions, provided by our consultants through a separately funded project, will be used to validate and refine the models. The project will enhance the cross disciplinary training of students.