John Lowengrub (University of California, Irvine)
Multiscale models of complex biological systems: Growth, patterning and morphogenesis
Complex biological systems such as developing tissues and growing tumors are characterized by nonlinear interactions among many dynamic components. Therefore, it is now clear more than ever that relying on experimental tools alone to understand these complex systems is not sufficient — mathematical, statistical, and computational approaches are becoming increasingly indispensable. In this course, we will develop and analyze mathematical models of selected complex biological and biomedical systems and show how these models can be simulated numerically. We demonstrate how to constrain and calibrate the models using experimental data and how both the models and their solutions provide insight into biological and biomedical systems. A major challenge in such studies is to properly integrate information across multiple scales that is increasingly more feasible to collect from experiments. We will discuss this point as well as advantages and disadvantages of various modeling approaches, which point the way to future studies.
Lecture 1. Image-based modeling. Here, we focus on Fisher-Kolmogorov-based models that can account for proliferation, invasion, deformation and mass effects. We apply the models to brain tumors and we demonstrate how multimodal medical scans can be used to calibrate the models. We discuss how the models can be personalized and can be used for treatment planning.
Lecture 2. Multiscale model development. Here, we discuss strategies for coarse-graining systems of individual cells to obtain continuum models at a variety of scales by borrowing ideas from statistical physics, materials science and applied mathematics. We present continuum models at the cell scale and demonstrate how to obtain new continuum models at the tissue-scale with parameters that can be directly obtained from cell scale measurements. We relate the new systems with previously developed models.
Lecture 3. Multiscale models of morphogenesis. The regulation of cell division, cell sizes and cell arrangements is central to tissue growth and morphogenesis. Here, we discuss mathematical modeling approaches of tissue morphogenesis. We account for feedback regulation of cell lineage progression and demonstrate how the emergence of patterned growth from which sharply-demarcated buds and fingers readily emerge, either spontaneously or in response to transient external signals.
Lecture 4. Multiscale models of tumor growth. Cancer arises in cells that are actively engaged in collective, coordinated, and tightly controlled behaviors that have been exquisitely tailored to ensure reliable size control, homeostasis, and response to injury. Many of the distinctive characteristics of cancers result from the fact that transformed cells continue to be bound by constraints and rules associated with such collective behaviors, even as they progressively escape from some of them. We develop, analyze and simulate mathematical models of the spatiotemporal dynamics of heterogeneous cell populations and dysregulated cell-to-cell signaling. We use the models to investigate the emergence and consequences of non-genetic heterogeneity, focusing on colon cancer as an example.