Multiscale models of breast cancer progression

Abstract

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

FIGURE 1

Schematic of the tumor microenvironment. Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. One of the central programs associated with this transition is angiogenesis. Tumor angiogenesis is stimulated by reduced oxygen tension (i.e., hypoxia) which up-regulates the secretion of pro-angiogenic signaling molecules, e.g., VEGF, Interleukin-6 (IL-6) and Interleukin- 8 (IL-8) by tumorigenic cells and other cell types in the tumor microenvironment. These signals then initiate autocrine and paracrine programs which shape the chemical, mechanical and cellular composition of the microenvironment.

FIGURE 2

Schematic of a generic bottom-up ABM strategy. A three-dimensional computational domain representing the microenvironment is discretized into well-mixed microcompartments. The extracellular state e.g., the concentration of pO₂ or VEGF in each of the microcompartments is governed by the solution of continuum mass balances equations (partial differential equations). Agents representing different cell-types, each equipped with perhaps many signal processing networks, are embedded into the computational microenvironment and allowed to evolve according to rules that are functions of the output of the signaling networks. The agents make decisions about possible actions e.g., move, proliferate, differentiate etc. by evaluating the network models. Thus, the decisions of the agents depend upon both the position and temporal state of the agent.