Multi-Scale Agent-Based Modeling of Cancer Cell Chemotaxis within a Microfluidic Assay: Investigating the Role of Receptor Dynamics and Ligand Isoforms

Chemotaxis is proposed to be a key mechanism that allows cancer cells to invade surrounding tissue and vasculature, and also to extravasate into distant locations leading to metastasis. The signaling axis comprised of the chemokine CXCL12 and its receptor CXCR4 has been implicated as a major chemotactic proponent in breast cancer and more than 20 other cancers. Inhibition of CXCR4 has not resulted in clinically successful cancer therapy, prompting the search for other targets. A second receptor, CXCR7, is also present in the breast tumor environment and can scavenge CXCL12. Understanding how CXCR7 can shape ligand gradients on a molecular level, and influence cancer cell chemotaxis within the tissue scale, is unclear. In addition, CXCL12 exists as multiple isoforms, yet studies probing its role in cancer have only focused on one isoform. These isoforms have varying affinities for cell surface receptors and glycosaminoglycans, as well as experimental device surfaces, ultimately changing the presentation of the ligand to the receptor.  These complex interactions are overlooked in standard non-physiologic cell culture models and confound our understanding of chemotactic gradient formation, sensing, and its role in cancer.

In order to investigate the molecular mechanisms that regulate gradient formation and cancer cell responses to these gradients, we constructed a data-driven multi-scale agent-based model that simulates cancer cell chemotaxis within a microfluidic assay. First, we use in vitro data to construct an ordinary differential model to describe ligand and receptor binding, internalization, recycling and degradation for both receptors. Second, we take these single-cell equations and embed them within an agent-based model describing how cells interact and chemotax within a microfluidic device. Thus the molecular scale behavior drives the cellular level decisions, which ultimately dictate the overall organization of the cells in the device. We build and validate the model based on data in Torisawa et al. (Integrative Biology 2:680-686, 2010). By performing uncertainty and sensitivity analyses with Latin Hypercube Sampling and Partial Rank Correlation Coefficients, we then identify and analyze processes that have the greatest influence on chemotaxis. We find that ligand and receptor dynamics play a large role in shaping gradients and thus modulating cell behavior. By incorporating the partitioning of CXCL12 from its soluble state to its glycosaminoglycan-, surface- and receptor-bound states in the molecular scale of our model, we can also investigate how different CXCL12 isoforms affect the gradient, concentration, and cell behavior. Overall, our model is able to provide information on how molecular- and cellular-scale events determine cellular organization in a microfluidic device, and can be extended to explore cell behavior in tissue in response to CXCL12.

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