Bayesian Spatio-Dynamic Modeling in Cell Motility Studies: Learning Nonlinear Taxic Fields Guiding the Immune Response

Abstract

We develop and analyze models of the spatio-temporal organization of lymphocytes in the lymph nodes and spleen. The spatial dynamics of these immune system white blood cells are influenced by biochemical fields and represent key components of the overall immune response to vaccines and infections. A primary goal is to learn about the structure of these fields that fundamentally shape the immune response. We define dynamic models of single-cell motion involving nonparametric representations of scalar potential fields underlying the directional biochemical fields that guide cellular motion. Bayesian hierarchical extensions define multicellular models for aggregating models and data on colonies of cells. Analysis via customized Markov chain Monte Carlo methods leads to Bayesian inference on cell-specific and population parameters together with the underlying spatial fields. Our case study explores data from multiphoton intravital microscopy in lymph nodes of mice, and we use a number of visualization tools to summarize and compare posterior inferences on the three-dimensional taxic fields.

KEY WORDS:

• Bayesian kernel regression
• Chemotaxis
• Hierarchical dynamic models
• Immune response monitoring
• Markov chain Monte Carlo
• Nonlinear stochastic dynamics
• Potential field gradients
• Radial basis regression
• Single-cell tracking
• State-space models
• Taxic responses

Acknowledgments

This work was partly supported by NIH contract contract HHSN268200500019C (Thomas B. Kepler), grant GM-41514 (Michael D. Cahalan), the George E. Hewitt Foundation for Medical Research (Melanie P. Matheu), and by the National Science Foundation under grant DMS-1106516 (Mike West). Any opinions, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the Hewitt Foundation, NIH, and/or NSF.