Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection.

Mark N Read,Jacqueline Bailey,Jon Timmis,Tatyana Chtanova

doi:10.1371/journal.pcbi.1005082

Abstract

The advent of two-photon microscopy now reveals unprecedented, detailed spatio-temporal data on cellular motility and interactions in vivo. Understanding cellular motility patterns is key to gaining insight into the development and possible manipulation of the immune response. Computational simulation has become an established technique for understanding immune processes and evaluating hypotheses in the context of experimental data, and there is clear scope to integrate microscopy-informed motility dynamics. However, determining which motility model best reflects in vivo motility is non-trivial: 3D motility is an intricate process requiring several metrics to characterize. This complicates model selection and parameterization, which must be performed against several metrics simultaneously. Here we evaluate Brownian motion, Lévy walk and several correlated random walks (CRWs) against the motility dynamics of neutrophils and lymph node T cells under inflammatory conditions by simultaneously considering cellular translational and turn speeds, and meandering indices. Heterogeneous cells exhibiting a continuum of inherent translational speeds and directionalities comprise both datasets, a feature significantly improving capture of in vivo motility when simulated as a CRW. Furthermore, translational and turn speeds are inversely correlated, and the corresponding CRW simulation again improves capture of our in vivo data, albeit to a lesser extent. In contrast, Brownian motion poorly reflects our data. Lévy walk is competitive in capturing some aspects of neutrophil motility, but T cell directional persistence only, therein highlighting the importance of evaluating models against several motility metrics simultaneously. This we achieve through novel application of multi-objective optimization, wherein each model is independently implemented and then parameterized to identify optimal trade-offs in performance against each metric. The resultant Pareto fronts of optimal solutions are directly contrasted to identify models best capturing in vivo dynamics, a technique that can aid model selection more generally. Our technique robustly determines our cell populations’ motility strategies, and paves the way for simulations that incorporate accurate immune cell motility dynamics.

Highlights

Cellular motility and interactions underlie many processes in the immune response, including lymphocyte recirculation through blood and lymphoid organs, their interactions with cells presenting specific antigen, and relocation to the specific tissues where they engage in protective immunity [1]
We find that Lévy walk offers an inferior capture of our data to another class of motility model, the correlated random walk, and this determination was possible because we are able to explicitly evaluate several motility metrics simultaneously
We evaluate several random walk models’, including Brownian motion, Lévy walk, and several correlated random walks, capacities to capture the motility dynamics of lymph node T cells responding to inflammation and neutrophils responding to sterile laser injury of the ear pinnae

Summary

Introduction

Cellular motility and interactions underlie many processes in the immune response, including lymphocyte recirculation through blood and lymphoid organs, their interactions with cells presenting specific antigen, and relocation to the specific tissues where they engage in protective immunity [1]. Agent-based simulations (ABS), wherein individual immune cells are simulated as discrete entities with their own state in a spatially explicit environment, have found widespread application in immunology, with far-ranging applications including: understanding granuloma development [7], Payers patch development [8], the search efficiency of lymphocytes in the lymph node [9, 10], the establishment and subsequent recovery from autoimmune disease [5], and the mechanisms underlying cancer [11]. There is clear scope to combine detailed spatio-temporal two-photon microscopy data with spatially-explicit agent-based simulation to further understanding of how cellular motility integrates with other immune processes to impact health. In the Lévy walk model, an agent’s motility is described by a sequence of randomly oriented straight line movements drawn from a power-law, long-tailed distribution [12]. Subsequent work has cast doubt on Lévy walk’s apparent pervasiveness in nature, owing to methodological discrepancies in its identification [18, 19]

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Discussion

Conclusion