Describing directional cell migration with a characteristic directionality time.

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration.

Technical advance: introducing a novel metric, directionality time, to quantify human neutrophil chemotaxis as a function of matrix composition and stiffness.

A direct consequence of cellular movement and navigation, migration incorporates elements of speed, direction, and persistence of motion. Current techniques to parameterize the trajectory of a chemotaxing cell most commonly pair migration speed with some measure of persistence by calculating MSD, RMS speed, TAD, and/or CI. We address inherent limitations in TAD and CI for comparative analysis by introducing two new analytical tools to quantify persistence: directionality index and directionality time. With the use of these tools, we show that the mechanical properties of the underlying substrate contribute significantly to the regulation of human neutrophil chemotaxis toward fMLP on Fgn-, Col-, and Fn-coated gels of varying elasticity. The ß1-integrin ligand Col demonstrated mechanosensitive speed. In contrast, ß2-integrin ligand Fgn supported mechanosensitive persistence. Fn, recognized by ß1 and ß2 integrins, mechanoregulated speed and persistence. Blocking ß2 integrins of cells migrating on Fn identified an underlying ß2-integrin-directed modulation of persistence. These data demonstrate that individual components of the neutrophil chemotactic response show integrin dependence and are finely tunable with different ligand, mechanotactic, and chemotactic cues, underscoring the need for sensitive analytical methods.

Stick-slip motion and elastic coupling in crawling cells.

Crawling cells exhibit a variety of cell shape dynamics, ranging from complex ruffling and bubbling to oscillatory protrusion and retraction. Periodic shape changes during cell migration are recorded in fast-moving fish epithelial keratocytes where sticking and slipping at opposite sides of the cell's broad trailing edge generate bipedal locomotion. Barnhart et al. [Biophys. J. 98, 933 (2010)] recently proposed a mechanical spring model specifically designed to capture bipedal locomotion in these cells. We extend their model by benchmarking the dynamics of four mechanical configurations against those of crawling keratocytes. Our analysis shows that elastic coupling to the cell nucleus is necessary to generate its lateral motion. We select one configuration to study the effects of cell elasticity, size, and aspect ratio on crawling dynamics. This configuration predicts that shape dynamics are highly dependent on the lamellipodial elasticity but less sensitive to elasticity at the trailing edge. The model predicts a wide range of dynamics seen in actual crawling keratocytes, including coherent bipedal, coherent nonbipedal, and decoherent motions. This work highlights how the dynamical behavior of crawling cells can be derived from mechanical properties through which biochemical factors may operate to regulate cellular locomotion.