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.