Changepoint Detection for Piecewise Linear Paths
Commonly studied intracellular cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of stationarity) along often unobserved microtubules. Our group’s approach has developed a segmentation analysis protocol which involves an in-house changepoint detection algorithm coupled with summary statistics that are robust with respect to the inevitable mistakes that changepoint detections algorithms make.
Black: “current” position of the lysosome.
Grayscale: “recent” positions, the lighter the farther in the past.
Red: the inferred position of the contact between the molecular motor and the microtubule.
Piecewise-linear approximation of cargo paths
We would like to infer the behavior of the molecular motors that transport the cargo, but because the motor heads are so small (~ 5 nm) they cannot be observed directly in live cells. Meanwhile, intracellular cargo can be quite large and “easily” visualized. The compromise is that diffusion is rapid and the observations are noisy compared to the speed of the walking motors.
Over the last decade graduate students Melanie Jensen and Linh Do and postdoc Keisha Cook have worked to develop a changepoint algorithm and inference protocol for automatically segmenting paths and reporting a “best-fit” piecewise linear approximation of cargo paths.
Try out a beta version of our change-in-velocity detection algorithm here:
https://stochastics-lab.shinyapps.io/changepoint/
We are close to submitting the theoretical support for this algorithm. For our most recent modeling and inference effort using the changepoint algorithm, see Keisha J. Cook’s lead author paper, “Considering experimental frame rates and robust segmentation analysis of piecewise-linear microparticle trajectories” which has just recently been accepted by Mathematical Biosciences and Engineering!