Tracking single particles and elongated filaments with nanometer precision

Abstract

Recent developments in image processing have greatly advanced our understanding of biomolecular processes in vitro and in vivo. In particular, using Gaussian models to fit the intensity profiles of nanometer-sized objects have enabled their two-dimensional localization with a precision in the one-nanometer range. Here, we present an algorithm to precisely localize curved filaments whose structures are characterized by subresolution diameters and micrometer lengths. Using surface-immobilized microtubules, fluorescently labeled with rhodamine, we demonstrate positional precisions of ∼2 nm when determining the filament centerline and ∼9 nm when localizing the filament tips. Combined with state-of-the-art single particle tracking we apply the algorithm 1), to motor-proteins stepping on immobilized microtubules, 2), to depolymerizing microtubules, and 3), to microtubules gliding over motor-coated surfaces.

Figure 1

Algorithm for tracking individual frames containing filaments and individual particles: (A) Workflow of the tracking algorithm with corresponding images for every step. Plus (+) symbols denote the center positions of individual particles, whereas center positions of filaments and filament segments are marked with a cross (x). Red lines indicate the orientation of the model or the centerline of the filament. (B) Intensity profiles for different regions (colors correspond to regions in Fig. 1A), the corresponding model, and the residuals after fitting.

Figure 2

Precision (68% confidence interval) of filament tracking: The smallest error of the values shown in the histograms is denoted as best and the overall error of the microtubule distribution is denoted as 68%. (A) Histogram of microtubule centerline errors. (B) Histogram of microtubule length errors. (C) Histogram of microtubule tip position errors. (D) Centerline localization of one microtubule compared to center position localization of one TetraSpeck Fluorescent Microsphere (diameter 200 nm) and one Qdot 705 ITK Streptavidin Conjugate. Plus (+) and cross (x) symbols denote the center positions (500 frames) of the microsphere and the QD. The black dot indicates the centroid of the particles and the black dotted lines the 68% confidence interval of the particle's centroid measurement. The red lines denote the centerlines of the microtubule (11 of the 500 frames). The black line indicates the averaged microtubule centerline and the black dotted line the 68% confidence interval of the microtubule's averaged centerline measurement.

Figure 3

Applications of the filament tracking algorithm: (A) Kymograph of two QDs transported by kinesin-1. (B) Trajectory of both QDs and the centerline of their corresponding microtubules (gray). (C) Distance to the track for both QDs, gray denotes the microtubule centerline. Positive values denote the left hand side, negative the right hand side (in the direction of movement). (D) Kymograph of microtubule depolymerized by the kinesin-13 MCAK (10 nM concentration). The dotted line marks the time when the MCAK solution was flowed in. (E) Decrease in microtubule length due to depolymerization. (F) Movement of the microtubule tips in respect to the initial center position of the microtubule. (G) Kymograph of microtubule gliding over a kinesin-1 coated surface. The dotted line marks the time, when the temperature was increased from 22°C to 38°C (temperature of the Peltier element attached to the flow cell containing the motility solution). (H) Distance along the path of the microtubule center position. (I) Instantaneous velocity of the microtubule center position.