MTrack: Automated Detection, Tracking, and Analysis of Dynamic Microtubules

Microtubules are polar, dynamic filaments fundamental to many cellular processes. In vitro reconstitution approaches with purified tubulin are essential to elucidate different aspects of microtubule behavior. To date, deriving data from fluorescence microscopy images by manually creating and analyzing kymographs is still commonplace. Here, we present MTrack, implemented as a plug-in for the open-source platform Fiji, which automatically identifies and tracks dynamic microtubules with sub-pixel resolution using advanced objection recognition. MTrack provides automatic data interpretation yielding relevant parameters of microtubule dynamic instability together with population statistics. The application of our software produces unbiased and comparable quantitative datasets in a fully automated fashion. This helps the experimentalist to achieve higher reproducibility at higher throughput on a user-friendly platform. We use simulated data and real data to benchmark our algorithm and show that it reliably detects, tracks, and analyzes dynamic microtubules and achieves sub-pixel precision even at low signal-to-noise ratios.


24
Microtubules are dynamic filaments essential for many cellular processes such as intracellular 25 transport, cell motility and chromosome segregation. They assemble from dimeric -tubulin 26 subunits that polymerize in a head-to-tail fashion into polar filaments [26] (Figure 1). Microtubules 27 show a behavior termed 'dynamic instability', which can be empirically described by four parameters: 28 (1) the polymerization velocity at which microtubules grow (vg), (2) the depolymerization velocity at 29 which microtubules shrink (vs), (3) the catastrophe frequency at which microtubules switch from 30 growth to shrinkage (fc), and (4) the rescue frequency at which microtubules switch from shrinkage 31 to growth (fs) [25]. This dynamic behavior is intrinsic to microtubules. In a cellular context, however, 32 the dynamic properties of microtubules are modulated by motors and accessory proteins known as 33 microtubule associated proteins (MAPs) [6,44,5,31,10]. In most cases, the cellular context is too 34 complex to study a single protein's contribution to microtubule dynamics. Therefore, biochemical 35 activities of individual proteins have primarily been characterized in vitro using purified components 36 and total-internal reflection fluorescence (TIRF) microscopy [32,37,15,24,7,12,39,3,13,46]. 37 Furthermore, microtubule dynamics are strongly affected by a set of drugs routinely used to treat 38 diseases such as cancer [17] and malaria [18]. Owing to their clinical relevance, it is a viable need to 39 understand the exact regulation of microtubule dynamics by a given drug and thereby elucidate 40

Figure 1. Microtubule Dynamics by TIRF Microscopy
A Schematic experimental design: Stabilized microtubule seeds (red) are bound to the coverglass by antibodies and serve as nucleation points for dynamic microtubules (green). One microtubule end usually shows higher growth rates (+) than the other end (-). Total internal reflection fluorescence (TIRF) microscopy selectively excites fluorophores in a restricted volume adjacent to the glass-water interface allowing the visualization of individual microtubules. B TIRF microscopy image of dynamic microtubules (green) grown from stabilized seeds (red).
the underlying molecular mechanisms. Given the growing interest in biochemical reconstitution 41 systems [6,44,9], automation of data analysis will unveil the full potential of the experimental 42 approaches as described above. 43 Quantitatively deriving dynamic microtubule parameters from fluorescence microscopy images by 44 manually creating and analyzing kymographs (spatial position over time) is still common practice 45 [49]. This limits the collection of statistically significant amounts of data. Moreover, manual 46 analysis can bias data collection and introduce variability. Thus, methods have been developed 47 that allow microtubule detection and/or tracking [48,4,23,30,8,34]. However, to date, there is 48 no fully automated workflow that provides detection and tracking of microtubules followed by 49 automated data analysis and statistics collection. Here, we present the software MTrack, which 50 detects, tracks, measures, and analyses the behavior of fluorescently labeled microtubules imaged 51 by TIRF microscopy (Supplementary Figure 1). MTrack is capable of automatically identifying and 52 tracking dynamically growing microtubules that potentially bend and cross with subpixel resolution, 53 even at high growth rates and low signal-to-noise ratios (SNR) using advanced objection recognition 54 and robust outlier removal. The software is easily accessible for users and developers since it can 55 be automated and is provided as an open-source Fiji [36] plug-in.

57
The MTrack software is organized in two consecutive modules that can be run independently. The 58 first module robustly detects microtubule seeds and tracks dynamic microtubules over time. The 59 second module interprets the length over time plots to extract relevant parameters of dynamic 60 instability and population statistics. on manually clicking each individual microtubule to be analyzed [4,34]. Therefore, our aim was to 67 develop an approach that robustly detects microtubule seeds in the image in a fully automated 68 fashion. It is essential to precisely determine the exact end point of each seed, as these are the 69 sites from which microtubules will subsequently grow and shrink. MTrack does so by using the 70 Maximally Stable Extremal Regions (MSER) algorithm [21, 28] to identify image areas belonging to 71 each seed, a sum of 2D Gaussians (SoG) model to accurately localize individual seeds, and finally a 72 Gaussian Mask fit [40] to determine the precise end point of each seed with subpixel resolution 73 ( Figure 2A). 74 The principle underlying MSER is a component tree, which computes every possible threshold of the 75 image thereby increasing the dimensionality of the input image by one (e.g. 2d > 3d, Supplementary 76 Movie 1). Stable regions within the component tree are those that do not significantly change over 77 multiple thresholds. Since microtubules can vary in size, are randomly oriented, potentially bent, 78 and are the main bright objects in the fluorescent image, the MSER detector performs accurately 79 without the need to make assumptions about shape, orientation, and size of regions. Successfully 80 detected microtubule seeds show a one-to-one assignment to ellipsoidal regions ( Figure 2A). Even 81 for low SNRs, the overall detection accuracy mostly depends on the density of microtubule seeds 82 ( Figure 2B). MTrack detects seeds with a close to 100% accuracy when the distance between seeds 83 is larger than 5 pixels, which is experimentally feasible. Using the region identified by MSER, we fit a tracking. We will show that fitting polynomial functions enables us to robustly track microtubules, 106 even when bending or crossing. 107 In more detail, MSER first detects an image region for each dynamic microtubule within each frame 108 of the fluorescent time-lapse movie (as described for seed detection). To initialize the iterative 109 microtubule detection within each MSER region, we need a start point and the guess of an end point. 110 The start point is fixed and defined by the detected seed end, while the end point is estimated by 111 the intersection of the current MSER region boundary with the projected growth direction from 112 the last successfully segmented frame, which can potentially be many frames away ( Figure 3A  The MTrack algorithm successfully tracks straight, bending and crossing microtubules over time. A First, MSER detects an image region (red ellipse) for each dynamic microtubule (blue). The seed end is then identified as a start point (green circle) and the end point (x) is estimated by the intersection of the current MSER region boundary with the projected growth direction (dashed line) from the last successfully segmented microtubule. These two points initialize a 2D SoG fit represented by a 3 order polynomial function. The actual length of the dynamic microtubule is calculated as the contour length (lc) of the final fit. This approach allows tracking of bending B and crossing C microtubules. D Tracking accuracy for straight and bending microtubules (SNR 10) was determined as the distance between the actual simulated position of the microtubule end (Δ actual ) and the position given by the tracking algorithm (Δ tracked ).   was robust even at experimentally relevant SNRs and did not depend on the filament orientation. 194 We then showed that allowing the final fit to follow a 3 order polynomial function enabled us to 195 track straight, bending, and crossing microtubules. The tracking accuracy achieved pixel resolution, 196 providing a close to molecular precision. (1) The sum is over the pixel co-ordinates ( , ) and is the pixel intensity at that position. represents Here, we have used the vector notation to represent the co-ordinates ( = 0, 1) for ( , ) co-ordinates 282 respectively and ⃗ represents the unity vector. The derivative with respect to the end point is also 283 similar to above with , being replaced by , and start being replaced by end . 284 3.2 Derivative with respect to 285 We define and 287 ,

288
For the derivative is 6 without the term and for derivative with respect to it is unity.
We now have two more parameters to determine and . is the inflection of the polynomial and These derivatives are the same as described for the line model. 302 303 The term is now determined by the other fit parameters and can be written as

Derivative with Respect to
We define a new term as 305 = + 2 ,start + 3 2 ,start The ⃗ can then be redefined as The derivative wrt can then be written as before 308 We define a term as 309 = − 2 ,start − ( ,start + ,end )

Derivative with Respect to Curvature (b)
Defining a vector ⃗ as The derivative with respect to can then be written as before The derivative with respect to can then be written as before In order to obtain the optimized set of parameters, we use the Levenberg-Marquradt solver to 327 minimize the sum of squared differences in Eq.1. The squared function can be written as

Line Parameters from MSER Ellipses
To do so, we perform Taylor expansion on the 2 function as is given by and the matrix is given by As the matrix is sparse, the second term containing the 2 order derivative is ignored and only 332 the first term is kept. We minimize the squared function with respect to delta and if the solution 333 is going towards minima the parameter is decreased by a factor of 10, else increased by the same 334 factor.

356
Each microtubule evolves according to a polynomial function, whose parameters are determined in 357 each frame using the function parameters of its evolution in the previous frame. Including prior 358 knowledge helps making good initial guesses for the localization to proceed in the current frame. 359 As the dynamic function of evolution of each microtubule is smooth and unique, the optimizer is 360 unlikely to make mistakes and if it does the program can recognize that by noting sharp changes 361 in the polynomial function parameters of growth of a given microtubule. Two special cases are 362 discussed with respect to colliding microtubules. with the PSF, adding a background, and rendering the final pixel intensities using a Poisson process. 378 The simulation code is available on   Polymerization velocity (vg) and depolymerization velocity (vs) are given in µm/min, catastrophe frequency (fc) and rescue frequency (fs) in s -1 .