Probing cytoskeletal modulation of passive and active intracellular dynamics using nanobody-functionalized quantum dots

The cytoplasm is a highly complex and heterogeneous medium that is structured by the cytoskeleton. How local transport depends on the heterogeneous organization and dynamics of F-actin and microtubules is poorly understood. Here we use a novel delivery and functionalization strategy to utilize quantum dots (QDs) as probes for active and passive intracellular transport. Rapid imaging of non-functionalized QDs reveals two populations with a 100-fold difference in diffusion constant, with the faster fraction increasing upon actin depolymerization. When nanobody-functionalized QDs are targeted to different kinesin motor proteins, their trajectories do not display strong actin-induced transverse displacements, as suggested previously. Only kinesin-1 displays subtle directional fluctuations, because the subset of microtubules used by this motor undergoes prominent undulations. Using actin-targeting agents reveals that F-actin suppresses most microtubule shape remodelling, rather than promoting it. These results demonstrate how the spatial heterogeneity of the cytoskeleton imposes large variations in non-equilibrium intracellular dynamics.

line) frames detected as directional runs by "multi-scale" (black and red) and "strict directional filtering" (grey and pink) algorithms (see methods) on an artificial dataset containing noisy directional runs interspersed with random motion intervals.
(g) Example of a directed motion trajectory of kinesin-1 (time color-coded crosses) with linear (red curve) and B-spline approximations. In the latter case the distances between internal control points are 6 µm (green) and 1 µm (dark blue). Scale bar: 1 m.  (a) Average direction autocorrelation (cosine between consecutive displacements) as a function of time delay (n is the same as in Fig. 3d).
(b) COS-7 cell fixed and stained for acetylated (left) and tyrosinated (middle) tubulin. Scale bar: 5 m.   The data are presented for two cases. The first is "strict directional filtering" when the trajectories were filtered based on angle between two consecutive displacements. The second is "multi-scale directional filtering", described in Materials and Methods section. SEM is indicated.  Pulse Length) were optimized from standard settings to achieve optimal efficiency and provided in Table S1. We found that the number of incorporated QDs per cell mainly is For imaging of QDs and actin cytoskeleton COS-7 cells (Fig.1 a,b) were electroporated with QDs as described above and after 30 minutes fixed with 4% formaldehyde in PBS solution.

Electroporation of COS-7 cells and functionalization of QDs
Actin was stained with Alexa Fluor 488 Phalloidin (A12379, Molecular Probes) according to manufacturer's protocol. Z-stacks were acquired in each channel (GFP and mCherry) with 60x objective and 300 nm spacing between planes (25-30 planes in total per stack). Stacks were deconvolved using the Huygens Professional package (Scientific Volume Imaging) and 3D Gaussian Blur of 1 pixel was applied using ImageJ.
We used the same setup for live imaging of microtubules only (for iMSD analysis, Fig. 4a,b) or simultaneous kinesin and microtubules (Fig. 3f,g ). COS-7 cells were either transfected with and mCherry-α-tubulin only or co-transfected with TagRFP The characteristic distribution of intensities from one experiment is presented at Fig. S1f. We pooled together results of three independent experiments to calculate the average number of GFP molecules bound to QDs reported in the main text. The values of integrated intensity of the GFP clusters colocalized with QDs-VHH GFP and QDs-VHH GFP (2x) from each experiment was normalized by the average integrated intensity of corresponding single GFP. We calculated mean values and standard deviation for resulting pooled GFP molecules counts for QDs-VHH GFP (N=2941) and QDs-VHH GFP (2x) (N=5591). The bleaching intensity traces (Fig.S1g,h) were filtered using Chung-Kennedy nonlinear edge-preserving filter with parameter values K = 1, M = 10, p = 4 9 .

Particle detection and trajectory analysis
Image processing routines were automated using ImageJ/FIJI macros or custom build plugins. MSD calculation, curve fitting and all other statistical and numerical data analysis were performed in Matlab (MATLAB R2011b; MathWorks) and GraphPad Prism (ver.5.02, GraphPad Software).

Particle detection and tracking. To track and characterize individual quantum dots movements
we used TrackMate plugin (v.2.5.0) for FIJI with subpixel LoG detector and "Simple LAP tracker" option 10 . Resulting trajectories were exported to MTrackJ ImageJ plugin 11 for manual inspection and correction. To get localization precision, each detected spot was further fitted with 2D Gaussian with initial parameters corresponding to the microscopes point spread function as described earlier using ImageJ Dom_Utrecht plugin v.0.9.2 12 . Only tracks longer than 12 (for diffusion) and 50 (for QD-kinesin trajectories) frames were selected for the further analysis.
Diffusion trajectory analysis. MSD and velocity autocorrelation curves together with diffusion coefficient calculations were performed using "msdanalyzer" Matlab class 13 . Ensemble diffusion coefficients were measured as a slope of the affine regression line fitted to the first 25% of weighted averaged MSD curves and divided by four (assuming two dimensional motion).

Motors runs analysis.
Detection of processive runs in trajectories was performed using two algorithms. The first one, called "strict directional filtering", is calculating the cosine between two consecutive velocity vectors for a given trajectory and finds segments where its value is above defined threshold. In this segment, the particle is assumed to move directionally.
Directional autocorrelation is used as a local directional persistence measure in multiple applications 13 . Each trajectory represents a set of particle coordinates i r  , where index i denotes the frame number. Corresponding velocity vectors were defined as  , where τ is the time between frames. The value of cosine was calculated as: To find runs we used the lower threshold value of 0.6, corresponding to an approximately 100° cone facing forward. Only runs longer than 0.5 seconds were taken into account. To address the efficiency of the algorithm we tested it on a dataset containing 500 artificial trajectories of 1000 frames each (20 frames per second). Each track represented diffusive motion with coefficient D=0.2 µm 2 /s interrupted by four randomly located continuous runs with exponential distribution of durations. During processive runs the speed was constant and the change of the angle between two consecutive velocity vectors was sampled from a Gaussian distribution with standard deviation of 15°. The efficiency of detection did not depend on the speed of runs (data not shown), but declined as the duration of runs became shorter, as shown on Fig. S2e. At the average duration of run equal to one second (comparable to characteristic experimental kinesin run length) the algorithm detected correctly 94% of frames containing processive movements with only 6% of false positives. For the velocity and length analysis (Fig.2i-k and Supplementary Table 3) we used this algorithm with threshold value of 0.6 and minimal number of frames in one run equal to 10.
The second algorithm, referred to as "multi-scale filtering", was developed to detect kinesin runs in the presence of microtubules displacements. In this case, processive runs maintain general direction of movement but can be locally disrupted by abrupt random movements. To overcome the strict local criteria of the first algorithm we used "non-local" directionality measure as: where positive integer k defines a window (time scale) of directionality. To find this kind of "disrupted" runs we used its average value over multiple time scales: Using this characteristic with K=9, we initially located those segments of trajectory where its value was above -0.1 and among them we picked only those longer than one second, where the average value of Spline fitting and curvature calculations. Segments of directional runs were fitted with nonperiodic cubic B-splines using "B-splines" Matlab package by Levente Hunyadi (http://www.mathworks.com/matlabcentral/fileexchange/27374-b-splines). In short, first the length of the run L was estimated as a total sum of displacements. The degree of approximation was defined by the average distance between spline's control points denoted l. The total number of control points was defines as n=[L/l]+1 and the number of knots as p = n + 6. The knot vector t points were equally spaced: Analysis of QD blinking (Fig. S1c) "In vitro" measurements of QDs blinking were performed by first diluting stock QD solution to 10 nM in PBS and running it through a flow chamber of the same design as in the "Stoichiometric quantification" section. As a result QDs were non-specifically immobilized on the coverslip. The flow chamber was further filled with imaging medium (PBS or 10mM MEA in PBS), sealed with vacuum grease and imaged on the same setup and with the same parameters as described for Fig. 1c-f (see "Rapid frame rate imaging" section). Three movies of from tracks as periods of continuous QDs emission. The cumulative distribution function of these durations is shown on Fig. S1c. For the "inside cell" condition we used the slow diffusing subpopulation of QDs also used in the dataset presented in Fig.1d-f, analyzed in the same manner.

SUPPLEMENTARY NOTE 1
Actin pore size estimation According to Eq.9 in reference 19 , for diffusion of a tracer with radius R through a network of filaments of radius r (when R size is compatible with r) , the inaccessible volume fraction is: where  is the volume fraction of overlapping filaments and can be approximated as D slow /D fast , a QD radius of R=15 nm, actin filament radius r=4 nm, we numerically solved the system of equations Eq.9-10 in 19 to estimate the pore size being equal to L=36 nm.