Name: quantifying cytoskeleton dynamics using differential dynamic microscopy
Uploaded: 2022-06-15T13:00:00
Duration: 6 min 37 s
Description: Watch this Scientific Journal Video about Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy at JoVE.com

Parts of this research were funded by a National Institutes of Health R15 Award (National Institute of General Medical Sciences award no. R15GM123420, awarded to R.M.R.-A. and R.J.M.), a Cottrell Scholar Award from the Research Corporation for Science Advancement (award no. 27459, awarded to R.J.M.), and a William M. Keck Foundation Research Grant (awarded to R.M.R-A.). GHK gratefully acknowledges financial support from the Dutch Research Council (NWO; project number VI.C.182.004 of the NWO Talent Programme).

NOTE: A Jupyter Notebook file containing the code to go along with each step in the following protocol can be found on the following GitHub repository, https://github.com/rmcgorty/PyDDM/tree/main/Examples. A PDF of that file is included in&#160;Supplementary File 1. Additionally, a walkthrough of the code and documentation of each function and class can be found on the website,&#160;https://rmcgorty.github.io/PyDDM/.
1. Software installation
<ol>
	<li>To follow along with the example DDM analysis files, install Jupyter Notebook for running the code. Install other required common Python packages, including NumPy and Matplotlib as well. These packages all come bundled with the Anaconda distribution (see&#160;https://www.anaconda.com/products/individual).&#160;</li>
	<li>Install the Python package xarray63. This package is necessary for organizing and storing metadata and analysis parameters. If using the Anaconda distribution, install xarray (along with its recommended dependencies) using the command: 
	conda install -c conda-forge xarray dask netCDF4 bottleneck</li>
	<li>Install the PyYAML package using the command: 
	conda install -c anaconda yaml 
	This package is necessary for reading metadata about the images to analyze and the parameters set by the user for analysis and fitting.</li>
	<li>Install the PyDDM package, by downloading from the GitHub repository or using the git command: 
	git clone&#160;https://github.com/rmcgorty/PyDDM.git</li>
</ol>
2. Planning the imaging sessions
<ol>
	<li>Choose the optimal available imaging modality and optical settings. As mentioned, DDM can be used with a number of microscopy methods.</li>
	<li>To assist in planning the appropriate objective lens and image size to use, determine the range of wavenumbers, q, that will be probed based on the pixel size and total image size. Confirm that the choice of magnification and field of view are optimal for the experiment, based on these calculations. For the images analyzed here, a 60x 1.4 NA objective and an image size of 256 x 256 pixels with a pixel size of 0.83 &#181;m were used for the active actin-microtubule composite network. For the images of beads embedded in a vimentin network, a 100x 1.4 NA objective and an image size of 512 x 512 pixels with a pixel size of 0.13 &#181;m were used. 
	NOTE: The minimum q is set by 2&#960;/N&#916;x, where the image size (assumed to be square) is N&#160;&#215; N pixels with a pixel size of &#916;x. The maximum q is the minimum of&#160;&#960;/&#916;x and 2&#960; NA/&#955;, where NA is the imaging objective&#39;s numerical aperture, and &#955; is the wavelength of light (for brightfield imaging, one can replace NA with (NAobjective + NAcondenser)/2).</li>
	<li>Next, consider the range of timescales to investigate. Typically, DDM analysis is done on sequences of at least 1000 frames.
	<ol>
		<li>To determine the appropriate frame rate, consider the expected time it will take for features in the sample to move a distance on the order of the minimum resolvable length scale (corresponding to the maximum&#160;q).</li>
		<li>In considering the upper limit of the range of timescales probed, recognize that, typically, the power spectrum of hundreds of&#160;image differences of a given lag time&#160;&#916;t are averaged together to provide sufficient statistics to reduce noise. Hence, acquire image sequences longer than the maximum timescale probed. 
		&#8203;NOTE: If an expected diffusion coefficient, D, or velocity, v, is known, then one can estimate expected characteristic decay times using&#160;&#964; = 1/Dq2&#160;or&#160;&#964; = 1/vq along with the range of q, which was determined based on the field of view and pixel size. The range of expected &#964; values over the accessible q-range can help guide the choice of frame rate and the number of frames to acquire.</li>
	</ol>
	</li>
</ol>
3. Sample preparation and image acquisition
NOTE: For details of the sample preparation and imaging settings used for the data presented in the representative results section, see previous publications from the authors11,51,64 and Supplementary File 2.
<ol>
	<li>Based on the consideration of the time and length scales to probe, acquire image sequences of, ideally, over 1000 frames. 
	NOTE: The code will analyze square images or square regions of interest within the image, so adjust the frame size accordingly.</li>
	<li>Save image sequences as a three-dimensional greyscale TIFF stack. Alternatively, the format used by Nikon Instruments systems, ND2 format, can be read by the installed package. If images are saved in some different format, use ImageJ or another imaging processing program to convert the images to a TIFF stack. 
	&#8203;NOTE: If using ND2 files, the package nd2reader from&#160;https://github.com/Open-Science-Tools/nd2reader must be installed.</li>
</ol>
4. Parameter setup
<ol>
	<li>Make a copy of the parameter file example_parameter_file.yml provided in the PyDDM code repository under the examples folder. Open this YAML file with a text editor like NotePad++ or the text editor in JupyterLab. See Supplementary File 2 for an example YAML parameters file used in the analysis of data presented in the representative results section.</li>
	<li>In the copied YAML file, provide the data directory and file name corresponding to the image sequence to be analyzed. Under the metadata section, provide the pixel size and frame rate.</li>
	<li>Under the Analysis_parameters section, provide details for how the DDM matrix should be calculated. Some parameters here are optional.
	<ol>
		<li>At a minimum, provide values for the parameters number_lag_times and last_lag_time. These correspond to the number of different lag times for which to calculate the DDM matrix and the longest lag time (in frames) to use, respectively. For the data of tracer beads in vimentin networks used here, the parameters number_lag_times and last_lag_time were 60 and 1000, respectively. The code will compute the DDM matrix for lag times from 1 frame (or some other minimum lag time if the optional parameter first_lag_time is specified) to the last_lag_time with logarithmic spacing. 
		NOTE: If M frames were acquired, one could calculate the DDM matrix for a lag time as large as M-1. However, with poor statistics at such a large lag time, the data is likely to be noisy. The longest lag time for which to calculate the DDM matrix will depend on the details of the data, but we suggest trying around one-third of the total image series duration.</li>
	</ol>
	</li>
	<li>Provide details for how the DDM matrix or the intermediate scattering function (ISF) should be fit in the Fitting_parameters section. Give the name of the model under the model parameter. Provide the initial guess, lower bound, and upper bound for each of the fitting parameters in the chosen model. 
	&#8203;NOTE: To display a list of the possible fitting models, run the function print_fitting_models. The models can also be found in the online documentation on the PyDDM website.</li>
</ol>
5. Calculating the DDM matrix
<ol>
	<li>Initialize an instance of the DDM_Analysis class. To do so, provide the metadata and analysis parameters discussed above by passing the filename, with the full file path included, of the YAML file to DDM_Analysis. Alternatively, pass the metadata and parameters as a Python dictionary data structure.</li>
	<li>Run the function calculate_DDM_matrix to calculate the DDM matrix. This calculation may take several minutes or longer depending on the frame size and the number of lag times. See Figure 2 for typical run times.</li>
	<li>Inspect the returned data, which will be in a data structure from the xarray package known as a Dataset. This data structure is stored under the attribute ddm_dataset. 
	NOTE: Not only the DDM matrix but also associated variables and metadata will be stored in this data structure. It will also be saved to disk in a Network Common Data Form (netCDF) format.</li>
	<li>Inspect the plots and figures, which will be generated and displayed. These figures are also saved as a PDF file in the data directory.
	<ol>
		<li>See that one of the generated plots shows the ensemble-averaged squared modulus of the Fourier-transformed images, <img alt="Equation031" src="/files/ftp_upload/63931/63931eq031.png" style="margin-bottom: 0px;" />&#160;as a function of q. By default, the code uses this to estimate the background parameter B. Estimate the background from <img alt="Equation031" src="/files/ftp_upload/63931/63931eq031.png" style="margin-bottom: 0px;" /> by assuming that, in the limit of large q, it will approach B/2, where B is the background.</li>
		<li>If <img alt="Equation031" src="/files/ftp_upload/63931/63931eq031.png" style="margin-bottom: 0px;" /> is not reaching a plateau at large q, then use another method for estimating B. To accomplish this, set the parameter background_method in either the YAML file or as an optional keyword argument to the function calculate_DDM_matrix. More details about the methods for estimating B are presented in the representative results section.</li>
	</ol>
	</li>
</ol>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/63931/63931fig2v2.jpg" /> 
Figure 2: Computation time for calculating the DDM matrix. In (A) and (B) the time for calculating the DDM matrix, <img alt="Equation009" src="/files/ftp_upload/63931/63931eq009.png" style="margin-bottom: 0px;" />, is shown. The data used in all cases is a movie of 5000 frames with an image size of 512 x 512 pixels. The DDM matrix was calculated for 30 lag times, logarithmically spaced between 1 frame (0.01 s) and 1000 frames (10 s). The code was run on an Intel i7-10700 2.90 GHz desktop computer with 32 GB RAM. In (A), the effect of varying how many image differences are used in computing the DDM matrix for each lag time is shown. For this, the images are binned to result in an image size of 256 x 256. For each lag time &#916;t, images separated by that&#160;&#916;t are subtracted and the resulting matrix is Fourier transformed. For a given &#916;t, all pairs of images separated by&#160;that&#160;&#916;t can be used (shown in blue), only non-overlapping image pairs can be used (e.g., frames 1 and 10, 10 and 19, etc.; shown in brown), or 300 image pairs or fewer can be used for each &#916;t. In (B), the effect of changing the image size on the computation time is shown. The images were binned either by grouping 2 x 2, 4 x 4, or 8 x 8 pixels, resulting in image sizes of 256 x 256, 128 x 128, or 64 x 64, respectively. For each, about 300 image pairs are used in computing the DDM matrix for each &#916;t. (C) From the DDM matrix, the intermediate scattering function (ISF) can be extracted. This is shown for the three cases in (A). The blue data points (with no offset) correspond to the ISF when the maximum number of image pairs are used for each &#916;t; the brown data points (with an offset of 0.1) correspond to the ISF when non-overlapping image pairs are used for each &#916;t; and the pink data points (with an offset of 0.2) correspond to the ISF when at most 300 image pairs are used for each &#916;t. The ISF found using non-overlapping image pairs shows noisiness at long &#916;t. For that case, few image pairs are used at long&#160;&#916;t (e.g., for&#160;&#916;t of 1000 frames, only 4 image pairs are used). (D) By fitting the ISF to an exponential function, the characteristic decay time, &#964;, for each wavenumber, q, is determined. In pink, results are shown after binning the original images by 2 x 2, resulting in an image size of 256 x 256. In gray, results are shown after binning by 8 x 8, resulting in an image size of 64 x 64. By binning the data, information about the dynamics at higher wavenumbers is lost, but calculating the DDM matrix for the 64 x 64 images is about 16x faster than for the 256 x 256 images. <a href="https://www.jove.com/files/ftp_upload/63931/63931fig2v2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
6. Fitting the DDM matrix or the ISF
<ol>
	<li>Initialize an instance of the DDM_Fit class. To do so, pass to DDM_Fit the filename of the YAML file containing the image metadata and parameters for fitting.</li>
	<li>Decide which model for the DDM matrix or the ISF to use for fitting the data. List the available models by executing the function print_fitting_models. Specify the model to be used in the YAML parameter file or by using the function reload_fit_model_by_name.</li>
	<li>Set the initial guesses and bounds for each parameter in the chosen model in the provided YAML parameter file. To change the initial guess for any parameter, use the function set_parameter_initial_guess. Set bounds for the parameters with the function set_parameter_bounds. For example, as seen in Supplementary File 2, for the data of tracer beads in the vimentin network, the initial guess for the decay time was 1 s and the bounds on that parameter were 0.01 s and 2000 s.</li>
	<li>Execute the fit with the function fit. Assign a variable to the output of this function to easily access the results. 
	&#8203;NOTE: This function can take many optional arguments. See the code documentation and provided examples for a list of such arguments and when to consider setting them to non-default values.</li>
</ol>
7. Interpreting the fit results
<ol>
	<li>Generate plots for inspecting the fits and the q-dependence of the fit parameters with the function fit_report. 
	NOTE: This function will generate a series of plots, which will also be saved as a PDF. Optional arguments to this function can be used to modify the plots produced.</li>
	<li>Among the generated plots will be a figure with 2 x 2 subplots showing the DDM matrix or ISF (depending on the chosen fitting model) at four q-values (specified as an optional argument to fit_report), along with the calculated DDM matrix or ISF using the model and best fit parameters. To plot the DDM matrix or ISF along with the best fit in an interactive way, use the class Browse_DDM_Fits as shown in the provided examples when the Jupyter Notebook environment is used.</li>
	<li>From the plot of the characteristic decay time&#160;&#964; vs. the wavenumber q, determine whether the dynamics follow diffusive, subdiffusive, ballistic, or some other type of motion. This can be done by looking for the power law relationship between&#160;&#964; and q. 
	&#8203;NOTE: On the log-log plot of&#160;&#964; vs. q generated by the function fit_report, three lines will be shown, corresponding to power law fits over a specified range of&#160;q values. The solid black line corresponds to fitting &#964; vs. q to a power law, &#964; = 1 / Kq&#946;, where K and&#160;&#946; are free parameters. The dashed line in orange corresponds to fitting to simple diffusion, &#964; = 1 / Dq2, where D is a diffusion coefficient. The dot-dashed line in blue corresponds to fitting to &#964; = 1 / vq, where v is a velocity.</li>
</ol>
8. Saving the results
<ol>
	<li>The results of the fit will be saved in a xarray dataset. Use the xarray function to_netcdf or Python&#39;s built-in pickle module to save this data structure to disk. Use the xarray function open_dataset to load these netCDF files.</li>
	<li>Use the function save_fit_results_to_excel to save the fit results, along with the data, to a worksheet file.</li>
</ol>

<ol>
	<li>Burla, F., Mulla, Y., Vos, B. E., Aufderhorst-Roberts, A., Koenderink, G. H. From mechanical resilience to active material properties in biopolymer networks. Nature Reviews Physics. 1 (4), 249-263 (2019).</li>
	<li>Amblard, F., Maggs, A. C., Yurke, B., Pargellis, A. N., Leibler, S. Subdiffusion and anomalous local viscoelasticity in actin networks. Physical Review Letters. 77 (21), 4470-4473 (1996).</li>
	<li>Mizuno, D., Tardin, C., Schmidt, C. F., MacKintosh, F. C. Nonequilibrium mechanics of active cytoskeletal networks. Science. 315 (5810), 370-373 (2007).</li>
	<li>Bendix, P. M. et al. A quantitative analysis of contractility in active cytoskeletal protein networks. Biophysical Journal. 94 (8), 3126-3136 (2008).</li>
	<li>Pelletier, V., Gal, N., Fournier, P., Kilfoil, M. L. Microrheology of microtubule solutions and actin-microtubule composite networks. Physical Review Letters. 102 (18), 188303 (2009).</li>
	<li>Stuhrmann, B., Soares e Silva, M., Depken, M., MacKintosh, F. C., Koenderink, G. H. Nonequilibrium fluctuations of a remodeling in vitro cytoskeleton. Physical Review E. 86 (2), 020901 (2012).</li>
	<li>Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M., Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature. 491 (7424), 431-434 (2012).</li>
	<li>Alvarado, J., Sheinman, M., Sharma, A., MacKintosh, F. C., Koenderink, G. H. Molecular motors robustly drive active gels to a critically connected state. Nature Physics. 9 (9), 591-597 (2013).</li>
	<li>Anderson, S. J. et al. Filament rigidity vies with mesh size in determining anomalous diffusion in cytoskeleton. Biomacromolecules. 20 (12),4380-4388 (2019).</li>
	<li>Anderson, S. J., Garamella, J., Adalbert, S., McGorty, R. J., Robertson-Anderson, R. M. Subtle changes in crosslinking drive diverse anomalous transport characteristics in actin-microtubule networks. Soft Matter. 17 (16), 4375-4385 (2021).</li>
	<li>Lee, G. et al. Myosin-driven actin-microtubule networks exhibit self-organized contractile dynamics. Science Advances. 7 (6), eabe4334 (2021).</li>
	<li>Wong, I. Y. et al. Anomalous diffusion probes microstructure dynamics of entangled F-actin networks. Physical Review Letters. 92 (17), 178101 (2004).</li>
	<li>K&#246;ster, S., Lin, Y.-C., Herrmann, H., Weitz, D. A. Nanomechanics of vimentin intermediate filament networks. Soft Matter. 6 (9), 1910-1914 (2010).</li>
	<li>Chandrakar, P. et al. Engineering stability, longevity, and miscibility of microtubule-based active fluids. Soft Matter. 18 (9), 1852-1835 (2022).</li>
	<li>Alvarado, J., Cipelletti, L., H. Koenderink, G. Uncovering the dynamic precursors to motor-driven contraction of active gels. Soft Matter. 15 (42), 8552-8565 (2019).</li>
	<li>Linsmeier, I. et al. Disordered actomyosin networks are sufficient to produce cooperative and telescopic contractility. Nature Communications. 7 (1), 12615 (2016).</li>
	<li>Stam, S. et al. Filament rigidity and connectivity tune the deformation modes of active biopolymer networks. Proceedings of the National Academy of Sciences. 114 (47), E10037-E10045 (2017).</li>
	<li>Malik-Garbi, M. et al. Scaling behaviour in steady-state contracting actomyosin networks. Nature Physics. 15 (5), 509-516 (2019).</li>
	<li>Berezney, J., Goode, B. L., Fraden, S., Dogic, Z. Extensile to contractile transition in active microtubule-actin composites generates layered asters with programmable lifetimes. Proceedings of the National Academy of Sciences. 119 (5), e2115895119 (2022).</li>
	<li>Roostalu, J., Rickman, J., Thomas, C., N&#233;d&#233;lec, F., Surrey, T. Determinants of polar versus nematic organization in networks of dynamic microtubules and mitotic motors. Cell. 175 (3), 796-808.e714 (2018).</li>
	<li>Cerbino, R., Trappe, V. Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical Review Letters. 100 (18), 188102 (2008).</li>
	<li>Giavazzi, F., Brogioli, D., Trappe, V., Bellini, T., Cerbino, R. Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond. Physical Review E. 80 (3), 031403 (2009).</li>
	<li>Giavazzi, F., Cerbino, R. Digital Fourier microscopy for soft matter dynamics. Journal of Optics. 16 (8), 083001 (2014).</li>
	<li>He, K., Spannuth, M., Conrad, J. C., Krishnamoorti, R. Diffusive dynamics of nanoparticles in aqueous dispersions. Soft Matter. 8 (47), 11933-11938 (2012).</li>
	<li>Lu, P. J. et al. Characterizing concentrated, multiply scattering, and actively driven fluorescent systems with confocal differential dynamic microscopy. Physical Review Letters. 108 (21), 218103 (2012).</li>
	<li>Giavazzi, F. et al. Viscoelasticity of nematic liquid crystals at a glance. Soft Matter. 10 (22), 3938-3949 (2014).</li>
	<li>Bayles, A. V., Squires, T. M., Helgeson, M. E. Dark-field differential dynamic microscopy. Soft Matter. 12 (8), 2440-2452 (2016).</li>
	<li>Wulstein, D. M., Regan, K. E., Robertson-Anderson, R. M., McGorty, R. Light-sheet microscopy with digital Fourier analysis measures transport properties over large field-of-view. Optics Express. 24 (18), 20881-20894 (2016).</li>
	<li>Richards, J. A., Martinez, V. A., Arlt, J. Particle sizing for flowing colloidal suspensions using flow-differential dynamic microscopy. Soft Matter. 17 (14), 3945-3953 (2021).</li>
	<li>Ferri, F. et al. Kinetics of colloidal fractal aggregation by differential dynamic microscopy. The European Physical Journal Special Topics. 199 (1), 139-148 (2011).</li>
	<li>Lanfranco, R. et al. Adaptable DNA interactions regulate surface triggered self assembly. Nanoscale. 12 (36), 18616-18620 (2020).</li>
	<li>Cho, J. H., Cerbino, R., Bischofberger, I. Emergence of multiscale dynamics in colloidal gels. Physical Review Letters. 124 (8), 088005 (2020).</li>
	<li>Giavazzi, F., Trappe, V., Cerbino, R. Multiple dynamic regimes in a coarsening foam. Journal of Physics: Condensed Matter. 33 (2), 024002 (2020).</li>
	<li>He, K. et al. Diffusive dynamics of nanoparticles in arrays of nanoposts. ACS Nano. 7 (6), 5122-5130 (2013).</li>
	<li>Jacob, J. D. C., He, K., Retterer, S. T., Krishnamoorti, R., Conrad, J. C. Diffusive dynamics of nanoparticles in ultra-confined media. Soft Matter. 11 (38), 7515-7524 (2015).</li>
	<li>Sentjabrskaja, T. et al. Anomalous dynamics of intruders in a crowded environment of mobile obstacles. Nature Communications. 7, 11133 (2016).</li>
	<li>Hitimana, E., Roopnarine, B. K., Morozova, S. Diffusive dynamics of charged nanoparticles in convex lens-induced confinement. Soft Matter. 18 (4), 832-840 (2022).</li>
	<li>Wilson, L. G. et al. Differential dynamic microscopy of bacterial motility. Physical Review Letters. 106 (1), 018101 (2011).</li>
	<li>Martinez, V. A. et al. Differential dynamic microscopy: a high-throughput method for characterizing the motility of microorganisms. Biophysical Journal. 103 (8), 1637-1647 (2012).</li>
	<li>Germain, D., Leocmach, M., Gibaud, T. Differential dynamic microscopy to characterize Brownian motion and bacteria motility. American Journal of Physics. 84 (3), 202-210 (2016).</li>
	<li>Croze, O. A. et al. Helical and oscillatory microswimmer motility statistics from differential dynamic microscopy. New Journal of Physics. 21 (6), 063012 (2019).</li>
	<li>Safari, M. S., Vorontsova, M. A., Poling-Skutvik, R., Vekilov, P. G., Conrad, J. C. Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters. Physical Review E. 92 (4), 042712 (2015).</li>
	<li>Wang, J., McGorty, R. Measuring capillary wave dynamics using differential dynamic microscopy. Soft Matter. 15 (37), 7412-7419 (2019).</li>
	<li>Cerbino, R., Giavazzi, F., Helgeson, M. E. Differential dynamic microscopy for the characterization of polymer systems. Journal of Polymer Science. 60 (7), 1079-1089 (2021).</li>
	<li>Cerbino, R., Cicuta, P. Perspective: differential dynamic microscopy extracts multi-scale activity in complex fluids and biological systems. The Journal of Chemical Physics. 147 (11), 110901 (2017).</li>
	<li>Drechsler, M., Giavazzi, F., Cerbino, R., Palacios, I. M. Active diffusion and advection in Drosophila oocytes result from the interplay of actin and microtubules. Nature Communications. 8 (1), 1-11 (2017).</li>
	<li>Burla, F., Sentjabrskaja, T., Pletikapic, G., Beugen, J. v., H. Koenderink, G. Particle diffusion in extracellular hydrogels. Soft Matter. 16 (5), 1366-1376 (2020).</li>
	<li>Regan, K., Wulstein, D., Rasmussen, H., McGorty, R., Robertson-Anderson, R. M. Bridging the spatiotemporal scales of macromolecular transport in crowded biomimetic systems. Soft Matter. 15 (6), 1200-1209 (2019).</li>
	<li>Wulstein, D. M., Regan, K. E., Garamella, J., McGorty, R. J., Robertson-Anderson, R. M. Topology-dependent anomalous dynamics of ring and linear DNA are sensitive to cytoskeleton crosslinking. Science Advances. 5 (12), eaay5912 (2019).</li>
	<li>Lee, G. et al. Active cytoskeletal composites display emergent tunable contractility and restructuring. Soft Matter. 17 (47), 10765-10776 (2021).</li>
	<li>Achiriloaie, D. H. et al. Kinesin and myosin motors compete to drive rich multi-phase dynamics in programmable cytoskeletal composites. arXiv:2112.11260 .(2021).</li>
	<li>Chen, X. et al. Coaxial differential dynamic microscopy for measurement of Brownian motion in weak optical field. Optics Express. 26 (24), 32083-32090 (2018).</li>
	<li>Reufer, M., Martinez, V. A., Schurtenberger, P., Poon, W. C. K. Differential dynamic microscopy for anisotropic colloidal dynamics. Langmuir. 28 (10), 4618-4624 (2012).</li>
	<li>Giavazzi, F., Haro-P&#233;rez, C., Cerbino, R. Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy. Journal of Physics: Condensed Matter. 28 (19), 195201 (2016).</li>
	<li>Cerbino, R., Piotti, D., Buscaglia, M., Giavazzi, F. Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters. Journal of Physics: Condensed Matter. 30 (2), 025901 (2017).</li>
	<li>Safari, M. S., Poling-Skutvik, R., Vekilov, P. G., Conrad, J. C. Differential dynamic microscopy of bidisperse colloidal suspensions. npj Microgravity. 3 (1), 21 (2017).</li>
	<li>Giavazzi, F., Pal, A., Cerbino, R. Probing roto-translational diffusion of small anisotropic colloidal particles with a bright-field microscope. The European Physical Journal E. 44 (4), 61 (2021).</li>
	<li>Schwarz-Linek, J. et al. Escherichia coli as a model active colloid: a practical introduction. Colloids and Surfaces B: Biointerfaces. 137, 2-16 (2016).</li>
	<li>Kurzthaler, C. et al. Probing the spatiotemporal dynamics of catalytic Janus particles with single-particle tracking and differential dynamic microscopy. Physical Review Letters. 121 (7), 078001 (2018).</li>
	<li>Mandal, S., Kurzthaler, C., Franosch, T., L&#246;wen, H. Crowding-enhanced diffusion: an exact theory for highly entangled self-propelled stiff filaments. Physical Review Letters. 125 (13), 138002 (2020).</li>
	<li>Norouzisadeh, M., Chraga, M., Cerchiari, G., Croccolo, F. The modern structurator: increased performance for calculating the structure function. The European Physical Journal E. 44 (12), 146 (2021).</li>
	<li>Gu, M., Luo, Y., He, Y., Helgeson, M. E., Valentine, M. T. Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E. 104 (3), 034610 (2021).</li>
	<li>Hoyer, S., Hamman, J. xarray: N-D labeled arrays and datasets in Python. Journal of Open Research Software. 5 (1), 10 (2017).</li>
	<li>Aufderhorst-Roberts, A., Koenderink, G. H. Stiffening and inelastic fluidization in vimentin intermediate filament networks. Soft Matter. 15 (36), 7127-7136 (2019).</li>
	<li>Guo, M. et al. The role of vimentin intermediate filaments in cortical and cytoplasmic mechanics. Biophysical Journal. 105 (7), 1562-1568 (2013).</li>
	<li>Lavenus, S. B., Tudor, S. M., Ullo, M. F., Vosatka, K. W., Logue, J. S. A flexible network of vimentin intermediate filaments promotes migration of amoeboid cancer cells through confined environments. Journal of Biological Chemistry. 295 (19), 6700-6709 (2020).</li>
	<li>Patteson, A. E. et al. Loss of vimentin enhances cell motility through small confining spaces. Small. 15 (50), 1903180 (2019).</li>
	<li>Lin, Y.-C. et al. Origins of elasticity in intermediate filament networks. Physical Review Letters. 104 (5), 058101 (2010).</li>
	<li>Pawelzyk, P., M&#252;cke, N., Herrmann, H., Willenbacher, N. Attractive interactions among intermediate filaments determine network mechanics in vitro. PLOS ONE. 9 (4), e93194 (2014).</li>
	<li>Schepers, A. V. et al. Multiscale mechanics and temporal evolution of vimentin intermediate filament networks. Proceedings of the National Academy of Sciences. 118 (27), e2102026118 (2021).</li>
	<li>Wu, H. et al. Effect of divalent cations on the structure and mechanics of vimentin intermediate filaments. Biophysical Journal. 119 (1), 55-64 (2020).</li>
	<li>Dogterom, M., Koenderink, G. H. Actin-microtubule crosstalk in cell biology. Nature Reviews Molecular Cell Biology. 20 (1), 38-54 (2019).</li>
	<li>Giavazzi, F., Malinverno, C., Scita, G., Cerbino, R. Tracking-free determination of single-cell displacements and division rates in confluent monolayers. Frontiers in Physics. 6, 120 (2018).</li>
	<li>Cho, J. H. Multiscale Probing of Colloidal Gelation Dynamics., Massachusetts Institute of Technology (2018).</li>
	<li>Krall, A. H., Weitz, D. A. Internal dynamics and elasticity of fractal colloidal gels. Physical Review Letters. 80 (4), 778-781 (1998).</li>
	<li>Bayles, A. V., Squires, T. M., Helgeson, M. E. Probe microrheology without particle tracking by differential dynamic microscopy. Rheologica Acta. 56 (11), 863-869 (2017).</li>
	<li>Edera, P., Bergamini, D., Trappe, V., Giavazzi, F., Cerbino, R. Differential dynamic microscopy microrheology of soft materials: a tracking-free determination of the frequency-dependent loss and storage moduli. Physical Review Materials. 1 (7), 073804 (2017).</li>
	<li>Wang, B., Kuo, J., Bae, S. C., Granick, S. When Brownian diffusion is not Gaussian. Nature Materials. 11 (6), 481-485 (2012).</li>
	<li>soft-matter/trackpy: Trackpy v0.5.0.&#160;Zenodo&#160;(2021).</li>
	<li>Crocker, J. C., Grier, D. G. Methods of digital video microscopy for colloidal studies. Journal of Colloid and Interface Science. 179 (1), 298-310 (1996).</li>
	<li>Nixon-Luke, R., Arlt, J., Poon, W. C. K., Bryant, G., Martinez, V. A. Probing the dynamics of turbid colloidal suspensions using differential dynamic microscopy. Soft Matter. 18 (9), 1856-1867 (2022).</li>
</ol>

The authors have nothing to disclose.

The software package described here uses DDM to analyze density fluctuations observed in images acquired using an optical microscope. Representative results from the data of tracer particles embedded in vimentin networks were first shown. The analysis of such data can be used to characterize the mesh size and stiffness of the network similarly to how single-particle tracking has been used in many past studies of cytoskeleton networks6,12,13. An advantage of using DDM over single-particle tracking is that DDM does not require the particles to be localized. Therefore, even in images where the particle density is too high or the particles too small to localize and track, DDM can still determine the dynamics. Where single-particle tracking would be advantageous is when inspecting particle-to-particle variability. With DDM, one finds the ensemble averaged dynamics whereas, with single-particle tracking, one may compute both a single particle&#39;s MSD and the ensemble-averaged MSD. However, DDM can be used to investigate heterogeneous dynamics by analyzing multiple regions of interest within a large field of view.
Next, representative results from data of fluorescently labeled filaments in an active network composed of two differently labeled cytoskeletal filament types were shown11. With this data, the ballistic motion was characterized without needing any localizable features within the image. Since DDM extracts the ensemble averaged dynamics with few user inputs, it makes comparing image series acquired with different conditions straightforward (e.g., comparing samples with different ratios of actin to microtubules or samples with different concentrations of myosin, as done in50). Additionally, using fluorescent imaging, we can investigate the dynamics of different components of a network using multicolor labeling. This was done in11,50, where the dynamics of actin and of microtubules were separately analyzed in an active actin-microtubule composite network using multicolor imaging. In the representative results section here, just the results from the microtubule channel were shown, but in previous work, we compared the dynamics of the microtubule and actin filaments11.
We note that these representative results showcase either passive subdiffusion or active ballistic motion. Importantly, DDM can be used to analyze systems where there is a crossover in the type of dynamics at intermediate time or length scales. As examples, Kurzthaler et al. used DDM with a system of active Janus colloids to explore active directed motion at short time scales and randomization of the orientation at longer time scales59; Giavazzi et al. used DDM with a coarsening foam and found a crossover in the dynamics corresponding to the length scale of a bubble33; and Cho et al. used DDM with colloidal gels and found three distinguishable regimes at different length scales spanning from the fractal clusters to the whole network32.
The data included in the representative results section were acquired with brightfield microscopy and laser-scanning confocal microscopy. However, as previously noted, DDM can be used with many imaging modalities. With any imaging modality, users should consider optical settings such as the degree of optical sectioning or the depth of field. A high degree of optical sectioning may reduce signal from out-of-focus objects, but one will not be able to accurately measure dynamics over timescales greater than the timescale for objects to move out of the depth of field25,28. A more thorough discussion of how the q-dependent depth of field affects DDM analysis can be found in22. For brightfield imaging, users may also need to consider the sample thickness. While for weakly scattering samples, thicker samples may provide more signal42, turbid samples may require modifying the analysis to account for multiple scattering81. Finally, for imaging methods that are not linear space invariant (that is, where the intensity recorded by the camera of an object depends on where that object is in the x-y sample plane), one may need to account for the linear space variance, as demonstrated with dark-field DDM27.
For those getting started with DDM, we wish to emphasize the importance of considering the spatial and temporal resolution. When inspecting the determined decay times as a function of wavenumber, it is important to mark the limits of one&#39;s resolution (i.e., the maximum and minimum lag times and the maximum wavenumber, as done in Figure 5). One should think carefully about these limits prior to collecting data so that the optimal objective lens, image size, frame rate, and movie duration can be selected. The other important consideration is how to estimate the background parameter B. Multiple methods for estimating the background have been used in the literature, and the effects of over- or underestimating B have been described in prior publications62,77. As shown in Figure 10, PyDDM allows users to implement different methods for estimating B, and we suggest new users try these methods and evaluate which are appropriate to use.
A strength of this package is its thorough documentation and walkthroughs featuring example data, the storage and organization of metadata to keep track of how analyses were performed, and the flexibility in how to analyze the DDM matrix (various fitting models, multiple methods for estimating the background parameter B, the ability to find the MSD). However, there are multiple aspects to this code that could be improved. Currently, the code has not been optimized for fast computation speed. Methods for speeding up the computation have been reported61,62, and these will be implemented in future releases. Additionally, we plan to implement recently reported methods to better estimate uncertainties and to employ simulations for guiding users to the appropriate ISF model62. For other improvements, we hope users will contact us with suggestions.

The cytoskeleton is a network of protein filaments that spans across the cytoplasm of eukaryotic cells, connecting the cell surface to the nucleus. It has unique material properties, providing mechanical protection against large and repeated mechanical loads, yet also driving dynamic cell shape changes1. Reconstituted cytoskeleton networks can give rise to a range of interesting dynamic behaviors, from the caging of embedded particles to ballistic motion driven by molecular motors2,3,4,5,6,7,8,9,10,11. Methods to analyze the dynamics of such networks include tracking the motion of embedded tracer microspheres6,7,12,13,14, image analysis to track the size of protein-dense clusters over time8, dynamic light scattering15, particle image velocimetry4,16,17,18,19, computing the power spectral density of images over time19, and kymograph analysis20. As more studies on reconstituted cytoskeleton networks are conducted, whether to understand cellular mechanics or active matter, robust, unbiased, and reproducible methods for characterizing the dynamics are increasingly necessary. Differential dynamic microscopy (DDM)21,22, a relatively new technique that has been used to study cytoskeleton dynamics, is one such technique that efficiently quantifies dynamics with few user-defined parameters. With the software package described here, researchers with little experience in programming or image analysis will be able to leverage DDM for their own work.
DDM is an image analysis technique to extract a sample&#39;s dynamics. Like particle tracking or particle image velocimetry, DDM requires a time series of images (often thousands of images), typically recorded with a microscope. Unlike particle tracking, individual features or tracer beads do not need to be localized (or even be localizable) in the image. Unlike both particle tracking and particle image velocimetry, one recovers the ensemble dynamics with DDM with relatively few user-specified parameters. With DDM, images are analyzed in Fourier space to determine the decay time of density fluctuations&#160;over a range of wavenumbers, q, where q = 2&#960;u, and u is the magnitude of the spatial frequencies, <img alt="Equation004" src="/files/ftp_upload/63931/63931eq004.png" />. One obtains scattering-like information but with real-space images acquired on a microscope21,22,23. Therefore, one can take advantage of the various contrast-generating methods of microscopy, such as widefield fluorescence22,24, confocal fluorescence25, polarized26, dark-field27, or light-sheet fluorescence28 microscopies. Furthermore, images used for DDM analysis may be used for particle tracking or particle image velocimetry to provide complementary information.
This combination of features from dynamic light scattering and optical microscopy makes DDM a powerful and versatile technique. Since its first description by Cerbino and Trappe in 200821, where DDM was demonstrated to measure the diffusion of 73 nm colloidal particles, DDM has been used to measure flowing colloids29, colloidal aggregation30,31, the viscoelasticity of nematic liquid crystals26, the dynamics of colloidal gels32, coarsening foams33, nanoparticles in confined environments34,35,36,37, bacterial motility38,39,40,41, the diffusion of weakly scattering protein clusters42, capillary waves at fluid interfaces43, and other systems. Those looking for a more complete listing of publications employing DDM can refer to thorough review papers on the subject22,23,44,45.
DDM has also been used to investigate the dynamics of biological networks. Drechsler et al. used DDM to measure the dynamics of actin in living Drosophila oocytes46. Burla et al. quantified the dynamics of tracer particles in networks of hyaluronan and hyaluronan-collagen composites47. Several uses of DDM to study the dynamics of tracer particles in reconstituted cytoskeleton networks9,10, the transport of DNA molecules in such networks48,49, and the dynamics of active reconstituted networks have also been documented11,50,51. An advantage of DDM in measuring the dynamics in such systems is that individual particles or molecules do not need to be localized and tracked. So, for example, the dynamics of DNA molecules in crowded environments can be measured with DDM despite the difficulty in tracking such small and non-spherical molecules. Furthermore, with fluorescence microscopy, one can use multi-color labeling to selectively measure the dynamics of individual constituents in a complex composite.
To perform DDM, a sequence of images is taken over time, I(x,y,t). For a given lag time, &#916;t, all (or a subset of) pairs of images separated by that lag time are found. The squared Fourier transform of the difference of each pair,
<img alt="Equation007" src="/files/ftp_upload/63931/63931eq007.png" style="margin-bottom: 0px;" />
is computed and averaged together. This quantity, <img alt="Equation008" src="/files/ftp_upload/63931/63931eq008.png" style="margin-bottom: 0px;" />, is radially averaged, provided that the dynamics are isotropic. This yields the DDM matrix (also referred to as the image structure function), <img alt="Equation009" src="/files/ftp_upload/63931/63931eq009.png" style="margin-bottom: 0px;" />. This process is shown graphically in Figure 1. To determine the sample&#39;s dynamics from this DDM matrix, the DDM matrix is assumed to take the form
<img alt="Equation010" src="/files/ftp_upload/63931/63931eq010.png" style="margin-bottom: 0px;" />
where A is the amplitude, which depends on the details of the microscope and the structure of the sample, B is the background, which depends on the noise in the images, and f&#160;(q, &#916;t) is the intermediate scattering function (ISF), which contains information about the dynamics21,22. In simple cases,
<img alt="Equation014" src="/files/ftp_upload/63931/63931eq014.png" style="margin-bottom: 0px;" />
where&#160;&#964; is a characteristic decay or decorrelation time. Such an ISF has been used in several studies employing DDM on ergodic systems like dilute colloidal suspensions21,24,27,37,40,52. However, other forms of the ISF can be used to model various types of dynamics. For example, one may use a cumulant expansion to model the ISF for polydisperse samples as
<img alt="Equation016" src="/files/ftp_upload/63931/63931eq016.png" style="margin-bottom: 0px;" />
where&#160;&#956; is a measure of the polydispersity42,53; if density fluctuations decay by two separate modes one may use an ISF like
<img alt="Equation018" src="/files/ftp_upload/63931/63931eq018.png" style="margin-bottom: 0px;" /> 26, 54, 55, 56, 57;
other ISFs can be used for swimming micro-organisms or other active particles38,39,40,41,58,59.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/63931/63931fig1v2.jpg" /> 
Figure 1: Overview of DDM analysis. From the time series of images, the Fourier transform of image differences is computed to calculate the DDM matrix. The DDM matrix can be fit to a model to determine the time scale of density fluctuations across a range of q values. <a href="https://www.jove.com/files/ftp_upload/63931/63931fig1v2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Here, the use of a DDM analysis software package developed in Python, PyDDM, is described. This software package builds on the work done by our research labs and other published studies over the last several years. Primary motivators for creating this software package include the need for (1) keeping track of and storing metadata and parameters used in the analysis; (2) thorough documentation with detailed examples of analysis from start to finish; and (3) an easy way to employ different (or create new) mathematical models for fitting the data (e.g., adding ISF models, such as ones recently developed for active filaments60, would be straightforward). Other software packages for DDM analysis also exist, though not all are well documented and written in an open-source programming language. For example, there is C++ code with computing on GPUs (https://github.com/peterlu/ConDDM)25, C++ code that uses Fourier transforms in time to speed up calculations (https://github.com/giovanni-cerchiari/diffmicro)61, MATLAB and Python versions (https://github.com/MathieuLeocmach/DDM)40, MATLAB code (https://sites.engineering.ucsb.edu/~helgeson/ddm.html)27, and MATLAB code with uncertainty quantification (https://github.com/UncertaintyQuantification/DDM-UQ)62. As this PyDDM package is well documented and provides a lot of flexibility in how the DDM matrix is calculated and analyzed, it can hopefully be useful to researchers looking to implement DDM regardless of their background in programming or image analysis.&#160;
The protocol shows how this software package can be used to quantify the dynamics of in vitro reconstituted cytoskeleton networks. This is done by using two distinct sets of imaging data: (1) images of submicron tracer particles embedded in a vimentin network taken with brightfield microscopy and (2) images of fluorescently labeled actin and microtubule filaments in an entangled composite network with myosin-driven activity taken with laser-scanning confocal microscopy. The analyses of these two datasets highlight notable strengths of DDM, including its ability to analyze images taken with a variety of imaging modalities (e.g., brightfield or confocal fluorescence), to extract dynamics from either embedded tracers or from labeled filaments, and to quantify a variety of dynamics (e.g., subdiffusive and constrained or ballistic).

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>CMOS camera, Orca-Flash 4.0</td>
			<td>Hamatsu</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>F-127 Pluronic</td>
			<td>Sigma Aldrich</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Jupyter Notebook</td>
			<td></td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Nanodrop</td>
			<td>Thermo Fisher</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Nikon Ti-Eclipse microscope</td>
			<td>Nikon</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>PLL-PEG-bio</td>
			<td>SuSos AG, D&#252;bendorf, Switzerland</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Polystyrene beads</td>
			<td>Sigma Aldrich</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>Protein dialysis mini-cassette</td>
			<td>Thermo Fisher</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>PyDDM</td>
			<td>University of San Diego</td>
			<td>N/A</td>
			<td>Open source software available from https://github.com/rmcgorty/PyDDM</td>
		</tr>
	</tbody>
</table>

quantifying cytoskeleton dynamics using differential dynamic microscopy

Cells can crawl, self-heal, and tune their stiffness due to their remarkably dynamic cytoskeleton. As such, reconstituting networks of cytoskeletal biopolymers may lead to a host of active and adaptable materials. However, engineering such materials with precisely tuned properties requires measuring how the dynamics depend on the network composition and synthesis methods. Quantifying such dynamics is challenged by variations across the time, space, and formulation space of composite networks. The protocol here describes how the Fourier analysis technique, differential dynamic microscopy (DDM), can quantify the dynamics of biopolymer networks and is particularly well suited for studies of cytoskeleton networks. DDM works on time sequences of images acquired using a range of microscopy modalities, including laser-scanning confocal, widefield fluorescence, and brightfield imaging. From such image sequences, one can extract characteristic decorrelation times of density fluctuations across a span of wave vectors. A user-friendly, open-source Python package to perform DDM analysis is also developed. With this package, one can measure the dynamics of labeled cytoskeleton components or of embedded tracer particles, as demonstrated here with data of intermediate filament (vimentin) networks and active actin-microtubule networks. Users with no prior programming or image processing experience will be able to perform DDM using this software package and associated documentation.

Watch this Scientific Journal Video about Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy at JoVE.com

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Differential dynamic microscopy (DDM) combines features of dynamic light scattering and microscopy. Here, the process of using DDM to characterize reconstituted cytoskeleton networks by quantifying the subdiffusive and caged dynamics of particles in vimentin networks and the ballistic motion of active myosin-driven actin-microtubule composites is presented.

Cells can crawl, self-heal, and tune their stiffness due to their remarkably dynamic cytoskeleton. As such, reconstituting networks of cytoskeletal ...

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