Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Our protocol can quantify dynamics in many systems using a range of optical microscopy techniques. We highlight how this method can, in particular, help characterize the dynamics of reconstituted cytoskeleton networks. The main advantage of using our Differential Dynamic Microscopy software package is that it is well-documented, has multiple example analysis files and can easily be adapted to study different types of dynamics.

Our software package can be used to quantify dynamics not only in reconstituted cytoskeleton networks, but also in other soft and biologically relevant materials. Based on the time and length scales to probe acquire image sequences of over 1, 000 frames using microscope control software, such as Micro-Manager. Under the examples folder provided in the PyDDM code repository, make a copy of the parameter file named, example_parameter_file.yml.

Open this EML file with a text editor like Notepad+or the text editor in JupyterLab. In the copied EML 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.

Under the analysis parameter section, select the parameters for calculation of the DDM matrix, such as the number of different lag times and the longest lag time. Provide details on the fitting of the DDM matrix or the intermediate scattering function in the fitting parameter section, such as the name of the model and model parameter, initial guess, lower bound and upper bound. Initialize an instance of the DDM analysis class by providing the metadata in the analysis parameters by passing the file name of the EML file with the full file path to DDM analysis.

Alternatively, pass the metadata and parameters as a Python dictionary data structure. Run the function to calculate the DDM matrix. Inspect the returned data with the associated variables and metadata, which are stored as a dataset in the Xarray package.

Then, inspect the plots and figures, which are saved as a PDF file and the data directory. One of these plots shows the default method for how the background is estimated. If needed, change the method in which the background is estimated using the parameter background method in either the EML file or as an optional keyword argument to the function calculate DDM matrix.

Initialize an instance of the DDM fit class by passing the file name of the EML file containing the image metadata and fitting parameters. List the available models by executing the function print fitting models. Specify the model to be used in the EML parameter file or by using the function reload fit model by name.

For each parameter in the chosen model, set the initial guesses and bounds if different from values specified in the EML file by using the functions set parameter initial guess and set parameter bounds. Execute the fit with the function fit. Generate plots for inspecting the fits in the q dependence of the fit parameters with the function fit report.

Check the output including the figure with two by two subplots showing the DDM matrix or ISF at four q values along with the fit. Use the class browse DDM fits in the Jupyter Notebook environment to plot the DDM matrix or ISF along with the best fit in an interactive way. Clicking on a point in the decay time versus wavenumber plot will show the data and fit.

Check the results of the fit saved in an Xarray dataset and use the function two netCDF or Python’s built-in pickle module to save this data structure to disk. DDM analysis was performed on the brightfield image series of 0.6 micron beads in a vimentin network and confocal microscope images from an active actin-microtubule composite network with spectrally distinct fluorescent labels. Intermediate scattering functions were plotted as a function of lag time at different wavenumbers and a network with a vimentin concentration of 19 micromolar and 34 micromolar.

The long lag time plateau of the function at a value well above zero indicates nonergodicity. The decay time tau plotted as a function of q for two networks with different vimentin concentrations show to sub-diffusive or confined motion. The nonergodicity parameters c plotted as a function of q squared for the network with 34 and 49 micromolar vimentin showed that the log of c was proportional to q squared as expected for confined motion.

The mean squared displacement versus lag time plots showed that the values determined from DDM agreed well with that found through single particle tracking. For the more concentrated network, the value plateaus at longer lag times. DDM matrix versus lag time for an active actin-microtubule composite network showed that the DDM matrix for a particular q value had a plateau at low lag times, then increased in further plateaued at large lag times.

The characteristic decay times tau from the fits to the DDM matrix show that the relationship between tau and q indicates ballistic motion. After developing this PyDDM software package, we used it to investigate the anisotropic and time-varying dynamics of active cytoskeleton networks and other systems.