3D single-molecule localization microscopy is utilized to probe the spatial positions and motion trajectories of fluorescently labeled proteins in living bacterial cells. The experimental and data analysis protocol described herein determines the prevalent diffusive behaviors of cytosolic proteins based on pooled single-molecule trajectories.
Single-molecule localization microscopy probes the position and motions of individual molecules in living cells with tens of nanometer spatial and millisecond temporal resolution. These capabilities make single-molecule localization microscopy ideally suited to study molecular level biological functions in physiologically relevant environments. Here, we demonstrate an integrated protocol for both acquisition and processing/analysis of single-molecule tracking data to extract the different diffusive states a protein of interest may exhibit. This information can be used to quantify molecular complex formation in living cells. We provide a detailed description of a camera-based 3D single-molecule localization experiment, as well as the subsequent data processing steps that yield the trajectories of individual molecules. These trajectories are then analyzed using a numerical analysis framework to extract the prevalent diffusive states of the fluorescently labeled molecules and the relative abundance of these states. The analysis framework is based on stochastic simulations of intracellular Brownian diffusion trajectories that are spatially confined by an arbitrary cell geometry. Based on the simulated trajectories, raw single-molecule images are generated and analyzed in the same way as experimental images. In this way, experimental precision and accuracy limitations, which are difficult to calibrate experimentally, are explicitly incorporated into the analysis workflow. The diffusion coefficient and relative population fractions of the prevalent diffusive states are determined by fitting the distributions of experimental values using linear combinations of simulated distributions. We demonstrate the utility of our protocol by resolving the diffusive states of a protein that exhibits different diffusive states upon forming homo- and hetero-oligomeric complexes in the cytosol of a bacterial pathogen.
Examining the diffusive behavior of biomolecules provides insight into their biological functions. Fluorescence microscopy-based techniques have become valuable tools for observing biomolecules in their native cell environment. Fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS)1 provide ensemble-averaged diffusive behaviors. Conversely, single-molecule localization microscopy enables observation of individual fluorescently tagged molecules with high spatial and temporal resolution2,3,4. Observing individual molecules is advantageous since a protein of interest may exist in different diffusive states. For example, two readily distinguishable diffusive states arise when a transcriptional regulator, such as CueR in Escherichia coli, diffuses freely in the cytosol or binds to a DNA sequence and becomes immobilized on the timescale of measurement5. Single-molecule tracking provides a tool for observing these different states directly, and sophisticated analyses are not required to resolve them. However, it becomes more challenging to resolve multiple diffusive states and their population fractions in cases where their diffusive rates are more similar. For example, due to the size dependence of the diffusion coefficient, different oligomerization states of a protein manifest themselves as different diffusive states6,7,8,9,10. Such cases require an integrated approach in terms of data acquisition, processing and analysis.
A critical factor influencing diffusive rates of cytosolic molecules is the effect of confinement by the cell boundary. The restrictions placed on molecular motion by a bacterial cell boundary cause a cytosolic molecules’ measured diffusion rate to appear slower than if the same motion had occurred in an unconfined space. For very slowly diffusing molecules, the effect of cellular confinement is negligible due to the lack of collisions with the boundary. In such cases, it may be possible to accurately resolve diffusive states by fitting the distributions of molecular displacements, r, or apparent diffusion coefficients, D*, using analytical models based on the equations for Brownian motion (random diffusion)11,12,13. However, for fast diffusing cytosolic molecules, the experimental distributions no longer resemble those obtained for unconfined Brownian motion due to collisions of diffusing molecules with the cell boundaries. Confinement effects must be accounted for to accurately determine the unconfined diffusion coefficients of the fluorescently labeled molecules. Several approaches have recently been developed to account for confinement effects either (semi-)analytically 5,14,15,16 or numerically through Monte Carlo simulations of Brownian diffusion6,10,16,17,18,19.
Here, we provide an integrated protocol for collecting and analyzing single-molecule localization microscopy data with a particular focus on single-molecule tracking. The end goal of the protocol is to resolve diffusive states of fluorescently labeled cytosolic proteins inside, in this case, rod-shaped bacterial cells. Our work builds on a previous protocol for single-molecule tracking, in which a DNA polymerase, PolI, was shown to exist in a DNA bound and unbound state by diffusion analysis20. Here, we expand single-molecule tracking analysis to 3D measurements and perform more realistic computational simulations to resolve and quantify multiple diffusive states simultaneously present in cells. The data is acquired using a home-built 3D super-resolution fluorescence microscope which is capable of determining the 3D position of fluorescent emitters by imaging with the double-helix point-spread-function (DHPSF)21,22. The raw single-molecule images are processed using custom-written software to extract the 3D single-molecule localizations, which are then combined into single-molecule trajectories. Thousands of trajectories are pooled to generate distributions of apparent diffusion coefficients. In a final step, the experimental distributions are fit with numerically generated distributions obtained through Monte-Carlo simulations of Brownian motion in a confined volume. We apply this protocol to resolve the diffusive states of the Type 3 secretion system protein YscQ in living Yersinia enterocolitica. Due to its modular nature, our protocol is generally applicable to any type of single-molecule or single-particle tracking experiment in arbitrary cell geometries.
1. Double-helix point-spread-function calibration
NOTE: Images described in this and the following sections are acquired using a custom built inverted fluorescence microscope, as described in Rocha et al.23. The same procedure is applicable to different microscope implementations designed for single-molecule localization and tracking microscopy2,3,4. All software for image acquisition and data processing described in this article is available (https://github.com/GahlmannLab2014/Single-Molecule-Tracking-Analysis.git).
2. Bacterial culture preparation
3. Data acquisition
4. Data processing
NOTE: A modified version of the Easy-DHPSF software24 is used in MATLAB for the analysis of the raw camera frames to extract single-molecule localizations. Easy-DHPSF is used specifically to fit DHPSF localizations in single-molecule imaging. Custom changes were made to implement Maximum Likelihood Estimation (MLE)-based fitting routine that accounts for the pixel-dependent noise characteristics of modern sCMOS cameras26. It was also modified to accept the image file type output from the HCImage Live program (.dcimg). For a more detailed explanation of the software and the individual steps, please see Lew et al.24
5. Data post-processing
6. Single-molecule tracking
NOTE: The following section is completed using custom-written software in MATLAB. This section describes the steps the software performs.
7. Monte-Carlo simulation of Brownian motion in a confined volume
NOTE: Create libraries of simulated apparent diffusion coefficient distributions by performing Monte Carlo simulations of Brownian motion confined to a cylindrical volume, using 64 values in the range of 0.05–20 µm2/s as input parameters (software available from the authors upon request). This range was chosen to cover the range of previously estimated diffusion coefficients of fluorescent (fusion) proteins in bacteria. 64 diffusion coefficients are used to sample this range sufficiently. This section is performed using custom-written software in MATLAB and describes the steps the software automatically takes. The rod-shaped Y. enterocolitica cells used here are approximated by a cylindrical volume of length l = 5 µm and diameter d = 0.8 µm.
8. Experimental apparent diffusion coefficient distribution fitting
NOTE: Fit experimentally measured distributions of apparent diffusion coefficients using linear combinations of the simulated distributions generated in the previous section (Monte-Carlo simulation of Brownian motion in a confined volume). This section is performed using custom-written software in MATLAB and describes the steps the software automatically takes. For more information and examples of application, please see Rocha et al.29
Under the experimental conditions described here (20,000 frames, trajectory length minimum of 4 localizations) and depending on the expression levels of the fluorescently labeled fusion proteins, approximately 200-3,000 localizations yielding 10-150 trajectories can be generated per cell (Figure 2a,b). A large number of trajectories is necessary to produce a well-sampled distribution of apparent diffusion coefficients. The size of FOV collected here is ~55 x 55 µm, with 10 FOV collected per experiment. Therefore, to obtain >5,000 trajectories per experiment each FOV should contain at least 50 cells. Ideally, the cell population should be made as dense as possible, but without having cells touch each other. If the cell density is too high, then the presence of touching or overlapping cells makes it challenging to segment them successfully using OUFTI(28), as described in Data Post Processing. Poor segmentation can lead to localizations and trajectories assigned incorrectly between cells.
Here, we present apparent diffusion coefficient data on the Y. enterocolitica Type 3 secretion protein YscQ, which we N-terminally labeled with the fluorescent protein eYFP. YscQ is a structural component of a membrane-spanning molecular machine, called the injectisome. The injectisome is comprised of over 20 different proteins, many of which are present in multiple copy numbers. Type 3 secretion injectisomes are broadly utilized by pathogenic gram-negative bacteria to deliver virulent effector proteins directly into host cell during infection. YscQ dynamically binds and unbinds to and from the cytosolic side of the injectisome. As a result, YscQ is also found freely diffusing in the cytosol. By applying the data acquisition, processing, and analysis protocol described above, we determined that unbound YscQ exists in at least 3 distinct diffusive states (Figure 3). These 3 diffusive states correspond to different homo- and hetero-oligomeric complexes of YscQ and other Type 3 secretion proteins23.
Figure 1: Optical diagram of microscope pathways. The microscope has a pathway for detection of fluorescence signal and a separate pathway for taking a phase contrast image. A motorized ‘flip-mirror’ is used to switch between the pathways. The camera detectors, excitation lasers, LED, and ‘flip-mirror’ are controlled remotely by computer. Please click here to view a larger version of this figure.
Figure 2: Single-molecule localizations and trajectories. (A). 3D single-molecule localizations of eYFP-YscQ in a Y. enterocolitica cell obtained in different frames (1,766 localizations). The localizations are overlaid on a phase contrast image of the cell. The green line indicates the cell outline based on the phase contrast image. (B). 3D single-molecule trajectories of eYFP-YscQ obtained from the localizations shown in panel A (142 trajectories). Different colors represent different single-molecule trajectories. Please click here to view a larger version of this figure.
Figure 3: Apparent diffusion coefficient distribution fitting of eYFP-YscQ in Y. enterocolitica. The apparent diffusion coefficient distribution for eYFP-YscQ in Y. enterocolitca was best fit with 3 diffusive states. Note that the probability density function (PDF) is shown here, while the data fitting was done by fitting the cumulative distribution function (CDF, Experimental Apparent Diffusion Coefficient Distribution Fitting). Figure adapted from Rocha et al23. Please click here to view a larger version of this figure.
Supplementary Figure 1. Microscope Control GUI. The microscope GUI controls the micropositioner of the stage, excitation lasers, LED, and cameras for fluorescence emission. Please click here to download this file.
Supplementary Figure 2. Easy-DHPSF GUI. The Easy-DHPSF software is used to extract single-molecule localizations from the DHPSF signals. Please click here to download this file.
Supplementary Figure 3. Oufti Segmentation. The open source software OUFTI28 is used to sement the cells. Here, the results of the cell segmentation are shown in green. Please click here to download this file.
Supplementary Figure 4. Selection of control points. Five points are selected in both the cell outline data and the localization data. The cell poles are used as reference points. These points are used to transform the data so that the cell outlines and localizations are correctly overlaid. Please click here to download this file.
Supplementary Figure 5. Delete unwanted cells. After the cell overlay, unwanted cells are manually deleted. Cells with unusually low/high amounts of localizations should be deleted, as well as any cells which are at the edge of the FOV. Please click here to download this file.
Supplementary Figure 6. Final overlay of cell outlines and localizations. After deletion of unwanted cells, the cell outlines and single-molecule localizations are finely transformed to get the final overlay. Localizations outside of cell outlines are deleted. Please click here to download this file.
Supplementary Mov. 1: Raw data for a single-molecule trajectory. Example of detection of eYFP-YscQ on the sCMOS camera. In frame 1, there is no fluorescence signal. In frames 2-10, fluorescence is detected from a single molecule. In each successive frame, the position and orientation of the DHPSF changes, indicating diffusion of this molecule. Finally, in frame 11, there is once again an absence in fluorescence signal, indicating the end of the trajectory. Each pixel is 108 x 108 nm. Please click here to download this file.
Supplementary Mov. 2: Raw data for a missed single-molecule trajectory. Frames 1-3 show fluorescence signal for a single emitter. However, frames 4-6 show the presence of two overlapping DHPSFs, indicating the presence of two emitters in close proximity. In such cases, the individual DHPSFs may not be correctly fit because of their overlap. Even if both DHPSFs are successfully fit, any trajectory observed containing these localizations would be discarded. Two or more localizations in the same cell may lead to incorrect assignments of localizations to a given trajectory. Each pixel is 108 x 108 nm. Please click here to download this file.
A critical factor for the successful application of the presented protocol is to ensure that single-molecule signals are well-separated from each other (i.e., they need to be sparse in space and in time (Supplementary Mov. 1)). If there is more than one fluorescing molecule in a cell at the same time, then localization could be incorrectly assigned to another molecules’ trajectory. This is referred to as the linking problem30. Experimental conditions, such as protein expression levels and excitation laser intensity can be chosen to avoid the linking problem. However, care should be taken to obtain wild-type protein expression levels to ensure representative results. Here, we used allelic replacements under the control of the native promoters instead of chemically inducible expression, to ensure native expression levels of the labeled proteins. Thus, the excitation laser intensity (for eYFP blinking) or the activation laser intensity (for photo-activatable fluorescent probes) can be used to control the concentration of active emitters in time. Alternatively, when chemical dye labeling is used in conjunction with HALO and SNAP tags31,32, then the dye concentration can be reduced until fluorescent signals are sparse enough to track single molecules33. The protocol presented here further eliminates the linking problem by discarding any trajectories for which two or more localizations are simultaneously present in the same cell (Supplementary Mov. 2). Thus, if single-molecule signals are too dense, a large amount of data is automatically discarded during processing. Under the excitation conditions used here (λex = 514 nm at 350 W/cm2), we obtained 10-150 trajectories per bacterial cell when acquiring 20,000 frames over the course of 8 min. On the other hand, if experimental conditions are chosen such that single-molecule signals are sparse, then the data acquisition throughput may be low, so that obtaining a sufficiently large number of single-molecule trajectories would require imaging additional cells in additional fields-of-view. Acquiring a large number of trajectories is beneficial, because the errors in the fitted parameters (the diffusion coefficients and the population fractions) decrease as the number of trajectories that are analyzed increase29.
Achieving large numbers of single-molecule trajectories requires high data-acquisition throughput. As a wide-field technique, single-molecule localization microscopy acquires data for each cell in the FOV simultaneously, and researchers have begun to take advantage of new sCMOS detectors that afford large FOVs26,34,35. However, excitation laser powers of several Watts are required to achieve uniform intensities sufficient for single-molecule localization microscopy throughout such large FOVs. Such laser powers may be above the damage threshold of commercially available objective lenses. Lenslet arrays employed to make the excitation laser intensities uniform in large FOVs may be able to circumvent this issue34. Additionally, optical aberrations become pronounced when imaging far away from the optical axis. As a result, the shape of the DHPSF may become too distorted to be successfully fit by a double Gaussian model employed in easy DHPSF. When imaging in an ultrawide FOV, more sophisticated spatially-varying PSF models are required36. To avoid these complicating factors, the data presented here were acquired in a relatively small FOV (diameter = 55 µm) and data from 10 FOVs were pooled to obtain more than 75,000 single-molecule trajectories.
Fitting of the experimentally measured apparent diffusion coefficient distributions with simulated distributions requires realistic simulation of the experimental data. Static and dynamic localization errors in camera-based tracking can affect the quality of the measurement11,13. Static localization errors are due to the finite numbers of photons collected per fluorescence emitter, which results in an imprecise PSF shape and thus result in single-molecule localizations of limited precision2,37,38. Dynamic localization errors arise due to moving emitters that generate blurred PSFs39. When an algorithm is applied to fit the shape of the PSF, motion-blurred images provide localizations with limited accuracy and precision39. In severe cases of rapid molecule movement, the image may be too distorted to fit, resulting in an unsuccessful fit and thus no recorded localization. Simulating spatially blurred PSFs with realistic signal to-noise ratios and localizing with the same fitting algorithm as experimental data accounts for both static and dynamic localization error. Second, rapidly diffusing molecules can be strongly confined to small volumes, such as the cytosol of a bacterial cell. As a result, the apparent diffusion coefficients are smaller, on average, than those expected for unconfined motion. Spatial confinement results in an overall left-shift of the distribution towards smaller diffusive values. Importantly, the shape of the distribution is no longer expressible as an analytical function. By explicitly accounting for static and dynamic localization errors due to motion blurring and confinement effects through stochastic simulations, realistic distributions can be obtained23.
The described diffusion analysis relies on two key assumptions regarding the dynamic behavior of the molecules in the biological environment. It assumes that diffusive states are described by confined Brownian motion and that they do not interconvert on the timescale of a single-molecule trajectory. We have experimentally verified that the assumption of confined Brownian motion is justified for free eYFP diffusion in Y. enterocolitica23. These results are in agreement with a number of studies in various bacterial species that have established that the motion of cytosolic proteins, fusion proteins, and biomolecular complexes smaller than 30 nm can be described by Brownian motion18,40,41,42,43,44,45. Non-specific collisions of small fluorescently labeled proteins with other cellular components may slow down the diffusion rates,45,46 but do not lead to deviations from Brownian diffusion. By contrast, specific interaction with cognate binding partners can produce a change in the diffusion coefficient, as recently shown for the Y. enterocolitica Type 3 secretion protein YscQ23. The validity of the second assumption is difficult to assess, especially for systems for which neither the diffusive states nor the binding kinetics are known. The situation is further complicated because any oligomerization states and binding kinetics measured in vitro, may not reflect the structures and dynamics that occur in vivo. A recent theoretical study based on the analysis framework presented here suggests that it may be possible to extract the state switching kinetics in addition to the diffusion coefficients and population fractions29.
In summary, we present an integrated protocol for resolving the diffusive states of fluorescently labeled molecules based on single-molecule trajectories measured in living bacterial cells. As presented here, the protocol is applied to 3D single-molecule localization microscopy using the double-helix PSF for imaging in Y. enterocolitica, a bacterial pathogen. However, with only a few modifications, the protocol can be applied to any type of 2D or 3D single-molecule localization microscopy and specimen geometry.
The authors have nothing to disclose.
We thank Alecia Achimovich and Ting Yan for critical reading of the manuscript. We thank Ed Hall, senior staff scientist in the Advanced Research Computing Services group at the University of Virginia, for help with setting up the optimization routines used in this work. Funding for this work was provided by the University of Virginia.
2,6-diaminopimelic acid | Chem Impex International | 5411 | Necessary for growth of Y. enterocolitica cells used. |
4f lenses | Thorlabs | AC508-080-A | f = 80mm, 2" |
514 nm laser | Coherent | Genesis MX514 MTM | Use for fluorescence excitation |
agarose | Inivtrogen | 16520100 | Used to make gel pads to mount liquid bacterial sample on microscope. |
ammonium chloride | Sigma Aldrich | A9434 | M2G ingredient. |
bandpass filter | Chroma | ET510/bp | Excitation pathway. |
Brain Heart Infusion | Sigma Aldrich | 53286 | Growth media for Y. enterocolitica. |
calcium chloride | Sigma Aldrich | 223506 | M2G ingredient. |
camera | Imaging Source | DMK 23UP031 | Camera for phase contrast imaging. |
dielectric phase mask | Double Helix, LLC | N/A | Produces DHPSF signal. |
disodium phosphate | Sigma Aldrich | 795410 | M2G ingredient. |
ethylenediaminetetraacetic acid | Fisher Scientific | S311-100 | Chelates Ca2+. Induces secretion in the T3SS. |
flip mirror | Newport | 8892-K | Allows for switching between fluorescence and phase contrast pathways. |
fluospheres | Invitrogen | F8792 | Fluorescent beads. 540/560 exication and emission wavelengths. 40 nm diameter. |
glass cover slip | VWR | 16004-302 | #1.5, 22mmx22mm |
glucose | Chem Impex International | 811 | M2G ingredient. |
immersion oil | Olympus | Z-81025 | Placed on objective lens. |
iron(II) sulfate | Sigma Aldrich | F0518 | M2G ingredient. |
long pass filter | Semrock | LP02-514RU-25 | Emission pathway. |
magnesium sulfate | Fisher Scientific | S25414A | M2G ingredient. |
microscope platform | Mad City Labs | custom | Platform for inverted microscope. |
nalidixic acid | Sigma Aldrich | N4382 | Y. enterocolitica cells used are resistant to nalidixic acid. |
objective lens | Olympus | 1-U2B991 | 60X, 1.4 NA |
Ozone cleaner | Novascan | PSD-UV4 | Used to eliminate background fluorescence on glass cover slips. |
potassium phosphate | Sigma Aldrich | 795488 | M2G ingredient. |
Red LED | Thorlabs | M625L3 | Illuminates sample for phase contrast imaging. 625nm. |
sCMOS camera | Hamamatsu | ORCA-Flash 4.0 V2 | Camera for fluorescence imaging. |
short pass filter | Chroma | ET700SP-2P8 | Emission pathway. |
Tube lens | Thorlabs | AC508-180-A | f=180 mm, 2" |
Yersinia enterocolitica dHOPEMTasd | N/A | N/A | Strain AD4442, eYFP-YscQ |
zero-order quarter-wave plate | Thorlabs | WPQ05M-514 | Excitation pathway. |