SMAUG: Analyzing single-molecule tracks with nonparametric Bayesian statistics.

Data Analysis

The analysis algorithms used are described in detail in the Theory section. All code and some test datasets are available as Supplementary Material .

Simulated SPT Trajectories

Simulations of SPT experiments were constructed with custom-built Matlab code (Matlab R2017b, The MathWorks). Each track was constructed with its duration drawn from a geometric distribution with expected value equal to ten time lapses. Each step along the track could belong to one of several mobility states with corresponding diffusion coefficient, D i . Mobility state labels were assigned for each localization by a random draw from the Transition Matrix. Steps along the trajectory were then constructed for movement in both the X and Y directions using a zero-mean Gaussian distribution with variance equal to 2 D i Δ t , where Δ t is the frame imaging time. Camera noise and motion blur were then applied to each dimension separately as described in [ 17 ]. The “realistic” range imaging parameters were based on reference [ 18 ]. A full description of the method for constructing the simulations is given in Supplementary Information Note 1 . In vitro experiments Fluoresbrite® microspheres with diameters of 100, 200, and 350 nm (Cat # 21636, Polysciences Inc.) in water were diluted 1:1 v/v with glycerol, and 5 μL of the 50% glycerol mixture was placed between two glass coverslips and imaged with a frame exposure time of 40 ms. The shutter was open during the entire image acquisition time with negligible dark time, leading to a total acquisition time of approximately 40 ms. Imaging was done in an Olympus IX71 inverted epifluorescence microscope with a 60× 1.20 NA water-immersion objective. Samples were excited by a 488 nm laser (Coherent Sapphire 488–50) with power density 140 W/cm 2 . The fluorescence emission was filtered with appropriate filters and imaged on a 512 × 512 pixel Photometrics Evolve electron-multiplying charge-coupled device (EMCCD) camera. Recorded single-molecule positions were detected and localized using home-built code as previously described [ 5 ], and connected into trajectories using the Hungarian algorithm [ 19 ].

Vibrio cholerae experiments

V. cholerae cells containing a chromosomal fusion of the photoactivatable red fluorescent protein, PAmCherry, to TcpP, a membrane-localized transcriptional regulator (TcpP-PAmCherry) as the sole source of TcpP. TcpP-PAmCherry is expressed at the native tcpP locus (strain LD51) and cells were grown under conditions known to stimulate TcpP-mediated expression of virulence genes [ 20 ] (LB rich media at pH 6.5 and 30 °C). Once cells reached mid log-phase they were diluted into M9 minimal media, and then imaged at room temperature on agarose pads using a 406-nm laser (Coherent Cube 405–100; 102 W/cm 2 ) for photo-activation and a 561-nm laser (Coherent-Sapphire 561–50; 163 W/cm 2 ) for imaging. Continual images were collected with a 40-ms exposure time per frame in an Olympus IX71 inverted epifluorescence microscope with a 100× 1.40 NA oil-immersion objective. The fluorescence emission was filtered with appropriate filters and imaged on a 512 × 512 pixel Photometrics Evolve EMCCD camera. Recorded single-molecule positions were detected and localized as previously described using home-built code [ 5 ], and connected into trajectories using the Hungarian algorithm [ 19 ].

B-cell receptor

(BCR) experiments The BCR dynamics were measured in CH27 mouse lymphoma B cells (RRID: CVCL_7178) as described in [ 21 ]. Briefly, cells were transiently expressing full-length versions of Lyn kinase or LAT2 (linker for activation of T cells 2)/LAB (linker for activation of B cells) conjugated to mEos3.2. Endogenous, plasma membrane-localized BCR was labeled for 10 min at room temperature with 5 mg/mL goat anti-mouse IgM (Jackson ImmunoResearch; RRID: AB_2338477) f(Ab)1 fragments conjugated to both silicon rhodamine (SiR) dye (Spirochrome, Switzerland) and biotin. Cells were imaged in a live-cell buffer compatible with BCR signaling both before and after the addition of 1μg/ml streptavidin, which clusters and activates receptors. Imaging was performed on an Olympus IX81-XDC inverted microscope with a cellTIRF module, a 100× UAPO TIRF objective (NA = 1.49), and active Z-drift correction (ZDC). Excitation of the SiR dye was accomplished using a 647 nm solid-state laser (OBIS, 100 mW, Coherent, Santa Clara, CA). Photoactivation of mEos3.2 was accomplished with a 405 nm diode laser (CUBE 405–50FP, Coherent) with excitation using a 561 nm solid-state laser (Sapphire 561 LP, Coherent). All images were taken on an iXon-897 EMCCD camera (Andor, CT) at approximately 45 frames/s with an exposure time of 20 ms. Recorded single-molecule positions were detected, localized, and connected into trajectories as described in [ 22 ]. Data acquired for Lyn was reported previously [ 21 ] and reanalyzed for this work.

Comparisons with other methods

We compared the ability of SMAUG to determine the underlying system parameters with other common analysis methods employed in the field: global cumulative probability distribution (CPDGlobal) [ 5 ], perturbation expectation-maximization (pEM) [ 7 ] and variational Bayes single-particle tracking (vbSPT) [ 16 ]. We analyzed the 4-state simulation described in Fig. 2 with these other methods ( SI Fig. S4 ). CPDGlobal is a curve-fitting method that constructs cumulative probability density (CPD) curves of the squared step sizes for several time lags and fits the whole set in a single “global” fitting step to an equation for K diffusive states. Because CPDGlobal cannot determine K from a dataset, we set this input value to the correct value of K = 4. The results show that CPDGlobal incorrectly identified either the diffusion coefficient, the weight fraction or both for all four states present in the system ( SI Fig. S4B ). The pEM method finds optimal estimates of parameter values with an iterative expectation-maximization algorithm, then bootstraps the results by sampling with replacement to attempt to get past local extrema to find globally optimal parameter values parameter values. Finally, pEM uncovers the true number of diffusive states while avoiding over-fitting by using a penalized global log-likelihood calculation. When there is no prior knowledge of the true number of states in the system, pEM draws an incorrect conclusion here: given our 4-state simulation data, pEM over-fit the true value and found the most likely model to be K = 6 ( SI Fig. S4C ). The parameter estimates from pEM for the true K = 4 states did more closely resemble the true values ( SI Fig. S4D ), though with less accuracy than SMAUG ( SI Fig. S4A ). Like SMAUG, vbSPT estimates parameter values within a Bayesian framework; vbSPT then uses a penalized log-likelihood to determine when the dataset has been over-fit. The vbSPT method under-fit the simulated data and found the most likely model to be K = 3, overshooting the slowest term and under estimating the upper end ( SI Fig. S4E ). These comparisons display the power of SMAUG to uncover the hidden information in an SPT experiment; other methods such as HMM-Bayes [ 31 ] were not appropriate for our data as these methods investigate if there exists directional diffusion in addition to normal diffusion within a single long trajectory, not among a whole dataset of related trajectories.

Supplementary Material 1 2