Uncovering diffusive states of the yeast membrane protein, Pma1, and how labeling method can change diffusive behavior

Abstract

We present and analyze video-microscopy-based single-particle-tracking measurements of the budding yeast (Saccharomyces cerevisiae) membrane protein, Pma1, fluorescently labeled either by direct fusion to the switchable fluorescent protein, mEos3.2, or by a novel, light-touch, labeling scheme, in which a 5 amino acid tag is directly fused to the C-terminus of Pma1, which then binds mEos3.2. The track diffusivity distributions of these two populations of single-particle tracks differ significantly, demonstrating that labeling method can be an important determinant of diffusive behavior. We also applied perturbation expectation maximization (pEMv2) (Koo and Mochrie in Phys Rev E 94(5):052412, 2016), which sorts trajectories into the statistically optimum number of diffusive states. For both TRAP-labeled Pma1 and Pma1-mEos3.2, pEMv2 sorts the tracks into two diffusive states: an essentially immobile state and a more mobile state. However, the mobile fraction of Pma1-mEos3.2 tracks is much smaller ([Formula: see text]) than the mobile fraction of TRAP-labeled Pma1 tracks ([Formula: see text]). In addition, the diffusivity of Pma1-mEos3.2's mobile state is several times smaller than the diffusivity of TRAP-labeled Pma1's mobile state. Thus, the two different labeling methods give rise to very different overall diffusive behaviors. To critically assess pEMv2's performance, we compare the diffusivity and covariance distributions of the experimental pEMv2-sorted populations to corresponding theoretical distributions, assuming that Pma1 displacements realize a Gaussian random process. The experiment-theory comparisons for both the TRAP-labeled Pma1 and Pma1-mEos3.2 reveal good agreement, bolstering the pEMv2 approach.

Fig. 1

Wide-field fluorescence microscopy images for four strains of S. cerevisiae: a Cells expressing the Pma1-mCherry direct fusion; b Cells expressing the Pma1-mEos3.2 direct fusion; c Cells expressing the Pma1-MEEVF/TRAP-mEos3.2 TRAP-peptide system; and d Cells expressing untagged Pma1 and TRAP-mEos3.2. In each case, the scale bars correspond to 3 μm

Fig. 2

Trajectories comprising four or more steps obtained from 20000 frames of wide-field PALM movies from cells with a Pma1-mEos3.2 and b TRAP-labeled Pma1. Trajectories comprising four or more steps obtained from 20000 frames of PALM movies, under TIRF illumination, from cells with c Pma1-mEos3.2 and d TRAP-labeled Pma1. In each panel, the scale bar represents 3 μm

Fig. 3

a Number of tracks and b probability versus track length plotted on logarithmic-linear axes for TRAP-labeled Pma1, shown in blue, and Pma1-mEos3.2, shown in pink. Overlap in the histograms is represented in bordeaux. Two is the minimum number of connected steps to be considered a track

Fig. 4

Comparison between the distributions of track diffusivities, $D$, for a experimental TRAP-labeled Pma1 and b experimental direct fusion data. In both cases, the track length equals four steps. The overall, unsorted, population-averaged distributions, shown as the light gray histograms, are plotted with the theoretical two-component curve, shown as the red curve, calculated using Eq. 12 and the pEMv2-found covariance values. The sorted track diffusivity distributions (dark and darker gray histograms) are shown with their corresponding single state theory curves (blue and cyan curves), given by Eq. 9. Overlap between histograms is denoted by a deep gray color

Fig. 5

Relative Bayesian Information Criterion $({\text{BIC}}_K-{\text{BIC}}_1)$ values versus number of diffusive states for TRAP-labeled Pma1 (blue) and Pma1-mEos3.2 trajectories (red). The highest relative BIC value occurs for two states

Fig. 6

Distribution of covariance elements a $S_0$ and b $S_1$, for experimental 4-step TRAP-labeled Pma1 tracks. The unsorted covariance distribution (light gray histogram) is plotted with the theoretical two-component curve (red curve) given by Eq. 11, and the fitted two-component curve (black dashed line). The tracks are sorted into two distributions representing the two distinct diffusive states found by pEMv2 (dark gray and darker gray histograms), and plotted with their single theory curves (blue and cyan curves), given by Eq. 4. Overlap between histograms is denoted by a deep gray color

Fig. 7

$p$ values versus KS statistic for TRAP-labeled Pma1 tracks, determined as described in the text by simulation, for state 1 $S_0$ (red) and $S_1$ (orange), and state 2 $S_0$ (blue) and $S_1$ (cyan). Also shown is the analytic $p$ value according to the Kolmogorov distribution. The black circles correspond to the experimental KS statistics for each track length and their corresponding $p$ values

Fig. 8

$p$ values versus $\sqrt{\frac{n_1{n}_2}{n_1+n_2}}\times \text{KS}$ statistic, for TRAP-labeled Pma1 tracks, determined as described in the text by simulation, for state 1 $S_0$ (red) and $S_1$ (orange) and state 2 $S_0$ (blue) and $S_1$ (cyan)

Fig. 9

Sorted CDFs for TRAP-labeled tracks. Shown are pEMv2-sorted experimental $S_0$ distributions (black dashed lines) for state 1 and state 2, compared to 40000 simulated tracks for state 1 (blue) and state 2 (cyan), plotted with pEMv2-sorted experimental $S_1$ distributions (black dashed lines) for state 1 and state 2, compared to 40000 simulated tracks for state 1 (red) and state 2 (magenta)

Fig. 10

Distribution of covariance elements, $S_0$ (a) and $S_1$ (b), for experimental direct-fusion tracks. The unsorted covariance distribution (light gray histogram) is plotted with the theoretical two-component curve (red curve) given by Eq. 11, and the fitted two-component curve (black dashed line). The tracks are sorted into two distributions representing the two distinct diffusive states found by pEMv2 (dark gray and darker gray histograms), and plotted with their single theory curves (blue and cyan curves), given by Eq. 4. Overlap between histograms is denoted by a deep gray color

Fig. 11

$p$ values versus KS statistic for direct-fusion tracks, determined as described in the text by simulation, for state 1 $S_0$ (red) and $S_1$ (orange), and state 2 $S_0$ (blue) and $S_1$ (cyan). Also shown is the analytic $p$ value according to the Kolmogorov distribution. The black circles correspond to the experimental KS statistics for each track length and their corresponding $p$ values

Fig. 12

$p$ values versus $\sqrt{\frac{n_1{n}_2}{n_1+n_2}}\times \text{KS}$ statistic, for direct-fusion tracks, determined as described in the text by simulation, for state 1 $S_0$ (red) and $S_1$ (orange) and state 2 $S_0$ (blue) and $S_1$ (cyan)

Fig. 13

Sorted CDFs of experimental direct-fusion data. CDFs for $S_0$-distributions and $S_1$-distributions (black dashed lines) for each sorted state, compared to theory curves for each state (blue and cyan lines for $S_0$ states 1 and 2; red and magenta for $S_1$, states 1 and 2, respectively)

Fig. 14

Comparison of the mean squared displacements (MSDs) for TRAP-labeled Pma1 trajectories sorted into state 1 (blue) and state 2 (cyan) across track length. Similarly, the MSDs of the experimental direct fusion data are plotted for state 1 (red) and state 2 (magenta). In each case, the state 2 MSDs have higher slopes than state 1