Depth-of-Focus Correction in Single-Molecule Data Allows Analysis of 3D Diffusion of the Glucocorticoid Receptor in the Nucleus

<div><p>Single-molecule imaging of proteins in a 2D environment like membranes has been frequently used to extract diffusive properties of multiple fractions of receptors. In a 3D environment the apparent fractions however change with observation time due to the movements of molecules out of the depth-of-field of the microscope. Here we developed a mathematical framework that allowed us to correct for the change in fraction size due to the limited detection volume in 3D single-molecule imaging. We applied our findings on the mobility of activated glucocorticoid receptors in the cell nucleus, and found a freely diffusing fraction of 0.49±0.02. Our analysis further showed that interchange between this mobile fraction and an immobile fraction does not occur on time scales shorter than 150 ms.</p></div

Calibration of the depth of field (DOF). eYFP was coated on a glass slide and the objective was moved by a piezo scanner (S1 Fig Data).

<p>The resulting peak-widths were fitted as previously described [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141080#pone.0141080.ref025" target="_blank">25</a>]. The data were subsequently fit to Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141080#pone.0141080.e001" target="_blank">1</a>) yielding the signal width at focus, <i>σ</i>₀ = 263 nm and the DOF = 750 nm. All data characterized by a width larger than √2 × 263 nm = 372 nm (dashed line) were discarded from further analysis.</p

Result of Eq (6) for DOF = 750 nm and four different time lags, t (S1 Fig Data).

<p>For a diffusion constant of D = 2 μm²/s the probability to reside inside the DOF after t = 10 ms is 0.79, whereas for D = 0.1 mm2/s the probability is 0.97.</p

Imaging of diffusing fluorophores inside the nucleus.

<p>Since the depth of focus (DOF = 750 nm) is shallow, molecules can diffuse in and out of the observation volume. This will deplete the relative contribution of the fast diffusing fraction to the analysis.</p

Single-molecule imaging and PICS analysis (S1 Fig Data).

<p><i>A</i>: Signal of individual eYFP-GR molecules on an emCCD camera. <i>B</i>: The signal of an individual molecule is fitted to a Gaussian yielding the position, the width and the strength of the signal. <i>C</i>: Distance calculation between molecules in subsequent frames. <i>D</i>: Cumulative distribution function (cdf) of distances of molecules in subsequent frames correlated by diffusion.</p

PICS analysis of glucocorticoid receptor at different time lags (S1 Fig Data).

<p>In blue the uncorrected result. A decrease of the fast fraction is observed. In green the result corrected by Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141080#pone.0141080.e008" target="_blank">8</a>) taking into account the DOF. The fast fraction stays constant for time lags at least up to 150 ms. Dashed lines are linear fits to the data. Error-bars represent the standard deviation.</p

Simulation result that shows depletion of the fast fraction for increasing time lags (S1 Fig Data).

<p>The time lag is given by the number of frames between detections. In blue the uncorrected result, in green the result after correction with Eq (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141080#pone.0141080.e008" target="_blank">8</a>).</p

Ligand structure determines the nuclear mobility of the GR.

<p>A range of natural and synthetic agonists (black bars) and an antagonists (red bar) were tested for their effect on the intranuclear mobility of the GR by both SMM (A) and FRAP (B–C) analysis. Multiple structural elements of the steroids are associated with a reduced mobility of the receptor. Altered mobility can be reflected in all aspects of mobility: a larger bound fraction (SMM; white bars and FRAP; white and light grey bars combined) a lower diffusion coefficient (in µm²/s, written in its corresponding bar in A) and longer immobilization times (C). (D and E) A mutation of phenylalanine 623 to alanine (F623A) prevents interactions of the 9-fluoro group of steroids within the ligand binding pocket of the GR. F623A YFP-GR still translocates completely to the nucleus after 3 hours of 1 µM prednisolone or Δ-fludrocortisone treatment (D). SMM analyses of nuclear F623A YFP-GR kinetics shows that the mobility of F623A YFP-GR is highly similar after either Δ-fludrocortisone or prednisolone treatment (black bars for the diffusing fraction, with their corresponding diffusion coefficient (in µm²/s) written within their corresponding bar; (E)). SMM: n = 20, FRAP: n = 30. Data represented as total fit ± SEM (of 3 separate PICS analyses) for SMM and as average of top 10% fits ± SEM for FRAP. Δ-flu; Δ-fludrocortisone, dex; dexamethasone, Predn; prednisolone, csol; cortisol, cort; corticosterone. The data for GR-dexamethasone is the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090532#pone-0090532-g002" target="_blank">Figure 2</a>.</p

Loss of either the DNA-binding or the ligand-binding domain results in a high GR mobility.

<p>(A) Schematic representation of three functional YFP-GR deletion mutants tested. (B and C) Fraction distributions as analyzed by SMM (B) and FRAP (C). Diffusion coefficients are written within the corresponding bars in B (in µm²/s). (D) Immobilization times of both bound fractions in FRAP. While loss of the AF-1 domain hardly affects GR's nuclear mobility, deletion of the DBD and especially the LBD leads to a very mobile receptor with reduced frequency and average duration of DNA-binding and a higher diffusion coefficient. SMM: n = 20, FRAP: n = 30. Data represented as total fit ± SEM (of 3 separate PICS analyses) for B and as average of top 10% fits ± SEM for C and D. The data for wild type GR is the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090532#pone-0090532-g003" target="_blank">Figure 3</a>.</p

SMM and FRAP analyses provide a consistent model of the intranuclear mobility of the GR.

<p>(A) A two-population fit of SMM analysis for dexamethasone-bound YFP-GR identifies two fractions of approximately equal size. (B) Both fractions show a linear increase in mean squared displacement (MSD) over time, but with a 40-fold difference in MSD. Diffusion coefficients (D_fast and D_slow) are calculated from a linear fit of the experimental data (dashed lines; D =  slope/4). The D_fast of 1.31 µm²/s fits to diffusing molecules, while the D_slow of only 0.03 µm²/s best fits to the slow movement of chromatin and the molecules bound to it. (C) A 3-population Monte Carlo simulation of the FRAP curve for dexamethasone-bound YFP-GR shows that half of the nuclear population is diffusing, while the remainder is subdivided into two bound fractions that differ in their immobilization times. The fraction size of the diffusing fraction is similar in size as that obtained from SMM analysis. (D) Both bound fractions are only transiently immobilized, with a 3-fold difference in duration. (A and B) Data represented as best fit ± SEM (of 3 separate PICS analyses). (C and D) Data represented as average of top 10% best fits ± SEM.</p