Depth-of-Focus Correction in Single-Molecule Data Allows Analysis of 3D Diffusion of the Glucocorticoid Receptor in the Nucleus
November
Depth-of-Focus Correction in Single-Molecule Data Allows Analysis of 3D Diffusion of the Glucocorticoid Receptor in the Nucleus
Rolf Harkes 0 1
Veer I. P. Keizer 0 1
Marcel J. M. Schaaf 0 1
Thomas Schmidt 0 1
0 1 Physics of Life Processes, Huygens-Kamerlingh Onnes Laboratory, Leiden University , Leiden , The Netherlands , 2 Institute of Biology Leiden (IBL), Leiden University , Leiden , The Netherlands
1 Editor: Jan Peter Tuckermann, University of Ulm , GERMANY
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.
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Competing Interests: The authors have declared
that no competing interests exist.
Since the initial camera-based observation of the diffusion of individual molecules in artificial
membranes [1], single-molecule imaging technology has yielded a plethora of novel insights
into the behavior of proteins and other membrane constituents in vitro [2–4], in cellulo [5–11]
and in vivo [12]. Single-molecule microscopy has been of great importance to quantify the
diffusive properties of membrane constituents. Diffusive properties consequently report faithfully
about the local structural properties of the membrane, the activation state of signaling
pathways [13], transport of membrane components [14], or cellular regulation processes [15,16].
For a homogeneous system in equilibrium, one would predict that the ensemble-averaged
mobility is hence governed by multiple populations, each reflecting a distinct molecular state
of its components. Indeed, experimental verifications of this prediction have ubiquitously been
found. Whether particle-averaged mean-squared displacement analysis [17], molecular
stepwidth distributions [18] or molecular squared-displacement distributions [19] were analyzed,
multiple populations have always been found in the analysis of receptor mobility in cells.
Given that single-molecule imaging permits to follow processes in time, there have been
many attempts to find transitions between states i.e. transitions in diffusive behavior. Those
Fig 1. Imaging of diffusing fluorophores inside the nucleus. 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.
should show up as change in the fraction size of different mobility when changing the time of
observation. Using gold [14] or quantum-dot labeling [20] of individual components, or by
labeling larger structure like liposomes [21] long time scales could be covered and switching
behavior has been observed.
Spurred by the success of single-molecule imaging in membrane biology and biophysics, in
recent years the technology has been further developed to permit single-molecule observations
of proteins in the 3D environment inside live eukaryotic cells [18,22,23]. In those experiments
individual proteins were imaged over time, their position analyzed in 3D to sub-wavelength
accuracy [24], and subsequently the mobility analyzed by step-length analysis. Similar to the
membrane constituents, mobility of cytosolic proteins appeared inhomogeneous and fractions
of different mobility were identified. Various research groups [18,22,23] realized that, unlike
when imaging on the 2D membrane surface, the apparent fraction size of the various
components depends on observation time. This is due to movements of molecules out of the
depthof-field of the observation volume: fast molecules will disappear faster compared to slow
molecules (Fig 1). Given typical values for the depth-of-field of 1 μm for both wide-field
[18,23] or selective-plane [22] illumination and typical diffusion constants of cytosolic proteins
of 10 μm2/s, the residency time of a molecule within the observation volumes reduces to <50
ms. Hence, in those earlier reports fraction sizes for short time-lags of 6.5 ms and 20 ms,
respectively, were reported to avoid any 3D artifact [18,22,23].
Here we present a mathematical framework that can correct for the change in fraction size
due to the limited detection volume in 3D single-molecule imaging. We applied our findings to
data on the mobility of activated glucocorticoid receptors (GR) in the nucleus of monkey
kidney (COS-1) cells. Our analysis showed that f (...truncated)