Fluorescence fluctuation spectroscopy: an invaluable microscopy tool for uncovering the biophysical rules for navigating the nuclear landscape

Nuclear architecture is fundamental to the manner by which molecules traverse the nucleus. The nucleoplasm is a crowded environment where dynamic rearrangements in local chromatin compaction locally rede ﬁ ne the space accessible toward nuclear protein diffusion. Here, we review a suite of methods based on ﬂ uorescence ﬂ uctuation spectroscopy (FFS) and how they have been employed to interrogate chromatin organization, as well as the impact this structural framework has on nuclear protein target search. From ﬁ rst focusing on a set of studies that apply FFS to an inert ﬂ uorescent tracer diffusing inside the nucleus of a living cell, we demonstrate the capacity of this technology to measure the accessibility of the nucleoplasm. Then with a baseline understanding of the exploration volume available to nuclear proteins during target search, we review direct applications of FFS to ﬂ uorescently labeled transcription factors (TFs). FFS can detect changes in TF mobility due to DNA binding, as well as the formation of TF complexes via changes in brightness due to oligomerization. Collectively, we ﬁ nd that FFS-based methods can uncover how nuclear proteins in general navigate the nuclear landscape.


Introduction
The genomic DNA of cells from all kingdoms of life is associated with general structuring proteins that package the genome and regulate access of DNA-binding proteins to their specific DNA sequence motifs [1,2]. In every human cell, ∼2 m of DNA is wrapped around histone proteins to form a string of nucleosomes, and the resulting chromatin fibers are compacted into a multilayered threedimensional chromatin network that fits within a nuclear volume with a diameter of 10 μm [3]. A significant question has been how DNA-binding proteins navigate the crowded nuclear interior and locate their binding sites within this complex chromatin network. Early studies suggested DNA-binding proteins locate their binding sites via a mixture of 3D diffusion and 1D translocation along DNA; so-called 'facilitated diffusion' [4]. However, more recent results showed that while some low abundance proteins in prokaryotes (such as the Lac repressor) may locate their target sites via facilitated diffusion, for higher abundance proteins and in eukaryotic cells, target search is likely dominated by 3D diffusion [5,6].
Diffusing molecules encounter chromatin with differing degrees of local compaction that may influence their diffusive route taken as well as their local concentration in different subnuclear regions due to size exclusion effects. For example, the dynamic rearrangements in nucleosome proximity that transform transcriptionally accessible euchromatin into silenced heterochromatin have been shown to locally redefine the space accessible to nuclear protein diffusion [7][8][9][10][11]. To what extent this chromatin organization plays an inhibitory or facilitatory role in guiding the diffusive route of nuclear factors to target destinations is not entirely understood. Furthermore, accessing this information with standard live cell imaging has proven to be technically challenging because the rearrangements in chromatin structure that control DNA template access occur on a fast timescale (micro to milliseconds) [7] and are well below the diffraction limit of light [12].
To interrogate the chromatin network organization within an intact nucleus and define the role this structural framework plays in nuclear factor navigation, two perspectives of investigation have emerged. The first approach is to directly study chromatin organization using electron microscopy [12], super-resolution optical microscopy [13][14][15], histone FRET microscopy [16][17][18][19], or techniques based on high throughput identification of DNA sequences that are in spatial proximity to one another in the nucleus [20][21][22][23][24]. The second perspective is to indirectly probe chromatin organization from the point of view of the molecules exploring this complex environment. By this approach, the accessibility of the nuclear landscape toward diffusing molecules is measured using methods such as fluorescence recovery after photobleaching (FRAP) [25][26][27][28][29], single particle tracking (SPT) [30][31][32][33][34] and fluorescence fluctuation spectroscopy (FFS) [35][36][37][38][39][40] (Figure 1). The application of SPT and FRAP to study nuclear factor dynamics within live cell nuclear architecture has recently been reviewed [41]. Thus here, we focus on methods based on FFS to uncover the biophysical rules for navigating the nuclear space. As outlined in Figure 1, FFS bridges insights derived from SPT with FRAP by detecting nuclear protein mobility at the single molecule level, but with the statistics to draw conclusions on population level events such as nuclear trafficking.
FFS describes a family of analytical methods that when coupled with live cell microscopy and genetically encoded fluorescent tags, can provide a measurement of nuclear protein diffusion, concentration and oligomerization in the context of live cell chromatin organization [35][36][37][38][39][40]. FFS methods rely on measuring fluctuations  in fluorescence intensity arising from a population of fluorescent molecules passing through a small observation volume [e.g. a confocal or two-photon point spread function (PSF)]. In the case of confocal laser scanning microscopy, the observation volume is either parked in a specific subcellular location of interest (single-point FFS) or scanned across a subcellular compartment (scanning FFS; Figure 2a-c). For every fluorescence fluctuation recorded, two aspects are analyzed. The first is the temporal spectrum, which reports on nuclear protein mobility and can be obtained from a temporal autocorrelation function (ACF) analysis (Figure 2d-g) [42,43]. The second is the amplitude spectrum, which quantifies the number and brightness (NB) (or oligomeric state) of a nuclear protein population and can be obtained from a moment analysis (Figure 2h-k) [44][45][46] or the generation of a photon counting histogram (PCH) [47]. In the case of scanning FFS, a key advantage is that a spatial component is introduced into the measurement (Figure 2c). Thus, in addition to mapping the local dynamics of a nuclear protein, the diffusive route or law by which it traverses the chromatin environment can be extracted via a spatiotemporal correlation analysis of distinct fluorescence fluctuations.
To demonstrate FFS as an invaluable tool for the study of nuclear architecture and investigate how this structural framework facilitates nuclear protein target search, here we review two types of FFS studies. The first type of study employs an inert fluorescent tracer in a living cell to probe chromatin network microstructure and organization on different temporal and spatial scales [7][8][9][10][11]. This approach provides a spatiotemporal analysis of the connectivity of the intranuclear landscape, onto which we can overlay a specific nuclear protein's dynamics derived from FRAP-, SPT-or FFS-based experiments. The second type of study is where FFS is applied directly to a biological nuclear protein of interest to track its change in mobility upon interaction with a target site or change in brightness upon complex formation [48][49][50][51][52][53]. The outcome of this series of studies is a statistical view of how nuclear protein target search is governed by nonspecific versus specific binding interactions and complex formation. This latter point is important since quantifying the impact of oligomer formation on transcription factor (TF) transport dynamics is currently unique to FFS.
Accessibility of the nuclear landscape toward three-dimensional molecular diffusion Evidence emerging from a series of FFS experiments suggests that modulation of protein access by chromatin is a general mechanism to guide molecules to their correct subnuclear location [7][8][9][10][11]. A key feature of these experiments is to apply FFS to study the mobility of an inert fluorescent tracer (such as free GFP) within a living cell to report on the permeability and therefore microstructure of the intracellular landscape. This approach was first combined with single-point FFS to study the impact of chromatin organization on molecular diffusion [9,11]. For example, in an initial study by Dross et al. [11], the diffusion coefficient of eGFP was derived at several different points inside the nucleus of a living cell and compared with local DNA density (Figure 3a-d). This experiment found that while eGFP mobility varied significantly within the cell nucleus, surprisingly, it did not correlate with chromatin density that was measured via histone H2B tagged to a red fluorescent protein [11]. At the same time, however, in a study by Bancaud et al. [9] the mobility of eGFP oligomers (dimers, pentamers and decamers) was found to be modulated by euchromatin versus heterochromatin. Specifically, the crowded environment of dense heterochromatin reduced the subdiffusive rate of these larger fluorescent tracers two-to three-fold and independently of the number of subunits within the eGFP oligomeric complex [9]. This DNA density-dependent change in mobility has since been observed for monomeric eGFP (albeit to a much subtler extent) when fluorescence fluctuation segments acquired along a scanning FFS experiment are sorted according to local DNA intensity and treated as independent single-point FFS measurements [10]. Collectively, these results suggest that chromatin density, which determines the available volume for molecules to occupy, dictates nuclear protein concentration and mobility. However, given that single-point FFS measures only the local diffusion coefficient of molecules within the PSF (∼0.3 μm), the spatial environment around the PSF and therefore the route the molecules take before crossing the observation volume is not observed. Thus, the diffusive route by which molecules access different subnuclear chromatin environments is not detected.
To investigate the spatial dependence of eGFP mobility within a larger chromatin environment and identify how molecules access different DNA density environments, we mapped the diffusive route of eGFP inside the nucleus of a living cell [7,54,55]. This was achieved by selecting a confocal line scan across regions of high and low DNA density within nuclei of cells stained with Hoechst 33342 (a common chromatin stain). By scanning the laser beam across a selected heterogeneous chromatin environment at a rate faster than eGFP diffusion, fluctuations due to eGFP translocation were recorded and spatiotemporally compared by pair correlation function ( pCF) analysis (Figure 3e-h). pCF analysis is a novel approach to spatiotemporal correlation spectroscopy that maps molecular flow along a scanning FFS measurement by calculating the time it takes fluorescent molecules to translocate between pairs of pixels [56]. When applied to free eGFP in a Hoechst-stained nucleus, pCF analysis can detect millisecond changes in local chromatin structure based on the arrival time of eGFP into and out of the chromatin environment [7]. Remarkably, we found that interphase chromatin contains disconnected channels of molecular flow associated with high and low DNA density, but with intermittent bursts of free diffusion between the channels (∼300 ms in duration) that are suggestive of localized fluctuations in chromatin structure. Interestingly, these bursts of 'communication' between the high DNA density channel to the low DNA density environment (where molecular transport is twice as efficient) are dependent on metabolic activity and disappear during mitotic chromosome condensation [54,55]. Collectively, the results from pCF analysis suggest the existence of a not-yet-understood interplay between chromatin organization and molecular flow inside the nucleus.
More recently, Baum et al. employed a related approach, a line-illuminating multi-focus fluorescence microscope, to measure GFP mobility over multiple scales in the nuclei of live cells [8]. This microscopy set-up couples the temporal resolution of single-point FCS (microsecond sampling frequency) with the spatial information offered from scanning FCS (sub-micrometer to several micrometers) via the parallelized acquisition of several hundred detection volumes (Figure 3i-l). Thus, a multiscale fluorescence correlation spectroscopy (msFCS) analysis can be performed that extends from an ACF to pCF analysis performed at different distances, Parallel line illumination offers both high temporal resolution (microseconds) and a spatial component contained within the measurement. (k) msFCS involves both application of the ACF (G(τ)) to each fluorescence fluctuation (F(t)) and spatial cross correlation (G(τ,δr)) of distinct fluorescence fluctuations (analogous to the pCF function). (l) A full description of eGFP mobility over multiple length scales (δr ≥ 0) is extracted via msFCS, and this enables the diffusive law by which eGFP explores different chromatin environments to be characterized. and therefore a mean square displacement analysis of protein transport [8]. Application of this technology to monomeric eGFP confirmed that the nucleus imposes mobility constraints in a scale-dependent manner, and from drug-induced chromatin de-condensation, identified local DNA density as the dominant obstacle restricting certain translocations. Interestingly, comparison of monomeric GFP with multimers of GFP showed that differently sized particles 'sense' distinct structured environments. Larger particles ( pentamers) diffuse more slowly and are excluded from certain regions whilst being trapped in other regions, whereas smaller particles (monomers and dimers) diffuse faster and can explore their local environment more thoroughly. This size dependence likely has a significant impact on a nuclear protein's target search mechanism and shifts the threshold for what DNA densities restrict molecular diffusion and access to different nuclear compartments.
FFS-based analysis of TF DNA target search within nuclear architecture FFS of an inert tracer's mobility inside the nucleus of a living cell has revealed that: (1) local chromatin structure modulates molecular mobility [9][10][11], (2) global chromatin network organization regulates the diffusive route of nuclear traffic [7,54,55] and (3) the size of the molecule undergoing diffusion influences the exploration volume that can be accessed [8,9]. Deviations from this baseline behavior occur upon binding of a TF to DNA (an immobile obstacle) [8,40,48,52], which is often accompanied by protein-protein interaction and or complex formation (e.g. homo-oligomerization) [35,[49][50][51]53,57]. SPT has proved to be a powerful technique to measure TF diffusion and residence times [41]; however, FFS methods can also access these variables often via simpler experiments. To detect, localize and characterize TF DNA-binding dynamics based on mobility alone, the temporal spectrum of the fluorescence fluctuation is analyzed (Figure 2d-g). In the simplest case, this is performed by an ACF analysis of a single-point FFS measurement that is subsequently fit to a modified diffusion model to account for DNA binding [40,42,43,58].
In an elegant study by Kaur et al. [52] single-point FFS was performed in a developing mouse embryo to investigate the mobility of the TF Oct4 during mammalian development [52]. Oct4 was tagged with photoactivatable GFP ( paGFP) to maintain the FFS requirement of a low fluorophore concentration. Then from ACF analysis of Oct4-paGFP movement in single nuclei, it was found that while 75% of Oct4 was freely diffusing, the remaining fraction underwent an anomalous subdiffusive process with a tens of millisecond dwell time. Comparison of the subdiffusive population with free paGFP and an Oct4-paGFP DNA-binding mutant revealed the anomalous component to be a specific property of Oct4 DNA interaction (Figure 4a,b). Furthermore, the anomalous component of Oct4 diffusion was selectively slowed down in the nuclei of pluripotent but not extra-embryonic cells [52]. Given the known role of Oct4 in the maintenance of pluripotency, this set of single-point FFS experiments suggest Oct4 nuclear mobility can accurately predict its functional activity, as confirmed by SPT [59]. TF mobility as a readout of specific DNA binding has since been employed in several different types of scanning FFS-based experiments, with the added advantage of this property being either spatially mapped [e.g. temporal image correlation spectroscopy (tICS)] [40,48,60] or analyzed by a spatiotemporal correlation function that infers mobility over multiple length scales [e.g. multiscale FCS or raster image correlation spectroscopy (RICS)] [8,49]. The aspects of nuclear protein mobility that these different FFS-based methods of analysis can quantify in a living cell are outlined and compared in Table 1.
To investigate if and how TF oligomerization influences DNA target search strategy, given that selfassociation has long been known to regulate TF function in prokaryotes, the amplitude spectrum of a fluorescence fluctuation provides a valuable additional dimension of information. The amplitude spectrum reports on the brightness of the fluorescent molecules that give rise to a measured fluorescence fluctuation, a property directly related to a fluorescent protein's oligomeric state (Figure 2h-k). In the case of a single-point FFS measurement, where the sampling frequency is fast (microseconds) and good statistics can be achieved, the different brightness species of a TF at a specific location can be extracted by constructing a PCH [47]. PCH analysis, however, requires access to a true photon counting detector. If this hardware is not available, an alternative method to recover the oligomeric state of a TF within a single-point FFS measurement is by moment analysis [44][45][46]. Moment-based brightness analysis of oligomerization has been applied to several TFs, and in each case, these FFS studies showed that self-association modulates TF DNA-binding activity [35,[49][50][51]53,57]. For example, it was found from tagging the glucocorticoid receptor (GR) with GFP (GFP-GR) that upon binding DNA, GFP-GR dimers form a tetrameric complex that is key to the GR activation pathway (Figure 4c,d).
A critical advantage of moment-based brightness analysis is its applicability to scanning FFS measurements when limited to the first and second moment (i.e. NB analysis) [48,49]. Unlike PCH analysis, which demands high statistics and is computationally too laborious to apply to all pixels within an image, NB analysis enables TF oligomerization to be spatially mapped in the context of live cell nuclear architecture, as has been done with Signal transducer and activator of transcription 3 (STAT3) [51,61]. With this approach, however, the average oligomeric state reported in each pixel can potentially mask the presence of a heterogeneous oligomeric population. Efforts have therefore been made to resolve the different species that can coexist in each pixel of an NB acquisition via the development of time resolved NB and enhanced NB [62,63]. An alternative approach is, however, to filter the different oligomeric species present based on mobility and how this detected oligomeric population evolves in space over time. To do this, we combined the capacity of pCF analysis to track molecular  Millisecond sampling frequency limits mobilities detected (D upto ∼30 mm 2 s −1 ). Spatial component in measurement enables higher statistics and further detection of heterogeneity in mobility rates and types. [10,36,[73][74] Pair correlation function (pCF) -Quantify the arrival time of a nuclear protein between pairs of points separated by a fixed or varying distance (δr > point spread function) -Detect location and size of barriers to diffusion Millisecond sampling frequency enables the diffusive route of a nuclear protein population to be mapped over a spatial scale of ∼0.3 to 1 mm. Pair correlation analysis can also now be applied radially in 2D frame scan acquisitions. [7,37,[54][55][56][75][76][77] Multiscale fluorescence correlation spectroscopy (msFCS) -Diffusion rate/type, binding kinetics (ACF) and arrival time between distinct locations (pCF) -Diffusion law (mean square displacement analysis) -Number of molecules in each pixel along line scan Microsecond sampling frequency enables fast mobilities to be detected alongside spatial information (e.g. molecular flow and diffusion law). Requires access to a line-illuminating multi-focus fluorescence microscope. [8] Pair correlation of molecular brightness (pCOMB) -Quantify the mobility of nuclear proteins as a function of oligomeric state and DNA density Spatial correlation of brightness fluctuations amplifies the presence of few higher order oligomers (perfect for TFs). [51] Frame scan Millisecond to second sampling + 2D spatial component -Determine the diffusion law by which proteins move (e.g. isotropic, confined or partitioned) [94][95][96][97] flow with moment-based detection of oligomerization events [51]. This method, termed pair correlation of molecular brightness ( pCOMB), tracks oligomer mobility by first amplifying the signal from the brightest species present and then filtering the dynamics of the extracted oligomeric population based on arrival time between two locations (Figure 4e,f ) [51]. Because TF mobility is in general limited upon interaction with the DNA network, pCOMB analysis is sensitive toward changes in oligomeric state that accompany nonspecific or specific DNA binding. Thus, coupled with the knowledge that nuclear protein size modulates exploration of the nucleoplasm, this technology has the potential to provide insight into how TFs employ self-association to navigate nuclear architecture and modulate DNA-binding activity.

Perspectives
• Importance in the field: The multilayered 3D arrangement of DNA into the chromatin network renders the nucleoplasm into an incredibly crowded environment and yet nuclear proteins efficiently navigate this structural framework to arrive at a target DNA sequence. How exactly nuclear organization regulates nuclear trafficking to maintain genome function is thus of great interest. As reviewed here, the evidence that has emerged from application of FFS to an inert tracer's mobility inside the nucleus is that modulation of protein access by chromatin constitutes a general mechanism to sequester molecules where they need to be for DNA-dependent activity. Importantly, the detected spatial compartmentalization of the nucleus that is imparted by chromatin is not static and rearranges on a spatiotemporal scale that is only visible when you observe it from the point of view of the molecules scanning the genome [7][8][9][10][11]. Thus, probing nuclear organization from the point of view of the DNA-binding proteins that read and copy genetic information is key.
• Summary of current thinking: FFS applied directly to fluorescently labeled TFs enables a unique perspective on DNA target search and how this process is regulated by nuclear architecture. The current thinking derived from FFS analysis of TF mobility is that the biophysical rules which govern inert protein navigation of the nucleoplasm also apply to TF transport, but with DNA-binding interactions of varying affinity overlaid, which result in TF accumulation at specific nuclear locations [48,49,52]. In many instances, the affinity of DNA interaction is increased by homo-oligomerization [50,53,57], and thus the measurement of both TF mobility and brightness (read out of oligomer formation) can serve as a powerful approach to spatiotemporally track TF activity [51].
• A comment on future directions: Given the nanoscale nature of the chromatin network [12], in the future it will be essential to develop methods that can probe intranuclear diffusion and TF complex formation at a higher resolution. One way to achieve this is to couple the FFS-based methods of nuclear protein analysis reviewed here (Table 1) with microscopy hardware that reduces the size of the observation volume. Efforts are already underway to do just this via the use of microscope systems with stimulated emission depletion (STED) [64,65] or, more recently, the Zeiss Airyscan detector [66]. These exciting new approaches to the acquisition of FFS data, combined with the use of bright organic dyes that can be linked to the target protein using Halo or SNAP-tags [67], will enable dynamics features such as chromatin accessibility or TF complex formation to be interrogated with unprecedented spatiotemporal resolution. Multiplexing super-resolution with FFS will undoubtedly facilitate our understanding of the interplay between chromatin structure and genome function.