In vivo pair correlation analysis of EGFP intranuclear diffusion reveals DNA-dependent molecular flow

Measuring protein-membrane interaction through radial fluorescence correlation in 2 dimensions

The cell membrane has a fundamental role in the cell life cycle but there's still much to be learned about its heterogeneous structure, regulation, and protein interaction. Additionally, the protein-membrane interaction is often overlooked when studying specific protein dynamics. In this work, we present a new tool for a better understanding of protein dynamics and membrane function using live cells and fast non-invasive techniques without the need for individual particle tracking. To this end, we used the 2D-pair correlation function (2D-pCF) to study protein interactions across cellular membranes. We performed numerical simulations and confocal experiments using a GAP-mEGFP fusion construct known to interact with the plasmatic membrane. Our results demonstrate that based on a quantitative correlation analysis as the 2D pair correlation of the signal intensities, is possible to characterize protein-membrane interactions in live systems and real-time. Combining experimental and numerical results this work presents a new powerful approach to the study of the dynamic protein-membrane interaction.

The Material Properties of the Cell Nucleus: A Matter of Scale

Chromatin regulatory processes physically take place in the environment of the cell nucleus, which is filled with the chromosomes and a plethora of smaller biomolecules. The nucleus contains macromolecular assemblies of different sizes, from nanometer-sized protein complexes to micrometer-sized biomolecular condensates, chromosome territories, and nuclear bodies. This multiscale organization impacts the transport processes within the nuclear interior, the global mechanical properties of the nucleus, and the way the nucleus senses and reacts to mechanical stimuli. Here, we discuss recent work on these aspects, including microrheology and micromanipulation experiments assessing the material properties of the nucleus and its subcomponents. We summarize how the properties of multiscale media depend on the time and length scales probed in the experiment, and we reconcile seemingly contradictory observations made on different scales. We also revisit the concept of liquid-like and solid-like material properties for complex media such as the nucleus. We propose that the nucleus can be considered a multiscale viscoelastic medium composed of three major components with distinct properties: the lamina, the chromatin network, and the nucleoplasmic fluid. This multicomponent organization enables the nucleus to serve its different functions as a reaction medium on the nanoscale and as a mechanosensor and structural scaffold on the microscale.

Correlation analyses reveal differential diffusion behavior of eisosomal proteins between mother and daughter cells

Eisosomes are nanoscale plasma membrane domains shaped as furrow-like invaginations. In Saccharomyces cerevisiae these relatively immobile and uniform structures are mainly composed of two cytoplasmic proteins Pil1 and Lsp1. The present work uses fluctuation of fluorescence signals and analytical methods to determine Pil1 and Lsp1 dynamics at different subcellular locations. Using scanning techniques and autocorrelation analysis we determine that the cytoplasmic pools of Pil1 and Lsp1 behave mainly by passive diffusion. Single-point FCS experiments performed at several subcellular locations reveal that Pil1 mobility is faster in daughter cells. Furthermore, pair correlation function analysis indicates a rapid dynamic of Pil1 near the plasma membrane of growing yeast buds, where the membrane is expected to be actively assembling eisosomes.

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells

The phase separation and aggregation of proteins are hallmarks of many neurodegenerative diseases. These processes can be studied in living cells using fluorescent protein constructs and quantitative live-cell imaging techniques, such as fluorescence recovery after photobleaching (FRAP) or the related fluorescence loss in photobleaching (FLIP). While the acquisition of FLIP images is straightforward on most commercial confocal microscope systems, the analysis and computational modeling of such data is challenging. Here, a novel model-free method is presented, which resolves complex spatiotemporal fluorescence-loss kinetics based on dynamic-mode decomposition (DMD) of FLIP live-cell image sequences. It is shown that the DMD of synthetic and experimental FLIP image series (DMD-FLIP) allows for the unequivocal discrimination of subcellular compartments, such as nuclei, cytoplasm, and protein condensates based on their differing transport and therefore fluorescence loss kinetics. By decomposing fluorescence-loss kinetics into distinct dynamic modes, DMD-FLIP will enable researchers to study protein dynamics at each time scale individually. Furthermore, it is shown that DMD-FLIP is very efficient in denoising confocal time series data. Thus, DMD-FLIP is an easy-to-use method for the model-free detection of barriers to protein diffusion, of phase-separated protein assemblies, and of insoluble protein aggregates. It should, therefore, find wide application in the analysis of protein transport and aggregation, in particular in relation to neurodegenerative diseases and the formation of protein condensates in living cells.

Radial pair correlation of molecular brightness fluctuations maps protein diffusion as a function of oligomeric state within live-cell nuclear architecture

Nuclear proteins can modulate their DNA binding activity and the exploration volume available during DNA target search by self-associating into higher-order oligomers. Directly tracking this process in the nucleoplasm of a living cell is, however, a complex task. Thus, here we present a microscopy method based on radial pair correlation of molecular brightness fluctuations (radial pCOMB) that can extract the mobility of a fluorescently tagged nuclear protein as a function of its oligomeric state and spatiotemporally map the anisotropy of this parameter with respect to nuclear architecture. By simply performing a rapid frame scan acquisition, radial pCOMB has the capacity to detect, within each pixel, protein oligomer formation and the size-dependent obstruction nuclear architecture imparts on this complex's transport across sub-micrometer distances. From application of radial pCOMB to an oligomeric transcription factor and DNA repair protein, we demonstrate that homo-oligomer formation differentially regulates chromatin accessibility and interaction with the DNA template.

Heterochromatic repeat clustering imposes a physical barrier on homologous recombination to prevent chromosomal translocations

Mouse pericentromeric DNA is composed of tandem major satellite repeats, which are heterochromatinized and cluster together to form chromocenters. These clusters are refractory to DNA repair through homologous recombination (HR). The mechanisms by which pericentromeric heterochromatin imposes a barrier on HR and the implications of repeat clustering are unknown. Here, we compare the spatial recruitment of HR factors upon double-stranded DNA breaks (DSBs) induced in human and mouse pericentromeric heterochromatin, which differ in their capacity to form clusters. We show that while DSBs increase the accessibility of human pericentromeric heterochromatin by disrupting HP1α dimerization, mouse pericentromeric heterochromatin repeat clustering imposes a physical barrier that requires many layers of de-compaction to be accessed. Our results support a model in which the 3D organization of heterochromatin dictates the spatial activation of DNA repair pathways and is key to preventing the activation of HR within clustered repeats and the onset of chromosomal translocations.

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DSBs at human pericentric HC are positionally stable and recruit HR factors

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Repeat clustering restricts Rad51 at the periphery of heterochromatin

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Human pericentromeric HC is more accessible to HR factors than mouse HC

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Inhibition of DSB relocation at clustered repeats leads to translocations

In vivo pair correlation microscopy reveals dengue virus capsid protein nucleocytoplasmic bidirectional movement in mammalian infected cells

Flaviviruses are major human disease-causing pathogens, including dengue virus (DENV), Zika virus, yellow fever virus and others. DENV infects hundreds of millions of people per year around the world, causing a tremendous social and economic burden. DENV capsid (C) protein plays an essential role during genome encapsidation and viral particle formation. It has been previously shown that DENV C enters the nucleus in infected cells. However, whether DENV C protein exhibits nuclear export remains unclear. By spatially cross-correlating different regions of the cell, we investigated DENV C movement across the nuclear envelope during the infection cycle. We observed that transport takes place in both directions and with similar translocation times (in the ms time scale) suggesting a bidirectional movement of both C protein import and export.Furthermore, from the pair cross-correlation functions in cytoplasmic or nuclear regions we found two populations of C molecules in each compartment with fast and slow mobilities. While in the cytoplasm the correlation times were in the 2-6 and 40-110 ms range for the fast and slow mobility populations respectively, in the cell nucleus they were 1-10 and 25-140 ms range, respectively. The fast mobility of DENV C in cytoplasmic and nuclear regions agreed with the diffusion coefficients from Brownian motion previously reported from correlation analysis. These studies provide the first evidence of DENV C shuttling from and to the nucleus in infected cells, opening new venues for antiviral interventions.

A survey of physical methods for studying nuclear mechanics and mechanobiology

It is increasingly appreciated that the cell nucleus is not only a home for DNA but also a complex material that resists physical deformations and dynamically responds to external mechanical cues. The molecules that confer mechanical properties to nuclei certainly contribute to laminopathies and possibly contribute to cellular mechanotransduction and physical processes in cancer such as metastasis. Studying nuclear mechanics and the downstream biochemical consequences or their modulation requires a suite of complex assays for applying, measuring, and visualizing mechanical forces across diverse length, time, and force scales. Here, we review the current methods in nuclear mechanics and mechanobiology, placing specific emphasis on each of their unique advantages and limitations. Furthermore, we explore important considerations in selecting a new methodology as are demonstrated by recent examples from the literature. We conclude by providing an outlook on the development of new methods and the judicious use of the current techniques for continued exploration into the role of nuclear mechanobiology.

Infection-induced chromatin modifications facilitate translocation of herpes simplex virus capsids to the inner nuclear membrane

Herpes simplex virus capsids are assembled and packaged in the nucleus and move by diffusion through the nucleoplasm to the nuclear envelope for egress. Analyzing their motion provides conclusions not only on capsid transport but also on the properties of the nuclear environment during infection. We utilized live-cell imaging and single-particle tracking to characterize capsid motion relative to the host chromatin. The data indicate that as the chromatin was marginalized toward the nuclear envelope it presented a restrictive barrier to the capsids. However, later in infection this barrier became more permissive and the probability of capsids to enter the chromatin increased. Thus, although chromatin marginalization initially restricted capsid transport to the nuclear envelope, a structural reorganization of the chromatin counteracted that to promote capsid transport later. Analyses of capsid motion revealed that it was subdiffusive, and that the diffusion coefficients were lower in the chromatin than in regions lacking chromatin. In addition, the diffusion coefficient in both regions increased during infection. Throughout the infection, the capsids were never enriched at the nuclear envelope, which suggests that instead of nuclear export the transport through the chromatin is the rate-limiting step for the nuclear egress of capsids. This provides motivation for further studies by validating the importance of intranuclear transport to the life cycle of HSV-1.

Dengue Virus Capsid-Protein Dynamics in Live Infected Cells Studied by Pair Correlation Analysis

It has become increasingly evident that unveiling the mechanisms of virus entry, assembly, and virion release is fundamental for identifying means for preventing viral spread and controlling viral disease. Due to virus mobility and structural and/or functional heterogeneity among viral particles, high spatiotemporal resolution single-virus/single-particle techniques are required to capture the behavior of viral particles inside infected cells.In this chapter, we present fluorescence imaging analysis methods for studying the mobility of fluorescently labeled dengue virus (DENV) proteins in live infected cells. Some of the most recent Fluorescence Fluctuation Spectroscopy (FFS) methods will be presented and, in particular, the pair Correlation Functions (pCF) approach will be discussed. The pCF method does not require individual molecule isolation, as in a particle-tracking experiment, to capture single viral protein behavior. In this regard, image acquisition is followed by the spatiotemporal cross-correlation function at increasing time delays, yielding a quantitative view of single-particle mobility in intact live infected cells.We provide a general overview and a practical guidance for the implementation of advanced FFS techniques, and the pair Correlation Functions analysis, as quantitative tools to reveal insights into previously unreported DENV mechanisms. We expect this protocol report will serve as an incentive for further applying correlation imaging studies in virology research.

Concepts to Reveal Parvovirus-Nucleus Interactions

Parvoviruses are small single-stranded (ss) DNA viruses, which replicate in the nucleoplasm and affect both the structure and function of the nucleus. The nuclear stage of the parvovirus life cycle starts at the nuclear entry of incoming capsids and culminates in the successful passage of progeny capsids out of the nucleus. In this review, we will present past, current, and future microscopy and biochemical techniques and demonstrate their potential in revealing the dynamics and molecular interactions in the intranuclear processes of parvovirus infection. In particular, a number of advanced techniques will be presented for the detection of infection-induced changes, such as DNA modification and damage, as well as protein-chromatin interactions.

Investigating Spatial Heterogeneity of Nanoparticles Movement in Live Cells with Pair-Correlation Microscopy and Phasor Analysis

How nanoparticles distribute in living cells and overcome cellular barriers are important criteria in the design of drug carriers. Pair-correlation microscopy is a correlation analysis of fluctuation in the fluorescence intensity obtained by a confocal line scan that can quantify the dynamic properties of nanoparticle diffusion including the number of mobile nanoparticles, diffusion coefficient, and transit time across a spatial distance. Due to the potential heterogeneities in nanoparticle properties and the complexity within the cellular environment, quantification of averaged auto- and pair-correlation profiles may obscure important insights into the ability of nanoparticles to deliver drugs. To overcome this issue, we used phasor analysis to develop a data standardizing method, which can segment the scanned line into several subregions according to diffusion and address the spatial heterogeneity of nanoparticles moving inside cells. The phasor analysis is a fit-free method that represents autocorrelation profiles for each pixel relative to free diffusion on the so-called phasor plots. Phasor plots can then be used to select subpopulations for which the auto- and pair-correlation analysis can be performed separately. We demonstrate the phasor analysis for pair-correlation microscopy for investigating 16 nm, Cy5-labeled silica nanoparticles diffusing across the plasma membrane and green fluorescent proteins (GFP) diffusing across nuclear envelope in MCF-7 cells.

Of numbers and movement - understanding transcription factor pathogenesis by advanced microscopy

Transcription factors (TFs) are life-sustaining and, therefore, the subject of intensive research. By regulating gene expression, TFs control a plethora of developmental and physiological processes, and their abnormal function commonly leads to various developmental defects and diseases in humans. Normal TF function often depends on gene dosage, which can be altered by copy-number variation or loss-of-function mutations. This explains why TF haploinsufficiency (HI) can lead to disease. Since aberrant TF numbers frequently result in pathogenic abnormalities of gene expression, quantitative analyses of TFs are a priority in the field. In vitro single-molecule methodologies have significantly aided the identification of links between TF gene dosage and transcriptional outcomes. Additionally, advances in quantitative microscopy have contributed mechanistic insights into normal and aberrant TF function. However, to understand TF biology, TF-chromatin interactions must be characterised in vivo, in a tissue-specific manner and in the context of both normal and altered TF numbers. Here, we summarise the advanced microscopy methodologies most frequently used to link TF abundance to function and dissect the molecular mechanisms underlying TF HIs. Increased application of advanced single-molecule and super-resolution microscopy modalities will improve our understanding of how TF HIs drive disease.

Navigating the crowd: visualizing coordination between genome dynamics, structure, and transcription

The eukaryotic genome is hierarchically structured yet highly dynamic. Regulating transcription in this environment demands a high level of coordination to permit many proteins to interact with chromatin fiber at appropriate sites in a timely manner. We describe how recent advances in quantitative imaging techniques overcome caveats of sequencing-based methods (Hi-C and related) by enabling direct visualization of transcription factors and chromatin at high resolution, from single genes to the whole nucleus. We discuss the contribution of fluorescence imaging to deciphering the principles underlying this coordination within the crowded nuclear space in living cells and discuss challenges ahead.

Spatiotemporal dynamics of 53BP1 dimer recruitment to a DNA double strand break

Tumor suppressor p53-binding protein 1 (53BP1) is a DNA repair protein essential for the detection, assessment, and resolution of DNA double strand breaks (DSBs). The presence of a DSB is signaled to 53BP1 via a local histone modification cascade that triggers the binding of 53BP1 dimers to chromatin flanking this type of lesion. While biochemical studies have established that 53BP1 exists as a dimer, it has never been shown in a living cell when or where 53BP1 dimerizes upon recruitment to a DSB site, or upon arrival at this nuclear location, how the DSB histone code to which 53BP1 dimers bind regulates retention and self-association into higher-order oligomers. Thus, here in live-cell nuclear architecture we quantify the spatiotemporal dynamics of 53BP1 oligomerization during a DSB DNA damage response by coupling fluorescence fluctuation spectroscopy (FFS) with the DSB inducible via AsiSI cell system (DIvA). From adopting this multiplexed approach, we find that preformed 53BP1 dimers relocate from the nucleoplasm to DSB sites, where consecutive recognition of ubiquitinated lysine 15 of histone 2A (H2AK15ub) and di-methylated lysine 20 of histone 4 (H4K20me2), leads to the assembly of 53BP1 oligomers and a mature 53BP1 foci structure.

Discrete Manhattan and Chebyshev pair correlation functions in k dimensions

Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in k dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.

Combined Selective Plane Illumination Microscopy and FRAP Maps Intranuclear Diffusion of NLS-GFP

Since its initial development in 1976, fluorescence recovery after photobleaching (FRAP) has been one of the most popular tools for studying diffusion and protein dynamics in living cells. Its popularity is derived from the widespread availability of confocal microscopes and the relative ease of the experiment and analysis. FRAP, however, is limited in its ability to resolve spatial heterogeneity. Here, we combine selective plane illumination microscopy (SPIM) and FRAP to create SPIM-FRAP, wherein we use a sheet of light to bleach a two-dimensional (2D) plane and subsequently image the recovery of the same image plane. This provides simultaneous quantification of diffusion or protein recovery for every pixel in a given 2D slice, thus moving FRAP measurements beyond these previous limitations. We demonstrate this technique by mapping both intranuclear diffusion of NLS-GFP and recovery of 53BP1-mCherry, a marker for DNA damage, in live MDA-MB-231 cells. SPIM-FRAP proves to be an order of magnitude faster than fluorescence-correlation-spectroscopy-based techniques for such measurements. We observe large length-scale (>∼500 nm) heterogeneity in the recovery times of NLS-GFP, which is validated against simulated data sets. 2D maps of NLS-GFP recovery times showed no pixel-by-pixel correlation with histone density, although slower diffusion was observed in nucleoli. Additionally, recovery of 53BP1-mCherry was observed to be slowed at sites of DNA damage. We finally developed a diffusion simulation for our SPIM-FRAP experiments to compare across techniques. Our measured diffusion coefficients are on the order of previously reported results, thus validating the quantitative accuracy of SPIM-FRAP relative to well-established methods. With the recent rise of accessibility of SPIM systems, SPIM-FRAP is set to provide a straightforward means of quantifying the spatial distribution of protein recovery or diffusion in living cells.

Back to the Future: Genetically Encoded Fluorescent Proteins as Inert Tracers of the Intracellular Environment

Over the past decades, the discovery and development of genetically encoded fluorescent proteins (FPs) has brought a revolution into our ability to study biologic phenomena directly within living matter. First, FPs enabled fluorescence-labeling of a variety of molecules of interest to study their localization, interactions and dynamic behavior at various scales-from cells to whole organisms/animals. Then, rationally engineered FP-based sensors facilitated the measurement of physicochemical parameters of living matter-especially at the intracellular level, such as ion concentration, temperature, viscosity, pressure, etc. In addition, FPs were exploited as inert tracers of the intracellular environment in which they are expressed. This oft-neglected role is made possible by two distinctive features of FPs: (i) the quite null, unspecific interactions of their characteristic β-barrel structure with the molecular components of the cellular environment; and (ii) their compatibility with the use of time-resolved fluorescence-based optical microscopy techniques. This review seeks to highlight the potential of such unique combinations of properties and report on the most significative and original applications (and related advancements of knowledge) produced to date. It is envisioned that the use of FPs as inert tracers of living matter structural organization holds a potential for several lines of further development in the next future, discussed in the last section of the review, which in turn can lead to new breakthroughs in bioimaging.

Dengue Virus Capsid Protein Dynamics Reveals Spatially Heterogeneous Motion in Live-Infected-Cells

Dengue is the single most important human viral infection transmitted by insects. The function of the viral proteins andtheir interactions with the host cell is under exhaustive investigation with the aim of identifying antiviral strategies. Here,using recombinant full-length dengue virus genomes, carrying a fluorescent mCherry fused to capsid, we studied biophysicalproperties of the viral protein during one infectious cycle in living cells. Dengue virus capsid protein associates to differentcellular compartments but its function in these locations is largely unknown. We evaluated the diffusion of capsid inside the celland determined a higher effective diffusion coefficient in the cytoplasm than in the nucleus. Using advanced fluorescencecorrelation methods, including the recently developed two-dimensional pair correlation analysis, we constructed for the first timehigh resolution maps of capsid mobility in an infected cell. We observed that the motion of capsid in the nucleoplasm-nucleolusinterface was highly organized, indicating an obstacle in this interface. Although nucleoli are membraneless structures, theydisplayed liquid-liquid phase separation. Once inside nucleoli, the protein showed isotropic mobility, indicating free diffusion orimmobilized capsid inside these structures. This is the first study presenting spatial and temporal dynamics of the dengue viruscapsid protein during infection.

Chromatin condensation fluctuations rather than steady-state predict chromatin accessibility

Chromatin accessibility to protein factors is critical for genome activities. However, the dynamic properties of chromatin higher-order structures that regulate its accessibility are poorly understood. Here, we took advantage of the microenvironment sensitivity of the fluorescence lifetime of EGFP-H4 histone incorporated in chromatin to map in the nucleus of live cells the dynamics of chromatin condensation and its direct interaction with a tail acetylation recognition domain (the double bromodomain module of human TAF_II250, dBD). We reveal chromatin condensation fluctuations supported by mechanisms fundamentally distinct from that of condensation. Fluctuations are spontaneous, yet their amplitudes are affected by their sub-nuclear localization and by distinct and competing mechanisms dependent on histone acetylation, ATP and both. Moreover, we show that accessibility of acetylated histone H4 to dBD is not restricted by chromatin condensation nor predicted by acetylation, rather, it is predicted by chromatin condensation fluctuations.

Pair Correlation Analysis Maps the Dynamic Two-Dimensional Organization of Natural Killer Cell Receptors at the Synapse

In living systems, the contact between cells is the basis of recognition, differentiation, and orchestration of an immune response. Obstacles and barriers to biomolecular motion, especially for receptors at cellular synapses, critically control these functions by creating an anisotropic environment. Whereas conventional fluorescence fluctuation methods, such as fluorescence correlation spectroscopy or fluorescence recovery after photobleaching, can only measure the isotropic diffusion of molecules, the two-dimensional pair correlation function (2D-pCF) approach probes the anisotropic paths at different spatial locations within an image, allowing the creation of high-resolution maps that can visualize and quantify how molecules move in a living cell. In this work, we show how the 2D-pCF method maps the environment in cellular synapses as perceived by natural killer (NK) cell receptors. In cultured human HLA null 721.221 cells, 2D-pCF reveals the motion of inhibitory receptor HLA-Cw4-YFP coexpressed with KIR3DL1 to be highly directional around specific loci, while these restrictions were absent in the case of HLA-B51-YFP coexpressed with KIR2DL1. Further, in freshly isolated educated (H-2D^d) and uneducated (MHC^-/-) primary murine NK cells, the 2D-pCF method shows significant differences in the paths taken by activating receptor NKp46 and inhibitory receptor Ly49A in educated compared to uneducated cells. Altogether, we demonstrate that the 2D-pCF method is very powerful in informing about the spatial organization of motion in cells. Our data support the hypothesis that flexibility in the spatial arrangement of membrane receptors, that is, the absence of barriers, is crucial for NK cell function.

Interferometric fluorescence cross correlation spectroscopy

Measuring transport properties like diffusion and directional flow is essential for understanding dynamics within heterogeneous systems including living cells and novel materials. Fluorescent molecules traveling within these inhomogeneous environments under the forces of Brownian motion and flow exhibit fluctuations in their concentration, which are directly linked to the transport properties. We present a method utilizing single photon interference and fluorescence correlation spectroscopy (FCS) to simultaneously measure transport of fluorescent molecules within aqueous samples. Our method, within seconds, measures transport in thousands of homogenous voxels (100 nm)³ and under certain conditions, eliminates photo-physical artifacts associated with blinking of fluorescent molecules. A comprehensive theoretical framework is presented and validated by measuring transport of quantum dots, associated with VSV-G receptor along cellular membranes as well as within viscous gels.

HEXIM1 Diffusion in the Nucleus Is Regulated by Its Interactions with Both 7SK and P-TEFb

How nuclear proteins diffuse and find their targets remains a key question in the transcription field. Dynamic proteins in the nucleus are classically subdiffusive and undergo anomalous diffusion, yet the underlying physical mechanisms are still debated. In this study, we explore the contribution of interactions to the generation of anomalous diffusion by the means of fluorescence spectroscopy and simulation. Using interaction-deficient mutants, our study indicates that HEXIM1 interactions with both 7SK RNA and positive transcription elongation factor b are critical for HEXIM1 subdiffusion and thus provides evidence of the effects of protein-RNA interaction on molecular diffusion. Numerical simulations allowed us to establish that the proportions of distinct oligomeric HEXIM1 subpopulations define the apparent anomaly parameter of the whole population. Slight changes in the proportions of these oligomers can lead to significant shifts in the diffusive features and recapitulate the modifications observed in cells with the various interaction-deficient mutants. By combining simulations and experiments, our work opens new prospects in which the anomaly α coefficient in diffusion becomes a helpful tool to infer alterations in molecular interactions.

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 redefine the space accessible toward nuclear protein diffusion. Here, we review a suite of methods based on fluorescence fluctuation 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 first focusing on a set of studies that apply FFS to an inert fluorescent 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 fluorescently 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 find that FFS-based methods can uncover how nuclear proteins in general navigate the nuclear landscape.

Characterizing proteins in their cellular environment: Examples of recent advances in quantitative fluorescence microscopy

Quantitative characterization of protein interactions, both intramolecular and intermolecular, is crucial in understanding the mechanisms and regulation of their function. In recent years, it has become possible to obtain such information on protein systems in live cells, from bacteria to mammalian cell lines. This review discusses recent advances in measuring protein folding, absolute concentration, oligomerization, diffusion, transport, and organization at super-resolution.

Phasor histone FLIM-FRET microscopy quantifies spatiotemporal rearrangement of chromatin architecture during the DNA damage response

To investigate how chromatin architecture is spatiotemporally organized at a double-strand break (DSB) repair locus, we established a biophysical method to quantify chromatin compaction at the nucleosome level during the DNA damage response (DDR). The method is based on phasor image-correlation spectroscopy of histone fluorescence lifetime imaging microscopy (FLIM)-Förster resonance energy transfer (FRET) microscopy data acquired in live cells coexpressing H2B-eGFP and H2B-mCherry. This multiplexed approach generates spatiotemporal maps of nuclear-wide chromatin compaction that, when coupled with laser microirradiation-induced DSBs, quantify the size, stability, and spacing between compact chromatin foci throughout the DDR. Using this technology, we identify that ataxia-telangiectasia mutated (ATM) and RNF8 regulate rapid chromatin decompaction at DSBs and formation of compact chromatin foci surrounding the repair locus. This chromatin architecture serves to demarcate the repair locus from the surrounding nuclear environment and modulate 53BP1 mobility.

Measuring Mobility in Chromatin by Intensity-Sorted FCS

The architectural organization of chromatin can play an important role in genome regulation by affecting the mobility of molecules within its surroundings via binding interactions and molecular crowding. The diffusion of molecules at specific locations in the nucleus can be studied by fluorescence correlation spectroscopy (FCS), a well-established technique based on the analysis of fluorescence intensity fluctuations detected in a confocal observation volume. However, detecting subtle variations of mobility between different chromatin regions remains challenging with currently available FCS methods. Here, we introduce a method that samples multiple positions by slowly scanning the FCS observation volume across the nucleus. Analyzing the data in short time segments, we preserve the high temporal resolution of single-point FCS while probing different nuclear regions in the same cell. Using the intensity level of the probe (or a DNA marker) as a reference, we efficiently sort the FCS segments into different populations and obtain average correlation functions that are associated to different chromatin regions. This sorting and averaging strategy renders the method statistically robust while preserving the observation of intranuclear variations of mobility. Using this approach, we quantified diffusion of monomeric GFP in high versus low chromatin density regions. We found that GFP mobility was reduced in heterochromatin, especially within perinucleolar heterochromatin. Moreover, we found that modulation of chromatin compaction by ATP depletion, or treatment with solutions of different osmolarity, differentially affected the ratio of diffusion in both regions. Then, we used the approach to probe the mobility of estrogen receptor-α in the vicinity of an integrated multicopy prolactin gene array. Finally, we discussed the coupling of this method with stimulated emission depletion FCS for performing FCS at subdiffraction spatial scales.

Comprehensive correlation analysis for super-resolution dynamic fingerprinting of cellular compartments using the Zeiss Airyscan detector

The availability of the Airyscan detector in the Zeiss LSM 880 has made possible the development of a new concept in fluctuation correlation spectroscopy using super-resolution. The Airyscan unit acquires data simultaneously on 32 detectors arranged in a hexagonal array. This detector opens up the possibility to use fluctuation methods based on time correlation at single points or at a number of points simultaneously, as well as methods based on spatial correlation in the area covered by the detector. Given the frame rate of this detector, millions of frames can be acquired in seconds, providing a robust statistical basis for fluctuation data. We apply the comprehensive analysis to the molecular fluctuations of free GFP diffusing in live cells at different subcellular compartments to show that at the nanoscale different cell environments can be distinguished by the comprehensive fluctuation analysis.

A potent, minimally invasive and simple strategy of enhancing intracellular targeted delivery of Tat peptide-conjugated quantum dots: organic solvent-based permeation enhancer

Targeted delivery of nanomaterials to specific intracellular locations is essential for the development of many nanomaterials-based biological applications. Thus far the targeting performance has been limited due to various intracellular transport barriers, especially intracellular vesicle trapping. Here we report the application of permeation enhancers based on organic solvents in small percentage to enhance the intracellular targeted delivery of nanomaterials. Previously permeation enhancers based on organic solvents and ionic liquids have been used in overcoming biological transport barriers at tissue, organ, and cellular levels, but this strategy has so far rarely been examined for its potential in facilitating transport of nanometer-scale entities across intracellular barriers, particularly intracellular vesicle trapping. Using the cell nucleus as a model intracellular target and Tat peptide-conjugated quantum dots (QDs-Tat) as a model nanomaterial-based probe, we demonstrate that a small percentage (e.g. 1%) of organic solvent greatly enhances nucleus targeting specificity as well as increasing endocytosis-based cellular uptake of QDs. We combine vesicle colocalization (DiO dye staining), vesicle integrity (calcein dye release), and single-particle studies (pair-correlation function microscopy) to investigate the process of organic solvent-enhanced vesicle escape of QDs-Tat. The organic solvent based vesicle escape-enhancing approach is found to be not only very effective but minimally invasive, resulting in high vesicle escape efficiency with no significant disruption to the membrane integrity of either intracellular vesicles or cells. This approach drastically outperforms the commonly used vesicle escape-enhancing agent (i.e., chloroquine, whose enhancement effect is based on disrupting vesicle integrity) in both potency and minimal invasiveness. Finally, we apply organic solvent-based targeting enhancement to improve the intracellular delivery of the anticancer drug doxorubicin (DOX).

Pair correlation functions for identifying spatial correlation in discrete domains

Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.

A Discontinuous Galerkin Model for Fluorescence Loss in Photobleaching

Fluorescence loss in photobleaching (FLIP) is a modern microscopy method for visualization of transport processes in living cells. This paper presents the simulation of FLIP sequences based on a calibrated reaction-diffusion system defined on segmented cell images. By the use of a discontinuous Galerkin method, the computational complexity is drastically reduced compared to continuous Galerkin methods. Using this approach on green fluorescent protein (GFP), we can determine its intracellular diffusion constant, the strength of localized hindrance to diffusion as well as the permeability of the nuclear membrane for GFP passage, directly from the FLIP image series. Thus, we present for the first time, to our knowledge, a quantitative computational FLIP method for inferring several molecular transport parameters in parallel from FLIP image data acquired at commercial microscope systems.

Visualization of barriers and obstacles to molecular diffusion in live cells by spatial pair-cross-correlation in two dimensions

Despite recent advances in optical super-resolution, we lack a method that can visualize the path followed by diffusing molecules in the cytoplasm or in the nucleus of cells. Fluorescence correlation spectroscopy (FCS) provides molecular dynamics at the single molecule level by averaging the behavior of many molecules over time at a single spot, thus achieving very good statistics but at only one point in the cell. Earlier image-based methods including raster-scan and spatiotemporal image correlation need spatial averaging over relatively large areas, thus compromising spatial resolution. Here, we use spatial pair-cross-correlation in two dimensions (2D-pCF) to obtain relatively high resolution images of molecular diffusion dynamics and transport in live cells. The 2D-pCF method measures the time for a particle to go from one location to another by cross-correlating the intensity fluctuations at specific points in an image. Hence, a visual map of the average path followed by molecules is created.

Mapping the Dynamics of the Glucocorticoid Receptor within the Nuclear Landscape

The distribution of the transcription machinery among different sub-nuclear domains raises the question on how the architecture of the nucleus modulates the transcriptional response. Here, we used fluorescence fluctuation analyses to quantitatively explore the organization of the glucocorticoid receptor (GR) in the interphase nucleus of living cells. We found that this ligand-activated transcription factor diffuses within the nucleus and dynamically interacts with bodies enriched in the coregulator NCoA-2, DNA-dependent foci and chromatin targets. The distribution of the receptor among the nuclear compartments depends on NCoA-2 and the conformation of the receptor as assessed with synthetic ligands and GR mutants with impaired transcriptional abilities. Our results suggest that the partition of the receptor in different nuclear reservoirs ultimately regulates the concentration of receptor available for the interaction with specific targets, and thus has an impact on transcription regulation.

Time-resolved biophysical approaches to nucleocytoplasmic transport

Molecules are continuously shuttling across the nuclear envelope barrier that separates the nucleus from the cytoplasm. Instead of being just a barrier to diffusion, the nuclear envelope is rather a complex filter that provides eukaryotes with an elaborate spatiotemporal regulation of fundamental molecular processes, such as gene expression and protein translation. Given the highly dynamic nature of nucleocytoplasmic transport, during the past few decades large efforts were devoted to the development and application of time resolved, fluorescence-based, biophysical methods to capture the details of molecular motion across the nuclear envelope. These methods are here divided into three major classes, according to the differences in the way they report on the molecular process of nucleocytoplasmic transport. In detail, the first class encompasses those methods based on the perturbation of the fluorescence signal, also known as ensemble-averaging methods, which average the behavior of many molecules (across many pores). The second class comprises those methods based on the localization of single fluorescently-labelled molecules and tracking of their position in space and time, potentially across single pores. Finally, the third class encompasses methods based on the statistical analysis of spontaneous fluorescence fluctuations out of the equilibrium or stationary state of the system. In this case, the behavior of single molecules is probed in presence of many similarly-labelled molecules, without dwelling on any of them. Here these three classes, with their respective pros and cons as well as their main applications to nucleocytoplasmic shuttling will be briefly reviewed and discussed.

Measuring Protein Movement, Oligomerization State, and Protein-Protein Interaction in Arabidopsis Roots Using Scanning Fluorescence Correlation Spectroscopy (Scanning FCS)

Scanning fluorescence correlation spectroscopy (scanning FCS) can be used to determine protein movement, oligomerization state, and protein-protein interaction. Here, we describe how to use the scanning FCS techniques of raster image correlation spectroscopy (RICS) and pair correlation function (pCF) to determine the rate and direction of protein movement. In addition, we detail how number and brightness (N&B) and cross-correlation analyses can be used to determine oligomerization state and binding ratios of protein complexes. We specifically describe how to acquire suitable images for scanning FCS analysis using the model plant Arabidopsis and how to perform the various analyses using the SimFCS software.

Pair correlation microscopy reveals the role of nanoparticle shape in intracellular transport and site of drug release

Nanoparticle size, surface charge and material composition are known to affect the uptake of nanoparticles by cells. However, whether nanoparticle shape affects transport across various barriers inside the cell remains unclear. Here we used pair correlation microscopy to show that polymeric nanoparticles with different shapes but identical surface chemistries moved across the various cellular barriers at different rates, ultimately defining the site of drug release. We measured how micelles, vesicles, rods and worms entered the cell and whether they escaped from the endosomal system and had access to the nucleus via the nuclear pore complex. Rods and worms, but not micelles and vesicles, entered the nucleus by passive diffusion. Improving nuclear access, for example with a nuclear localization signal, resulted in more doxorubicin release inside the nucleus and correlated with greater cytotoxicity. Our results therefore demonstrate that drug delivery across the major cellular barrier, the nuclear envelope, is important for doxorubicin efficiency and can be achieved with appropriately shaped nanoparticles.

Quantitative imaging of mammalian transcriptional dynamics: from single cells to whole embryos

Probing dynamic processes occurring within the cell nucleus at the quantitative level has long been a challenge in mammalian biology. Advances in bio-imaging techniques over the past decade have enabled us to directly visualize nuclear processes in situ with unprecedented spatial and temporal resolution and single-molecule sensitivity. Here, using transcription as our primary focus, we survey recent imaging studies that specifically emphasize the quantitative understanding of nuclear dynamics in both time and space. These analyses not only inform on previously hidden physical parameters and mechanistic details, but also reveal a hierarchical organizational landscape for coordinating a wide range of transcriptional processes shared by mammalian systems of varying complexity, from single cells to whole embryos.

Dynamics of intracellular processes in live-cell systems unveiled by fluorescence correlation microscopy

Fluorescence fluctuation-based methods are non-invasive microscopy tools especially suited for the study of dynamical aspects of biological processes. These methods examine spontaneous intensity fluctuations produced by fluorescent molecules moving through the small, femtoliter-sized observation volume defined in confocal and multiphoton microscopes. The quantitative analysis of the intensity trace provides information on the processes producing the fluctuations that include diffusion, binding interactions, chemical reactions and photophysical phenomena. In this review, we present the basic principles of the most widespread fluctuation-based methods, discuss their implementation in standard confocal microscopes and briefly revise some examples of their applications to address relevant questions in living cells. The ultimate goal of these methods in the Cell Biology field is to observe biomolecules as they move, interact with targets and perform their biological action in the natural context. © 2016 IUBMB Life, 69(1):8-15, 2017.

Diffusion Tensor Analysis by Two-Dimensional Pair Correlation of Fluorescence Fluctuations in Cells

In a living cell, the movement of biomolecules is highly regulated by the cellular organization into subcompartments that impose barriers to diffusion, can locally break the spatial isotropy, and ultimately guide these molecules to their targets. Despite the pivotal role of these processes, experimental tools to fully probe the complex connectivity (and accessibility) of the cell interior with adequate spatiotemporal resolution are still lacking. Here, we show how the heterogeneity of molecular dynamics and the location of barriers to molecular motion can be mapped in live cells by exploiting a two-dimensional (2D) extension of the pair correlation function (pCF) analysis. Starting from a time series of images collected for the same field of view, the resulting 2D pCF is calculated in the proximity of each point for each time delay and allows us to probe the spatial distribution of the molecules that started from a given pixel. This 2D pCF yields an accurate description of the preferential diffusive routes. Furthermore, we combine this analysis with the image-derived mean-square displacement approach and gain information on the average nanoscopic molecular displacements in different directions. Through these quantities, we build a fluorescence-fluctuation-based diffusion tensor that contains information on speed and directionality of the local dynamical processes. Contrary to classical fluorescence correlation spectroscopy and related methods, this combined approach can distinguish between isotropic and anisotropic local diffusion. We argue that the measurement of this iMSD tensor will contribute to advance our understanding of the role played by the intracellular environment in the regulation of molecular diffusion at the nanoscale.

Dynamic Organization of SecA and SecY Secretion Complexes in the B. subtilis Membrane

In prokaryotes, about one third of cellular proteins are translocated across the plasma membrane or inserted into it by concerted action of the cytoplasmic ATPase SecA and the universally conserved SecYEG heterotrimeric polypeptide-translocating pore. Secretion complexes have been reported to localize in specific subcellular sites in Bacillus subtilis. In this work, we used a combination of total internal reflection microscopy, scanning fluorescence correlation spectroscopy, and pair correlation function to study the localization and dynamics of SecA and SecY in growing Bacillus subtilis cells. Both SecA and SecY localized in transient and dynamic foci in the cytoplasmic membrane, which displayed no higher-level organization in helices. Foci of SecA and SecY were in constant flux with freely diffusing SecA and SecY molecules. Scanning FCS confirmed the existence of populations of cellular SecA and SecY molecules with a wide range of diffusion coefficients. Diffusion of SecY as an uncomplexed molecular species was short-lived and only local while SecY complexed with its protein partners traversed distances of over half a micrometer in the cell.

Tracking transcription factor mobility and interaction in Arabidopsis roots with fluorescence correlation spectroscopy

To understand complex regulatory processes in multicellular organisms, it is critical to be able to quantitatively analyze protein movement and protein-protein interactions in time and space. During Arabidopsis development, the intercellular movement of SHORTROOT (SHR) and subsequent interaction with its downstream target SCARECROW (SCR) control root patterning and cell fate specification. However, quantitative information about the spatio-temporal dynamics of SHR movement and SHR-SCR interaction is currently unavailable. Here, we quantify parameters including SHR mobility, oligomeric state, and association with SCR using a combination of Fluorescent Correlation Spectroscopy (FCS) techniques. We then incorporate these parameters into a mathematical model of SHR and SCR, which shows that SHR reaches a steady state in minutes, while SCR and the SHR-SCR complex reach a steady-state between 18 and 24 hr. Our model reveals the timing of SHR and SCR dynamics and allows us to understand how protein movement and protein-protein stoichiometry contribute to development.

Quantifying the dynamics of the oligomeric transcription factor STAT3 by pair correlation of molecular brightness

Oligomerization of transcription factors controls their translocation into the nucleus and DNA-binding activity. Here we present a fluorescence microscopy analysis termed pCOMB (pair correlation of molecular brightness) that tracks the mobility of different oligomeric species within live cell nuclear architecture. pCOMB amplifies the signal from the brightest species present and filters the dynamics of the extracted oligomeric population based on arrival time between two locations. We use this method to demonstrate a dependence of signal transducer and activator of transcription 3 (STAT3) mobility on oligomeric state. We find that on entering the nucleus STAT3 dimers must first bind DNA to form STAT3 tetramers, which are also DNA-bound but exhibit a different mobility signature. Examining the dimer-to-tetramer transition by a cross-pair correlation analysis (cpCOMB) reveals that chromatin accessibility modulates STAT3 tetramer formation. Thus, the pCOMB approach is suitable for mapping the impact oligomerization on transcription factor dynamics.

Exploring the dynamics of cell processes through simulations of fluorescence microscopy experiments

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments.

Spatially Resolved Quantification of Chromatin Condensation through Differential Local Rheology in Cell Nuclei Fluorescence Lifetime Imaging

The linear sequence of DNA encodes access to the complete set of proteins that carry out cellular functions. Yet, much of the functionality appropriate for each cell is nested within layers of dynamic regulation and organization, including a hierarchy of chromatin structural states and spatial arrangement within the nucleus. There remain limitations in our understanding of gene expression within the context of nuclear organization from an inability to characterize hierarchical chromatin organization in situ. Here we demonstrate the use of fluorescence lifetime imaging microscopy (FLIM) to quantify and spatially resolve chromatin condensation state using cell-permeable, DNA-binding dyes (Hoechst 33342 and PicoGreen). Through in vitro and in situ experiments we demonstrate the sensitivity of fluorescence lifetime to condensation state through the mechanical effects that accompany the structural changes and are reflected through altered viscosity. The establishment of FLIM for resolving and quantifying chromatin condensation state opens the door for single-measurement mechanical studies of the nucleus and for characterizing the role of genome structure and organization in nuclear processes that accompany physiological and pathological changes.

Spatio-Temporal Regulation of Rac1 Mobility by Actin Islands

Rho GTPases play important roles in many aspects of cell migration, including polarity establishment and organizing actin cytoskeleton. In particular, the Rho GTPase Rac1 has been associated with the generation of protrusions at leading edge of migrating cells. Previously we showed the mobility of Rac1 molecules is not uniform throughout a migrating cell (Hinde E et. al. PNAS 2013). Specifically, the closer a Rac1 molecule is to the leading edge, the slower the molecule diffuses. Because actin-bound Rac1 diffuses slower than unbound Rac1, we hypothesized that regions of high actin concentration, called "actin islands", act as diffusive traps and are responsible for the non-uniform diffusion observed in vivo. Here, in silico model simulations demonstrate that equally spaced actin islands can regulate the time scale for Rac1 diffusion in a manner consistent with data from live-cell imaging experiments. Additionally, we find this mechanism is robust; different patterns of Rac1 mobility can be achieved by changing the actin islands' positions or their affinity for Rac1.

Advanced fluorescence microscopy methods for the real-time study of transcription and chromatin dynamics

In this contribution we provide an overview of the recent advances allowed by the use of fluorescence microscopy methods in the study of transcriptional processes and their interplay with the chromatin architecture in living cells. Although the use of fluorophores to label nucleic acids dates back at least to about half a century ago,¹ two recent breakthroughs have effectively opened the way to use fluorescence routinely for specific and quantitative probing of chromatin organization and transcriptional activity in living cells: namely, the possibility of labeling first the chromatin loci and then the mRNA synthesized from a gene using fluorescent proteins. In this contribution we focus on methods that can probe rapid dynamic processes by analyzing fast fluorescence fluctuations.

Chromatin dynamics during DNA repair revealed by pair correlation analysis of molecular flow in the nucleus

Chromatin dynamics modulate DNA repair factor accessibility throughout the DNA damage response. The spatiotemporal scale upon which these dynamics occur render them invisible to live cell imaging. Here we present a believed novel assay to monitor the in vivo structural rearrangements of chromatin during DNA repair. By pair correlation analysis of EGFP molecular flow into chromatin before and after damage, this assay measures millisecond variations in chromatin compaction with submicron resolution. Combined with laser microirradiation we employ this assay to monitor the real-time accessibility of DNA at the damage site. We find from comparison of EGFP molecular flow with a molecule that has an affinity toward double-strand breaks (Ku-EGFP) that DNA damage induces a transient decrease in chromatin compaction at the damage site and an increase in compaction to adjacent regions, which together facilitate DNA repair factor recruitment to the lesion with high spatiotemporal control.