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Transcription factor (TF) proteins regulate gene expression by binding to specific sites on the genome. In the facilitated diffusion model, an optimized search process is achieved by the TF alternating between 3D diffusion in the bulk and 1D diffusion along DNA. While undergoing 1D diffusion, the protein can switch from a search mode for fast diffusion along nonspecific DNA to a recognition mode for stable binding to specific DNA. It was recently noticed that, for a small TF domain protein, reorientations on DNA happen between the nonspecific and specific DNA binding. We here conducted all-atom molecular dynamics simulations with steering forces to reveal the protein-DNA binding free energetics, confirming that the search and recognition modes are distinguished primarily by protein orientations on the DNA. As the binding free energy difference between the specific and nonspecific DNA system slightly deviates from that being estimated directly from dissociation constants on 15-bp DNA constructs, we hypothesize that the discrepancy can come from DNA sequences flanking the 6-bp central binding sites that impact on the dissociation kinetics measurements. The hypothesis is supported by a simplified spherical protein-DNA model along with stochastic simulations and kinetic modeling.

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.

Biophysical modeling of development started with Alan Turing. His two-morphogen reaction-diffusion model was a radical but powerful simplification. Despite its apparent limitations, the model captured real developmental processes that only recently have been validated at the molecular level in many systems. The precision and robustness of reaction-diffusion patterning, despite boundary condition-dependence, remain active areas of investigation in developmental biology.

Flagellar length control in Chlamydomonas is a tractable model system for studying the general question of organelle size regulation. We have previously proposed that the diffusive return of the kinesin motor that powers intraflagellar transport can play a key role in length regulation. Here, we explore how the motor speed and diffusion coefficient for the return of kinesin-2 affect flagellar growth kinetics. We find that the system can exist in two distinct regimes, one dominated by motor speed and one by diffusion coefficient. Depending on length, a flagellum can switch between these regimes. Our results indicate that mutations can affect the length in distinct ways. We discuss our theory's implication for flagellar growth influenced by beating and provide possible explanations for the experimental observation that a beating flagellum is usually longer than its immotile mutant. These results demonstrate how our simple model can suggest explanations for mutant phenotypes.

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.

A number of enzymes reportedly exhibit enhanced diffusion in the presence of their substrates, with a Michaelis-Menten-like concentration dependence. Although no definite explanation of this phenomenon has emerged, a physical picture of enzyme self-propulsion using energy from the catalyzed reaction has been widely considered. Here, we present a kinematic and thermodynamic analysis of enzyme self-propulsion that is independent of any specific propulsion mechanism. Using this theory, along with biophysical data compiled for all enzymes so far shown to undergo enhanced diffusion, we show that the propulsion speed required to generate experimental levels of enhanced diffusion exceeds the speeds of well-known active biomolecules, such as myosin, by several orders of magnitude. Furthermore, the minimal power dissipation required to account for enzyme enhanced diffusion by self-propulsion markedly exceeds the chemical power available from enzyme-catalyzed reactions. Alternative explanations for the observation of enhanced enzyme diffusion therefore merit stronger consideration.

An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies.

Multiple-particle tracking (MPT) is a microscopy technique capable of simultaneously tracking hundreds to thousands of nanoparticles in a biological sample and has been used extensively to characterize biological microenvironments, including the brain extracellular space (ECS). Machine learning techniques have been applied to MPT data sets to predict the diffusion mode of nanoparticle trajectories as well as more complex biological variables, such as biological age. In this study, we develop a machine learning pipeline to predict and investigate changes to the brain ECS due to injury using supervised classification and feature importance calculations. We first validate the pipeline on three related but distinct MPT data sets from the living brain ECS-age differences, region differences, and enzymatic degradation of ECS structure. We predict three ages with 86% accuracy, three regions with 90% accuracy, and healthy versus enzyme-treated tissue with 69% accuracy. Since injury across groups is normally compared with traditional statistical approaches, we first used linear mixed effects models to compare features between healthy control conditions and injury induced by two different oxygen glucose deprivation exposure times. We then used machine learning to predict injury state using MPT features. We show that the pipeline predicts between the healthy control, 0.5 h OGD treatment, and 1.5 h OGD treatment with 59% accuracy in the cortex and 66% in the striatum, and identifies nonlinear relationships between trajectory features that were not evident from traditional linear models. Our work demonstrates that machine learning applied to MPT data is effective across multiple experimental conditions and can find unique biologically relevant features of nanoparticle diffusion., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Weak protein interactions are associated with a broad array of biological functions and are often implicated in molecular dysfunction accompanying human disease. In addition, these interactions are a critical determinant in the effective manufacturing, stability, and administration of biotherapeutic proteins. Despite their prominence, much remains unknown about how molecular attributes influence the hydrodynamic and thermodynamic contributions to the overall interaction mechanism. To systematically probe these contributions, we have evaluated self-interaction in a diverse set of proteins that demonstrate a broad range of behaviors from attractive to repulsive. Analysis of the composite trending in the data provides a convenient interconversion among interaction parameters measured from the concentration dependence of the molecular weight, diffusion coefficient, and sedimentation coefficient, as well as insight into the relationship between thermodynamic and hydrodynamic interactions. We find relatively good agreement between our data and a model for interacting hard spheres in the range of weak self-association. In addition, we propose an empirically derived, general scaling relationship applicable across a broad range of self-association and repulsive behaviors., Competing Interests: Declaration of interests The authors were employees of Sanofi during the work described in this manuscript and may hold shares and/or stock options in the company. In response to reasonable requests, noncommercially available materials and experimental protocols, that Sanofi has the right to provide, will be made available to not-for-profit or academic requesters upon completion of a material transfer agreement. Requests may be made by contacting the corresponding author., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Measuring the compaction of a protein or complex is key to our understanding of the interactions within and between biomolecules. Experimentally, protein compaction is often probed either by estimating the radius of gyration (R g ) obtained from small-angle x-ray scattering (SAXS) experiments or the hydrodynamic radius (R h ) obtained, for example, by pulsed field gradient NMR (PFG NMR) spectroscopy. PFG NMR experiments generally report on the translational diffusion coefficient, which in turn can be used to estimate R h using an internal standard to account for sample viscosity and uncertainty about the gradient strength. 1,4-Dioxane is one such commonly used internal standard, and the reference value of R h is therefore important. We have revisited the basis for the commonly used reference value for the R h of dioxane (2.12 Å) that is used to convert measured diffusion coefficients into a hydrodynamic radius. We followed the same approach that was used to establish the current reference value by measuring SAXS and PFG NMR data for a set of seven different proteins and using these as standards. Our analysis shows that the current R h reference value for dioxane R h is underestimated, and we instead suggest a new value of 2.27 ± 0.04 Å. Using this updated reference value results in a ∼7% increase in R h values for proteins whose hydrodynamic radii have been measured by PFG NMR. These results are particularly important when the absolute value of R h is of interest such as when determining or validating ensemble descriptions of intrinsically disordered proteins., Competing Interests: Declaration of interests K.L.-L. holds stock options in and is a consultant for Peptone Ltd., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Mechanical and biochemical cues intricately activate Yes-associated protein (YAP), which is pivotal for the cellular responses to these stimuli. Recent findings reveal an unexplored role of YAP in influencing the apoptotic process. It has been shown that, on soft matrices, YAP is recruited to small adhesions, phosphorylated at Y357, and translocated into the nucleus triggering apoptosis. Interestingly, YAP Y357 phosphorylation is significantly reduced in larger mature focal adhesions on stiff matrices. Building upon these novel insights, we have developed a stochastic model to delve deeper into the complex dynamics of YAP phosphorylation within integrin adhesions. Our findings emphasize several key points: firstly, increasing the cytosolic diffusion rate of YAP correlates with higher levels of phosphorylated YAP (pYAP); secondly, increasing the number of binding sites and distributing them across the membrane surface, mimicking smaller adhesions, leads to higher pYAP levels, particularly at lower diffusion rates. Moreover, we show that the binding and release rate of YAP to adhesions as well as adhesion lifetimes significantly influence the size effect of adhesion-induced YAP phosphorylation. The results highlight the complex and dynamic interplay between adhesion lifetime, the rate of pYAP unbinding from adhesions, and dephosphorylation rates, collectively shaping overall pYAP levels. In summary, our work advances the understanding of YAP mechanotransduction and opens avenues for experimental validation., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Biochemical signaling pathways often involve proteins with multiple, modular interaction domains. Signaling activates binding sites, such as by tyrosine phosphorylation, which enables protein recruitment and growth of networked protein assemblies. Although widely observed, the physical properties of the assemblies, as well as the mechanisms by which they function, remain largely unknown. Here we examine molecular mobility within LAT:Grb2:SOS assemblies on supported membranes by single-molecule tracking. Trajectory analysis reveals a discrete temporal transition to subdiffusive motion below a characteristic timescale, indicating that the LAT:Grb2:SOS assembly has the dynamical structure of a loosely entangled polymer. Such dynamical analysis is also applicable in living cells, where it offers another dimension on the characteristics of cellular signaling assemblies.

Brightness analysis of fluorescence fluctuation experiments has been used to successfully measure the oligomeric state of proteins at the plasma membrane, in the nucleoplasm, and in the cytoplasm of living cells. Here we extend brightness analysis to the nuclear envelope (NE), a double membrane barrier separating the cytoplasm from the nucleoplasm. Results obtained by applying conventional brightness analysis to fluorescently tagged proteins within the NE exhibited an unusual concentration dependence. Similarly, the autocorrelation function of the fluorescence fluctuations exhibited unexpected changes with protein concentration. These observations motivated the application of mean-segmented Q analysis, which identified the existence of a fluctuation process distinct from molecular diffusion in the NE. We propose that small changes in the separation of the inner and outer nuclear membrane are responsible for the additional fluctuation process, as suggested by results obtained for luminal and nuclear membrane-associated EGFP-tagged proteins. Finally, we applied these insights to study the oligomerization of the luminal domains of two nuclear membrane proteins, nesprin-2 and SUN2, which interact transluminally to form a nuclear envelope-spanning linker molecular bridge known as the linker of the nucleoskeleton and cytoskeleton complex.

The response of lipid bilayers to osmotic stress is an important part of cellular function. Recent experimental studies showed that when cell-sized giant unilamellar vesicles (GUVs) are exposed to hypotonic media, they respond to the osmotic assault by undergoing a cyclical sequence of swelling and bursting events, coupled to the membrane's compositional degrees of freedom. Here, we establish a fundamental and quantitative understanding of the essential pulsatile behavior of GUVs under hypotonic conditions by advancing a comprehensive theoretical model of vesicle dynamics. The model quantitatively captures the experimentally measured swell-burst parameters for single-component GUVs, and reveals that thermal fluctuations enable rate-dependent pore nucleation, driving the dynamics of the swell-burst cycles. We further extract constitutional scaling relationships between the pulsatile dynamics and GUV properties over multiple timescales. Our findings provide a fundamental framework that has the potential to guide future investigations on the nonequilibrium dynamics of vesicles under osmotic stress.

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.

Despite the importance of speed in synaptic transmission, in many synapses, neurotransmitters bind to their receptors at rates that appear to be slower than the diffusion limit. This assessment is generally based on a comparison with the Smoluchowski limit rather than an independent experimental analysis. In many synapses, miniature excitatory postsynaptic currents (mEPSCs) are controlled by the interplay between binding to receptors and diffusion of the neurotransmitter out of the synaptic cleft. A model for mEPSCs that incorporates these features was used to evaluate published data showing that elevated viscosity increases mEPSC amplitude. With diffusion-limited binding, the model predicts that raising the viscosity will decrease the amplitude rather than increase it. Diffusion-independent binding predicts an increase that is larger than that observed. To explore the intermediate behavior between the diffusion-limited and diffusion-independent extremes, a general expression for intermolecular rates was used that depends on both collision frequency and intrinsic reactivity. This analysis yielded an estimate for collision frequency that is about an order of magnitude above the measured rate of association and an order of magnitude below the Smoluchowski limit., Competing Interests: Declaration of interests The author declares no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

A mesh of cytoskeletal fibers, consisting of microtubules, intermediate filaments, and fibrous actin, prevents the Brownian diffusion of particles with a diameter larger than 0.10 μm, such as vesicular stomatitis virus ribonucleoprotein (RNP) particles, in mammalian cells. Nevertheless, RNP particles do move in random directions but at a lower rate than Brownian diffusion, which is thermally driven. This nonthermal biological transport process is called "active diffusion" because it is driven by ATP. The ATP powers motor proteins such as myosin II. The motor proteins bend and cross-link actin fibers, causing the mesh to jiggle. Until recently, little was known about how RNP particles get through the mesh. It has been customary to analyze the tracks of particles like RNPs by computing the slope of the ensemble-averaged mean-squared displacement of the particles as a signature of mechanism. Although widely used, this approach "loses information" about the timing of the switches between physical mechanisms. It has been recently shown that machine learning composed of variational Bayesian analysis, Gaussian mixture models, and hidden Markov models can use "all the information" in a single track to reveal that that the positions of RNP particles are spatially clustered. Machine learning assigns a number, called a state, to each cluster. RNP particles remain in one state for 0.2-1.0 s before switching (hopping) to a different state. This earlier work is here extended to analyze the movements of a particle within a state and to determine particle directionality within and between states., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Polyethylene glycol (PEG) conjugation provides a protective modification that enhances the pharmacokinetics and solubility of proteins for therapeutic use. A knowledge of the structural ensemble of these PEGylated proteins is necessary to understand the molecular details that contribute to their hydrodynamic and colligative properties. Because of the large size and dynamic flexibility of pharmaceutically important PEGylated proteins, the determination of structure is challenging. In addition, the hydration of these conjugates that contain large polymers is difficult to determine with traditional methods that identify only first shell hydration water, which does not account for the complete hydrodynamic volume of a macromolecule. Here, we demonstrate that structural ensembles, generated by coarse-grained simulations, can be analyzed with HullRad and used to predict sedimentation coefficients and concentration-dependent hydrodynamic and diffusion nonideality coefficients of PEGylated proteins. A knowledge of these concentration-dependent properties enhances the ability to design and analyze new modified protein therapeutics. HullRad accomplishes this analysis by effectively accounting for the complete hydration of a macromolecule, including that of flexible polymers., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Plasma membrane fluidity is an important phenotypic feature that regulates the diffusion, function, and folding of transmembrane and membrane-associated proteins. In bacterial cells, variations in membrane fluidity are known to affect respiration, transport, and antibiotic resistance. Membrane fluidity must therefore be tightly regulated to adapt to environmental variations and stresses such as temperature fluctuations or osmotic shocks. Quantitative investigation of bacterial membrane fluidity has been, however, limited due to the lack of available tools, primarily due to the small size and membrane curvature of bacteria that preclude most conventional analysis methods used in eukaryotes. Here, we develop an assay based on total internal reflection-fluorescence correlation spectroscopy (TIR-FCS) to directly measure membrane fluidity in live bacteria via the diffusivity of fluorescent membrane markers. With simulations validated by experiments, we could determine how the small size, high curvature, and geometry of bacteria affect diffusion measurements and correct subsequent measurements for unbiased diffusion coefficient estimation. We used this assay to quantify the fluidity of the cytoplasmic membranes of the Gram-positive bacteria Bacillus subtilis (rod-shaped) and Staphylococcus aureus (coccus) at high (37°C) and low (20°C) temperatures in a steady state and in response to a cold shock, caused by a shift from high to low temperature. The steady-state fluidity was lower at 20°C than at 37°C, yet differed between B. subtilis and S. aureus at 37°C. Upon cold shock, the membrane fluidity decreased further below the steady-state fluidity at 20°C and recovered within 30 min in both bacterial species. Our minimally invasive assay opens up exciting perspectives for the study of a wide range of phenomena affecting the bacterial membrane, from disruption by chemicals or antibiotics to viral infection or change in nutrient availability., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Interleaflet coupling-the influence of one leaflet on the properties of the opposing leaflet-is a fundamental plasma membrane organizational principle. This coupling is proposed to participate in maintaining steady-state biophysical properties of the plasma membrane, which in turn regulates some transmembrane signaling processes. A prominent example is antigen (Ag) stimulation of signaling by clustering transmembrane receptors for immunoglobulin E (IgE), FcεRI. This transmembrane signaling depends on the stabilization of ordered regions in the inner leaflet for sorting of intracellular signaling components. The resting inner leaflet has a lipid composition that is generally less ordered than the outer leaflet and that does not spontaneously phase separate in model membranes. We propose that interleaflet coupling can mediate ordering and disordering of the inner leaflet, which is poised in resting cells to reorganize upon stimulation. To test this in live cells, we first established a straightforward approach to evaluate induced changes in membrane order by measuring inner leaflet diffusion of lipid probes by imaging fluorescence correlation spectroscopy, by imaging fluorescence correlation spectroscopy (ImFCS), before and after methyl-α-cyclodexrin (mαCD)-catalyzed exchange of outer leaflet lipids (LEX) with exogenous order- or disorder-promoting phospholipids. We examined the functional impact of LEX by monitoring two Ag-stimulated responses: recruitment of cytoplasmic Syk kinase to the inner leaflet and exocytosis of secretory granules (degranulation). Based on the ImFCS data in resting cells, we observed global increase or decrease of inner leaflet order when outer leaflet is exchanged with order- or disorder-promoting lipids, respectively. We find that the degree of both stimulated Syk recruitment and degranulation correlates positively with LEX-mediated changes of inner leaflet order in resting cells. Overall, our results show that resting-state lipid ordering of the outer leaflet influences the ordering of the inner leaflet, likely via interleaflet coupling. This imposed lipid reorganization modulates transmembrane signaling stimulated by Ag clustering of IgE-FcεRI., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Biophysical Society. All rights reserved.)

The cell membrane organization has an essential functional role through the control of membrane receptor confinement in micro- or nanodomains. Several mechanisms have been proposed to account for these properties, although some features have remained controversial, notably the nature, size, and stability of cholesterol- and sphingolipid-rich domains or lipid rafts. Here, we probed the effective energy landscape acting on single-nanoparticle-labeled membrane receptors confined in raft nanodomains- epidermal growth factor receptor (EGFR), Clostridium perfringens ε-toxin receptor (CPεTR), and Clostridium septicum α-toxin receptor (CSαTR)-and compared it with hop-diffusing transferrin receptors. By establishing a new analysis pipeline combining Bayesian inference, decision trees, and clustering approaches, we systematically classified single-protein trajectories according to the type of effective confining energy landscape. This revealed the existence of only two distinct organization modalities: confinement in a quadratic energy landscape for EGFR, CPεTR, and CSαTR (A), and free diffusion in confinement domains resulting from the steric hindrance due to F-actin barriers for transferrin receptor (B). The further characterization of effective confinement energy landscapes by Bayesian inference revealed the role of interactions with the domain environment in cholesterol- and sphingolipid-rich domains with (EGFR) or without (CPεTR and CSαTR) interactions with F-actin to regulate the confinement energy depth. These two distinct mechanisms result in the same organization type (A). We revealed that the apparent domain sizes for these receptor trajectories resulted from Brownian exploration of the energy landscape in a steady-state-like regime at a common effective temperature, independently of the underlying molecular mechanisms. These results highlight that confinement domains may be adequately described as interaction hotspots rather than rafts with abrupt domain boundaries. Altogether, these results support a new model for functional receptor confinement in membrane nanodomains and pave the way to the constitution of an atlas of membrane protein organization., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific locations is accomplished through a combination of passive diffusion and active transport by molecular motors that ballistically move along a network of cytoskeletal filaments. Although motor-based transport is known to be necessary to overcome cytoplasmic crowding and the limited range of diffusion within reasonable timescales, the topological features of the cytoskeletal network that regulate transport efficiency and robustness have not been established. Using a continuum diffusion model, we observed that the time required for cellular transport was minimized when the network was localized near the nucleus. In simulations that explicitly incorporated network spatial architectures, total filament mass was the primary driver of network transit times. However, filament traps that redirect cargo back to the nucleus caused large variations in network transport. Filament polarity was more important than filament orientation in reducing average transit times, and transport properties were optimized in networks with intermediate motor on and off rates. Our results provide important insights into the functional constraints on intracellular transport under which cells have evolved cytoskeletal structures, and have potential applications for enhancing reactions in biomimetic systems through rational transport network design.

Quantifying the forces between and within macromolecules is a necessary firststep in understanding the mechanics of molecular structure, protein folding,and enzyme function and performance. In such macromolecular settings, dynamicsingle-molecule force spectroscopy (DFS) has been used to distort bonds. Theresulting responses, in the form of rupture forces, work applied, andtrajectories of displacements, have been used to reconstruct bond potentials.Such approaches often rely on simple parameterizations of one-dimensional bondpotentials, assumptions on equilibrium starting states, and/or large amounts oftrajectory data. Parametric approaches typically fail at inferringcomplex-shaped bond potentials with multiple minima, while piecewise estimationmay not guarantee smooth results with the appropriate behavior at largedistances. Existing techniques, particularly those based on work theorems, alsodo not address spatial variations in the diffusivity that may arise fromspatially inhomogeneous coupling to other degrees of freedom in themacromolecule, thereby presenting an incomplete picture of the overall bonddynamics. To solve these challenges, we have developed a comprehensiveempirical Bayesian approach that incorporates data and regularization termsdirectly into a path integral. All experiemental and statistical parameters inour method are estimated empirically directly from the data. Upon testing ourmethod on simulated data, our regularized approach requires fewer data andallows simultaneous inference of both complex bond potentials and diffusivityprofiles.

Dimethyl sulfoxide (DMSO) has been broadly used in biology as a cosolvent, a cryoprotectant, and an enhancer of membrane permeability, leading to the general assumption that DMSO-induced structural changes in cell membranes and their hydration water play important functional roles. Although the effects of DMSO on the membrane structure and the headgroup dehydration have been extensively studied, the mechanism by which DMSO invokes its effect on lipid membranes and the direct role of water in this process are unresolved. By directly probing the translational water diffusivity near unconfined lipid vesicle surfaces, the lipid headgroup mobility, and the repeat distances in multilamellar vesicles, we found that DMSO exclusively weakens the surface water network near the lipid membrane at a bulk DMSO mole fraction (XDMSO) of 0.1, DMSO enters the lipid interface and restricts the lipid headgroup motion. We postulate that DMSO acts as an efficient cryoprotectant even at low concentrations by exclusively disrupting the water network near the lipid membrane surface, weakening the cohesion between water and adhesion of water to the lipid headgroups, and so mitigating the stress induced by the volume change of water during freeze-thaw.

Cells control organelle size with great precision and accuracy to maintain optimal physiology, but the mechanisms by which they do so are largely unknown. Cilia and flagella are simple organelles in which a single measurement, length, can represent size. Maintenance of flagellar length requires an active transport process known as intraflagellar transport, and previous measurements suggest that a length-dependent feedback regulates intraflagellar transport. But the question remains: how is a length-dependent signal produced to regulate intraflagellar transport appropriately? Several conceptual models have been suggested, but testing these models quantitatively requires that they be cast in mathematical form. Here, we derive a set of mathematical models that represent the main broad classes of hypothetical size-control mechanisms currently under consideration. We use these models to predict the relation between length and intraflagellar transport, and then compare the predicted relations for each model with experimental data. We find that three models-an initial bolus formation model, an ion current model, and a diffusion-based model-show particularly good agreement with available experimental data. The initial bolus and ion current models give mathematically equivalent predictions for length control, but fluorescence recovery after photobleaching experiments rule out the initial bolus model, suggesting that either the ion current model or a diffusion-based model is more likely correct. The general biophysical principles of the ion current and diffusion-based models presented here to measure cilia and flagellar length can be generalized to measure any membrane-bound organelle volume, such as the nucleus and endoplasmic reticulum.

The image-mean square displacement technique applies the calculation of the mean square displacement commonly used in single-molecule tracking to images without resolving single particles. The image-mean square displacement plot obtained is similar to the mean square displacement plot obtained using the single-particle tracking technique. This plot is then used to reconstruct the protein diffusion law and to identify whether the labeled molecules are undergoing pure isotropic, restricted, corralled, transiently confined, or directed diffusion. In our study total internal reflection fluorescence microscopy images were taken of Cholera toxin subunit B (CtxB) membrane-labeled NIH 3T3 mouse fibroblasts and MDA 231 MB cells. We found a population of CTxB undergoing purely isotropic diffusion and one displaying restricted diffusion with corral sizes ranging from 150 to ∼1800 nm. We show that the diffusion rate of CTxB bound to GM1 is independent of the size of the confinement, suggesting that the mechanism of confinement is different from the mechanism controlling the diffusion rate of CtxB. We highlight the potential effect of continuous illumination on the diffusion mode of CTxB. We also show that aggregation of CTxB/GM1 in large complexes occurs and that these aggregates tend to have slower diffusion rates.

Diffusion of a fluorescent protein within a cell has been measured using either fluctuation-based techniques (fluorescence correlation spectroscopy (FCS) or raster-scan image correlation spectroscopy) or particle tracking. However, none of these methods enables us to measure the diffusion of the fluorescent particle at each pixel of the image. Measurement using conventional single-point FCS at every individual pixel results in continuous long exposure of the cell to the laser and eventual bleaching of the sample. To overcome this limitation, we have developed what we believe to be a new method of scanning with simultaneous construction of a fluorescent image of the cell. In this believed new method of modified raster scanning, as it acquires the image, the laser scans each individual line multiple times before moving to the next line. This continues until the entire area is scanned. This is different from the original raster-scan image correlation spectroscopy approach, where data are acquired by scanning each frame once and then scanning the image multiple times. The total time of data acquisition needed for this method is much shorter than the time required for traditional FCS analysis at each pixel. However, at a single pixel, the acquired intensity time sequence is short; requiring nonconventional analysis of the correlation function to extract information about the diffusion. These correlation data have been analyzed using the phasor approach, a fit-free method that was originally developed for analysis of FLIM images. Analysis using this method results in an estimation of the average diffusion coefficient of the fluorescent species at each pixel of an image, and thus, a detailed diffusion map of the cell can be created.

Models of biological diffusion-reaction systems require accurate classification of the underlying diffusive dynamics (e.g., Fickian, subdiffusive, or superdiffusive). We use a renormalization group operator to identify the anomalous (non-Fickian) diffusion behavior from a short trajectory of a single molecule. The method provides quantitative information about the underlying stochastic process, including its anomalous scaling exponent. The classification algorithm is first validated on simulated trajectories of known scaling. Then it is applied to experimental trajectories of microspheres diffusing in cytoplasm, revealing heterogeneous diffusive dynamics. The simplicity and robustness of this classification algorithm makes it an effective tool for analysis of rare stochastic events that occur in complex biological systems.

Puffs are local Ca(2+) signals that arise by Ca(2+) liberation from the endoplasmic reticulum through the concerted opening of tightly clustered inositol trisphosphate receptors/channels (IP3Rs). The locations of puff sites observed by Ca(2+) imaging remain static over several minutes, whereas fluorescence recovery after photobleaching (FRAP) experiments employing overexpression of fluorescently tagged IP3Rs have shown that the majority of IP3Rs are freely motile. To address this discrepancy, we applied single-molecule imaging to locate and track type 1 IP3Rs tagged with a photoswitchable fluorescent protein and expressed in COS-7 cells. We found that ∼ 70% of the IP3R1 molecules were freely motile, undergoing random walk motility with an apparent diffusion coefficient of ∼ 0.095 μm s(-1), whereas the remaining molecules were essentially immotile. A fraction of the immotile IP3Rs were organized in clusters, with dimensions (a few hundred nanometers across) comparable to those previously estimated for the IP3R clusters underlying functional puff sites. No short-term (seconds) changes in overall motility or in clustering of immotile IP3Rs were apparent following activation of IP3/Ca(2+) signaling. We conclude that stable clusters of small numbers of immotile IP3Rs may underlie local Ca(2+) release sites, whereas the more numerous motile IP3Rs appear to be functionally silent.

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

Using a coarse-grained lipid and peptide model, we show that the free energy stabilization of amyloid-β in heterogeneous lipid membranes is predicted to have a dependence on asymmetric distributions of cholesterol compositions across the membrane leaflets. We find that a highly asymmetric cholesterol distribution that is depleted on the exofacial leaflet but enhanced on the cytofacial leaflet of the model lipid membrane thermodynamically favors membrane retention of a fully embedded Aβ peptide. However, in the case of cholesterol redistribution that increases concentration of cholesterol on the exofacial layer, typical of aging or Alzheimer's disease, the free energy favors peptide extrusion of the highly reactive N-terminus into the extracellular space that may be vulnerable to aggregation, oligomerization, or deleterious oxidative reactivity.

Diffusion determines the turnover of biomolecules in liquid-liquid phase-separated condensates. We considered the mean square displacement and thus the diffusion constant for simple model systems of peptides GGGGG, GGQGG, and GGVGG in aqueous solutions after phase separation by simulating atomic-level models. These solutions readily separate into aqueous and peptide-rich droplet phases. We noted the effect of the peptides being in a solvated, surface, or droplet state on the peptide's diffusion coefficients. Both sequence and peptide conformational distribution were found to influence diffusion and condensate turnover in these systems, with sequence dominating the magnitude of the differences. We found that the most compact structures for each sequence diffused the fastest in the peptide-rich condensate phase. This model result may have implications for turnover dynamics in signaling systems., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions-creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim-leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Due to the high concentration of proteins, nucleic acids, and other macromolecules, the bacterial cytoplasm is typically described as a crowded environment. However, the extent to which each of these macromolecules individually affects the mobility of macromolecular complexes, and how this depends on growth conditions, is presently unclear. In this study, we sought to quantify the crowding experienced by an exogenous 40 nm fluorescent particle in the cytoplasm of E. coli under different growth conditions. By performing single-particle tracking measurements in cells selectively depleted of DNA and/or mRNA, we determined the contribution to crowding of mRNA, DNA, and remaining cellular components, i.e., mostly proteins and ribosomes. To estimate this contribution to crowding, we quantified the difference of the particle's diffusion coefficient in conditions with and without those macromolecules. We found that the contributions of the three classes of components were of comparable magnitude, being largest in the case of proteins and ribosomes. We further found that the contributions of mRNA and DNA to crowding were significantly larger than expected based on their volumetric fractions alone. Finally, we found that the crowding contributions change only slightly with the growth conditions. These results reveal how various cellular components partake in crowding of the cytoplasm and the consequences this has for the mobility of large macromolecular complexes., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Phosphatidylinositol (3,4,5)-trisphosphate (PIP3) is a signaling lipid on the plasma membrane that plays a fundamental role in cell signaling with a strong impact on cell physiology and diseases. It is responsible for the protruding edge formation, cell polarization, macropinocytosis, and other membrane remodeling dynamics in cells. It has been shown that the membrane confinement and curvature affects the wave formation of PIP3 and F-actin. But, even in the absence of F-actin, a complex self-organization of the spatiotemporal PIP3 waves is observed. In recent findings, we have shown that these waves can be guided and pinned on strongly bended Dictyostelium membranes caused by molecular crowding and curvature-limited diffusion. Based on these experimental findings, we investigate the spatiotemporal PIP3 wave dynamics on realistic three-dimensional cell-like membranes to explore the effect of curvature-limited diffusion, as observed experimentally. We use an established stochastic reaction-diffusion model with enzymatic Michaelis-Menten-type reactions that mimics the dynamics of Dictyostelium cells. As these cells mimic the three-dimensional shape and size observed experimentally, we found that the PIP3 wave directionality can be explained by a Hopf-like and a reverse periodic-doubling bifurcation for uniform diffusion and curvature-limited diffusion properties. Finally, we compare the results with recent experimental findings and discuss the discrepancy between the biological and numerical results., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Interstitial fluid flow is a feature of many solid tumors. In vitro experiments have shown that such fluid flow can direct tumor cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis (cell migration up stress gradients) and autologous chemotaxis (downstream cell movement in response to flow-induced gradients of self-secreted chemoattractants). In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow. We use a kinetic description for the cell velocity probability density function, and model the flow-dependent mechanical and chemical stimuli as forcing terms that bias cell migration upstream and downstream. Using velocity-space averaging, we reformulate the model as a system of continuum equations for the spatiotemporal evolution of the cell volume fraction and flux in response to forcing terms that depend on the local direction and magnitude of the mechanochemical cues. We specialize our model to describe a one-dimensional cell layer subject to fluid flow. Using a combination of numerical simulations and asymptotic analysis, we delineate the parameter regime where transitions from downstream to upstream cell migration occur. As has been observed experimentally, the model predicts downstream-oriented chemotactic migration at low cell volume fractions, and upstream-oriented tensotactic migration at larger volume fractions. We show that the locus of the critical volume fraction, at which the system transitions from downstream to upstream migration, is dominated by the ratio of the rate of chemokine secretion and advection. Our model also predicts that, because the tensotactic stimulus depends strongly on the cell volume fraction, upstream, tensotaxis-dominated migration occurs only transiently when the cells are initially seeded, and transitions to downstream, chemotaxis-dominated migration occur at later times due to the dispersive effect of cell diffusion., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

A spiral wavefront (WF), generated by a cardiac rotor that drifts between surface electrodes during atrial fibrillation, exhibits frequency changes inconsistent with classical Doppler effect (CDE) phenomena. Recent clinical studies reveal three repeatedly observed events--1) side-dependent frequency changes across the path of the rotor, 2) one additional WF strike on the higher frequency side, and 3) a reversal of WF strike sequence--which constitute a diametrical property of spinning WF sources. A linear ray model is first used to reveal and develop the diametrical phenomena. Mathematical models of an Archimedean spiral and a spiral generated by the diffusion equation are developed and compared. Each formulation predicts the diametrical property that CDE does not capture and illuminates the occurrence of a strong side and weak side with respect to the rotor path. Whereas CDE exhibits higher and lower frequencies from approaching and receding sources of WFs, respectively, spiral rotors generate higher and lower frequencies on opposite sides of the migration path. This motivates the reconsideration of mapping and ablation strategies that have traditionally been based on identifying sites of the dominant frequency. While this research aims to characterize the path of a spiral rotor during atrial fibrillation accurately, the results are applicable in other fields of science and engineering in which rotating spiral waves occur., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We present a quantitative fluctuation-based assay to measure the degree of local chromatin compaction and investigate how chromatin density regulates the diffusive path adopted by an inert protein in dividing cells. The assay uses CHO-K1 cells coexpressing untagged enhanced green fluorescent protein (EGFP) and histone H2B tagged mCherry. We measure at the single-cell level the EGFP localization and molecular flow patterns characteristic of each stage of chromatin compaction from mitosis through interphase by means of pair-correlation analysis. We find that the naturally occurring changes in chromatin organization impart a regulation on the spatial distribution and temporal dynamics of EGFP within the nucleus. Combined with the analysis of Ca(2+) intracellular homeostasis during cell division, EGFP flow regulation can be interpreted as the result of controlled changes in chromatin compaction. For the first time, to our knowledge, we were able to probe chromatin compaction on the micrometer scale, where the regulation of molecular diffusion may become relevant for many cellular processes.

Here we address the impact nuclear architecture has on molecular flow within the mitotic nucleus of live cells as compared to interphase by the pair correlation function method. The mitotic chromatin is found to allow delayed but continuous molecular flow of EGFP in and out of a high chromatin density region, which, by pair correlation function analysis, is shown as a characteristic arc shape that appears upon entry and exit. This is in contrast to interphase chromatin, which regulates flow between different density chromatin regions by means of a mechanism which turns on and off intermittently, generating discrete bursts of EGFP. We show that the interphase bursts are maintained by metabolic energy, whereas the mitotic mechanism of regulation responsible for the arc is not sensitive to ATP depletion. These two distinct routes of molecular flow were concomitantly measured in the Caenorhabditis elegans germ line, which indicates a conservation of mechanism on a scale more widespread than cell type or organism.

Prefibrillar oligomers of proteins are suspected to be the primary pathogenic agents in several neurodegenerative diseases. A key approach for elucidating the pathogenic mechanisms is to probe the existence of oligomers directly in living cells. In this work, we were able to monitor the process of aggregation of Concanavalin A in live cells. We used number and brightness analysis, two-color cross number and brightness analysis, and Raster image correlation spectroscopy to obtain the number of molecules, aggregation state, and diffusion coefficient as a function of time and cell location. We observed that binding of Concanavalin A to the membrane and the formation of small aggregates paralleled cell morphology changes, indicating progressive cell compaction and death. Upon protein aggregation, we observed increased membrane water penetration as reported by Laurdan generalized polarization imaging.

In developing and self-renewing tissues, terminally differentiated (TD) cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit-amplifying) cell stages, which ultimately give rise to TD cells. As the tissue reaches a tightly controlled steady-state size, cells at different lineage stages assume distinct spatial locations within the tissue. Although tissue stratification appears to be genetically specified, the underlying mechanisms that direct tissue lamination are not yet completely understood. Herein, we use modeling and simulations to explore several potential mechanisms that can be utilized to create stratification during developmental or regenerative growth in general systems and in the model system, the olfactory epithelium of mouse. Our results show that tissue stratification can be generated and maintained through controlling spatial distribution of diffusive signaling molecules that regulate the proliferation of each cell type within the lineage. The ability of feedback molecules to stratify a tissue is dependent on a low TD death rate: high death rates decrease tissue lamination. Regulation of the cell cycle lengths of stem cells by feedback signals can lead to transient accumulation of stem cells near the base and apex of tissue.

Molecular diffusion and transport are fundamental processes in physical, chemical, biochemical, and biological systems. However, current approaches to measure molecular transport in cells and tissues based on perturbation methods such as fluorescence recovery after photobleaching are invasive, fluctuation correlation methods are local, and single-particle tracking requires the observation of isolated particles for relatively long periods of time. We propose to detect molecular transport by measuring the time cross-correlation of fluctuations at a pair of locations in the sample. When the points are farther apart than two times the size of the point spread function, the maximum of the correlation is proportional to the average time a molecule takes to move from a specific location to another. We demonstrate the method by simulations, using beads in solution, and by measuring the diffusion of molecules in cellular membranes. The spatial pair cross-correlation method detects barriers to diffusion and heterogeneity of diffusion because the time of the correlation maximum is delayed in the presence of diffusion barriers. This noninvasive, sensitive technique follows the same molecule over a large area, thereby producing a map of molecular flow. It does not require isolated molecules, and thus many molecules can be labeled at the same time and within the point spread function.

Calmodulin (CaM) is the major pathway that transduces intracellular Ca2+ increases to the activation of a wide variety of downstream signaling enzymes. CaM and its target proteins form an integrated signaling network believed to be tuned spatially and temporally to control CaM's ability to appropriately pass signaling events downstream. Here, we report the spatial diffusivity and availability of CaM labeled with enhanced green fluorescent protein (eGFP)-CaM, at basal and elevated Ca2+,quantified by the novel fluorescent techniques of raster image scanning spectroscopy and number and brightness analysis. Our results show that in basal Ca2+ conditions cytoplasmic eGFP-CaM diffuses at a rate of 10 microm(2)/s, twofold slower than the noninteracting tracer, eGFP, indicating that a significant fraction of CaM is diffusing bound to other partners. The diffusion rate of eGFP-CaM is reduced to 7 microm(2)/s when a large (646 kDa) target protein Ca2+/CaM-dependent protein kinase II is coexpressed in the cells. In addition, the presence of Ca2+/calmodulin-dependent protein kinase II, which can bind up to 12 CaM molecules per holoenzyme, increases the stoichiometry of binding to an average of 3 CaMs per diffusive molecule. Elevating intracellular Ca2+ did not have a major impact on the diffusion of CaM complexes. These results present us with a model whereby CaM is spatially modulated by target proteins and support the hypothesis that CaM availability is a limiting factor in the network of CaM-signaling enzymes.

Increasing evidence points to a dynamical compartmentalization of the cell nucleus, yet the mechanisms by which interphase chromatin moves and is positioned within nuclei remain unclear. Here, we study the dynamics of chromatin in vivo applying a novel particle-tracking method in a two-photon microscope that provides approximately 10-fold higher spatial and temporal resolutions than previous measurements. We followed the motion of a chromatin sequence containing a lac-operator repeat in cells stably expressing lac repressor fused with enhanced green fluorescent protein, observing long periods of apparent constrained diffusion interrupted by relatively abrupt jumps of approximately 150 nm lasting 0.3-2 s. During these jumps, the particle moved an average of four times faster than in the periods between jumps and in paths more rectilinear than predicted for random diffusion motion. Additionally, the jumps were sensitive to the temperature and absent after ATP depletion. These experimental results point to an energy-dependent mechanism driving fast motion of chromatin in interphase cells.

Single-point fluorescence correlation spectroscopy (FCS) allows measurements of fast diffusion and dynamic processes in the microsecond-to-millisecond time range. For measurements on living cells, image correlation spectroscopy (ICS) and temporal ICS extend the FCS approach to diffusion times as long as seconds to minutes and simultaneously provide spatially resolved dynamic information. However, ICS is limited to very slow dynamics due to the frame acquisition rate. Here we develop novel extensions to ICS that probe spatial correlations in previously inaccessible temporal windows. We show that using standard laser confocal imaging techniques (raster-scan mode) not only can we reach the temporal scales of single-point FCS, but also have the advantages of ICS in providing spatial information. This novel method, called raster image correlation spectroscopy (RICS), rapidly measures during the scan many focal points within the cell providing the same concentration and dynamic information of FCS as well as information on the spatial correlation between points along the scanning path. Longer time dynamics are recovered from the information in successive lines and frames. We exploit the hidden time structure of the scan method in which adjacent pixels are a few microseconds apart thereby accurately measuring dynamic processes such as molecular diffusion in the microseconds-to-seconds timescale. In conjunction with simulated data, we show that a wide range of diffusion coefficients and concentrations can be measured by RICS. We used RICS to determine for the first time spatially resolved diffusions of paxillin-EGFP stably expressed in CHOK1 cells. This new type of data analysis has a broad application in biology and it provides a powerful tool for measuring fast as well as slower dynamic processes in cellular systems using any standard laser confocal microscope.

Images obtained with a laser-scanning microscope contain a time structure that can be exploited to measure fast dynamics of molecules in solution and in cells. The spatial correlation approach provides a simple algorithm to extract this information. We describe the analysis used to process laser-scanning images of solutions and cells to obtain molecular diffusion constant in the microsecond to second timescale.