Effect of loops on the mean-square displacement of Rouse-model chromatin.

Chromatin polymer dynamics are commonly described using the classical Rouse model. The subsequent discovery, however, of intermediate-scale chromatin organization known as topologically associating domains (TADs) in experimental Hi-C contact maps for chromosomes across the tree of life, together with the success of loop extrusion factor (LEF) model in explaining TAD formation, motivates efforts to understand the effect of loops and loop extrusion on chromatin dynamics. This paper seeks to fulfill this need by combining LEF-model simulations with extended Rouse-model polymer simulations to investigate the dynamics of chromatin with loops and dynamic loop extrusion. We show that loops significantly suppress the averaged mean-square displacement (MSD) of a gene locus, consistent with recent experiments that track fluorescently labeled chromatin loci. We also find that loops reduce the MSD's stretching exponent from the classical Rouse-model value of 1/2 to a loop-density-dependent value in the 0.45-0.40 range. Remarkably, stretching exponent values in this range have also been observed in recent experiments [Weber et al., Phys. Rev. Lett. 104, 238102 (2010)0031-900710.1103/PhysRevLett.104.238102; Bailey et al., Mol. Biol. Cell 34, ar78 (2023)1059-152410.1091/mbc.E23-04-0119]. We also show that the dynamics of loop extrusion itself negligibly affects chromatin mobility. By studying static "rosette" loop configurations, we also demonstrate that chromatin MSDs and stretching exponents depend on the location of the locus in question relative to the position of the loops and on the local friction environment.

Imaging Proteins Sensitive to Direct Fusions Using Transient Peptide-Peptide Interactions.

Fluorescence microscopy enables specific visualization of proteins in living cells and has played an important role in our understanding of the protein subcellular location and function. Some proteins, however, show altered localization or function when labeled using direct fusions to fluorescent proteins, making them difficult to study in live cells. Additionally, the resolution of fluorescence microscopy is limited to ∼200 nm, which is 2 orders of magnitude larger than the size of most proteins. To circumvent these challenges, we previously developed LIVE-PAINT, a live-cell super-resolution approach that takes advantage of short interacting peptides to transiently bind a fluorescent protein to the protein-of-interest. Here, we successfully use LIVE-PAINT to image yeast membrane proteins that do not tolerate the direct fusion of a fluorescent protein by using peptide tags as short as 5-residues. We also demonstrate that it is possible to resolve multiple proteins at the nanoscale concurrently using orthogonal peptide interaction pairs.

Uncovering diffusive states of the yeast membrane protein, Pma1, and how labeling method can change diffusive behavior.

We present and analyze video-microscopy-based single-particle-tracking measurements of the budding yeast (Saccharomyces cerevisiae) membrane protein, Pma1, fluorescently labeled either by direct fusion to the switchable fluorescent protein, mEos3.2, or by a novel, light-touch, labeling scheme, in which a 5 amino acid tag is directly fused to the C-terminus of Pma1, which then binds mEos3.2. The track diffusivity distributions of these two populations of single-particle tracks differ significantly, demonstrating that labeling method can be an important determinant of diffusive behavior. We also applied perturbation expectation maximization (pEMv2) (Koo and Mochrie in Phys Rev E 94(5):052412, 2016), which sorts trajectories into the statistically optimum number of diffusive states. For both TRAP-labeled Pma1 and Pma1-mEos3.2, pEMv2 sorts the tracks into two diffusive states: an essentially immobile state and a more mobile state. However, the mobile fraction of Pma1-mEos3.2 tracks is much smaller ([Formula: see text]) than the mobile fraction of TRAP-labeled Pma1 tracks ([Formula: see text]). In addition, the diffusivity of Pma1-mEos3.2's mobile state is several times smaller than the diffusivity of TRAP-labeled Pma1's mobile state. Thus, the two different labeling methods give rise to very different overall diffusive behaviors. To critically assess pEMv2's performance, we compare the diffusivity and covariance distributions of the experimental pEMv2-sorted populations to corresponding theoretical distributions, assuming that Pma1 displacements realize a Gaussian random process. The experiment-theory comparisons for both the TRAP-labeled Pma1 and Pma1-mEos3.2 reveal good agreement, bolstering the pEMv2 approach.

Loops and the activity of loop extrusion factors constrain chromatin dynamics.

The chromosomes-DNA polymers and their binding proteins-are compacted into a spatially organized, yet dynamic, three-dimensional structure. Recent genome-wide chromatin conformation capture experiments reveal a hierarchical organization of the DNA structure that is imposed, at least in part, by looping interactions arising from the activity of loop extrusion factors. The dynamics of chromatin reflects the response of the polymer to a combination of thermal fluctuations and active processes. However, how chromosome structure and enzymes acting on chromatin together define its dynamics remains poorly understood. To gain insight into the structure-dynamics relationship of chromatin, we combine high-precision microscopy in living Schizosaccharomyces pombe cells with systematic genetic perturbations and Rouse model polymer simulations. We first investigated how the activity of two loop extrusion factors, the cohesin and condensin complexes, influences chromatin dynamics. We observed that deactivating cohesin, or to a lesser extent condensin, increased chromatin mobility, suggesting that loop extrusion constrains rather than agitates chromatin motion. Our corresponding simulations reveal that the introduction of loops is sufficient to explain the constraining activity of loop extrusion factors, highlighting that the conformation adopted by the polymer plays a key role in defining its dynamics. Moreover, we find that the number of loops or residence times of loop extrusion factors influence the dynamic behavior of the chromatin polymer. Last, we observe that the activity of the INO80 chromatin remodeler, but not the SWI/SNF or RSC complexes, is critical for ATP-dependent chromatin mobility in fission yeast. Taking the data together, we suggest that thermal and INO80-dependent activities exert forces that drive chromatin fluctuations, which are constrained by the organization of the chromosome into loops.

Extrusion of chromatin loops by a composite loop extrusion factor.

Chromatin loop extrusion by structural maintenance of chromosome (SMC) complexes is thought to underlie intermediate-scale chromatin organization inside cells. Motivated by a number of experiments suggesting that nucleosomes may block loop extrusion by SMCs, such as cohesin and condensin complexes, we introduce and characterize theoretically a composite loop extrusion factor (composite LEF) model. In addition to an SMC complex that creates a chromatin loop by encircling two threads of DNA, this model includes a remodeling complex that relocates or removes nucleosomes as it progresses along the chromatin, and nucleosomes that block SMC translocation along the DNA. Loop extrusion is enabled by SMC motion along nucleosome-free DNA, created in the wake of the remodeling complex, while nucleosome rebinding behind the SMC acts as a ratchet, holding the SMC close to the remodeling complex. We show that, for a wide range of parameter values, this collection of factors constitutes a composite LEF that extrudes loops with a velocity, comparable to the velocity of remodeling complex translocation on chromatin in the absence of SMC, and much faster than loop extrusion by an isolated SMC that is blocked by nucleosomes.

Covariance distributions in single particle tracking.

Several recent experiments, including our own experiments in the fission yeast, Schizosaccharomyces pombe, have characterized the motions of gene loci within living nuclei by measuring the locus position over time, then proceeding to obtain the statistical properties of this motion. To address the question of whether a population of such single-particle tracks, obtained from many different cells, corresponds to a single mode of diffusion, we derive theoretical equations describing the probability distribution of the displacement covariance, assuming the displacement itself is a zero-mean multivariate Gaussian random variable. We also determine the corresponding theoretical means, variances, and third central moments. Bolstering the theory is good agreement between its predictions and the results obtained for various simulated and measured data sets, including simulated particle trajectories undergoing simple and anomalous diffusion, and the measured trajectories of an optically trapped bead in water, and in a viscoelastic polymer solution. We also show that, for sufficiently long tracks, each covariance distribution in all of these examples is well-described by a skew-normal distribution with mean, variance, and skewness given by the theory. However, for the experimentally measured motion of a gene locus in S. pombe, we find that the first two covariance distributions are wider than predicted, although the third and subsequent covariance distributions are well-described by theory. This observation suggests that the origin of the theory-experiment discrepancy in this case is associated with localization noise, which influences only the first two covariances. Thus, we hypothesized that the discrepancy is caused by locus-to-locus heterogeneity in the localization noise, of independent measurements of the same tagged site. Indeed, simulations implementing heterogeneous localization noise revealed that the excess covariance widths can be largely recreated on the basis of heterogeneous noise. Thus, we conclude that the motion of gene loci in fission yeast is consistent with a single mode of diffusion.

PAINT using proteins: A new brush for super-resolution artists.

PAINT (points accumulation for imaging in nanoscale topography) refers to methods that achieve the sparse temporal labeling required for super-resolution imaging by using transient interactions between a biomolecule of interest and a fluorophore. There have been a variety of different implementations of this method since it was first described in 2006. Recent papers illustrate how transient peptide-protein interactions, rather than small molecule binding or DNA oligonucleotide duplex formation, can be employed to perform PAINT-based single molecule localization microscopy (SMLM). We discuss the different approaches to PAINT using peptide and protein interactions, and their applications in vitro and in vivo. We highlight the important parameters to consider when selecting suitable peptide-protein interaction pairs for such studies. We also note the opportunities for protein scientists to apply their expertise in guiding the choice of peptide and protein pairs that are used. Finally, we discuss the potential for expanding super-resolution imaging methods based on transient peptide-protein interactions, including the development of simultaneous multicolor imaging of multiple proteins and the study of very high and very low abundance proteins in live cells.

A versatile image analysis platform for three-dimensional nuclear reconstruction.

Nuclear morphology is indicative of cellular health in many contexts. In order to robustly and quantitatively measure nuclear size and shape, numerous experimental methods leveraging fluorescence microscopy have been developed. While these methods are useful for quantifying two-dimensional morphology, they often fail to accurately represent the three-dimensional structure of the nucleus, thus omitting important spatial and volumetric information. To address the need for a more accurate image analysis modality, we have developed a software platform that faithfully reconstructs membrane surfaces in three dimensions with sub-pixel resolution. Here, we showcase its broad applicability across species and nuclear scale, as well as provide information on how to employ this platform for diverse experimental systems.

Applying Perturbation Expectation-Maximization to Protein Trajectories of Rho GTPases.

Single-particle tracking (SPT) enables the ability to noninvasively probe the diffusive motions of individual proteins inside living cells at sub-diffraction-limit resolution. The stochastic motions of diffusing Rho GTPases encode information concerning its interactions with binding partners and with its local environment. By identifying Rho GTPases' diffusive states, insight can thus be gained into the spatiotemporal in vivo biochemistry inside live cells at a single-molecule resolution. Here we present perturbation expectation-maximization (pEM), a computational method which simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors: (1) the number of diffusive states, (2) the properties of each such diffusive state, and (3) the probabilities of each trajectory to a respective diffusive state. We provide a step-by-step guide to pEM and discuss considerations for its practical applications, including pEM's capabilities and limitations.

Multiplexed fluctuation-dissipation-theorem calibration of optical tweezers inside living cells.

In order to apply optical tweezers-based force measurements within an uncharacterized viscoelastic medium such as the cytoplasm of a living cell, a quantitative calibration method that may be applied in this complex environment is needed. We describe an improved version of the fluctuation-dissipation-theorem calibration method, which has been developed to perform in situ calibration in viscoelastic media without prior knowledge of the trapped object. Using this calibration procedure, it is possible to extract values of the medium's viscoelastic moduli as well as the force constant describing the optical trap. To demonstrate our method, we calibrate an optical trap in water, in polyethylene oxide solutions of different concentrations, and inside living fission yeast (S. pombe).

Systems-level approach to uncovering diffusive states and their transitions from single-particle trajectories.

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, an accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum-likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean-square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions that give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.

Improved Determination of Subnuclear Position Enabled by Three-Dimensional Membrane Reconstruction.

Many aspects of chromatin biology are influenced by the nuclear compartment in which a locus resides, from transcriptional regulation to DNA repair. Further, the dynamic and variable localization of a particular locus across cell populations and over time makes analysis of a large number of cells critical. As a consequence, robust and automatable methods to measure the position of individual loci within the nuclear volume in populations of cells are necessary to support quantitative analysis of nuclear position. Here, we describe a three-dimensional membrane reconstruction approach that uses fluorescently tagged nuclear envelope or endoplasmic reticulum membrane marker proteins to precisely map the nuclear volume. This approach is robust to a variety of nuclear shapes, providing greater biological accuracy than alternative methods that enforce nuclear circularity, while also describing nuclear position in all three dimensions. By combining this method with established approaches to reconstruct the position of diffraction-limited chromatin markers-in this case, lac Operator arrays bound by lacI-GFP-the distribution of loci positions within the nuclear volume with respect to the nuclear periphery can be quantitatively obtained. This stand-alone image analysis pipeline should be of broad practical utility for individuals interested in various aspects of chromatin biology, while also providing, to our knowledge, a new conceptual framework for investigators who study organelle shape.

Domain morphology, boundaries, and topological defects in biophotonic gyroid nanostructures of butterfly wing scales.

Many organisms in nature have evolved sophisticated cellular mechanisms to produce photonic nanostructures and, in recent years, diverse crystalline symmetries have been identified and related to macroscopic optical properties. However, because we know little about the distributions of domain sizes, the orientations of photonic crystals, and the nature of defects in these structures, we are unable to make the connection between the nanostructure and its development and functionality. We report on nondestructive studies of the morphology of chitinous photonic crystals in butterfly wing scales. Using spatially and angularly resolved x-ray diffraction, we find that the domains are highly oriented with respect to the whole scale, indicating growth from scale boundaries. X-ray coherent diffractive imaging reveals two types of crystalline domain interfaces: abrupt changes between domains emerging from distinct nucleation sites and smooth transitions with edge dislocations presumably resulting from internal stresses during nanostructure development. Our study of the scale structure reveals new aspects of photonic crystal growth in butterfly wings and shows their similarity to block copolymer materials. It opens new avenues to exploration of fundamental processes underlying the growth of biological photonic nanostructures in a variety of species.

Designed Proteins as Novel Imaging Reagents in Living Escherichia coli.

Fluorescence imaging is a powerful tool to study protein function in living cells. Here, we introduce a novel imaging strategy that is fully genetically encodable, does not require the use of exogenous substrates, and adds a minimally disruptive tag to the protein of interest (POI). Our method was based on a set of designed tetratricopeptide repeat affinity proteins (TRAPs) that specifically and reversibly interact with a short, extended peptide tag. We co-expressed the TRAPs fused to fluorescent proteins (FPs) and the peptide tags fused to the POIs. We illustrated the method using the Escherichia coli protein FtsZ and showed that our system could track distinct FtsZ structures under both low and high expression conditions in live cells. We anticipate that our imaging strategy will be a useful tool for imaging the subcellular localization of many proteins, especially those recalcitrant to imaging by direct tagging with FPs.

Promoting convergence: The integrated graduate program in physical and engineering biology at Yale University, a new model for graduate education.

In 2008, we established the Integrated Graduate Program in Physical and Engineering Biology (IGPPEB) at Yale University. Our goal was to create a comprehensive graduate program to train a new generation of scientists who possess a sophisticated understanding of biology and who are capable of applying physical and quantitative methodologies to solve biological problems. Here we describe the framework of the training program, report on its effectiveness, and also share the insights we gained during its development and implementation. The program features co-teaching by faculty with complementary specializations, student peer learning, and novel hands-on courses that facilitate the seamless blending of interdisciplinary research and teaching. It also incorporates enrichment activities to improve communication skills, engage students in science outreach, and foster a cohesive program cohort, all of which promote the development of transferable skills applicable in a variety of careers. The curriculum of the graduate program is integrated with the curricular requirements of several Ph.D.-granting home programs in the physical, engineering, and biological sciences. Moreover, the wide-ranging recruiting activities of the IGPPEB serve to enhance the quality and diversity of students entering graduate school at Yale. We also discuss some of the challenges we encountered in establishing and optimizing the program, and describe the institution-level changes that were catalyzed by the introduction of the new graduate program. The goal of this article is to serve as both an inspiration and as a practical "how to" manual for those who seek to establish similar programs at their own institutions. © 2016 by The International Union of Biochemistry and Molecular Biology, 44(6):537-549, 2016.

Extracting Diffusive States of Rho GTPase in Live Cells: Towards In Vivo Biochemistry.

Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and demonstrate that pEM is capable of uncovering the proper number of underlying diffusive states with an accurate characterization of their diffusion properties. We then apply pEM to experimental protein trajectories of Rho GTPases, an integral regulator of cytoskeletal dynamics and cellular homeostasis, in vivo via single particle tracking photo-activated localization microscopy. Remarkably, pEM uncovers 6 distinct diffusive states conserved across various Rho GTPase family members. The variability across family members in the propensities for each diffusive state reveals non-redundant roles in the activation states of RhoA and RhoC. In a resting cell, our results support a model where RhoA is constantly cycling between activation states, with an imbalance of rates favoring an inactive state. RhoC, on the other hand, remains predominantly inactive.

Cross-Scale Integrin Regulation Organizes ECM and Tissue Topology.

The diverse morphologies of animal tissues are underlain by different configurations of adherent cells and extracellular matrix (ECM). Here, we elucidate a cross-scale mechanism for tissue assembly and ECM remodeling involving Cadherin 2, the ECM protein Fibronectin, and its receptor Integrin α5. Fluorescence cross-correlation spectroscopy within the zebrafish paraxial mesoderm mesenchyme reveals a physical association between Integrin α5 on adjacent cell membranes. This Integrin-Integrin complex correlates with conformationally inactive Integrin. Cadherin 2 stabilizes both the Integrin association and inactive Integrin conformation. Thus, Integrin repression within the adherent mesenchymal interior of the tissue biases Fibronectin fibrillogenesis to the tissue surface lacking cell-cell adhesions. Along nascent somite boundaries, Cadherin 2 levels decrease, becoming anti-correlated with levels of Integrin α5. Simultaneously, Integrin α5 clusters and adopts the active conformation and then commences ECM assembly. This cross-scale regulation of Integrin activation organizes a stereotypic pattern of ECM necessary for vertebrate body elongation and segmentation.

The tethering of chromatin to the nuclear envelope supports nuclear mechanics.

The nuclear lamina is thought to be the primary mechanical defence of the nucleus. However, the lamina is integrated within a network of lipids, proteins and chromatin; the interdependence of this network poses a challenge to defining the individual mechanical contributions of these components. Here, we isolate the role of chromatin in nuclear mechanics by using a system lacking lamins. Using novel imaging analyses, we observe that untethering chromatin from the inner nuclear membrane results in highly deformable nuclei in vivo, particularly in response to cytoskeletal forces. Using optical tweezers, we find that isolated nuclei lacking inner nuclear membrane tethers are less stiff than wild-type nuclei and exhibit increased chromatin flow, particularly in frequency ranges that recapitulate the kinetics of cytoskeletal dynamics. We suggest that modulating chromatin flow can define both transient and long-lived changes in nuclear shape that are biologically important and may be altered in disease.

Structural Diversity of Arthropod Biophotonic Nanostructures Spans Amphiphilic Phase-Space.

Many organisms, especially arthropods, produce vivid interference colors using diverse mesoscopic (100-350 nm) integumentary biophotonic nanostructures that are increasingly being investigated for technological applications. Despite a century of interest, precise structural knowledge of many biophotonic nanostructures and the mechanisms controlling their development remain tentative, when such knowledge can open novel biomimetic routes to facilely self-assemble tunable, multifunctional materials. Here, we use synchrotron small-angle X-ray scattering and electron microscopy to characterize the photonic nanostructure of 140 integumentary scales and setae from ∼127 species of terrestrial arthropods in 85 genera from 5 orders. We report a rich nanostructural diversity, including triply periodic bicontinuous networks, close-packed spheres, inverse columnar, perforated lamellar, and disordered spongelike morphologies, commonly observed as stable phases of amphiphilic surfactants, block copolymer, and lyotropic lipid-water systems. Diverse arthropod lineages appear to have independently evolved to utilize the self-assembly of infolding lipid-bilayer membranes to develop biophotonic nanostructures that span the phase-space of amphiphilic morphologies, but at optical length scales.

Routes to DNA accessibility: alternative pathways for nucleosome unwinding.

The dynamic packaging of DNA into chromatin is a key determinant of eukaryotic gene regulation and epigenetic inheritance. Nucleosomes are the basic unit of chromatin, and therefore the accessible states of the nucleosome must be the starting point for mechanistic models regarding these essential processes. Although the existence of different unwound nucleosome states has been hypothesized, there have been few studies of these states. The consequences of multiple states are far reaching. These states will behave differently in all aspects, including their interactions with chromatin remodelers, histone variant exchange, and kinetic properties. Here, we demonstrate the existence of two distinct states of the unwound nucleosome, which are accessible at physiological forces and ionic strengths. Using optical tweezers, we measure the rates of unwinding and rewinding for these two states and show that the rewinding rates from each state are different. In addition, we show that the probability of unwinding into each state is dependent on the applied force and ionic strength. Our results demonstrate not only that multiple unwound states exist but that their accessibility can be differentially perturbed, suggesting possible roles for these states in gene regulation. For example, different histone variants or modifications may facilitate or suppress access to DNA by promoting unwinding into one state or the other. We anticipate that the two unwound states reported here will be the basis for future models of eukaryotic transcriptional control.