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An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome. [ABSTRACT FROM AUTHOR]

Euchromatin is an accessible phase of genetic material containing genes that encode proteins with increased expression levels. The structure of euchromatin in vitro has been described as a 30-nm fiber formed from ordered nucleosome arrays. However, recent advances in microscopy have revealed an in vivo euchromatin architecture that is much more disordered, characterized by variable-length linker DNA and sporadic nucleosome clusters. In this work, we develop a theoretical model to elucidate factors contributing to the disordered in vivo architecture of euchromatin. We begin by developing a 1D model of nucleosome positioning that captures the interactions between bound epigenetic reader proteins to predict the distribution of DNA linker lengths between adjacent nucleosomes. We then use the predicted linker lengths to construct 3D chromatin configurations consistent with the physical properties of DNA within the nucleosome array, and we evaluate the distribution of nucleosome cluster sizes in those configurations. Our model reproduces experimental cluster-size distributions, which are dramatically influenced by the local pattern of epigenetic marks and the concentration of reader proteins. Based on our model, we attribute the disordered arrangement of euchromatin to the heterogeneous binding of reader proteins and subsequent short-range interactions between bound reader proteins on adjacent nucleosomes. By replicating experimental results with our physics-based model, we propose a mechanism for euchromatin organization in the nucleus that impacts gene regulation and the maintenance of epigenetic marks. [ABSTRACT FROM AUTHOR]

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross-over between two and four at contour lengths on the order of 30 kilo-base pairs. The anomalously high fractal dimension D = 4 is due to the inability of extruded loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times (Δ t) longer than tens of minutes to be proportional to Δ t 1/3. We validate our results with hybrid molecular dynamics--Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin, explaining the physical reason for TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation. [ABSTRACT FROM AUTHOR]

SignificanceEssential for sexual reproduction, meiosis is a specialized cell division required for the production of haploid gametes. Critical to this process are the pairing, recombination, and segregation of homologous chromosomes (homologs). While pairing and recombination are linked, it is not known how many linkages are sufficient to hold homologs in proximity. Here, we reveal that random diffusion and the placement of a small number of linkages are sufficient to establish the apparent "pairing" of homologs. We also show that colocalization between any two loci is more dynamic than anticipated. Our study provides observations of live interchromosomal dynamics during meiosis and illustrates the power of combining single-cell measurements with theoretical polymer modeling.

Short-range interactions and long-range contacts drive the 3D folding of structured proteins. The proteins’ structure has a direct impact on their biological function. However, nearly 40% of the eukaryotes proteome is composed of intrinsically disordered proteins (IDPs) and protein regions that fluctuate between ensembles of numerous conformations. Therefore, to understand their biological function, it is critical to depict how the structural ensemble statistics correlate to the IDPs’ amino acid sequence. Here, using small-angle X-ray scattering and time-resolved Förster resonance energy transfer (trFRET), we study the intramolecular structural heterogeneity of the neurofilament low intrinsically disordered tail domain (NFLt). Using theoretical results of polymer physics, we find that the Flory scaling exponent of NFLt subsegments correlates linearly with their net charge, ranging from statistics of ideal to self-avoiding chains. Surprisingly, measuring the same segments in the context of the whole NFLt protein, we find that regardless of the peptide sequence, the segments’ structural statistics are more expanded than when measured independently. Our findings show that while polymer physics can, to some level, relate the IDP’s sequence to its ensemble conformations, long-range contacts between distant amino acids play a crucial role in determining intramolecular structures. This emphasizes the necessity of advanced polymer theories to fully describe IDPs ensembles with the hope that it will allow us to model their biological function. [ABSTRACT FROM AUTHOR]

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities. [ABSTRACT FROM AUTHOR]

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases--a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase--that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions. [ABSTRACT FROM AUTHOR]

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome., Competing Interests: Competing interests statement:The authors declare no competing interest.

Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety. [ABSTRACT FROM AUTHOR]

Many multidomain proteins contain disordered linkers that regulate interdomain contacts, and thus the effective concentrations that govern intramolecular reactions. Effective concentrations are rarely measured experimentally, and therefore little is known about how they relate to linker architecture. We have directly measured the effective concentrations enforced by disordered protein linkers using a fluorescent biosensor. We show that effective concentrations follow simple geometric models based on polymer physics, offering an indirect method to probe the structural properties of the linker. The compaction of the disordered linker depends not only on net charge, but also on the type of charged residues. In contrast to theoretical predictions, we found that polyampholyte linkers can contract to similar dimensions as globular proteins. Hydrophobicity has little effect in itself, but aromatic residues lead to strong compaction, likely through π-interactions. Finally, we find that the individual contributors to chain compaction are not additive. We thus demonstrate that direct measurement of effective concentrations can be used in systematic studies of the relationship between sequence and structure of intrinsically disordered proteins. A quantitative understanding of the relationship between effective concentration and linker sequence will be crucial for understanding disorder-based allosteric regulation in multidomain proteins. [ABSTRACT FROM AUTHOR]

Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC-EC and EC-TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC-TVEC transition) emulate the functional form of the birefringence-macromolecular strain relationship based on Peterlin's theory. We quantify the duration and strain between the IC/VC-EC and the EC-TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time. [ABSTRACT FROM AUTHOR]

Mammalian chromatin is spatially organized at many scales showing two prominent features in interphase: (i) alternating regions (1-10 Mb) of active and inactive chromatin that spatially segregate into different compartments, and (ii) domains (<1 Mb), that is, regions that preferentially interact internally [topologically associating domains (TADs)] and are central to gene regulation. There is growing evidence that TADs are formed by active extrusion of chromatin loops by cohesin, whereas compartmentalization is established according to local chromatin states. Here, we use polymer simulations to examine how loop extrusion and compartmental segregation work collectively and potentially interfere in shaping global chromosome organization. A model with differential attraction between euchromatin and heterochromatin leads to phase separation and reproduces compartmentalization as observed in Hi-C. Loop extrusion, essential for TAD formation, in turn, interferes with compartmentalization. Our integrated model faithfully reproduces Hi-C data from puzzling experimental observations where altering loop extrusion also led to changes in compartmentalization. Specifically, depletion of chromatin-associated cohesin reduced TADs and revealed finer compartments, while increased processivity of cohesin strengthened large TADs and reduced compartmentalization; and depletion of the TAD boundary protein CTCF weakened TADs while leaving compartments unaffected. We reveal that these experimental perturbations are special cases of a general polymer phenomenon of active mixing by loop extrusion. Our results suggest that chromatin organization on the megabase scale emerges from competition of nonequilibrium active loop extrusion and epigenetically defined compartment structure. [ABSTRACT FROM AUTHOR]

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

We analyze the response of a single nucleosome to tension, which serves as a prototypical biophysical measurement where tension-dependent deformation alters transition kinetics. We develop a statistical-mechanics model of a nucleosome as a wormlike chain bound to a spool, incorporating fluctuations in the number of bases bound, the spool orientation, and the conformations of the unbound polymer segments. With the resulting free-energy surface, we perform dynamic simulations that permit a direct comparison with experiments. This simple approach demonstrates that the experimentally observed structural states at nonzero tension are a consequence of the tension and that these tension-induced states cease to exist at zero tension. The transitions between states exhibit substantial deformation of the unbound polymer segments. The associated deformation energy increases with tension; thus, the application of tension alters the kinetics due to tension-induced deformation of the transition states. This mechanism would arise in any system where the tether molecule is deformed in the transition state under the influence of tension. [ABSTRACT FROM AUTHOR]

The stochasticity of chromosome organization was investigated by fluorescently labeling genetic loci in live Escherichia coil cells. In spite of the common assumption that the chromosome is well modeled by an unstructured polymer, measurements of the locus distributions reveal that the E. coli chromosome is precisely organized into a nucleoid filament with a linear order. Loci in the body of the nucleoid show a precision of positioning within the cell of better than 10% of the cell length. The precision of interlocus distance genomically-proximate loci was better than 4% of the cell length. The measured dependence of the precision of interlocus distance on genomic distance singles out intranucleoid interactions as the mechanism responsible for chromosome organization. From the magnitude of the variance, we infer the existence of an as-yet- uncharacterized higher-order DNA organization in bacteria. We demonstrate that both the stochastic and average structure of the nucleoid is captured by a fluctuating elastic filament model. [ABSTRACT FROM AUTHOR]

Thermal fluctuations agitate molecules in solution over a broad range of times and distances. By passively watching the shape fluctuations of a thermally driven biomolecule, one can infer properties of the underlying interactions that determine the motion. We applied this concept to single molecules of fluorescently labeled A-DNA, a key model system for polymer physics. In contrast to most other single-molecule DNA experiments, we examined the unstretched, equilibrium state of DNA by using an anti-Brownian electrokinetic trap to confine the center of mass of the DNA without perturbing its internal dynamics. We analyze the long- wavelength conformational normal modes, calculate their spring constants, and measure linear and nonlinear couplings between modes. The modes show strong signs of nonlinear hydrodynamics. a feature of the underlying equations of polymer dynamics that has not previously been reported and is neglected in the widely used Rouse and Zimm approximations. [ABSTRACT FROM AUTHOR]

yon Willebrand factor (VWF), a protein present in our circulatory system, is necessary to stop bleeding under high shear-stress conditions as found in small blood vessels. The results presented here help unravel how an increase in hydrodynamic shear stress activates VWF's adhesion potential, leading to the counterintuitive phenomena of enhanced adsorption rate under strong shear conditions. Using a microfluidic device, we were able to mimic a wide range of bloodflow conditions and directly visualize the conformational dynamics of this protein under shear flow. In particular, we find that VWF displays a reversible globule-stretch transition at a critical shear rate γ̇crit in the absence of any adsorbing surface. Computer simulations reproduce this sharp transition and identify the large size of VWF's repeating units as one of the keys for this unique hydrodynamic activation. In the presence of an adsorbing collagen substrate, we find a large increase in the protein adsorption at the same critical shear rate, suggesting that the globule unfolding in bulk triggers the surface adsorption in the case of a collagen substrate, which provides a sufficient density of binding sites. Monitoring the adsorption process of multiple VWF fibers, we were able to follow the formation of an immobilized network that constitutes a ‘sticky’ grid necessary for blood platelet adhesion under high shear flow. Because areas of high shear stress coincide with a higher chance for vessel wall damage by mechanical forces, we identified the shear-induced increase in the binding probability of VWF as an effective self-regulating repair mechanism of our microvascular system. [ABSTRACT FROM AUTHOR]

Despite recent progress in visualization experiments, the mechanism underlying chromosome segregation in bacteria still remains elusive. Here we address a basic physical issue associated with bacterial chromosome segregation, namely the spatial organization of highly confined, self-avoiding polymers (of nontrivial topology) in a rod-shaped cell-like geometry. Through computer simulations, we present evidence that, under strong confinement conditions. topologically distinct domains of a polymer complex effectively repel each other to maximize their conformational entropy, suggesting that duplicated circular chromosomes could partition spontaneously. This mechanism not only is able to account for the spatial separation per se but also captures the major features of the spatiotemporal organization of the duplicating chromosomes observed in Escherichia coil and Caulobacter crescentus. [ABSTRACT FROM AUTHOR]

The molecular motor myosin V (MyoV) exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is the hand-over-hand stepping by a swinging lever arm movement toward the plus end of actin filaments. Single-molecule experiments have also shown that the motor "foot stomps," with one hand detaching and rebinding to the same site, and back-steps under sufficient load. The complete taxonomy of MyoV's load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are not understood. Using a polymer model, we develop an analytical theory to describe the minimal physical properties that govern motor dynamics. We solve the first-passage problem of the head reaching the target-binding site, investigating the competing effects of backward load, strain in the leading head biasing the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. We derive a stall force formula, determined by lever arm compliance and chemical cycle rates. By exploring the MyoV design space, we predict that it is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle and changes in the architecture of the lever arm.

Molecular dynamics simulations are used to model proteins that diffuse to DNA, bind, and dissociate; in the absence of any explicit interaction between proteins, or between templates, binding spontaneously induces local DNA compaction and protein aggregation. Small bivalent proteins form into rows [as on binding of the bacterial histone-like nucleoid-structuring protein (H-NS)], large proteins into quasi-spherical aggregates (as on nanoparticle binding), and cylinders with eight binding sites (representing octameric nucleosomal cores) into irregularly folded clusters (like those seen in nucleosomal strings). Binding of RNA polymerase II and a transcription factor (NFκB) to the appropriate sites on four human chromosomes generates protein clusters analogous to transcription factories, multiscale loops, and intrachromosomal contacts that mimic those found in vivo. We suggest that this emergent behavior of clustering is driven by an entropic bridging-induced attraction that minimizes bending and looping penalties in the template.