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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]

Understanding and characterizing semi-crystalline models with crystalline and amorphous segments is crucial for industrial applications. A coarse-grained molecular dynamics (CGMD) simulations study probed the crystal network formation in high-density polyethylene (HDPE) from melt, and shed light on tensile properties for microstructure analysis. Modified Paul–Yoon–Smith (PYS/R) forcefield parameters are used to compute the interatomic forces among the PE chains. The isothermal crystallization at 300 K and 1 atm predicts the multi-nucleus crystal growth; moreover, the lamellar crystal stems and amorphous region are alternatively oriented. A one-dimensional density distribution along the alternative lamellar stems further confirms the ordering of the lamellar-stack orientation. Using this plastic model preparation approach, the semi-crystalline model density ( ρ c r ) of ca. 0.913 g·cm−3 and amorphous model density ( ρ a m ) of ca. 0.856 g·cm−3 are obtained. Furthermore, the ratio of ρ c r / ρ a m ≈ 1.06 is in good agreement with computational (≈1.096) and experimental (≈1.14) data, ensuring the reliability of the simulations. The degree of crystallinity ( χ c ) of the model is ca. 52% at 300 K. Nevertheless, there is a gradual increase in crystallinity over the specified time, indicating the alignment of the lamellar stems during crystallization. The characteristic stress–strain curve mimicking tensile tests along the z-axis orientation exhibits a reversible sharp elastic regime, tensile strength at yield ca. 100 MPa, and a non-reversible tensile strength at break of 350%. The cavitation mechanism embraces the alignment of lamellar stems along the deformation axis. The study highlights an explanatory model of crystal network formation for the PE model using a PYS/R forcefield, and it produces a microstructure with ordered lamellar and amorphous segments with robust mechanical properties, which aids in predicting the microstructure–mechanical property relationships in plastics under applied forces. [ABSTRACT FROM AUTHOR]

Single‐molecule force spectroscopy is a powerful tool for the quantitative investigation of the biophysics, polymer physics and mechanochemistry of individual polymer strands. One limitation of this technique is that the attachment between the tip of the atomic force microscope and the covalent or noncovalent analyte in a given pull is typically not strong enough to sustain the force at which the event of interest occurs, which makes the experiments time‐consuming and inhibits throughput. Here we report a polyelectrolyte handle for single‐molecule force spectroscopy that offers a combination of high (several hundred pN) attachment forces, good (~4%) success in obtaining a high‐force (>200 pN) attachment, a non‐fouling detachment process that allows for repetition, and specific attachment locations along the polymer analyte. [ABSTRACT FROM AUTHOR]

The nuclear pore complex (NPC) is a critical gateway regulating molecular transport between the nucleus and cytoplasm. It allows small molecules to pass freely, while larger molecules require nuclear transport receptors to traverse the barrier. This selective permeability is maintained by phenylalanine-glycine-rich nucleoporins (FG-Nups), intrinsically disordered proteins that fill the NPC’s central channel. The disordered and flexible nature of FG-Nups complicates their spatial characterization with conventional structural biology techniques. To address this challenge, polymer physics offers a valuable framework for describing FG-Nup behavior, reducing their complex structures to a few key parameters. In this review, we explore how polymer physics models FG-Nups using these parameters and discuss experimental efforts to quantify them in various contexts, providing insights into the conformational properties of FG-Nups.

Carbohydrate polymers are promising materials for an eco-friendly future due to their biodegradability and abundance in nature. However, due to their molecular characteristics and hydrophilicity, are often complicated to be investigated via spectroscopic methods. Thermoplastic starch plasticized by glycerol was prepared through melt processing conditions using twin screw extruder. Here we show how the presence of water molecules affects the dielectric response and charge transport dynamics over broad frequency (10−1 to 107 Hz) and temperature (− 140 to 150 oC) ranges. Overall, 7 dielectric processes were observed and differentiation between electronic and ionic conductivities was achieved. Two segmental relaxation processes were observed for each sample, ascribed to the starch-rich and glycerol-rich phases. Although the timescales of the two segmental relaxations were found different, both arise from the same temperature, giving thus an alternative explanation on what is reported in the literature. The origin of the σ-relaxation was attributed to hydrogen ions and was found to be proportional to the ionic conductivity according to the Barton, Nakajima and Namikawa relation. The presence of water molecules was found to enhance the ionic conductivity, indicating that water contributes charge carriers when compared to the dried sample. [ABSTRACT FROM AUTHOR]

Synthetic control over the shape, size, and interactions between nanoscale building blocks remains an open challenge in self‐assembly. Here, we propose to engineer triblock, star‐like polymers to design patterning on nanoparticles. We developed a theory that characterizes the structural organization of grafted polymers as a function of parameters such as grafting density, chain length, block fractions, and core shape/sizes. Stripe‐like patterning and corner/edge patch formation on arbitrarily shaped cores are readily accessible using our framework, all of which can be a priori predicted. Lastly, we employ assembly simulations to show that the resulting particles provide tighter control over structural and orientational orderings during self‐assembly. More importantly, they offer a way to pattern directional interactions that can override face–face alignment tendencies intrinsic to each core geometry. Our theory, therefore, creates a new handle for tuning nanoscale synthesis, enabling designs of complex building blocks that can target novel assemblies for materials fabrication. [ABSTRACT FROM AUTHOR]

Staudinger taught us that macromolecules were made up of covalently bonded monomer repeat units chaining up as polymer chains. This paradigm is not challenged in this paper. The main question raised in polymer physics remains: how do these long chains interact and move as a group when submitted to shear deformation at high temperature when they are viscous liquids? The current consensus is that we need to distinguish two cases: the deformation of "un-entangled chains" for macromolecules with molecular weight, M, smaller than Me, "the entanglement molecular weight", and the deformation of "entangled" chains for M > Me. The current paradigm stipulates that the properties of polymers derive from the statistical characteristics of the macromolecule itself, the designated statistical system that defines the thermodynamic state of the polymer. The current paradigm claims that the viscoelasticity of un-entangled melts is well described by the Rouse model and that the entanglement issues raised when M > Me, are well understood by the reptation model introduced by de Gennes and colleagues. Both models can be classified in the category of "chain dynamics statistics". In this paper, we examine in detail the failures and the current challenges facing the current paradigm of polymer rheology: the Rouse model for un-entangled melts, the reptation model for entangled melts, the time–temperature superposition principle, the strain-induced time dependence of viscosity, shear-refinement and sustained-orientation. The basic failure of the current paradigm and its inherent inability to fully describe the experimental reality is documented in this paper. In the discussion and conclusion sections of the paper, we suggest that a different solution to explain the viscoelasticity of polymer chains and of their "entanglement" is needed. This requires a change in paradigm to describe the dynamics of the interactions within the chains and across the chains. A brief description of our currently proposed open dissipative statistical approach, "the Grain-Field Statistics", is presented. [ABSTRACT FROM AUTHOR]

Understanding and characterizing semi-crystalline models with crystalline and amorphous segments is crucial for industrial applications. A coarse-grained molecular dynamics (CGMD) simulations study probed the crystal network formation in high-density polyethylene (HDPE) from melt, and shed light on tensile properties for microstructure analysis. Modified Paul–Yoon–Smith (PYS/R) forcefield parameters are used to compute the interatomic forces among the PE chains. The isothermal crystallization at 300 K and 1 atm predicts the multi-nucleus crystal growth; moreover, the lamellar crystal stems and amorphous region are alternatively oriented. A one-dimensional density distribution along the alternative lamellar stems further confirms the ordering of the lamellar-stack orientation. Using this plastic model preparation approach, the semi-crystalline model density (ρcr) of ca. 0.913 g·cm−3 and amorphous model density (ρam) of ca. 0.856 g·cm−3 are obtained. Furthermore, the ratio of ρcr/ρam ≈ 1.06 is in good agreement with computational (≈1.096) and experimental (≈1.14) data, ensuring the reliability of the simulations. The degree of crystallinity (χc) of the model is ca. 52% at 300 K. Nevertheless, there is a gradual increase in crystallinity over the specified time, indicating the alignment of the lamellar stems during crystallization. The characteristic stress–strain curve mimicking tensile tests along the z-axis orientation exhibits a reversible sharp elastic regime, tensile strength at yield ca. 100 MPa, and a non-reversible tensile strength at break of 350%. The cavitation mechanism embraces the alignment of lamellar stems along the deformation axis. The study highlights an explanatory model of crystal network formation for the PE model using a PYS/R forcefield, and it produces a microstructure with ordered lamellar and amorphous segments with robust mechanical properties, which aids in predicting the microstructure–mechanical property relationships in plastics under applied forces.

Medical devices often include polymeric components, which contain additives or contaminants that may leach into patients and pose a health risk. Previously, we proposed a mass transport model that conservatively estimates the leaching kinetics and only requires the solute's diffusion coefficient in the polymer, D, to be specified. Because determining D experimentally is time‐consuming, we also parameterized empirical models to estimate worst‐case D values using only the solute molecular weight, Mw. These models were based on a modest database and were limited to 19 polymers and larger solutes (Mw>100 g/mol). Here, we assemble a much larger database, which enables us to construct more accurate models using a robust statistical approach, expanding the coverage to 50 device‐relevant polymers and smaller solutes (Mw<100 g/mol). Then, we demonstrate several applications of these bounds, including modeling the release kinetics. Finally, we observe an interesting phenomenon, a discontinuous drop in D of up to 25,000× for solutes with Mw>50 g/mol in glassy polymers. Using molecular simulations and cheminformatics tools, we propose a novel definition of the effective diameter of free volume channels in polymers, and we show that solutes larger than this channel size diffuse much more slowly. [ABSTRACT FROM AUTHOR]

Molecular simulations are now an essential part of modern chemistry and physics, especially for the investigation of macromolecules. They have evolved into mature approaches that can be used effectively to understand the structure-to-property relationships of diverse macromolecular systems. In this article, we provide a tutorial on molecular simulations, focusing on the technical and practical aspects. Several prominent and classical simulation methods and software are introduced. The applications of molecular simulations in various directions of macromolecular science are then featured by representative systems, including self-assembly, crystallization, chemical reaction, and some typical non-equilibrium systems. This tutorial paper provides a useful overview of molecular simulations in the rapid progress of macromolecular science, and suggests guidance for researchers who start exploiting molecular simulations in their study. [ABSTRACT FROM AUTHOR]

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]

Genetic information is stored in very long DNA molecules, which are folded to form chromatin, a similarly long polymer fibre that is ultimately organised into chromosomes. The organisation of chromatin is fundamental to many cellular functions, from the expression of the genetic information to cell division. As a long polymer, chromatin is very flexible and may adopt a myriad of shapes. Globally, the polymer physics governing chromatin dynamics is very well understood. But chromatin is not uniform and regions of it, with chemical modifications and bound effectors, form domains and compartments through mechanisms not yet clear. Polymer models have been successfully used to investigate these mechanisms to explain cytological observations and build hypothesis for experimental validation. Many different approaches to conceptualise chromatin in polymer models can be envisioned and each reflects different aspects. Here, we compare recent approaches that aim at reproducing prominent features of interphase chromatin organisation: the compartmentalisation into eu- and heterochromatin compartments, the formation of a nucleolus, chromatin loops and the rosette and Rabl conformations of interphase chromosomes. We highlight commonalities and contradictions that point to a modulation of the mechanisms involved to fine degree. Consolidating models will require the inclusion of yet hidden or neglected parameters.

A representation of polymer self‐consistent field theory equivalent to quantum density functional theory is given in terms of non‐orthogonal basis sets. Molecular integrals and self‐consistent equations for spherically symmetric systems using Gaussian basis functions are given, and the binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron self‐interaction correction is adopted and the Pauli‐exclusion principle is enforced through ideas of polymer excluded‐volume. The atoms hydrogen through neon are examined without some approximations which permit cancellation of errors and spontaneous shell structure is observed. Correlations are neglected in the interest of simplicity and comparisons are made with Hartree–Fock theory. The implications of the Pauli‐exclusion potential and its approximate form are discussed, and the Pauli model is analyzed using scaling theory for the uniform electron density case where the correct form of the Thomas–Fermi quantum kinetic energy and the Dirac exchange correction are recovered. [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]

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein's equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics" as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada's work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler's geometrodynamics. They were added to it in the 1960s by Geroch. Ranada's solutions of source-free Maxwell's equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole. [ABSTRACT FROM AUTHOR]

DNA and mRNA are essential aspects of cells. They are responsible for much of the genomic activity that takes place in a cell, and are significant macromolecules for research in cell and molecular biology. DNA and mRNA are polymers, molecules that are composed of repeating subunits known as monomers. In the past, a number of theoretical models that elucidate the physical properties of polymers have been proposed to the scientific community. These models include the Freely-Jointed Chain, Freely-Rotating Chain, Worm-Like Chain, and Gaussian Chain Models. In this paper, I make use of such theoretical models in polymer physics, and derive a number of theoretical models that correlate DNA, its respective pre-mRNA strand, and the corresponding post-mRNA strand in a eukaryotic cell. Furthermore, graphical representations of some of the mathematical models derived in the paper are also rendered. Based on this, the theoretical models formulated in this paper can be applied to research in the fields of mathematical biology, biophysics, biochemistry, and cell/molecular biology.

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide. [ABSTRACT FROM AUTHOR]

In the present work, molecular dynamics simulations are carried out based on the bead‐spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse‐Weissnberg number (WiR>>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug‐of‐war ongoing for each load‐bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist‐like interchain couplings as long as WiR > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges. [ABSTRACT FROM AUTHOR]

Biomolecular condensation and phase separation are increasingly understood to play crucial roles in cellular compartmentalization and spatiotemporal regulation of cell machinery implicated in function and pathology. A key aspect of current research is to gain insight into the underlying physical mechanisms of these processes. Accordingly, concepts of soft matter and polymer physics, the thermodynamics of mixing, and material science have been utilized for understanding condensation mechanisms of multivalent macromolecules resulting in viscoelastic mesoscopic supramolecular assemblies. Here, we focus on two topological concepts that have recently been providing key mechanistic understanding in the field. First, we will discuss how percolation provides a network-topology-related framework that offers an interesting paradigm to understand the complex networking of dense 'connected' condensate structures and, therefore, their phase behavior. Second, we will discuss the idea of entanglement as another topological concept that has deep roots in polymer physics and important implications for biomolecular condensates. We will first review some historical developments and fundamentals of these concepts, then we will discuss current advancements and recent examples. Our discussion ends with a few open questions and the challenges to address them, hinting at unveiling fresh possibilities for the modification of existing knowledge as well as the development of new concepts relevant to condensate science. [ABSTRACT FROM AUTHOR]

Recent studies in polymer physics have created macro-scale analogs to solute microscopic polymer chains like DNA by inducing diffusive motion on a chain of beads. These bead chains have persistence lengths of O(10) links and undergo diffusive motion under random fluctuations like vibration. We present a bead chain model within a new stochastic forcing system: an air fluidizing bed of granular media. A chain of spherical 6 mm resin beads crimped onto silk thread are buffeted randomly by the multiphase flow of grains and low density rising air “bubbles”. We “thermalize” bead chains of various lengths at different fluidizing airflow rates, while X-ray imaging captures a projection of the chains’ dynamics within the media. With modern 3D printing techniques, we can better represent complex polymers by geometrically varying bead connections and their relative strength, e.g., mimicking the variable stiffness between adjacent nucleotide pairs of DNA. We also develop Discrete Element Method (DEM) simulations to study the 3D motion of the bead chain, where the bead chain is represented by simulated spherical particles connected by linear and angular spring-like bonds. In experiment, we find that the velocity distributions of the beads follow exponential distributions rather than the Gaussian distributions expected from polymers in solution. Through use of the DEM simulation, we find that this difference can likely be attributed to the distributions of the forces imparted onto the chain from the fluidized bed environment. We anticipate expanding this study in the future to explore a wide range of chain composition and confinement geometry, which will provide insights into the physics of large biopolymers.

Staudinger taught us that macromolecules were made up of covalently bonded monomer repeat units chaining up as polymer chains. This paradigm is not challenged in this paper. The main question raised in polymer physics remains: how do these long chains interact and move as a group when submitted to shear deformation at high temperature when they are viscous liquids? The current consensus is that we need to distinguish two cases: the deformation of “un-entangled chains” for macromolecules with molecular weight, M, smaller than Me, “the entanglement molecular weight”, and the deformation of “entangled” chains for M > Me. The current paradigm stipulates that the properties of polymers derive from the statistical characteristics of the macromolecule itself, the designated statistical system that defines the thermodynamic state of the polymer. The current paradigm claims that the viscoelasticity of un-entangled melts is well described by the Rouse model and that the entanglement issues raised when M > Me, are well understood by the reptation model introduced by de Gennes and colleagues. Both models can be classified in the category of “chain dynamics statistics”. In this paper, we examine in detail the failures and the current challenges facing the current paradigm of polymer rheology: the Rouse model for un-entangled melts, the reptation model for entangled melts, the time–temperature superposition principle, the strain-induced time dependence of viscosity, shear-refinement and sustained-orientation. The basic failure of the current paradigm and its inherent inability to fully describe the experimental reality is documented in this paper. In the discussion and conclusion sections of the paper, we suggest that a different solution to explain the viscoelasticity of polymer chains and of their “entanglement” is needed. This requires a change in paradigm to describe the dynamics of the interactions within the chains and across the chains. A brief description of our currently proposed open dissipative statistical approach, “the Grain-Field Statistics”, is presented.

Elastomers used in everyday life are always reinforced with rigid nanoparticles (carbon black or silica). The addition of rigid nanoparticles to an elastomer gives it very specific viscoelastic properties. In this article, we discuss the current understanding of mechanical properties of a polymer matrix around its glass transition, focusing on the situation of polymers confined between two rigid surfaces with a nanometric gap. Then, we will explain how the properties of the matrix can help to understand the properties of filled or reinforced elastomers. We will then explain that in reinforced rubbers, the mechanical properties are dominated by stress propagation between neighboring aggregates through a nanometric polymer gap, thus by confined polymer bridges. We will discuss how knowledge of the dynamics of confined polymers allows us to understand the temperature dependence, the pressure dependence and the non-linearities observed for strain below 0.1 of reinforced elastomers.

Fluorescence resonance energy transfer (FRET) is a non‐invasive characterization method for studying molecular structures and dynamics, providing high spatial resolution at nanometer scale. Over the past decades, FRET‐based measurements are developed and widely implemented in synthetic polymer systems for understanding and detecting a variety of nanoscale phenomena, enabling significant advances in polymer science. In this review, the basic principles of fluorescence and FRET are briefly discussed. Several representative research areas are highlighted, where FRET spectroscopy and imaging can be employed to reveal polymer morphology and kinetics. These examples include understanding polymer micelle formation and stability, detecting guest molecule release from polymer host, characterizing supramolecular assembly, imaging composite interfaces, and determining polymer chain conformations and their diffusion kinetics. Finally, a perspective on the opportunities of FRET‐based measurements is provided for further allowing their greater contributions in this exciting area. [ABSTRACT FROM AUTHOR]

Spatial organization of chromatin plays a critical role in genome regulation. Previously, various types of affinity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways and perturb the chromatin. Here, we construct a polymer physics model following the mechanistic scheme of Topoisomerase-II, an enzyme resolving topological constraints of chromatin, and investigate how it affects interphase chromatin organization. Our computer simulations demonstrate Topoisomerase-II’s ability to phase separate chromatin into eu- and heterochromatic regions with a characteristic wall-like organization of the euchromatic regions. We realized that the ability of the euchromatic regions to cross each other due to enzymatic activity of Topoisomerase-II induces this phase separation. This realization is based on the physical fact that partial absence of self-avoiding interaction can induce phase separation of a system into its self-avoiding and non-self-avoiding parts, which we reveal using a mean-field argument. Furthermore, motivated from recent experimental observations, we extend our model to a bidisperse setting and show that the characteristic features of the enzymatic activity-driven phase separation survive there. The existence of these robust characteristic features, even under the non-localized action of the enzyme, highlights the critical role of enzymatic activity in chromatin organization.

Recent super-resolution imaging technologies enable tracing chromatin conformation with nanometer-scale precision at the single-cell level. They revealed, for example, that human chromosomes fold into a complex three-dimensional structure within the cell nucleus that is essential to establish biological activities, such as the regulation of the genes. Yet, to decode from imaging data the molecular mechanisms that shape the structure of the genome, quantitative methods are required. In this review, we consider models of polymer physics of chromosome folding that we benchmark against multiplexed FISH data available in human loci in IMR90 fibroblast cells. By combining polymer theory, numerical simulations and machine learning strategies, the predictions of the models are validated at the single-cell level, showing that chromosome structure is controlled by the interplay of distinct physical processes, such as active loop-extrusion and thermodynamic phase-separation. [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]

Dissolving microneedle (DMN)-assisted transdermal drug delivery (TDD) has received attention from the scientific community in recent years due to its ability to control the rate of drug delivery through its design, the choice of polymers, and its composition. The dissolution of the polymer depends strongly on the polymer-solvent interaction and polymer physics. Here, we developed a mathematical model based on the physicochemical parameters of DMNs and polymer physics to determine the drug release profiles. An annular gap width is defined when the MN is inserted in the skin, accumulating interstitial fluid (ISF) from the surrounding skin and acting as a boundary layer between the skin and the MN. Poly(vinylpyrrolidone) (PVP) is used as a model dissolving polymer, and ceftriaxone is used as a representative drug. The model agrees well with the literature data for ex vivo permeation studies, along with the percent height reduction of the MN. Based on the suggested mathematical model, when loading 0.39 mg of ceftriaxone, the prediction indicates that approximately 93% of the drug will be cleared from the bloodstream within 24 h. The proposed modeling strategy can be utilized to optimize drug transport behavior using DMNs.

Spontaneous locomotion is a common feature of most metazoan cells, generally attributed to the properties of actomyosin networks. This force-producing machinery has been studied down to the most minute molecular details, especially in lamellipodium-driven migration. Nevertheless, how actomyosin networks work inside contraction-driven amoeboid cells still lacks unifying principles. Here, using stable motile blebs from HeLa cells as a model amoeboid motile system, we imaged the dynamics of the actin cortex at the single filament level and revealed the co-existence of three distinct rheological phases. We introduce "advected percolation," a process where rigidity percolation and active advection synergize, spatially organizing the actin network's mechanical properties into a minimal and generic locomotion mechanism. Expanding from our observations on simplified systems, we speculate that this model could explain, down to the single actin filament level, how amoeboid cells, such as cancer or immune cells, can propel efficiently through complex 3D environments., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)

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.

Within cell nuclei, several biophysical processes occur in order to allow the correct activities of the genome such as transcription and gene regulation. To quantitatively investigate such processes, polymer physics models have been developed to unveil the molecular mechanisms underlying genome functions. Among these, phase-separation plays a key role since it controls gene activity and shapes chromatin spatial structure. In this paper, we review some recent experimental and theoretical progress in the field and show that polymer physics in synergy with numerical simulations can be helpful for several purposes, including the study of molecular condensates, gene-enhancer dynamics, and the three-dimensional reconstruction of real genomic regions. [ABSTRACT FROM AUTHOR]

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future. Mechanistic models provide testable hypotheses on principles of genome folding. It is common to start from a basic model and gradually introduce more ingredients to account for more experimental findings. In the transcription factor (TF) model, multivalent chromatin-binding proteins cluster through positive feedback, resulting in phase separation. This 'bridging-induced attraction' explains the biogenesis of nuclear bodies and the formation of active and inactive chromosome compartments. In the loop extrusion (LE) model, structural maintenance of chromosomes (SMC) proteins drive the growth of chromatin loops. LE explains the formation of topologically associating domains and the bias favouring convergent CCCTC-binding factor (CTCF) loops. The highly predictive heteromorphic polymer (HiP-HoP) model combines the TF and LE models and includes chromatin heteromorphicity. It can be used to predict 3D chromatin structure genome-wide. [ABSTRACT FROM AUTHOR]

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018) [53]), where the manifold is defined by the level set of constraint functions, and the probability distribution may involve the pseudodeterminant of the Jacobian of the constraints, as arises in physical sampling problems. The algorithm is easy to implement and scales well to problems with thousands of dimensions and with complex sets of constraints provided their Jacobian retains sparsity. The algorithm uses direct linear algebra and requires a single matrix factorization per proposal point, which enhances its efficiency over previously proposed methods but becomes the computational bottleneck of the algorithm in high dimensions. We test the algorithm on several examples inspired by soft-matter physics and materials science to study its complexity and properties. • Introduces numerical algorithm for sampling probability distribution on a manifold. • Manifold is defined by level set of constraint functions, such as bond-distances. • Algorithm is efficient in problems with thousands of dimensions. • Requires one sparse matrix factorization per proposal point. • Tested on examples from soft-matter physics with "soft" constraints. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide.

Biomolecular condensation and phase separation are increasingly understood to play crucial roles in cellular compartmentalization and spatiotemporal regulation of cell machinery implicated in function and pathology. A key aspect of current research is to gain insight into the underlying physical mechanisms of these processes. Accordingly, concepts of soft matter and polymer physics, the thermodynamics of mixing, and material science have been utilized for understanding condensation mechanisms of multivalent macromolecules resulting in viscoelastic mesoscopic supramolecular assemblies. Here, we focus on two topological concepts that have recently been providing key mechanistic understanding in the field. First, we will discuss how percolation provides a network-topology-related framework that offers an interesting paradigm to understand the complex networking of dense ‘connected’ condensate structures and, therefore, their phase behavior. Second, we will discuss the idea of entanglement as another topological concept that has deep roots in polymer physics and important implications for biomolecular condensates. We will first review some historical developments and fundamentals of these concepts, then we will discuss current advancements and recent examples. Our discussion ends with a few open questions and the challenges to address them, hinting at unveiling fresh possibilities for the modification of existing knowledge as well as the development of new concepts relevant to condensate science.

The pairing of homologous chromosomes (homologs) in meiosis is essential for distributing the correct numbers of chromosomes into haploid gametes. In budding yeast, pairing depends on the formation of 150 to 200 Spo11-mediated double-strand breaks (DSBs) that are distributed among 16 homolog pairs, but it is not known if all, or only a subset, of these DSBs contribute to the close juxtaposition of homologs. Having established a system to measure the position of fluorescently tagged chromosomal loci in three-dimensional space over time, we analyzed locus trajectories to determine how frequently and how long loci spend colocalized or apart. Continuous imaging revealed highly heterogeneous cell-to-cell behavior of foci, with the majority of cells exhibiting a “mixed” phenotype where foci move into and out of proximity, even at late stages of prophase, suggesting that the axial structures of the synaptonemal complex may be more dynamic than anticipated. The observed plateaus of the mean-square change in distance (MSCD) between foci informed the development of a biophysical model of two diffusing polymers that captures the loss of centromere linkages as cells enter meiosis, nuclear confinement, and the formation of Spo11-dependent linkages. The predicted number of linkages per chromosome in our theoretical model closely approximates the small number (approximately two to four) of estimated synapsis-initiation sites, suggesting that excess DSBs have negligible effects on the overall juxtaposition of homologs. These insights into the dynamic interchromosomal behavior displayed during homolog pairing demonstrate the power of combining time-resolved in vivo analysis with modeling at the granular level. [ABSTRACT FROM AUTHOR]

In higher eukaryotes, chromosomes have a complex three‐dimensional (3D) conformation in the cell nucleus serving vital functional purposes, yet their folding principles remain poorly understood at the single‐molecule level. Here, we summarize recent approaches from polymer physics to comprehend the physical mechanisms underlying chromatin architecture. In particular, we focus on two models that have been supported by recent, growing experimental evidence, the Loop Extrusion model and the Strings&Binders phase separation model. We discuss their key ingredients, how they compare to experimental data and some insight they provide on chromatin architecture and gene regulation. Progress in that research field are opening the possibility to predict how genomic mutations alter the network of contacts between genes and their regulators and how that is linked to genetic diseases, such as congenital disorders and cancer. [ABSTRACT FROM AUTHOR]

The development of novel experimental technologies able to map genome-wide chromatin contacts, as Hi-C, GAM or SPRITE, allowed to derive detailed information about the spatial structure of chromosomes in the cell nucleus. They revealed that the genome has a complex spatial organisation, which is highly connected with its activity. In the last years, such an abundance of experimental data prompted the development of quantitative models based on Polymer Physics to describe the chromatin architecture, clarifying many aspects about the molecular mechanisms underlying genome folding. Efficient algorithms are thus fundamental to perform massive numerical simulations for testing the accuracy of these models and provide a good description for small genomic regions or for whole chromosomes. Here, we consider the performances of Molecular Dynamics (MD) implementation of commonly used polymer physics models. Such models can be combined with Machine Learning approaches informed with experimental data to produce more accurate descriptions of real genomic regions. However, the execution times increase as a power-law with the size of the input data, which ultimately reflects the complexity of the investigated system. The best strategy is therefore a convenient trade-off between the accuracy in the description and the availability of computational resources. The combination of innovative experimental data and polymer physics theories allow to reconstruct the 3D genome structure. This is achieved by the use of machine learning approaches and massive parallel computing. Efficient algorithms and computational resources are then fundamental to produce models of increasingly high accuracy. [ABSTRACT FROM AUTHOR]

Abstract Background Structural maintenance of chromosomes (SMC) complexes are central organizers of chromatin architecture throughout the cell cycle. The SMC family member condensin is best known for establishing long-range chromatin interactions in mitosis. These compact chromatin and create mechanically stable chromosomes. How condensin contributes to chromatin organization in interphase is less well understood. Results Here, we use efficient conditional depletion of fission yeast condensin to determine its contribution to interphase chromatin organization. We deplete condensin in G2-arrested cells to preempt confounding effects from cell cycle progression without condensin. Genome-wide chromatin interaction mapping, using Hi-C, reveals condensin-mediated chromatin interactions in interphase that are qualitatively similar to those observed in mitosis, but quantitatively far less prevalent. Despite their low abundance, chromatin mobility tracking shows that condensin markedly confines interphase chromatin movements. Without condensin, chromatin behaves as an unconstrained Rouse polymer with excluded volume, while condensin constrains its mobility. Unexpectedly, we find that condensin is required during interphase to prevent ongoing transcription from eliciting a DNA damage response. Conclusions In addition to establishing mitotic chromosome architecture, condensin-mediated long-range chromatin interactions contribute to shaping chromatin organization in interphase. The resulting structure confines chromatin mobility and protects the genome from transcription-induced DNA damage. This adds to the important roles of condensin in maintaining chromosome stability.

The nuclear pore complex (NPC) is a critical gateway regulating molecular transport between the nucleus and cytoplasm. It allows small molecules to pass freely, while larger molecules require nuclear transport receptors to traverse the barrier. This selective permeability is maintained by phenylalanine-glycine-rich nucleoporins (FG-Nups), intrinsically disordered proteins that fill the NPC's central channel. The disordered and flexible nature of FG-Nups complicates their spatial characterization with conventional structural biology techniques. To address this challenge, polymer physics offers a valuable framework for describing FG-Nup behavior, reducing their complex structures to a few key parameters. In this review, we explore how polymer physics models FG-Nups using these parameters and discuss experimental efforts to quantify them in various contexts, providing insights into the conformational properties of FG-Nups.

Summary: All kingdoms of life have evolved tip‐growing cells able to mine their environment or deliver cargo to remote targets. The basic cellular processes supporting these functions are understood in increasing detail, but the multiple interactions between them lead to complex responses that require quantitative models to be disentangled. Here, I review the equations that capture the fundamental interactions between wall mechanics and cell hydraulics starting with a detailed presentation of James Lockhart's seminal model. The homeostatic feedbacks needed to maintain a steady tip velocity are then shown to offer a credible explanation for the pulsatile growth observed in some tip‐growing cells. Turgor pressure emerges as a central variable whose role in the morphogenetic process has been a source of controversy for more than 50 yr. I argue that recasting Lockhart's work as a process of chemical stress relaxation can clarify how cells control tip growth and help us internalise the important but passive role played by turgor pressure in the morphogenetic process. [ABSTRACT FROM AUTHOR]

The effects of molecular weight ( M w ) of polystyrene (PS) latex particles on optical and electrical percolations of multi-walled carbon nanotube (MWCNT)-added nanocomposite films were reported. Three different latex particle solutions, each having different M w , were first mixed with MWCNT dispersions at various mass fractions between 0 and 20 wt.% to prepare nanocomposites, and then the drop-casting method was employed to coat glass substrates by nanocomposite films. Surface resistivity, photon transmission and scanning electron microscopy measurements were performed on prepared films. As a result, the M w of latex particles had no influence on both optical, φ o and electrical percolation, φ c thresholds and the same threshold values were determined as 1.5 wt.%. Upon decreasing the latex M w , a steady reduction from 3.99 to 2.28 was observed for the critical exponents of electrical percolation, β c whereas almost similar critical exponents of optical percolation (averaged β o ≈ 0.20) were found without any trend. [ABSTRACT FROM AUTHOR]

Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modelling such systems is realistic description of the steric repulsion between nearby polymers. Previous models of the polymeric excluded volume interaction have the deficit of being non-analytic, being computationally expensive, or allowing polymers to erroneously cross each other. A recent solution to these issues, implemented in the MEDYAN simulation platform, uses analytical expressions obtained from integrating an interaction kernel along the lengths of two polymer segments to describe their repulsion. Here, we extend this model by re-deriving it for lower-dimensional geometrical configurations, deriving similar expressions using a steeper interaction kernel, comparing it to other commonly used potentials, and showing how to parameterise these models. We also generalise this new integrated style of potential by introducing a segmental Lennard-Jones potential, which enables modelling both attractive and repulsive interactions in semi-flexible polymer networks. These results can be further generalised to facilitate the development of effective interaction potentials for other finite elements in simulations of softmatter systems. [ABSTRACT FROM AUTHOR]