Polymer Physics Research Articles

Combinatorics and topological weights of chromatin loop networks.

Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, both in the case where TUs are labeled and where they are unlabeled. We then combine these mathematical results with those of computer simulations aimed at finding the inter-TU energy required to form a target loop network. We show that different topologies are vastly different in terms of both their combinatorial weight and energy of formation. We explain the latter result qualitatively by computing the topological weight of a given network-i.e., its partition function in statistical mechanics language-in the approximation where excluded volume interactions are neglected. Our results show that networks featuring local loops are statistically more likely with respect to networks including more nonlocal contacts. We suggest our classification of loop networks, together with our estimate of the combinatorial and topological weight of each network, will be relevant to catalog three-dimensional structures of chromatin fibers around eukaryotic genes, and to estimate their relative frequency in both simulations and experiments.

Stereocomplex crystallization of equimolar Poly(L-lactic acid)/Poly(D-lactic acid) blends from melt with lowered chain entanglements

Understanding polymer crystallization at the molecular level is one of the key open questions of polymer physics. Here, high molecular weight equimolar poly(L-lactic acid)/poly(D-lactic acid) (PLLA/PDLA) blends with lowered chain entanglements are prepared by the freeze-drying method. The role of chain entanglements in stereocomplex (SC) crystallization is explored. A significant increase in the crystallization kinetics of SC is observed with decreasing the entanglement density, and thus highly crystallized SC is obtained in the PLLA/PDLA blends by a process of non-isothermal crystallization. With reducing the chain entanglements of PLLA/PDLA blends, an intriguing phenomenon that SC crystallization stops at a high temperature around 200 °C and starts again at ∼160 °C on continuous cooling is observed, verifying the new concept of “poisoning by purity”. Further studies reveal that the PLLA/PDLA blends with lowered chain entanglements are more likely to form regularly folded SC lamellae, which nucleate and grow at higher temperatures. Meanwhile, the reduced chain entanglements also reduce the activation energy for chain diffusion. These two effects may be the main reason for the significantly accelerated crystallization kinetics of SC. This study provides a new idea for producing highly crystallized SC in PLLA products to improve their thermal resistance and other properties.

Molecular Weight-Dependent Physiochemical Behaviors of Calcium Carbonate Chains.

The regulation of physiochemical behaviors by changing molecular weights is an important cornerstone of polymer physics. However, similar correlations between molecular weights and properties have not been discovered in inorganic ionic compounds. In this work, we prepared a calcium carbonate specimen with a semiflexible chain topology analogous to those of polymers. The molecular weights of the calcium carbonate chains, which ranged from 3400 to 54 100 Da, were directly correlated to their physiochemical behaviors, including gel point, zero shear viscosity, and plateau modulus. The calcium carbonate chains showed similar polymeric characteristics, including shear thinning, thixotropy, entropic elasticity, and viscoelasticity. These features agreed with recent theories and formulas in polymer physics textbooks. On the basis of this understanding, the mechanical properties of calcium carbonate-based gels could be altered by changing their molecular weights. This study could represent a fusion of inorganic chemistry and polymer physics with similar molecular weight-dependent behaviors and material properties, establishing an alternative pathway for designing future inorganic materials.

Compaction and Segregation of DNA in Escherichia coli.

Theoretical and experimental approaches have been applied to study the polymer physics underlying the compaction of DNA in the bacterial nucleoid. Knowledge of the compaction mechanism is necessary to obtain a mechanistic understanding of the segregation process of replicating chromosome arms (replichores) during the cell cycle. The first part of this review discusses light microscope observations demonstrating that the nucleoid has a lower refractive index and thus, a lower density than the cytoplasm. A polymer physics explanation for this phenomenon was given by a theory discussed at length in this review. By assuming a phase separation between the nucleoid and the cytoplasm and by imposing equal osmotic pressure and chemical potential between the two phases, a minimal energy situation is obtained, in which soluble proteins are depleted from the nucleoid, thus explaining its lower density. This theory is compared to recent views on DNA compaction that are based on the exclusion of polyribosomes from the nucleoid or on the transcriptional activity of the cell. These new views prompt the question of whether they can still explain the lower refractive index or density of the nucleoid. In the second part of this review, we discuss the question of how DNA segregation occurs in Escherichia coli in the absence of the so-called active ParABS system, which is present in the majority of bacteria. How is the entanglement of nascent chromosome arms generated at the origin in the parental DNA network of the E. coli nucleoid prevented? Microscopic observations of the position of fluorescently-labeled genetic loci have indicated that the four nascent chromosome arms synthesized in the initial replication bubble segregate to opposite halves of the sister nucleoids. This implies that extensive intermingling of daughter strands does not occur. Based on the hypothesis that leading and lagging replichores synthesized in the replication bubble fold into microdomains that do not intermingle, a passive four-excluding-arms model for segregation is proposed. This model suggests that the key for segregation already exists in the structure of the replication bubble at the very start of DNA replication; it explains the different patterns of chromosome arms as well as the segregation distances between replicated loci, as experimentally observed.

Scaling of the linear viscoelasticity of entangled poly(ethylene oxide) aqueous solutions

The dynamic modulus of polymer solutions and melts can be expressed as a universal function of reduced frequency when the modulus is scaled by a characteristic value according to the scaling theory of polymer physics. Although the plot of the scaled modulus as a function of the scaled frequency supports the theory, it suffers from considerable scattered distribution of data points around the hypothetical master curve. Compared with the master curve of the time–temperature superposition (TTS) of polymer melts, the master curve of polymer solutions has poor quality. Furthermore, the scale factors of polymer solutions may not show a clear dependency on molecular weight and concentrations. Experimental errors and molecular weight distribution appear to enhance the inaccuracy of the master curve. Therefore, we apply a global optimization for the superposition of the viscoelastic data of polymer solutions with various molecular weights and concentrations. The global optimization resulted in the superposition of data as accurate as that of TTS. Furthermore, the numerically determined shift factors, which were relative scale factors, showed clear dependences on molecular weight and concentrations. We compared our global optimization with previous scaling methodologies.

Multiscale modelling of chromatin 4D organization in SARS-CoV-2 infected cells

SARS-CoV-2 can re-structure chromatin organization and alter the epigenomic landscape of the host genome, but the mechanisms that produce such changes remain unclear. Here, we use polymer physics to investigate how the chromatin of the host genome is re-organized upon infection with SARS-CoV-2. We show that re-structuring of A/B compartments can be explained by a re-modulation of intra-compartment homo-typic affinities, which leads to the weakening of A-A interactions and the enhancement of A-B mixing. At the TAD level, re-arrangements are physically described by a reduction in the loop extrusion activity coupled with an alteration of chromatin phase-separation properties, resulting in more intermingling between different TADs and a spread in space of the TADs themselves. In addition, the architecture of loci relevant to the antiviral interferon response, such as DDX58 or IFIT, becomes more variable within the 3D single-molecule population of the infected model, suggesting that viral infection leads to a loss of chromatin structural specificity. Analysing the time trajectories of pairwise gene-enhancer and higher-order contacts reveals that this variability derives from increased fluctuations in the chromatin dynamics of infected cells. This suggests that SARS-CoV-2 alters gene regulation by impacting the stability of the contact network in time.

Polymer Physics behind the Gel-Spinning of UHMWPE Fibers.

Gel-spinning of ultra-high molecular weight polyethylene (UHMWPE) fibers has attracted great interest in academia and industry since its birth and commercialization in the 1980s, due to unique properties such as high modulus, low density, and excellent chemical resistance. However, the high viscosity and long relaxation time greatly complicate processing. In industry, solvents, like decalin and paraffin oil, usually disentangle the physical networks and promote final drawability. From extruding the polymer solution to post-solid-stretching, many polymer physics problems that accompany high-modulus fiber gel-spinning should be understood and addressed. In this review, by detailed discussions about the effect of entanglements and intracrystalline chain dynamics on the mechanical properties of UHMWPE, theoretical descriptions of the structure formation of disentangled UHMWPE crystals, and the origin of high modulus and strength of final fibers are provided. Several physical intrinsic key factors are also discussed, revealing why UHMWPE is an ideal material for producing high-performance fibers.

Polymer physics view of peripheral chromatin: de Gennes' self-similar carpet.

Using scaling arguments to model peripheral chromatin localized near the inner surface of the nuclear envelope (NE) as a flexible polymer chain, we discuss the structural properties of the peripheral chromatin composed of alternating lamin-associated domains (LADs) and inter-LADs. Modeling the attraction of LADs to NE by de Gennes' self-similar carpet, which treats the chromatin layer as a polymer fractal, explains two major experimental observations. (i) The high density of chromatin close to the nuclear periphery decays to a constant density as the distance to the periphery increases. (ii) Due to the decreasing mesh size towards the nuclear periphery, the chromatin carpet inside NE excludes molecules (via nonspecific interactions) above a threshold size that depends on the distance from the nuclear periphery.

Map conformational landscapes of intrinsically disordered proteins with polymer physics quantities

Disordered proteins are conformationally flexible proteins that are biologically important and have been implicated in devastating diseases such as Alzheimer’s disease and cancer. Unlike stably folded structured proteins, disordered proteins sample a range of different conformations that needs to be accounted for. Here, we treat disordered proteins as polymer chains, and compute a dimensionless quantity called instantaneous shape ratio (Rs), as Rs = Ree2/Rg2, where Ree is end-to-end distance and Rg is radius of gyration. Extended protein conformations tend to have high Ree compared with Rg, and thus have high Rs values, whereas compact conformations have smaller Rs values. We use a scatter plot of Rs (representing shape) against Rg (representing size) as a simple map of conformational landscapes. We first examine the conformational landscape of simple polymer models such as Random Walk, Self-Avoiding Walk, and Gaussian Walk (GW), and we notice that all protein/polymer maps lie within the boundaries of the GW map. We thus use the GW map as a reference and, to assess conformational diversity, we compute the fraction of the GW conformations (fC) covered by each protein/polymer. Disordered proteins all have high fC scores, consistent with their disordered nature. Each disordered protein accesses a different region of the reference map, revealing differences in their conformational ensembles. We additionally examine the conformational maps of the nonviral gene delivery vector polyethyleneimine at various protonation states, and find that they resemble disordered proteins, with coverage of the reference map decreasing with increasing protonation state, indicating decreasing conformational diversity. We propose that our method of combining Rs and Rg in a scatter plot generates a simple, meaningful map of the conformational landscape of a disordered protein, which in turn can be used to assess conformational diversity of disordered proteins.

Molecular simulation-guided and physics-informed constitutive modeling of highly stretchable hydrogels with dynamic ionic bonds

Adaptive polymers are being designed with dynamic molecular bonds or chain interactions to respond with external stimuli with unparalleled mechanical properties and multifunctionality. An elegant example is to substantially enhance the stretchability and toughness of hydrogels through the use of ionic bond interactions. To assist the materials design and applications, a predictive theory is in high demand. However, existing multi-scale mechanics models often rely on empirical assumptions and relationships derived from polymer chemistry or physics to describe the evolution of microscale details under external stimuli, which are challenging to be validated experimentally. This study introduces a new methodology to develop constitutive theories for stretchable hydrogels based on insights garnered from molecular dynamics (MD) simulations. The continuum-level viscoelastic theory establishes the thermodynamics framework for stress-strain relationships, while MD simulations inform the evolution mechanisms of microscale bond interactions and network rearrangements, such as the bond distance and network relaxation time. These insights are then properly formulated based on polymer physics principles and fed into the continuum-level model. The resulting constitutive theory closely captures the stress responses at various loading conditions observed in experiments, as well as the microscale system volume and bond distance uncovered in MD simulations. Parametric studies are conducted to investigate the influences of various loading and material parameters on the mechanical properties of the materials, including loading rates, network crosslinking density, maximum strain, and bonding strength. Overall, the study establishes the connection between microscale network structure and mechanical responses of stretchable hydrogels with dynamic ionic bonds. It also offers practical guidance for optimizing material structures and loading conditions to enhance energy absorption and dissipation capabilities. The modeling approach can be extended to the study of other adaptive polymers with different dynamic bonds to create more precise and physically meaningful constitutive models.

Tuning Dielectric Constant of P3HT by Ultrasound-Induced Aggregation

Poly(3-hexylthiophene) (P3HT), a semiconducting polymer, is integral to the development of organic electronic devices. Its optoelectronic properties are significantly influenced by the nature of its intermolecular interactions, predominantly classified as J-type and H-type couplings. This study investigates the effect of sonication on the dielectric properties of P3HT, focusing on the transition from J-type (or less prominent H-type) to H-type intermolecular interactions, accompanied by disorder-order transformation. The research determined that sonication leads to a significant change in the dielectric properties of P3HT by forming distinct ordered regions interspersed within disordered or quasi-ordered areas. Specifically, there is an observable transition from J-type to H-type aggregation, which has profound effects on the material's electronic structure and optoelectronic performance. This transition was confirmed by changes in the absorption and photoluminescence spectra, indicating a more localized electronic character and the formation of non-emissive excitons in the case of H-aggregates. Increased dielectric constant after sonication is attributed to interface polarization, especially the Maxwell-Wagner-Sillars polarization. This effect is likely because new interfaces are created between the ordered regions and disordered/quasi-ordered regions within the P3HT material, where charges can accumulate as a result of disorder-order transformation. Our research contributes to the broader understanding of polymer physics and the development of organic electronic devices by showing how the manipulation of microstructural environments can control material properties.

Curvature controls beading in soft coated elastic cylinders: Finite wavemode instability and localized modulations

Axisymmetric beading instabilities in soft, elongated cylinders have been observed in a plethora of scenarios, ranging from cellular nanotunnels and nerves in biology to swollen cylinders and electrospun fibers in polymer physics. One of the common geometrical features that can be seen in these systems is the finite wavelength of the emerging pattern. However, modelling studies often predict that the instability has an infinite wavelength, which can be associated with localized necking or bulging. In this paper, we consider a soft elastic cylinder with a thin coating that resists bending, as described by the Helfrich free energy functional. The bending stiffness and natural mean curvature of the coating are two novel features whose competition against bulk elasticity and capillarity is investigated. For intermediate values of the bending stiffness, a linear stability analysis reveals that the mismatch between the current and natural mean curvature of the coating can lead to patterns emerging with a finite wavelength. This analysis creates a continuous bridge between the classical solutions of the shape equation obtained from the Helfrich functional and a curvature-controlled zero-wavemode instability, similar to the one induced by the competition between bulk elasticity and capillarity. A weakly non-linear analysis predicts that the criticality of the bifurcation depends on the controlling parameter, with both supercritical and subcritical bifurcations possible. When capillarity is introduced, the criticality of the bifurcation changes in a non-trivial way.

Swelling behavior of sodium lignosulfonate grafted polyacrylic acid highly absorbent hydrogels with two-phase structure

There exist two theories on the swelling behavior of cross-linked polymer networks treated by statistical thermodynamic and scalar methods, respectively. These two theories predict inconsistent network chain length dependence of the swelling ratio. The swelling of biopolymer gels is analysed with scaling laws from polymer physics, as an alternative for the classical Flory-Rehner theory. In this paper, the swelling data of sodium lignosulfonate grafted polyacrylic acid cross-linked networks in good solvents are reanalyzed, and it is pointed out that these networks are a typical model network conforming to the two-phase structural picture. For the swelling behavior of gels in the semi-dilute regime we derive the scaling theory based swelling equations, which make them compact and universal character.

Molecular Crowding: The History and Development of a Scientific Paradigm.

It is now generally accepted that macromolecules do not act in isolation but "live" in a crowded environment, that is, an environment populated by numerous different molecules. The field of molecular crowding has its origins in the far 80s but became accepted only by the end of the 90s. In the present issue, we discuss various aspects that are influenced by crowding and need to consider its effects. This Review is meant as an introduction to the theme and an analysis of the evolution of the crowding concept through time from colloidal and polymer physics to a more biological perspective. We introduce themes that will be more thoroughly treated in other Reviews of the present issue. In our intentions, each Review may stand by itself, but the complete collection has the aspiration to provide different but complementary perspectives to propose a more holistic view of molecular crowding.

Review on Crystallization Strategies for Polymer Single Crystals

Polymer physics has evolved significantly over the past century, transitioning from the early recognition of the chain structure of polymers to a mature field integrating principles from statistical mechanics, thermodynamics, and condensed matter physics. As an important part of polymer physics, polymer single crystals are crucial for understanding molecular structures and behaviors, enhancing material properties, and enabling precise functionalization. They offer insights into polymer crystallization kinetics, serve as templates for nanofabrication, and have applications in electronics, sensors, and biomedical fields. However, due to the complexity of molecular chain movement, the formation of polymer single crystals is still very difficult. Over the decades, numerous researchers have dedicated themselves to unraveling the mysteries of polymer single crystals, yielding substantial findings. This paper focus on the historical evolution and advancements in polymer single crystal research, aiming to offer valuable insights and assistance to fellow researchers in this field.

Chromatin structure from high resolution microscopy: Scaling laws and microphase separation.

Recent advances in experimental fluorescence microscopy allow high accuracy determination (resolution of 50nm) of the three-dimensional physical location of multiple (up to ∼10^{2}) tagged regions of the chromosome. We investigate publicly available microscopy data for two loci of the human Chr21 obtained from multiplexed fluorescence in situ hybridization (FISH) methods for different cell lines and treatments. Inspired by polymer physics models, our analysis centers around distance distributions between different tags with the aim being to unravel the chromatin conformational arrangements. We show that for any specific genomic site, there are (at least) two different conformational arrangements of chromatin, implying coexisting distinct topologies which we refer to as phase α and phase β. These two phases show different scaling behaviors: the former is consistent with a crumpled globule, while the latter indicates a confined, but more extended conformation, such as a looped domain. The identification of these distinct phases sheds light on the coexistence of multiple chromatin topologies and provides insights into the effects of cellular context and/or treatments on chromatin structure.

A Tale of Two Chains: Geometries of a Chain Model and Protein Native State Structures.

Linear chain molecules play a central role in polymer physics with innumerable industrial applications. They are also ubiquitous constituents of living cells. Here, we highlight the similarities and differences between two distinct ways of viewing a linear chain. We do this, on the one hand, through the lens of simulations for a standard polymer chain of tethered spheres at low and high temperatures and, on the other hand, through published experimental data on an important class of biopolymers, proteins. We present detailed analyses of their local and non-local structures as well as the maps of their closest contacts. We seek to reconcile the startlingly different behaviors of the two types of chains based on symmetry considerations.

Using polymer physics quantities to map conformational landscapes of disordered proteins

Using polymer physics quantities to map conformational landscapes of disordered proteins

Extensional Flow-Induced Concentration Gradient in Entangled Polymer Solutions with Chemically Identical Species.

Entangled polymer solutions show different rheological behavior from melts in fast extensional flow. This discrepancy is not expected according to the classic tube model and is an urgent issue to be solved in polymer physics. While in the tube model the polymer concentration is considered to be homogeneous, we show that extensional flow-induced concentration gradient may happen in polymer solutions even with chemically identical solutes and solvents. Through labeling an aggregation-induced emission (AIE) probe on oligomeric solvents, the flow-induced concentration gradient is visualized by combining extensional rheology and ex situ fluorescence microscopy. Microdomains of oligomeric solvents with a length scale of tens of micrometers are observed, and their influence on rheological behavior cannot be ignored.

Energy renormalization for temperature transferable coarse-graining of silicone polymer.

The bottom-up prediction of thermodynamic and mechanical behaviors of polymeric materials based on molecular dynamics (MD) simulation is of critical importance in polymer physics. Although the atomistically informed coarse-grained (CG) model can access greater spatiotemporal scales and retain essential chemical specificity, the temperature-transferable CG model is still a big challenge and hinders widespread application of this technique. Herein, we use a silicone polymer, i.e., polydimethylsiloxane (PDMS), having an incredibly low chain rigidity as a model system, combined with an energy-renormalization (ER) approach, to systematically develop a temperature-transferable CG model. Specifically, by introducing temperature-dependent ER factors to renormalize the effective distance and cohesive energy parameters, the developed CG model faithfully preserved the dynamics, mechanical and conformational behaviors compared with the target all-atomistic (AA) model from glassy to melt regimes, which was further validated by experimental data. With the developed CG model featuring tremendously improved computational efficiency, we systematically explored the influences of cohesive interaction strength and temperature on the dynamical heterogeneity and mechanical response of polymers, where we observed consistent trends with other linear polymers with varying chain rigidity and monomeric structures. This study serves as an extension of our proposed ER approach of developing temperature transferable CG models with diverse segmental structures, highlighting the critical role of cohesive interaction strength on CG modeling of polymer dynamics and thermomechanical behaviors.