Why Single-Chain Nanoparticles from Weak Polyelectrolytes Can Be Synthesized at Large Scale in Concentrated Solution?

Here, the unresolved question of why single-chain nanoparticles (SCNPs) prepared from a weak polyelectrolyte (PE) precursor can be synthesized on a large is addresses, unlike SCNPs obtained from an equivalent neutral (nonamphiphilic) polymer precursor. The combination of the standard elastic single-chain nanoparticles (ESN) model -developed for neutral chains- with the classical scaling theory of PE solutions provides the key. Essentially, the long-range repulsion between electrostatic blobs in a weak PE precursor restricts the cross-linking process during SCNPs formation to the interior of each blob. Consequently, the maximum concentration at which PE-SCNPs can be prepared without interchain cross-linking is not determined by the full size of the PE precursor but, instead, by the smaller size of its electrostatic blobs. Therefore, PE-SCNPs can be synthesized up to a critical concentration where electrostatic blobs from different chains touch each other. This concentration can be 30 times higher than that for non-PE polymer precursors. Upon progressive dilution, the size of PE-SCNPs synthesized in concentrated solution increases until it reaches the bigger size of PE-SCNPs prepared under highly diluted conditions. PE-SCNPs do not adopt a globular conformation either in concentrated or in diluted solution. It shows that the main model predictions agree with experimental results.

Nonmonotonic Composition Dependence of Viscosity upon Adding Single-Chain Nanoparticles to Entangled Polymers.

Well-characterized single-chain nanoparticles (SCNPs), synthesized from a linear polystyrene precursor through an intramolecular [4 + 4] thermal cycloaddition cross-linking reaction in dilute conditions, were added to entangled polystyrene melts at different concentrations. Starting from the pure linear melt, which is much more viscous than the melt of SCNPs, the zero-shear viscosity increased upon the addition of nanoparticles and reached a maximum before eventually dropping to the value of the SCNP melt. Molecular simulations reveal the origin of this unexpected behavior, which is the interplay of the very different compositional dependences of the dynamics of the two components. The SCNPs become much slower than the linear chains as their concentration decreases because they are threaded by the linear chains, reaching a maximum viscosity which is higher than that of the linear chains at a fraction of about 20%. This behavior is akin to that of single-loop ring polymers when added to linear matrices. This finding provides insights into the design and use of SCNPs as effective entropic viscosity modifiers of polymers and contributes to the discussion of the physics of loopy structures.

Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids.

Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.

Small-Molecule Allosteric Inhibitors of Human Aspartate Transcarbamoylase Suppress Proliferation of Bone Osteosarcoma Epithelial Cells.

Aspartate transcarbamoylase (ATC) is the first committed step in de novo pyrimidine biosynthesis in eukaryotes and plants. A potent transition state analog of human ATCase (PALA) has previously been assessed in clinical trials for the treatment of cancer, but was ultimately unsuccessful. Additionally, inhibition of this pathway has been proposed to be a target to suppress cell proliferation in E. coli, the malarial parasite and tuberculosis. In this manuscript we screened a 70-member library of ATC inhibitors developed against the malarial and tubercular ATCases for inhibitors of the human ATC. Four compounds showed low nanomolar inhibition (IC50 30-120 nM) in an in vitro activity assay. These compounds significantly outperform PALA, which has a triphasic inhibition response under identical conditions, in which significant activity remains at PALA concentrations above 10 µM. Evidence for a druggable allosteric pocket in human ATC is provided by both in vitro enzyme kinetic, homology modeling and in silico docking. These compounds also suppress the proliferation of U2OS osteoblastoma cells by promoting cell cycle arrest in G0/G1 phase. This report provides the first evidence for an allosteric pocket in human ATC, which greatly enhances its druggability and demonstrates the potential of this series in cancer therapy.

Consensus Pharmacophore Strategy For Identifying Novel SARS-Cov-2 Mpro Inhibitors from Large Chemical Libraries.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main Protease (Mpro) is an enzyme that cleaves viral polyproteins translated from the viral genome and is critical for viral replication. Mpro is a target for anti-SARS-CoV-2 drug development, and multiple Mpro crystals complexed with competitive inhibitors have been reported. In this study, we aimed to develop an Mpro consensus pharmacophore as a tool to expand the search for inhibitors. We generated a consensus model by aligning and summarizing pharmacophoric points from 152 bioactive conformers of SARS-CoV-2 Mpro inhibitors. Validation against a library of conformers from a subset of ligands showed that our model retrieved poses that reproduced the crystal-binding mode in 77% of the cases. Using models derived from a consensus pharmacophore, we screened >340 million compounds. Pharmacophore-matching and chemoinformatics analyses identified new potential Mpro inhibitors. The candidate compounds were chemically dissimilar to the reference set, and among them, demonstrating the relevance of our model. We evaluated the effect of 16 candidates on Mpro enzymatic activity finding that seven have inhibitory activity. Three compounds (1, 4, and 5) had IC50 values in the midmicromolar range. The Mpro consensus pharmacophore reported herein can be used to identify compounds with improved activity and novel chemical scaffolds against Mpro. The method developed for its generation is provided as an open-access code (https://github.com/AngelRuizMoreno/ConcensusPharmacophore) and can be applied to other pharmacological targets.

Host genetic regulation of human gut microbial structural variation.

Although the impact of host genetics on gut microbial diversity and the abundance of specific taxa is well established1-6, little is known about how host genetics regulates the genetic diversity of gut microorganisms. Here we conducted a meta-analysis of associations between human genetic variation and gut microbial structural variation in 9,015 individuals from four Dutch cohorts. Strikingly, the presence rate of a structural variation segment in Faecalibacterium prausnitzii that harbours an N-acetylgalactosamine (GalNAc) utilization gene cluster is higher in individuals who secrete the type A oligosaccharide antigen terminating in GalNAc, a feature that is jointly determined by human ABO and FUT2 genotypes, and we could replicate this association in a Tanzanian cohort. In vitro experiments demonstrated that GalNAc can be used as the sole carbohydrate source for F. prausnitzii strains that carry the GalNAc-metabolizing pathway. Further in silico and in vitro studies demonstrated that other ABO-associated species can also utilize GalNAc, particularly Collinsella aerofaciens. The GalNAc utilization genes are also associated with the host's cardiometabolic health, particularly in individuals with mucosal A-antigen. Together, the findings of our study demonstrate that genetic associations across the human genome and bacterial metagenome can provide functional insights into the reciprocal host-microbiome relationship.

Identification and characterization of a small molecule that activates thiosulfate sulfurtransferase and stimulates mitochondrial respiration.

The enzyme Thiosulfate sulfurtransferase (TST, EC 2.8.1.1), is a positive genetic predictor of diabetes type 2 and obesity. As increased TST activity protects against the development of diabetic symptoms in mice, an activating compound for TST may provide therapeutic benefits in diabetes and obesity. We identified a small molecule activator of human TST through screening of an inhouse small molecule library. Kinetic studies in vitro suggest that two distinct isomers of the compound are required for full activation as well as an allosteric mode of activation. Additionally, we studied the effect of TST protein and the activator on TST activity through mitochondrial respiration. Molecular docking and molecular dynamics (MD) approaches supports an allosteric site for the binding of the activator, which is supported by the lack of activation in the Escherichia coli. mercaptopyruvate sulfurtransferase. Finally, we show that increasing TST activity in isolated mitochondria increases mitochondrial oxygen consumption.

Phage display sequencing reveals that genetic, environmental, and intrinsic factors influence variation of human antibody epitope repertoire.

Phage-displayed immunoprecipitation sequencing (PhIP-seq) has enabled high-throughput profiling of human antibody repertoires. However, a comprehensive overview of environmental and genetic determinants shaping human adaptive immunity is lacking. In this study, we investigated the effects of genetic, environmental, and intrinsic factors on the variation in human antibody repertoires. We characterized serological antibody repertoires against 344,000 peptides using PhIP-seq libraries from a wide range of microbial and environmental antigens in 1,443 participants from a population cohort. We detected individual-specificity, temporal consistency, and co-housing similarities in antibody repertoires. Genetic analyses showed the involvement of the HLA, IGHV, and FUT2 gene regions in antibody-bound peptide reactivity. Furthermore, we uncovered associations between phenotypic factors (including age, cell counts, sex, smoking behavior, and allergies, among others) and particular antibody-bound peptides. Our results indicate that human antibody epitope repertoires are shaped by both genetics and environmental exposures and highlight specific signatures of distinct phenotypes and genotypes.

Validity of Effective Potentials in Crowded Solutions of Linear and Ring Polymers with Reversible Bonds.

We perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology on the potential by employing linear and ring backbones for the precursor (unbonded) polymer, finding that it leads to qualitatively different effective potentials. In the linear and ring cases the potentials can be described by Gaussians and generalized exponentials, respectively. The interactions are more repulsive for the ring topology, in analogy with known results in the absence of bonding. We also investigate the effect of the specific sequence of the reactive groups along the backbone (periodic or with different degrees of randomness), establishing that it has a significant impact on the effective potentials. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both polymers have the same types of reactive sites and intermolecular bonds can be formed. We test the validity of the effective potentials in solution, in a broad range of concentrations from high dilution to far above the overlap concentration. For this purpose, we compare simulations of the effective fluid and test particle route calculations with simulations of the real all-monomer system. Very good agreement is found for the reversible linear polymers, indicating that unlike in their nonbonding counterparts many-body effects are minor even far above the overlap concentration. The agreement for the reversible rings is less satisfactory, and at high concentration the real system does not show the clustering behavior predicted by the effective potential. Results similar to the former ones are found for the partial self-correlations in ring/linear mixtures. Finally, we investigate the possibility of creating, at high concentrations, a gel of two interpenetrated reversible networks. For this purpose we simulate a 50/50 two-component mixture of reversible polymers with orthogonal chemistry for the reactive sites, so that intermolecular bonds are only formed between polymers of the same component. As predicted by both the theoretical phase diagram and the simulations of the effective fluid, the two networks in the all-monomer mixture do not interpenetrate, and phase separation (demixing) is observed instead.

Synthetic Peptides That Antagonize the Angiotensin-Converting Enzyme-2 (ACE-2) Interaction with SARS-CoV-2 Receptor Binding Spike Protein.

The SARS-CoV-2 viral spike protein S receptor-binding domain (S-RBD) binds ACE2 on host cells to initiate molecular events, resulting in intracellular release of the viral genome. Therefore, antagonists of this interaction could allow a modality for therapeutic intervention. Peptides can inhibit the S-RBD:ACE2 interaction by interacting with the protein-protein interface. In this study, protein contact atlas data and molecular dynamics simulations were used to locate interaction hotspots on the secondary structure elements α1, α2, α3, ß3, and ß4 of ACE2. We designed a library of discontinuous peptides based upon a combination of the hotspot interactions, which were synthesized and screened in a bioluminescence-based assay. The peptides demonstrated high efficacy in antagonizing the SARS-CoV-2 S-RBD:ACE2 interaction and were validated by microscale thermophoresis which demonstrated strong binding affinity (∼10 nM) of these peptides to S-RBD. We anticipate that such discontinuous peptides may hold the potential for an efficient therapeutic treatment for COVID-19.

Characterization of gut microbial structural variations as determinants of human bile acid metabolism.

Bile acids (BAs) facilitate intestinal fat absorption and act as important signaling molecules in host-gut microbiota crosstalk. BA-metabolizing pathways in the microbial community have been identified, but it remains largely unknown how the highly variable genomes of gut bacteria interact with host BA metabolism. We characterized 8,282 structural variants (SVs) of 55 bacterial species in the gut microbiomes of 1,437 individuals from two cohorts and performed a systematic association study with 39 plasma BA parameters. Both variations in SV-based continuous genetic makeup and discrete clusters showed correlations with BA metabolism. Metagenome-wide association analysis identified 809 replicable associations between bacterial SVs and BAs and SV regulators that mediate the effects of lifestyle factors on BA metabolism. This is the largest microbial genetic association analysis to demonstrate the impact of bacterial SVs on human BA composition, and it highlights the potential of targeting gut microbiota to regulate BA metabolism through lifestyle intervention.

In Silico Design and Selection of New Tetrahydroisoquinoline-Based CD44 Antagonist Candidates.

CD44 promotes metastasis, chemoresistance, and stemness in different types of cancer and is a target for the development of new anti-cancer therapies. All CD44 isoforms share a common N-terminal domain that binds to hyaluronic acid (HA). Herein, we used a computational approach to design new potential CD44 antagonists and evaluate their target-binding ability. By analyzing 30 crystal structures of the HA-binding domain (CD44HAbd), we characterized a subdomain that binds to 1,2,3,4-tetrahydroisoquinoline (THQ)-containing compounds and is adjacent to residues essential for HA interaction. By computational combinatorial chemistry (CCC), we designed 168,190 molecules and compared their conformers to a pharmacophore containing the key features of the crystallographic THQ binding mode. Approximately 0.01% of the compounds matched the pharmacophore and were analyzed by computational docking and molecular dynamics (MD). We identified two compounds, Can125 and Can159, that bound to human CD44HAbd (hCD44HAbd) in explicit-solvent MD simulations and therefore may elicit CD44 blockage. These compounds can be easily synthesized by multicomponent reactions for activity testing and their binding mode, reported here, could be helpful in the design of more potent CD44 antagonists.

Advances in the Multi-Orthogonal Folding of Single Polymer Chains into Single-Chain Nanoparticles.

The folding of certain proteins (e.g., enzymes) into perfectly defined 3D conformations via multi-orthogonal interactions is critical to their function. Concerning synthetic polymers chains, the "folding" of individual polymer chains at high dilution via intra-chain interactions leads to so-called single-chain nanoparticles (SCNPs). This review article describes the advances carried out in recent years in the folding of single polymer chains into discrete SCNPs via multi-orthogonal interactions using different reactive chemical species where intra-chain bonding only occurs between groups of the same species. First, we summarize results from computer simulations of multi-orthogonally folded SCNPs. Next, we comprehensively review multi-orthogonally folded SCNPs synthesized via either non-covalent bonds or covalent interactions. Finally, we conclude by summarizing recent research about multi-orthogonally folded SCNPs prepared through both reversible (dynamic) and permanent bonds.

Crowded solutions of single-chain nanoparticles under shear flow.

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Repositioning of Etravirine as a Potential CK1ε Inhibitor by Virtual Screening.

CK1ε is a key regulator of WNT/ß-catenin and other pathways that are linked to tumor progression; thus, CK1ε is considered a target for the development of antineoplastic therapies. In this study, we performed a virtual screening to search for potential CK1ε inhibitors. First, we characterized the dynamic noncovalent interactions profiles for a set of reported CK1ε inhibitors to generate a pharmacophore model, which was used to identify new potential inhibitors among FDA-approved drugs. We found that etravirine and abacavir, two drugs that are approved for HIV infections, can be repurposed as CK1ε inhibitors. The interaction of these drugs with CK1ε was further examined by molecular docking and molecular dynamics. Etravirine and abacavir formed stable complexes with the target, emulating the binding behavior of known inhibitors. However, only etravirine showed high theoretical binding affinity to CK1ε. Our findings provide a new pharmacophore for targeting CK1ε and implicate etravirine as a CK1ε inhibitor and antineoplastic agent.

Pranlukast Antagonizes CD49f and Reduces Stemness in Triple-Negative Breast Cancer Cells.

INTRODUCTION: Cancer stem cells (CSCs) drive the initiation, maintenance, and therapy response of breast tumors. CD49f is expressed in breast CSCs and functions in the maintenance of stemness. Thus, blockade of CD49f is a potential therapeutic approach for targeting breast CSCs. In the present study, we aimed to repurpose drugs as CD49f antagonists. MATERIALS AND METHODS: We performed consensus molecular docking using a subdomain of CD49f that is critical for heterodimerization and a collection of pharmochemicals clinically tested. Molecular dynamics simulations were employed to further characterize drug-target binding. Using MDA-MB-231 cells, we evaluated the effects of potential CD49f antagonists on 1) cell adhesion to laminin; 2) mammosphere formation; and 3) cell viability. We analyzed the effects of the drug with better CSC-selectivity on the activation of CD49f-downstream signaling by Western blot (WB) and co-immunoprecipitation. Expressions of the stem cell markers CD44 and SOX2 were analyzed by flow cytometry and WB, respectively. Transactivation of SOX2 promoter was evaluated by luciferase reporter assays. Changes in the number of CSCs were assessed by limiting-dilution xenotransplantation. RESULTS: Pranlukast, a drug used to treat asthma, bound to CD49f in silico and inhibited the adhesion of CD49f+ MDA-MB-231 cells to laminin, indicating that it antagonizes CD49f-containing integrins. Molecular dynamics analysis showed that pranlukast binding induces conformational changes in CD49f that affect its interaction with ß1-integrin subunit and constrained the conformational dynamics of the heterodimer. Pranlukast decreased the clonogenicity of breast cancer cells on mammosphere formation assay but had no impact on the viability of bulk tumor cells. Brief exposure of MDA-MB-231 cells to pranlukast altered CD49f-dependent signaling, reducing focal adhesion kinase (FAK) and phosphatidylinositol 3-kinase (PI3K) activation. Further, pranlukast-treated cells showed decreased CD44 and SOX2 expression, SOX2 promoter transactivation, and in vivo tumorigenicity, supporting that this drug reduces the frequency of CSC. CONCLUSION: Our results support the function of pranlukast as a CD49f antagonist that reduces the CSC population in triple-negative breast cancer cells. The pharmacokinetics and toxicology of this drug have already been established, rendering a potential adjuvant therapy for breast cancer patients.

Scaffolding-Induced Property Modulation of Chemical Space.

Physicochemical property switching of chemical space is of great importance for optimization of compounds, for example, for biological activity. Cyclization is a key method to control 3D and other properties. A two-step approach, which involves a multicomponent reaction followed by cyclization, is reported to achieve the transition from basic moieties to charge neutral cyclic derivatives. A series of multisubstituted oxazolidinones, oxazinanones, and oxazepanones as well as their thio and sulfur derivatives are synthesized from readily available building blocks with mild conditions and high yields. Like a few other methods, MCR and cyclization allow for the collective transformation of a large chemical space into a related one with different properties.

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent.

This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time-temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.

Deformability and solvent penetration in soft nanoparticles at liquid-liquid interfaces.

HYPOTHESIS: The internal topology of soft nanoparticles - regular (ideal) vs disordered (realistic) networks - and its intrinsic deformability (degree of cross-linking) influences solvent permeability (uptake, invasive and mixing capacities) under interfacial confinement. METHODOLOGY: By means of large-scale molecular dynamics simulations we study nanogels at liquid-liquid (A-B) interfaces covering the whole range of cross-linking degrees and interfacial strengths. The nanogel permeability is analyzed with a grid representation that accounts for the surface fluctuations and adds to the density profiles the exact number of liquid particles inside the nanogel. Unlike in previous investigations, excluded volume interactions are considered for all the particles (monomers and liquids). FINDINGS: Nanogel's permeability is intrinsically related to the particle deformability. Ideal networks show higher values of the total liquid uptake and the invasive capacity (A-particles in B-side and vice versa) than realistic networks, though differences vanish in the limit of rigid interfaces. Uptake and invasion are optimized at a cross-linking degree that depends on the interfacial strength, tending to ~15-20% for moderate and stiff interfaces. As the interfacial strength increases, the miscibility inside the nanogel is enhanced by a factor of up to 5 with respect to the bare interface, with the disordered networks providing a better mixing than their ideal counterparts.

Facile Access to Completely Deuterated Single-Chain Nanoparticles Enabled by Intramolecular Azide Photodecomposition.

Access to completely deuterated single-chain nanoparticles (dSCNPs) has remained an unresolved issue. Herein, the first facile and efficient procedure to produce dSCNPs is reported, which comprises: i) the use of commercially available perdeuterated cyclic ether monomers as starting reagents, ii) a ring-opening copolymerization process performed in bulk to produce a neat dSCNP precursor, iii) a standard azidation reaction to decorate this precursor with azide moieties, and iv) a facile intramolecular azide photodecomposition step carried out under UV irradiation at high dilution providing with highly valuable, completely deuterated soft nano-objects from the precursor. dSCNPs are used to investigate by means of neutron-scattering measurements the form factor (radius of gyration, scaling exponent) of polyethylene oxide (PEO) chains in nanocomposites with different amounts of dSCNPs. Moreover, to illustrate the possibilities offered by the synthetic route disclosed in this communication for potential applications, the significant reduction in viscosity observed in a pure melt of polyether-based single-chain nanoparticles when compared to a melt of the corresponding linear polymer chains is shown.