Polymer Folding Research Articles

Folding behaviors of two-dimensional flexible polymers.

Unlike one-dimensional polymers, the theoretical framework on the behaviors of two-dimensional (2D) polymers is far from completeness. In this study, we model single-layer flexible 2D polymers of different sizes and examine their scaling behaviors in solution, represented by Rg ∼ Lν, where Rg is the radius of gyration and L is the side length of a 2D polymer. We find that the scaling exponent ν is 0.96 for a good solvent and 0.64 for under poor solvent condition. Interestingly, we observe a previously unnoticed phenomenon: under intermediate solvent conditions, the 2D polymer folds to maintain a flat structure, and as L becomes larger, multiple folded structures emerge. We introduce a shape parameter Q to diagram the relationship of folded structures with the polymer size and solvent condition. Theoretically, we explain the folding transitions by the competition between bending and solvophobic free energies.

Self‐Adaptive Synthesis of Non‐Covalent Crosslinkers while Folding Single‐Chain Polymers

AbstractPeptide folding is a dynamic process driven by non‐covalent cross‐linking leading to functional nanostructures for essential biochemical activities. However, replicating this process in synthetic systems is challenging due to the difficulty in mimicking nature‘s real‐time regulation of non‐covalent crosslinking for single‐chain polymer folding. Here, we address this by employing anionic dithiol building blocks to create macrocyclic disulfides as non‐covalent crosslinkers that adapted to the folding process. Initially, small macrocycles facilitated a low degree folding of a polycation. Then, this preorganized structure catalysed the production of larger macrocycles that enhanced the folding conversely. The self‐adaptive synthesis was verified through the encapsulation of an anticancer drug, showing an updated production distribution of non‐covalent crosslinkers and maximizing drug‐loading efficiency against drug‐resistant cancer in vitro. Our research advances the understanding of molecular systems by exploring species evolution via the structural dynamics of polymer folding. Additionally, adaptive synthesis enables controlled, sequential folding of synthetic polymers, with the potential to mimic protein functions.

Self-Adaptive Synthesis of Non-Covalent Crosslinkers while Folding Single-Chain Polymers.

Peptide folding is a dynamic process driven by non-covalent cross-linking leading to functional nanostructures for essential biochemical activities. However, replicating this process in synthetic systems is challenging due to the difficulty in mimicking nature's real-time regulation of non-covalent crosslinking for single-chain polymer folding. Here, we address this by employing anionic dithiol building blocks to create macrocyclic disulfides as non-covalent crosslinkers that adapted to the folding process. Initially, small macrocycles facilitated a low degree folding of a polycation. Then, this preorganized structure catalysed the production of larger macrocycles that enhanced the folding conversely. The self-adaptive synthesis was verified through the encapsulation of an anticancer drug, showing an updated production distribution of non-covalent crosslinkers and maximizing drug-loading efficiency against drug-resistant cancer in vitro. Our research advances the understanding of molecular systems by exploring species evolution via the structural dynamics of polymer folding. Additionally, adaptive synthesis enables controlled, sequential folding of synthetic polymers, with the potential to mimic protein functions.

Conformational modulation and polymerization-induced folding of proteomimetic peptide brush polymers.

Peptide-brush polymers generated by graft-through living polymerization of peptide-modified monomers exhibit high proteolytic stability, therapeutic efficacy, and potential as functional tandem repeat protein mimetics. Prior work has focused on polymers generated from structurally disordered peptides that lack defined conformations. To obtain insight into how the structure of these polymers is influenced by the folding of their peptide sidechains, a set of polymers with varying degrees of polymerization was prepared from peptide monomers that adopt α-helical secondary structure for comparison to those having random coil structures. Circular dichroism and nuclear magnetic resonance spectroscopy confirm the maintenance of the secondary structure of the constituent peptide when polymerized. Small-angle X-ray scattering (SAXS) studies reveal the solution-phase conformation of PLPs in different solvent environments. In particular, X-ray scattering shows that modulation of solvent hydrophobicity, as well as hydrogen bonding patterns of the peptide sidechain, plays an important role in the degree of globularity and conformation of the overall polymer, with polymers of helical peptide brushes showing less spherical compaction in conditions where greater helicity is observed. These structural insights into peptide brush folding and polymer conformation inform the design of these proteomimetic materials with promise for controlling and predicting their artificial fold and morphology.

PH-Controlled Reversible Folding of Copolymers via Formation of β-sheet Secondary Structures.

Protein functions are enabled by their perfectly arranged 3D structure, which is the result of a hierarchical intramolecular folding process. Sequence-defined polypeptide chains form locally ordered secondary structures (i.e., α-helix and β-sheet) through hydrogen bonding between the backbone amides, shaping the overall tertiary structure. To generate similarly complex macromolecular architectures based on synthetic materials, a plethora of strategies have been developed to induce and control the folding of synthetic polymers. However, the degree of complexity of the structure-driving ensemble of interactions demonstrated by natural polymers is unreached, as synthesizing long sequence-defined polymers with functional backbones remains a challenge. Herein, we report the synthesis of hybrid peptide-N,N-Dimethylacrylamide copolymers via radical Ring-Opening Polymerization (rROP) of peptide containing macrocycles. The resulting synthetic polymers contain sequence-defined regions of β-sheet encoding amino acid sequences. Exploiting the pH responsiveness of the embedded sequences, protonation or deprotonation in water induces self-assembly of the peptide strands at an intramacromolecular level, driving polymer chain folding via formation of β-sheet secondary structures. We demonstrate that the folding behavior is sequence dependent and reversible.

PH‐Controlled Reversible Folding of Copolymers via Formation of β‐sheet Secondary Structures

AbstractProtein functions are enabled by their perfectly arranged 3D structure, which is the result of a hierarchical intramolecular folding process. Sequence‐defined polypeptide chains form locally ordered secondary structures (i.e., α‐helix and β‐sheet) through hydrogen bonding between the backbone amides, shaping the overall tertiary structure. To generate similarly complex macromolecular architectures based on synthetic materials, a plethora of strategies have been developed to induce and control the folding of synthetic polymers. However, the degree of complexity of the structure‐driving ensemble of interactions demonstrated by natural polymers is unreached, as synthesizing long sequence‐defined polymers with functional backbones remains a challenge. Herein, we report the synthesis of hybrid peptide‐N,N‐Dimethylacrylamide copolymers via radical Ring‐Opening Polymerization (rROP) of peptide containing macrocycles. The resulting synthetic polymers contain sequence‐defined regions of β‐sheet encoding amino acid sequences. Exploiting the pH responsiveness of the embedded sequences, protonation or deprotonation in water induces self‐assembly of the peptide strands at an intramacromolecular level, driving polymer chain folding via formation of β‐sheet secondary structures. We demonstrate that the folding behavior is sequence dependent and reversible.

High-yield and chirality-selective isolation of single-walled carbon nanotubes using conjugated polymers and small molecular chaperones.

Single-walled carbon nanotubes (SWCNTs) have potential for a wide range of applications in diverse fields, but the heterogeneous properties of the synthesized mixtures of SWCNT types hinder the realization of these aspirations. Recent developments in extractive purification methods of polychiral SWCNT mixtures have somewhat gradually alleviated this problem, but either the yield or purity of the obtained fractions remains unsatisfactory. In this work, we showed the possibility of simultaneously achieving both the aforementioned goals, commonly considered mutually exclusive, via the enhancement of the capabilities of the conjugated polymer extraction (CPE) technique. We found that combining small molecular species, which alone are unwanted in the system, with a selective poly(9,9'-dioctylfluorenyl-2,7-diyl-alt-6,6'-(2,2'-bipyridine)) polymer increased the concentration of the harvested SWCNTs by an order of magnitude while maintaining near-monochiral purity of the materials. The conducted modeling revealed that the presence of these additives facilitated the folding of conjugated polymers around (6,5) SWCNTs, leading to a substantial increase in the concentration and quality of the SWCNT suspension. The obtained results lay the foundation for the widescale implementation of the CPE of usually scarcely available chirality-defined SWCNTs owing to the molecular chaperones expediting the folding of the conjugated polymers.

Solvent Dependent Folding of an Amphiphilic Polyaramid.

A series of synthetic alternating and amphiphilic aromatic amide polymers were synthesized by a step growth polymerization. Alternating meta- and para-linkages were introduced to force the polymer chain into a helical shape in the highly polar solvent water. The polymers were analyzed by 1H NMR spectroscopy and SEC in polar aprotic solvents such as DMSO and DMF. However, the polymers also showed good solubility in water. 1H NMR spectroscopy, small-angle X-ray scattering, and dynamic light scattering provided clear evidence of polymer folding in water but not DMF. We employed parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) to simulate the free energy surfaces of an analogous model polymer in DMF and water. The simulations gave a molecular model of an unfolded structure in DMF and a helically folded tubular structure in water.

Supramolecular Polymer Polymorphism: Spontaneous Helix-Helicoid Transition through Dislocation of Hydrogen-Bonded π-Rosettes.

Polymorphism, a phenomenon whereby disparate self-assembled products can be formed from identical molecules, has incited interest in the field of supramolecular polymers. Conventionally, the monomers that constitute supramolecular polymers are engineered to facilitate one-dimensional aggregation and, consequently, their polymorphism surfaces primarily when the states of assembly differ significantly. This engenders polymorphs of divergent dimensionalities such as one- and two-dimensional aggregates. Notwithstanding, realizing supramolecular polymer polymorphism, wherein polymorphs maintain one-dimensional aggregation, persists as a daunting challenge. In this work, we expound upon the manifestation of two supramolecular polymer polymorphs formed from a large discotic supramolecular monomer (rosette), which consists of six hydrogen-bonded molecules with an extended π-conjugated core. These polymorphs are generated in mixtures of chloroform and methylcyclohexane, attributable to distinctly different disc stacking arrangements. The face-to-face (minimal displacement) and offset (large displacement) stacking arrangements can be predicated on their distinctive photophysical properties. The face-to-face stacking results in a twisted helix structure. Conversely, the offset stacking induces inherent curvature in the supramolecular fiber, thereby culminating in a hollow helical coil (helicoid). While both polymorphs exhibit bistability in nonpolar solvent compositions, the face-to-face stacking attains stability purely in a kinetic sense within a polar solvent composition and undergoes conversion into offset stacking through a dislocation of stacked rosettes. This occurs without the dissociation and nucleation of monomers, leading to unprecedented helicoidal folding of supramolecular polymers. Our findings augment our understanding of supramolecular polymer polymorphism, but they also highlight a distinctive method for achieving helicoidal folding in supramolecular polymers.

Structure and energetics of hydroxyl‐terminated polybutadiene via density functional theory

AbstractHydroxyl‐terminated polybutadiene (HTPB) is a commonly used binding polymer in industry to produce polyurethanes. HTPB synthesis via allylic radical propagation leads to varied compositions and conformations that govern the bulk physical and mechanical properties of this polymer. While HTPB is incredibly well studied, its enthalpy of formation is still an open question and is critical to understanding the energetic contributions of the binding polymer in propellant formulations. This study investigates a series of HTPB polymers of experimentally relevant size and composition to understand the effects of conformations and monomer compositions on enthalpies of formation. The distribution of component monomer species comprising HTPB polymers is shown to have a significant effect on the condensed phase enthalpy of formation. The present study provides a best estimate of 331.2±50.3 kJ/mol or 150.7±22.9 kJ/kg for the condensed phase enthalpy of formation for commercially available HTPB formulations. The effects of the polymer folding motifs are smaller but distinct, with more highly folded structures exhibiting lower enthalpies of formation.

Protein-Inspired Control over Synthetic Polymer Folding for Structured Functional Nanoparticles in Water.

The folding of proteins into functional nanoparticles with defined 3D structures has inspired chemists to create simple synthetic systems mimicking protein properties. The folding of polymers into nanoparticles in water proceeds via different strategies, resulting in the global compaction of the polymer chain. Herein, we review the different methods available to control the conformation of synthetic polymers and collapse/fold them into structured, functional nanoparticles, such as hydrophobic collapse, supramolecular self-assembly, and covalent cross-linking. A comparison is made between the design principles of protein folding to synthetic polymer folding and the formation of structured nanocompartments in water, highlighting similarities and differences in design and function. We also focus on the importance of structure for functional stability and diverse applications in complex media and cellular environments.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

Source Code - Polymer folding through active processes recreates features of genome organization

Source Code - Polymer folding through active processes recreates features of genome organization

Machine-guided path sampling to discover mechanisms of molecular self-organization

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

Investigating flexible and semi-flexible polymers using solid-state nanopores.

Following the rise of nanopore DNA sequencing, nanopore sensors are showing great potential for characterizing and ultimately decoding information from other types of biotic and abiotic polymers. In particular, nanostructured DNA molecules are being proposed to store digital information for archival applications or as barcodes for multiplexed biomarker detection and solid-state nanopores are being used to decode them. However, progress in this area requires better understanding of the molecular mechanisms for translocation both at the theoretical and experimental level to optimize these applications, even with recent progress. Here we investigate the influence of polymer flexibility on translocation times and folding dynamics during polymer translocation through solid-state nanopores ranging in size from 5 to 15 nm on 10–15-nm-thick SiN membranes. We design DNA with modulated flexibilities by leaving gaps in one of the strands making up the DNA double helix. In doing so we create block-polymers consisting of rigid double stranded pieces held together by flexible single stranded parts of DNA. As expected, we observe that folding happens preferentially on these ssDNA sections in the structured polymer and propose this as a mechanism to control the folding of longer polymers by restricting folding to the ends of the molecule, leaving large internal blocks of the polymer unfolded. This strategy to limit polymer folding inside a pore can be used to tackle one of the major challenges of data storage and barcode readout using solid-state nanopores.

Sensitive Transfer-Free Wafer-Scale Graphene Microphones.

During the past decades micro-electromechanical microphones have largely taken over the market for portable devices, being produced in volumes of billions yearly. Because performance of current devices is near the physical limits, further miniaturization and improvement of microphones for mobile devices poses a major challenge that requires breakthrough device concepts, geometries, and materials. Graphene is an attractive material for enabling these breakthroughs due to its flexibility, strength, nanometer thinness, and high electrical conductivity. Here, we demonstrate that transfer-free 7 nm thick multilayer graphene (MLGr) membranes with diameters ranging from 85–155 to 300 μm can be used to detect sound and show a mechanical compliance up to 92 nm Pa–1, thus outperforming commercially available MEMS microphones of 950 μm with compliances around 3 nm Pa–1. The feasibility of realizing larger membranes with diameters of 300 μm and even higher compliances is shown, although these have lower yields. We present a process for locally growing graphene on a silicon wafer and realizing suspended membranes of patterned graphene across through-silicon holes by bulk micromachining and sacrificial layer etching, such that no transfer is required. This transfer-free method results in a 100% yield for membranes with diameters up to 155 μm on 132 fabricated drums. The device-to-device variations in the mechanical compliance in the audible range (20–20000 Hz) are significantly smaller than those in transferred membranes. With this work, we demonstrate a transfer-free method for realizing wafer-scale multilayer graphene membranes that is compatible with high-volume manufacturing. Thus, limitations of transfer-based methods for graphene microphone fabrication such as polymer contamination, crack formation, wrinkling, folding, delamination, and low-tension reproducibility are largely circumvented, setting a significant step on the route toward high-volume production of graphene microphones.

Thermal and redox properties of Donor–Acceptor foldamers consisting of tetrathiafulvalene and viologen

Donor–acceptor (DA)-type foldamers consisting of tetrathiafulvalene (TTF) and viologen (V2+) units were synthesized. In those foldamers, tri(ethylene glycol)-substituted DA units were alternatively connected via the folding point of catechol. The synthesis of TV2+-2mer, V2+TV2+-3mer, and V2+TV2+TV2+-5mer were confirmed by 1H and 13C NMR and high-resolution ESI-MS spectra. Thermal and electrochemical properties were characterized through temperature-dependent UV–Vis spectroscopy and cyclic voltammetry, respectively. Despite the weak molecular interaction between the tri(ethylene glycol)-substituted TTF and V2+ molecules, the foldamers formed the charge-transfer (CT) complex because of the tethered structure of the DA units on the catechol unit. The melting curve analysis of the polymer folding indicated that the degree of polymer folding was <50% at room temperature due to weak CT interactions. It was confirmed that the thermal stability of the folded state increased with the number of DA units. The oligomers were chemically oxidized, and the changes in their UV–Vis spectra were monitored. For V2+T•+V2+T•+V2+-5mer, intramolecular TTF radical dimer was formed. In the cyclic voltammogram, the redox reactions of the TTF and V2+ units were observed at the positive and negative potentials, respectively. When the V2+ unit was fully reduced to the neutral state, the oligomers became insoluble in acetonitrile. The stepwise conformation change of the V2+TV2+TV2+-5mer (folded, hooped, and extended states) in response to the oxidation states of the TTF unit (neutral, radical cation, and di-cation) was discussed with the help of computational modeling (ONIOM(M06:UFF) method).

Controlling Amphiphilic Polymer Folding beyond the Primary Structure with Protein-Mimetic Di(Phenylalanine).

While methods for polymer synthesis have proliferated, their functionality pales in comparison to natural biopolymers-strategies are limited for building the intricate network of noncovalent interactions necessary to elicit complex, protein-like functions. Using a bioinspired di(phenylalanine) acrylamide (FF) monomer, we explored the impact of various noncovalent interactions in generating ordered assembled structures. Amphiphilic copolymers were synthesized that exhibit β-sheet-like local structure upon collapsing into single-chain assemblies in aqueous environments. Systematic analysis of a series of amphiphilic copolymers illustrated that the global collapse is primarily driven by hydrophobic forces. Hydrogen-bonding and aromatic interactions stabilize local structure, as β-sheet-like interactions were identified via circular dichroism and thioflavin T fluorescence. Similar analysis of phenylalanine (F) and alanine-phenylalanine acrylamide (AF) copolymers found that distancing the aromatic residue from the polymer backbone is sufficient to induce β-sheet-like local structure akin to the FF copolymers; however, the interactions between AF subunits are less stable than those formed by FF. Further, hydrogen-bond donating hydrophilic monomers disrupt internal structure formed by FF within collapsed assemblies. Collectively, these results illuminate design principles for the facile incorporation of multiple facets of protein-mimetic, higher-order structure within folded synthetic polymers.

Organometallic single-chain polymer nanoparticles via intra-chain cross-linking with dinuclear μ-halo(diene)Rh(I) complexes

An approach towards the expansion of Rh(I)-containing single-chain polymer nanoparticles (SCNPs) using linear polymers and μ-halo(diene)Rh(I) dimers as cross-linkers in high dilution was explored. Initially, the effects of utilizing different anionic ligands, i.e., halides, together with various labile alkene ligands, such as ethylene, 1,5-cyclooctadiene and 1,5-hexadiene, on the stability and activity of the resulting Rh(I) cross-linking complexes were examined. While the ethylene complexes for bromide and iodide bridges resulted too unstable and the 1,5-cyclooctadiene ligand produced inert complexes, the 1,5-hexadiene ligands provided the proper equilibrium of stability and lability to achieve efficient polymer folding. Thus, a range of new organometallic nanoparticles could be obtained via a direct exchange between the 1,5-hexadiene labile ligands of the Rh(I) complexes, and the corresponding 1,5-hexadiene elements present in ROMP derived 1,5-polycyclooctadiene (PCOD) and 1,4-polybutadiene (PBD). Notably, SEC analysis of the single-chain nanoparticles both for PCOD and PBD revealed the expected decrease in the hydrodynamic radius (Rh) of the parent polymer, indicating that other anions can also be used as elements in the cross-linking moieties to form these organometallic nanoparticles. Moreover, all of the Rh-SCNPs displayed intrinsic semi-conductivities in the range of similar undoped organic conjugated polymers, expanding the possible uses of this methodology for many applications.

Polymer cyclization for the emergence of hierarchical nanostructures

The creation of synthetic polymer nanoobjects with well-defined hierarchical structures is important for a wide range of applications such as nanomaterial synthesis, catalysis, and therapeutics. Inspired by the programmability and precise three-dimensional architectures of biomolecules, here we demonstrate the strategy of fabricating controlled hierarchical structures through self-assembly of folded synthetic polymers. Linear poly(2-hydroxyethyl methacrylate) of different lengths are folded into cyclic polymers and their self-assembly into hierarchical structures is elucidated by various experimental techniques and molecular dynamics simulations. Based on their structural similarity, macrocyclic brush polymers with amphiphilic block side chains are synthesized, which can self-assemble into wormlike and higher-ordered structures. Our work points out the vital role of polymer folding in macromolecular self-assembly and establishes a versatile approach for constructing biomimetic hierarchical assemblies.