On the conformational structure of a stiff homopolymer

Modulation of flexo-rigid balance in photoresponsive thymine grafted copolymers towards designing smart healable coating

Efficacy and durability of the photovoltaic device mandates its protection against hot, humid weather condition, high energy of UV light and unwanted scratches. Such challenges can be mitigated by smart polymeric coating with inherent properties e.g. hydrophobicity to prevent moisture, optimal viscocity for better processibility and crack-healing. The hydrophobic polymers TP1-TP4 containing pendant photo-crosslinkable thymine moieties are designed that undergo [2 + 2] photocycloaddition upon UVB irradiation and can be dynamically reverted back upon irradiation with UVC light. A judicious control of solvent environment, chain length, functionality% and concentration of the polymers regulate the aspects of photodimerization thereby, rendering intra or inter-chain collapse to form diverse nanostructures. Photodimerization of the thymine moieties renders coil to globule transformation in dilute condition whereas irradiation performed at high macromolecular concentration regime exhibits higher order nanostructures. The photoresponsive chain collapse leads to the formation of rigid crosslinked domains within flexible polymer chains akin to the hard-soft phases of thermoplastic elastomers. Such rigidification of the crosslinked segments endows a tool to photomodulate the glass transition temperature (T g) that can dynamically revert back upon decrosslinking. Further, the structural modulation of the polymers is explored towards autonomic and nonautonomic self-healing behaviour at ambient conditions. Moreover, the self-healing efficacy can be tuned with the film thickness and it remains unaltered upon using solar simulator or direct sunlight. Overall, such hydrophobic low T g polymers display photo-regulated self-healing mechanism consisting of both autonomic and non-autonomic self-healing and may find applications in designing smart protective coatings for photovoltaic devices.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

The phase behavior of polyethylene ring chains

The equilibrium properties of an isolated polyethylene ring chain are studied by using molecular dynamics (MD) simulations. The results of an 80-bond linear chain are also presented, which are in agreement with previous studies of square-well chains and Lennard-Jones (LJ) homopolymers. Mainly, we focus on the collapse of polyethylene ring chains. At high temperatures, a fully oblate structure is observed for the ring chains with different chain lengths. For such an oblate structure, a shape factor of delta(*)=0.25 and a rodlike scaling relation between the radius of gyration and chain lengths could be deduced easily in theory, and the same results are obtained by our MD simulations. Such an oblate structure can be obtained by Monte Carlo simulation only for sufficient stiff ring chains. When the temperature decreases, an internal energy barrier is observed. This induces a strong peak in the heat capacity, denoting a gas-liquid-like transition. This energy barrier comes mainly from the local monomer-monomer interactions, i.e., the bond-stretching, the bond-bending, and the torsion potentials. A low temperature peak is also observed in the same heat capacity curve, representing a liquid-solid-like transition. These numerical simulation results support a two-stage collapse of polyethylene ring chains; however, the nature should be different from the square-well and LJ ring chains.

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.

On the formation of rings-on-a-string conformations in a single polyelectrolyte chain: A possible scenario

Recent single-molecular observations have revealed that a single giant DNA molecule assumes (micro) phase separated structures upon the addition of condensing agents. Electron and atomic force microscopy have clearly shown the coexistence of ordered tori and disordered coil structures within a single DNA molecule. Motivated by these experimental findings, we theoretically investigated the collapse transition of a single polyelectrolyte chain driven by the addition of condensing guest molecules. We found that the transition behavior critically depends on the degree of the surviving charge inside the torus. When the torus is charged, even slightly, "rings-on-a-string" structures are expected for a sufficiently long chain, owing to the combinational entropy of segment state distribution along the chain and the unique property of the stability of charged torus.

Stretching globular polymers. I. Single chains

We review the force-extension behavior of polymers collapsed in poor solvent, modified to include the effects of semiflexibility and considered for globules with "ordered" and "disordered" internal structures. A series of ordered globules is used as a model for the unbinding of a disordered globule beneath its glass transition and for multiple-repeat proteins such as the poly-Ig-domain titin used in atomic force microscopy studies. These single-chain results form the foundation for the treatment of cross-linked networks of globular polymers.

Time study of DNA condensate morphology: implications regarding the nucleation, growth, and equilibrium populations of toroids and rods

It is well known that multivalent cations cause free DNA in solution to condense into nanometer-scale particles with toroidal and rod-like morphologies. However, it has not been shown to what degree kinetic factors (e.g., condensate nucleation) versus thermodynamic factors (e.g., DNA bending energy) determine experimentally observed relative populations of toroids and rods. It is also not clear how multimolecular DNA toroids and rods interconvert in solution. We have conducted a series of condensation studies in which DNA condensate morphology statistics were measured as a function of time and DNA structure. Here, we show that in a typical in vitro DNA condensation reaction, the relative rod population 2 min after the initiation of condensation is substantially greater than that measured after morphological equilibrium is reached (ca. 20 min). This higher population of rods at earlier time points is consistent with theoretical studies that have suggested a favorable kinetic pathway for rod nucleation. By using static DNA loops to alter the kinetics and thermodynamics of condensation, we further demonstrate that reported increases in rod populations associated with decreasing DNA length are primarily due to a change in the thermodynamics of DNA condensation, rather than a change in the kinetics of condensate nucleation or growth. The results presented also reveal that the redistribution of DNA from rods to toroids is mediated through the exchange of DNA strands with solution.

Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

We establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O3 nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter c = (W2l)(L2pi)2. We also discuss the stability of the toroid states and propose the low-energy effective Green's function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.

Stability of toroid and rodlike globular structures of a single stiff-chain macromolecule for different bending potentials

We study the effect of the bending potential on the stability of toroidal and rodlike globules which are typical collapsed conformations of a single stiff-chain macromolecule. We perform numerical calculations in the framework of the bead-stick model of a polymer chain. The intrinsic structure of globules is also analyzed. It was shown that the bending potential affects the packing geometry of bundles in a toroidal globule in the ground state. This potential also influences the bends at the ends of a rodlike globule: both the shape of the loops and the number of bonds in each loop have been investigated numerically as well as by Monte Carlo computer simulations performed for a separate loop. Our main results are (1) the shape of the bending potential could be possibly seen from the geometry of a globule; (2) toroidal globules are always more favorable than the rodlike ones.

Coupling between helix-coil and coil-globule transitions in helical polymers

We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which could be a helix, a random coil, an amorphous globule, or one of various other globular states which carry residual helical strands. We study the boundaries between states and provide further insight into the physics of the system with a detailed analysis of the order parameter and other properties.

Single Molecule Nanoparticles of the Conjugated Polymer MEH−PPV, Preparation and Characterization by Near-Field Scanning Optical Microscopy

We have developed a straightforward method for producing a stable, aqueous suspension of hydrophobic, fluorescent pi-conjugated polymer nanoparticles consisting primarily of individual conjugated polymer molecules. Features of the method are the facile preparation, purity, unique optical properties, and small size (approximately 5-10 nm) of the resulting nanoparticles. The results of TEM, scanning force microscopy, and near-field scanning optical microscopy of particles cast from the suspension indicate that the particles are single conjugated polymer molecules. The NSOM results yield estimates of the optical cross-sections of individual conjugated polymer molecules. The UV-vis absorption spectra of the nanoparticle suspensions indicate a reduction in conjugation length attributed to deformations of the polymer backbone. Fluorescence spectra of the aqueous nanoparticle suspensions indicate interactions between segments of the polymer chain and intramolecular energy transfer.

Toroid formation in charge neutralized flexible or semi-flexible biopolymers: potential pathway for assembly of DNA carriers

BACKGROUND

The theoretical state diagram for semi-flexible macromolecules such as DNA predicts that a tightly wound toroid can be a stable structure. Experimentally, toroids roughly 100 nm in diameter are routinely observed for DNA in the presence of multivalent cations at low DNA concentration. Theory also predicts toroids can form between non-DNA semi-flexible polymers and multivalent counterions. This phenomenon provides a means to co-package DNA with functionalized anionic polymers to create gene delivery systems.

METHODS AND RESULTS

We show using electron microscopy that non-DNA polymers (polylysine, polyglutamic acid, and dextran sulfate) form toroids when mixed with multi- or polyvalent ions of opposite charge. The non-DNA toroids are similar in diameter to ones made with DNA. The results using dextran sulfate, a semi-flexible polymer, are explained by current theory. However, theory predicts that high flexibility in polypeptides should discourage their incorporation into stable toroids. To explain these latter observations we propose that charge neutralization facilitates secondary structure formation, which confers stiffness, thereby allowing stable toroids for the polypeptides studied. We measured the secondary structure of the toroid-forming polypeptides using circular dichroism (CD). The CD spectrum indicates the polypeptides undergo transitions from non-ordered structures (random coil) to ordered secondary structures (either alpha-helix or beta-sheet) upon charge neutralization which supports the hypothesis. The type of secondary structure is dependent on the type of multivalent counterion used to form the toroids. Formation of the polypeptide toroids confers resistance to heat denaturation of the resulting polypeptide secondary structure. The CD spectrum of DNA in a toroid also is changed from that of uncomplexed DNA, but all of the counterions used to form DNA toroids created structures with similar CD spectra in the DNA region (250-290 nm).

CONCLUSIONS

The toroid structure obtained using DNA is observed in other semi-flexible non-DNA polymers such as dextran sulfate, and also in flexible polymers such as polylysine and polyglutamic acid upon charge neutralization with multivalent counterions. In the flexible polymers we propose that this phenomenon is due to induction of secondary structure upon charge neutralization, which decreases polymer flexibility, i.e. increases polymer stiffness, to enable toroid formation. These results have significant implications for the co-assembly of non-DNA anionic polymers with DNA to create nanoscopic gene carriers.

Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions

Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.

Emergence of multiple tori structures in a single polyelectrolyte chain

We investigated the collapsed structure of a weakly charged wormlike chain under a moderate concentration of 1:1 electrolyte solution. By assuming a torus as a grand state, we found that the size of a torus is determined by the balance between surface energy and electrostatic energy, which leads to a finite torus thickness almost independent of the chain contour length. Owing to this unique characteristic, a long charged wormlike chain forms multiple tori structure as a collapsed product, which is never seen with a neutral wormlike chain. These features were confirmed by a Monte Carlo simulation.

Metastable and stable states of xanthan polyelectrolyte complexes studied by atomic force microscopy

The compaction of the semiflexible polysaccharide xanthan with selected multi- and polyvalent cations was studied. Polyelectrolyte complexes prepared at concentrations of 1-2 microg/ml were observed by tapping mode atomic force microscopy. High-molecular-weight xanthan compacted with chitosan yields a blend of mainly toroidal and metastable structures and a small fraction of rod-like species. Polyelectrolyte complexes of xanthan with polyethylenimine and trivalent chromium yielded similar structures or alternatively less well packed species. Racquet-type morphologies were identified as kinetically trapped states occurring on the folding path toward the energetically stable state of the toroids. Thermal annealing yielded a shift of the distribution of xanthan-chitosan morphologies toward this stable state. Ensembles of toroidal and rod-like morphologies of the xanthan-chitosan structures, collected using an asphericity index, were analyzed. The mean height of the toroids increased upon heating, with a selective increase in the height range above 2 nm. It is suggested that the observed metastable structures are formed from the high-molecular-weight fraction of xanthan and that these are driven toward the toroidal state, being a low-energy state, following annealing. Considered a model system for condensation of semiflexible polymers, the compaction of xanthan by chitosan captures the system at various stages in the folding toward a low-energy state and thus allows experimental analyses of these intermediates and their evolution.

Thermodynamical properties of simple models of protein-like heteropolymers

The lattice approximation of a heteropolymer chain as a model of a single polypeptide was used in the computer simulation. The residues of a model polypeptide were represented by the chain of alpha-carbons located on a very flexible [310] lattice. The force field that mimic the intramolecular interactions contained the long-range contact potential between the residues and the local preferences in forming helical structures. The chain consisted of two types of residues that had different hydrophobicity. The simulations were performed by means of the Replica Exchange Monte Carlo method combined with the Histogram method. The series of simulations were carried out to investigate the influence of both components of the force field on the transition temperature and the characteristics of the coil-to-globule transition. The properties of low-temperature ordered structures were determined. The thermodynamical description of the model chain was also given. The phase transition was found to be sharp and cooperative for longer chains and strong helical potential. The collapsed globule contained the strongly hydrophobic residues inside the globule while the remaining residues were mainly located close to the globule surface.

Cryoelectron microscopy of lambda phage DNA condensates in vitreous ice: the fine structure of DNA toroids

DNA toroids produced by the condensation of lambda phage DNA with hexammine cobalt (III) have been investigated by cryoelectron microscopy. Image resolution obtained by this technique has allowed unprecedented views of DNA packing within toroidal condensates. Toroids oriented coplanar with the microscope image plane exhibit circular fringes with a repeat spacing of 2.4 nm. For some toroids these fringes are observed around almost the entire circumference of the toroid. However, for most toroids well-defined fringes are limited to less than one-third of the total toroid circumference. Some toroids oriented perpendicular to the image plane reveal DNA polymers organized in a hexagonal close-packed lattice; however, for other toroids alternative packing arrangements are observed. To aid interpretation of electron micrographs, three-dimensional model toroids were generated with perfect hexagonal DNA packing throughout, as well as more physically realistic models that contain crossover points between DNA loops. Simulated transmission electron microscopy images of these model toroids in different orientations faithfully reproduce most features observed in cryoelectron micrographs of actual toroids.

Unmasking electronic energy transfer of conjugated polymers by suppression of O(2) quenching

The photochemistry of poly[2-methoxy, 5-(2'-ethyl-hexyloxy)-p-phenylene-vinylene] (MEH-PPV) has been found to be highly dependent on the presence of O(2), which increases singlet exciton quenching dramatically. Spectroscopy on isolated single molecules of MEH-PPV in polycarbonate films that exclude O(2) reveals two distinct polymer conformations with fluorescence maxima near 555 and 580 nanometers wavelength, respectively. Time-resolved single-molecule data demonstrate that the 580-nanometer conformation exhibits a "landscape" for intramolecular electronic energy relaxation with a "funnel" that contains a 580-nanometer singlet exciton trap at the bottom. The exciton traps can be converted to exciton quenchers by reaction with O(2). Conformationally induced, directed-energy transfer is arguably a critical dynamical process that is responsible for many of the distinctive photophysical properties of conjugated polymers.

Collapse of stiff conjugated polymers with chemical defects into ordered, cylindrical conformations

The optical, electronic and mechanical properties of synthetic and biological materials consisting of polymer chains depend sensitively on the conformation adopted by these chains. The range of conformations available to such systems has accordingly been of intense fundamental as well as practical interest, and distinct conformational classes have been predicted, depending on the stiffness of the polymer chains and the strength of attractive interactions between segments within a chain. For example, flexible polymers should adopt highly disordered conformations resembling either a random coil or, in the presence of strong intrachain attractions, a so-called 'molten globule'. Stiff polymers with strong intrachain interactions, in contrast, are expected to collapse into conformations with long-range order, in the shape of toroids or rod-like structures. Here we use computer simulations to show that the anisotropy distribution obtained from polarization spectroscopy measurements on individual poly[2-methoxy-5-(2'-ethylhexyl)oxy-1,4-phenylenevinylene] polymer molecules is consistent with this prototypical stiff conjugated polymer adopting a highly ordered, collapsed conformation that cannot be correlated with ideal toroid or rod structures. We find that the presence of so-called 'tetrahedral chemical defects', where conjugated carbon-carbon links are replaced by tetrahedral links, divides the polymer chain into structurally identifiable quasi-straight segments that allow the molecule to adopt cylindrical conformations. Indeed, highly ordered, cylindrical conformations may be a critical factor in dictating the extraordinary photophysical properties of conjugated polymers, including highly efficient intramolecular energy transfer and significant local optical anisotropy in thin films.