Theory of the rod-to-coil transition in polydiacetylene

A theory is proposed for the rod to coil transition in polydiacetylene 4BCMU and related polymers which is based on the hypothesis that the high-temperature (yellow) phase consists predominantly of the cis structure, while the low-temperature (red) phase is trans. Because the occurrence of a cis-trans interface is energetically costly, the correlation length for either isomer remains long and the transition is sharp, much like the helix-coil transition in the theory of Zimm and Bragg. The transition is driven by the higher entropy of the cis isomer, which is free to coil, unlike the trans or butatriene forms. The theory gives excellent agreement with optical absorption measurements and is consistent with all other experimental data for this system.     

Empirical force-field assessment: The interplay between backbone torsions and noncovalent term scaling

The kinetic and thermodynamic aspects of the helix-coil transition in polyalanine-based peptides have been studied at the ensemble level using a distributed computing network. This study builds on a previous report, which critically assessed the performance of several contemporary force fields in reproducing experimental measurements and elucidated the complex nature of helix-coil systems. Here we consider the effects of modifying backbone torsions and the scaling of noncovalent interactions. Although these elements determine the potential of mean force between atoms separated by three covalent bonds (and thus largely determine the local conformational distributions observed in simulation), we demonstrate that the interplay between these factors is both complex and force field dependent. We quantitatively assess the heliophilicity of several helix-stabilizing potentials as well as the changes in heliophilicity resulting from such modifications, which can "make or break" the accuracy of a given force field, and our findings suggests that future force field development may need to better consider effect that vary with peptide length. This report also serves as an example of the utility of distributed computing in analyzing and improving upon contemporary force fields at the level of absolute ensemble equilibrium, the next step in force field development.     

激光光散射研究聚(N-异丙基丙烯酰胺)单链及其智能凝胶微球在水中的相变(下)

（接上期）２聚（Ｎ－异丙基丙烯酰胺）微凝胶在水中的体积相变２．１理论部分凝胶体积相变热力学：聚合物凝胶的溶胀和蜷缩可以用膨胀因子α＝（Ｖ／Ｖ０）１／３＝（ΦＴ／ΦΘ）１／３来表征，其中ΦΘ的ΦＴ分别是温度Θ和Ｔ下凝胶网络的体积分数。在平均场理论中，中...     

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.     

Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram

The coil-globule transition in rigid-chain amphiphilic macromolecules was studied by means of computer simulation, and the phase diagrams for such molecules in the solvent quality-persistence length coordinates were constructed. It was shown that the type of phase diagram depends to a substantial extent on the degree of polymerization of a macromolecule. Relatively short amphiphilic macromolecules in the poor-solvent region always form a spherical globule, with the transition to this globule involving one or two intermediate conformations. These are the disk globule if the Kuhn segment is relatively large and the string of spherical micelles or the disk globule in the case of relative flexible chains. The phase diagram of a long rodlike amphiphilic chain turned out to be even more complex. Namely, three characteristic regions were distinguished in the region of a poor solvent, depending on the chain rigidity: the region of a cylindrical globule without certain order in the main chain, the region of the cylindrical globule with blobs having the collagen ordering of the chain, and the region of coexistence of collagen-like and toroidal globules. In the intermediate transitional region, not only conformations of strings of spherical micelle beads but also the necklace conformations in which the polymer chain in each bead has collagen ordering can occur in this case.     

Side-chain and backbone ordering in homopolymers

In order to study the relation between backbone and side-chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu(10), Gln(10), Asp(10), Asn(10), and Lys(10) were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e., Glu(10), and Gln(10), exhibit a second transition at lower temperatures connected with side-chain ordering. This occurs in the gas phase as well as in solvent, although the character of the side-chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e., Asp(10) and Asn(10), side-chain ordering takes place over a wide temperature range and exhibits no phase transition-like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side-chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side-chain ordering in Lys(10), whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition-like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.     

Proton transfer-induced conformational changes and melting in designed peptides in the gas phase

The conformations of protonated RA15K, RA20K and RA15H (R = arginine, A = alanine, K = lysine, and H = histidine) have been examined in the gas phase as a function of temperature. These peptides were designed so that intramolecular proton transfer will trigger conformational changes between a helix (proton sequestered at the C-terminus) and globule (proton sequestered at the N-terminus). Kinetically controlled structural transitions occur below 400 K (from helix to globule for RA15H, and from globule to helix for RA15K and RA20K). As the temperature is raised, the compact globule found at room temperature expands, accesses more configurations, and becomes entropically favored. At around 500 K, the RA15K and RA20K helices undergo a melting transition. The transition is broad, as expected for a phase transition in a finite system, and becomes narrower as the peptide size increases. In the helical conformation, the two basic residues are well separated; as a result, the proton transfer necessary to drive the melting transition probably involves a mobile proton. For doubly protonated RA15K, a dumbbell-like conformation (resulting from repulsion between the two protonated basic residues) is found at high temperature.     

Temperature-dependent helix-coil transition of an alanine based peptide

The helix-coil transition of a synthetic alpha-helical peptide (the D-Arg peptide), Ac-YGG(KAAAA)(3)-CO-D-Arg-CONH(2), was studied by static far-UV circular dichroism (CD) and time-resolved infrared spectroscopy coupled with the laser-induced temperature-jump technique for rapid relaxation initiation. Equilibrium thermal unfolding measurements of the D-Arg peptide monitored by CD spectroscopy reveal an apparent two-state helix-coil transition, with a thermal melting temperature around 10 degrees C. Time-resolved infrared (IR) measurements following a laser-induced temperature jump, however, reveal biphasic (or multiphasic) relaxation kinetics. The fast phase rises within the 20 ns response time of the detection system. The slow phase has a decay lifetime of approximately 140 ns at 300 K and exhibits monotonic temperature dependence with an apparent activation energy around 15.5 kcal/mol.     

Effect of low-molecular impurity on the melting of DNA-type macromolecules

Thermodynamics of the melting of a DNA-type macromolecule is studied theoretically. Elements of the macromolecule are able to annex a low-molecular impurity from the solvent (e.g., metal ions). Two models of the annexing of the impurity to the macromolecule are analyzed. It is shown that the concentration dependence of the helix-coil phase transition temperature is describable by a non-monotonic function in the case of certain relations between parameters.     

Microphase Separation within a Comb Copolymer with Attractive Side Chains: A Computer Simulation Study

Computer simulation modelling of a flexible comb copolymer with attractive interactions between the monomer units of the side chains is performed. The conditions for the coil‐globule transition, induced by the increase of attractive interaction, ε, between side chain monomer units, are analysed for different values of the number of monomer units in the backbone, N, in the side chains, n, and between successive grafting points, m. It is shown that the coil‐globule transition of such a copolymer corresponds to a first‐order phase transition. The energy of attraction (ε) required for the realisation of the coil‐globule transition decreases with increasing n and decreasing m. The coil‐globule transition is accompanied by significant aggregation of side chain units. The resulting globule has a complex structure. In the case of a relatively short backbone (small value of N), the globule consists of a spherical core formed by side chains and an enveloping shell formed by the monomer units of the backbone. In the case of long copolymers (large value of N), the side chains form several spherical micelles while the backbone is wrapped on the surfaces of these micelles and between them.     

Diagram of State of Stiff Amphiphilic Macromolecules

Summary: We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of polymerization. Relatively short amphiphilic molecules always form a spherical globule in a poor solvent, and the coil-globule transition includes one or two intermediate conformations, depending on the chain's stiffness. These are a disk-like globule in case of high enough Kuhn segment length, and a pearl necklace-like structure of spherical micelles and a disk-like globule in case of relatively flexible chains. The phase diagram of a long stiff amphiphilic chain was found to be more complex still. Thus three specific regions can be distinguished in the poor solvent region, depending on the chain stiffness. These correspond to a cylindrical globule without any specific backbone ordering, a cylindrical globule containing blobs with collagen-like ordering of the chain, and co-existence of collagen-like and toroidal globules. In the intermediate transition region in this case, apart from the pearl necklace-like conformations with spherical micelles, necklace conformations can be also observed where the polymeric chain has collagen-like ordering within each bead.     

Conformational relaxation dynamics of a poly(N-isopropylacrylamide) aqueous solution measured using the laser temperature jump transient grating method

We observed phase transition and phase relaxation processes of a poly(N-isopropylacrylamide) (PNIPAM) aqueous solution using the heterodyne transient grating (HD-TG) method combined with the laser temperature jump technique. The sample temperature was instantaneously raised by about 1.0 K after irradiation of a pump pulse to crystal violet (CV) molecules for heating, and the phase transition was induced for the sample with an initial temperature just below the lower critical solution temperature (LCST); the following phase relaxation dynamics was observed. Turbidity relaxation was observed in both the turbidity and HD-TG responses, while another relaxation process was observed only in the HD-TG response, namely via the refractive index change. It is suggested that this response is due to formation of globule molecules or their assemblies since they would have nothing to do with turbidity change but would affect the refractive index, which is dependent on the molar volume of a chemical species. Furthermore, the grating spacing dependence of the HD-TG responses suggests that the response was caused by the counter propagating diffusion of the coil molecules as a reactant species and the globule molecules as a product species and the lifetime of the globule molecules ranged from 1.5 to 5 seconds. Thus, we conclude that the turbidity reflects the dynamics of aggregate conditions, not molecular conditions. The coil and globule sizes were estimated from the obtained diffusion coefficient. The sizes of the coil molecules did not change at the initial temperatures below the LCST but increased sharply as it approaches LCST. We propose that the coil-state molecules associate due to hydrophobic interaction when the initial temperature was higher than LCST minus 0.5 K and that the globule-state molecules generated from the coil-state molecules showed a similar trend in temperature. The phase transition was also induced by heating under a microscope, and the relaxation process was followed using the fluorescence peak shift of a fluorescent molecule-labeled PNIPAM. The result also supports the existence of a globule molecule or its assembly remains for several seconds in the phase relaxation.     

Coupling between transport phenomena and conformational transitions: Isothermal water transport and “asymmetric osmotic pressure” across a “membrane phase” promoted by a helix-coil transition

A membrane system is described consisting of an aqueous concentrated solution of poly-L-lysine bounded by two rigid conventional membranes permeable to water and to small ions but impervious to the polymer. When a large and steady pH difference is maintained between two external isoosmotic solutions α and β, a vertical volume flow may be observed from the acid solution to the basic solution across the membrane. The flow may give rise to a pressure difference between the basic and the acid solution corresponding to a non-equilibrium steady state of the system. These effects, first reported by Liquori et al. [1] are extensively analyzed from a thermodynamic point of view.It is shown that the pH gradient across the membrane maintains a conformational gradient of poly-L-lysine which is known to undergo a pH regulated helix-coil transition. The latter gradient in turn determines a gradient of chemical potential of water within the membrane phase acting as the main driving force of the volume flow.Using the flux equations of irreversible thermodynamics in connection with a model of helix-coil transition proposed by the author [3,4] compact equations are derived for the isobaric volume flow across the membrane phase and the steady state osmotic pressure in agreement with the experimental results.Possible implications of this study in connection with active transport phenomena across biological membranes are discussed.     

Mechanical Unfolding of a Homopolymer Globule: Applied Force versus Applied Deformation

We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force the globule unfolds as a whole without formation of an intermediate state. The value of the threshold force and the corresponding jump in the distance between chain ends increase with a deterioration of the solvent quality and / or with an increase in the degree of polymerization. This way of globule unfolding is compared with that in the D-ensemble, when the distance between chain ends is imposed.     

The effect of surface treatment on the alignment and phase transition of a polypeptide liquid crystal

Poly(γ-benzyl-L-glutamate) (PBLG), was utilized as a surface coating agent in order to obtain parallel molecular orientation in thin layers of PBLG liquid-crystalline solutions confined between coated surfaces. It was found that in a thickness range much larger than the cholesteric pitch value, the texture was predominantly planar cholesteric. At film thickness comparable or smaller than the pitch, isotropic spherulites developed from a homeotropic nematic phase. Because of the coupling between the solution concentration and nematic director, as well as large differences in the elastic moduli of PBLG liquid-crystalline solutions, the long-range intermolecular interaction was unfavorable. Competition between parallel orientation induced by the surface coating of PBLG and inherent perpendicular orientation induced by PBLG molecules in the bulk would favor a short-range helix-coil transition mechanism, which results into a reentrant isotropic phase.     

Thermodynamics of the DNA helix-coil transition

The thermodynamics of the DNA helix-coil transition is studied, starting from the thermodynamical potential difference between the states helix and coil; this potential difference is understood as the difference in free energies. With only three parameters obtained from experimental data different quantities of the T₂ phage DNA molecule are calculated. It is observed that the phase transition is of second order.     

Knots in globule and coil phases of a model polyethylene

We examine the statistics of knots with numerical simulations of a simplified model of polyethylene. We can simulate polymers of up to 1000 monomers (each representing roughly three CH(2) groups), at a range of temperatures spanning coil (good solvent) and globule (bad solvent) phases. We quantify the abundance of knots in the globule phase and in confined polymers, and their rarity in the swollen phase. Since our polymers are open, we consider (and test) various operational definitions for knots, which are rigorously defined only for closed chains. We also associate a typical size with individual knots, which are found to be small (tight and localized) in the swollen phase but large (loose and spread out) in the dense phases.     

Fine structure and formation mechanism of particulate phase‐inversion poly(vinylidene fluoride) membranes

The structure and formation mechanism of a microporous phase‐inversion poly(vinylidene fluoride) (PVDF) membrane exhibiting a relatively loosely packed agglomerate of semicrystalline globules are explored. The membrane has been prepared by the coagulation of a solution of PVDF in dimethylformamide by the action of 1‐octanol, which is a soft nonsolvent. Experimental observations pertain to the globule surface, which is dominated by a grainy nanostructure; the globular interior, which exhibits a range of fine structures (e.g., twisted sheets and treelike branches); and the globule–globule connections, which exhibit a sheetlike or ropelike structure. On the basis of the observed structural details and phase diagram considerations, it is proposed that the membrane structure is the result of a unique combination of a polymer crystallization and a liquid–liquid phase‐separation process, with end‐result globular structural features of remarkable uniformity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1578–1588, 2003     

Phase behavior in thin films of cylinder-forming ABA block copolymers: mesoscale modeling

The phase behavior of cylinder-forming ABA block copolymers in thin films is modeled in detail using dynamic density functional theory and compared with recent experiments on polystyrene-block-polybutadiene-block-polystyrene triblock copolymers. Deviations from the bulk structure, such as wetting layer, perforated lamella, and lamella, are identified as surface reconstructions. Their stability regions are determined by an interplay between surface fields and confinement effects. Our results give evidence for a general mechanism governing the phase behavior in thin films of modulated phases.     

Macromolecules in a blend of poor and amphiphilic solvents

The globular state of the homopolymer macromolecule in a blend composed of a poor solvent and an amphiphilic solvent (substrate), whose molecules tend to be aligned with the solvent concentration gradient in the inhomogeneity region, was theoretically studied. The size of a homogeneous globule and the substrate concentration in its volume were calculated in terms of a bulk approximation. After the transition of the macromolecule from the coil to the globule state, its volume first decreases with a decrease in temperature and then begins to grow due to substrate molecules penetrating the globule. The substrate concentration in the globule insignificantly exceeds that outside the globule at identical second virial coefficients of interaction between monomer units and between substrate molecules. The expression for the free energy functional depending on the volume fractions of the components and on the orientation of substrate molecules was examined in the ground-state approximation. The orientation effect leads to narrowing of the surface layer and to a decrease in the surface tension of the homogeneous globule, thereby increasing its stability with respect to the transition to the unfolded-coil state.