Folding a nonbiological polymer into a compact multihelical structure

The only molecules that are currently known to fold into unique three-dimensional conformations and perform sophisticated functions are biological polymers - proteins and some RNA molecules. Our aim is to create a nonbiological sequence-specific polymer that folds in aqueous solution. Toward that end, we synthesized sequence-specific 30mer, 45mer, and 60mer peptoid oligomers (N-substituted glycine polymers) consisting of 15mer units we chained together by disulfide and oxime linkages to mimic the helical bundle structures commonly found in proteins. Because these 15mer sequences were previously shown to form defined helical structures that aggregate together at submillimolar concentrations, we expected that by covalently linking multiple 15mers together, they might fold as helical bundles. To probe whether they folded, we used fluorescence resonance energy transfer (FRET) reporter groups. We found that certain constructs fold up with a hydrophobic core and have cooperative folding transitions. Such molecules may ultimately provide a platform for designing specific functions resembling those of proteins.     

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.     

Folding of ubiquitin: a simple model describes the strange kinetics

The ubiquitin mutant UbG folding experiments of Sabelko et al., in which "strange kinetics" were observed, are interpreted in terms of a simple kinetic model. A minimal set of states consisting of a semicompact globule, two off-pathway traps, and the native state are included; the fully unfolded state is not considered because folding to the semicompact globule is fast. Both the low- and the high-temperature experiments of Sabelko et al. are fitted by a system of kinetic equations determining the transitions between these states. It is possible that cold- and heat-denaturated states of UbG are the basis of the off-pathway traps. The fits of the kinetic model to the experimental results provides an estimate of the rate constants for the various reaction channels and show how their contributions vary with temperature. Introduction of an on-pathway intermediate instead of one of the off-pathway traps does not lead to agreement with the experiments.     

Folding time distributions as an approach to protein folding kinetics

A 27-residue lattice heteropolymer subject to Monte Carlo dynamics on a simple cubic lattice is studied over a range of temperatures. Folding time distributions are used to obtain information concerning the details of folding kinetics. The results are compared with those from methods based on mean force surfaces expressed in terms of a reduced set of variables and on a disconnectivity graph for the same system. A detailed analysis of the folding trajectories is given, and the importance of dead-end traps in determining the folding time is demonstrated. We show that the calculated folding kinetics can be modeled by a system of kinetic equations, with the essential rate constants determined from the Monte Carlo simulations and the resulting folding time distributions. The kinetic equations make possible an analysis of the variation of the importance of different channels with temperature. In particular, we show that the presence of intermediates may be masked in the folding time distributions, with the mean folding time being independent of the height of the barrier between the intermediates and collapsed globule state of the system. This and other results demonstrate that care has to be used in interpreting experimental folding data in terms of the underlying kinetics. Correspondingly, simulations are shown to have to satisfy certain requirements to obtain proper sampling of the dead-end traps.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Crystallization kinetics in relation to polymer processing

Phase distribution of quenched samples has been determined by a deconvolution procedure of WAXS spectra in a wide range of cooling rates. The informations collected together with isothermal and DSC results provide a very wide set of data on the crystallization kinetics of polymers relevant which covers conditions encountered in most polymer processing operations. They have been compared with predictions of a non-isothermal crystallization model assuming two independent and parallel crystallization processes competing during solidification.     

Temperature effects for isothermal polymer crystallization kinetics

We adopt the cluster size distribution model to investigate the effect of temperature on homogeneous nucleation and crystal growth for isothermal polymer crystallization. The model includes the temperature effects of interfacial energy, nucleation rate, growth and dissociation rate coefficients, and equilibrium solubility. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different temperatures. The denucleation (Ostwald ripening effect) is also investigated by comparing moment and numerical solutions of the population balance equations. Agreement between the model results and temperature-sensitive experimental measurements for different polymer systems required strong temperature dependence for the crystal-melt interfacial energy.     

On the kinetics of polymer degradation in solution

Poly(2,2,2-trichloroethyl methacrylate), PTCMA, was irradiated in dilute dichloromethane solution with 16 MeV electron pulses of^{6 0}Co γ-rays. Both in the presence and absence of O₂, G(S)=9–10 was found at [PTCMA]<9 g/dm³. Indirect and direct radiation effects contributed to main-chain scission at a ratio of 7∶3. In contrast to earlier findings with dioxane solutions, at concentrations of up to 20 g/dm³ indications of crosslinking were not obtained. With CH₂Cl₂ solutions two modes of light scattering intensity (LSI) decrease were detected indicating the existence of two different macroradicals, one generated by the direct and the other by the indirect action of radiation. These radicals decayed with rate constants of 1.0·10³ s^?1 and 1.4·10¹ s^?1 and also reacted with C₂H₅SH with rate constants of 8·10⁴M^?1·s^?1 and 1·10³M^?1·s^?1, respectively. In O₂-saturated solutions both radicals formed peroxyl radicals, PO₂, wich combined generating products whose decomposition involved main-chain scission. The combination of PO₂-radicals was rate-determining in the consecutive series of reactions as inferred from the 2nd order decrease of the LSI.     

Folding kinetics of a naturally occurring helical peptide: implication of the folding speed limit of helical proteins

The folding mechanism and dynamics of a helical protein may strongly depend on how quickly its constituent alpha-helices can fold independently. Thus, our understanding of the protein folding problem may be greatly enhanced by a systematic survey of the folding rates of individual alpha-helical segments derived from their parent proteins. As a first step, we have studied the relaxation kinetics of the central helix (L9:41-74) of the ribosomal protein L9 from the bacterium Bacillus stearothermophilus , in response to a temperature-jump ( T-jump) using infrared spectroscopy. L9:41-74 has been shown to exhibit unusually high helicity in aqueous solution due to a series of side chain-side chain interactions, most of which are electrostatic in nature, while still remaining monomeric over a wide concentration range. Thus, this peptide represents an excellent model system not only for examining how the folding rate of naturally occurring helices differs from that of the widely studied alanine-based peptides, but also for estimating the folding speed limit of (small) helical proteins. Our results show that the T-jump induced relaxation rate of L9:41-74 is significantly slower than that of alanine-based peptides. For example, at 11 degrees C its relaxation time constant is about 2 micros, roughly seven times slower than that of SPE(5), an alanine-rich peptide of similar chain length. In addition, our results show that the folding rate of a truncated version of L9:41-74 is even slower. Taken together, these results suggest that individual alpha-helical segments in proteins may fold on a time scale that is significantly slower than the folding time of alanine-based peptides. Furthermore, we argue that the relaxation rate of L9:41-74 measured between 8 and 45 degrees C provides a realistic estimate of the ultimate folding rate of (small) helical proteins over this temperature range.     

Cure kinetics of epoxy resin and thermoplastic polymer

The cure kinetics and morphology of diglycidyl ether of bisphenol A (DGEBA) modified with polyvinyl acetate (PVAc) using diaminodiphenylmethane (DDM) as hardener were investigated through differential scanning calorimetry (DSC) and environmental scanning electron microscopy (ESEM). Isothermal curing measurements were carried out at 150, 120 and 80°C. The kinetic parameters were obtained using the general autocatalytic chemically controlled model. The comparison of the kinetic data indicates that the presence of PVAc does not change the autocatalytic nature of the cure reaction. Two T _g’s were observed in the fully cured samples of the modified systems. ESEM micrographies confirm the biphasic morphology.     

Phase behavior and photocrosslinking kinetics of semi-interpenetrating polymer networks prepared from miscible polymer blends

Mixtures of polystyrene derivatives (PSCS) and poly(vinyl methyl ether) (PVME) were made photocrosslinkable by chemically labeling PSCS chains with photoreactive anthracene. Miscibility of these anthracene-labeled PSCS/PVME blends was examined by light scattering under several crosslinking conditions in the one-phase region via photodimerization of anthracenes. As the reaction proceeds, the coexistence curve of PSCS/PVME blends shifts toward the low temperature side. By following the changes in concentration of anthracenes with irradiation time, it was found that the crosslinking reaction of PSCS chains in the blends does not follow the mean-field kinetics. However, it can be well expressed by the Kohlrausch–Williams–Watts (KWW) relaxation mechanism, indicating that the crosslinking reaction proceeds inhomogeneously in the blends. By scaling the reaction time with the average reaction rate obtained from the KWW equation modified for the reaction kinetics, all the crosslinking data obtained in the miscible region of the reacted blends fall on a single master curve. These experimental results suggest the universal behavior of the photocrosslinking kinetics obtained under the “shallow quench” conditions in the region far away from the coexistence curve of the reacting blends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 455–462, 1998     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

The kinetics of KNO3 sorption by crown-containing polymer

The kinetics of sorption of KNO₃ from aqueous solutions by a granulated polymer containing fragments of dibenzo-18-crown-6 was studied. Internal diffusion of the electrolyte in the polymer was shown to be a rate-limiting step of sorption of KNO₃. The effective coefficient of diffusion of the electrolyte in the polymer was calculated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1549–1551, August, 1997.     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

Folding and unfolding kinetics of DNA hairpins in flowing solution by multiparameter fluorescence correlation spectroscopy

Dynamic equilibrium between the folded and unfolded conformations of single stranded DNA hairpin molecules containing polythymine hairpin loops was investigated using simultaneous two-beam fluorescence cross-correlation spectroscopy and single beam autocorrelation spectroscopy. The hairpins were end-labeled with a fluorescent dye and a quencher, such that folding and unfolding of the DNA hairpin primary structure caused the dye fluorescence to fluctuate on the same characteristic time scale as the folding and unfolding reaction. These fluctuations were observed as the molecules flowed sequentially between two spatially offset, microscopic detection volumes. Cross-correlation analysis of fluorescence from the two detection volumes revealed the translational diffusion and flow properties of the hairpins, as well as the average molecular occupancy of the two volumes. Autocorrelation analysis of the fluorescence from the individual detection volumes revealed the kinetics of hairpin folding and unfolding, with the parameters relating to diffusion, flow, and molecular occupancy constrained to the values determined from the cross-correlation analysis. This allowed unambiguous characterization of the folding and unfolding kinetics, without the need to determine the hydrodynamic properties by analyzing a separate control sample. The analysis revealed nonexponential relaxation kinetics and DNA size-dependent folding times characteristic of dynamic heterogeneity in the DNA hairpin-forming mechanism.     

磁场影响聚合物本体结晶动力学的机理分析

在经典的热力学理论基础上,探讨了磁场对聚合物本体结晶过程的成核与生长的影响,建立了相关结晶动力学理论方程.初步认为,磁场产生的＂磁结晶效应＂可能是由于晶相与非晶相之间磁化率差异导致了两相之间磁化能的差异,也可能由于聚合物体系在结晶前会形成一种有序相,减小了体系的熵值,进而改变了结晶过程中的体系自由能,影响其成核与晶体生长,乃至整个结晶动力学方程.利用Matlab软件结合PLLA的各结晶参数值,绘制了结晶自由能与各成核临界参数之间的函数图像.结果表明,在低过冷度下,较小的自由能扰动可能导致较大的晶核临界参数变化.     

Crosslinking kinetics studies on interpenetrating polymer network powder coatings

IPN powder coatings were prepared which were composed of (A) a pendant double bond-containing acrylic resin made by reacting m-isopropenyl-α-α-dimethylbenzyl isocyanate (TMI) and a hydroxyl-containing acrylic resin and (B) a bisphenol type epoxy resin of high molecular weight cured by means of a carboxylic acid-containing acrylic resin. Crosslinking kinetics studies were carried out by using a computerized differential scanning calorimeter (DSC). A computer program was designed to simulate the curing reactions of the IPN powder coatings by using the individual kinetic parameters obtained from DSC. The simulated results from the computer program are very close to the results from experimental thermograms (by DSC). Therefore, this methodology provides an efficient tool to simplify and predict kinetic studies of crosslinking reactions in current or new IPN powder coating systems.