Chain Fluctuations Research Articles

Dielectric Relaxation of Monodisperse Linear Polyisoprene: Contribution of Constraint Release

cis-Polyisoprene (PI) has the type A dipole parallel along the chain backbone so that the end-to-end fluctuation of PI chains results in slow dielectric relaxation. Comparison of dielectric and viscoelastic data of PI has revealed several interesting features related to the entanglement dynamics, for example, success and failure of the full dynamic tube dilation (DTD) picture for monodisperse linear and star PI, respectively [see a review: Watanabe, H. Polym. J. 2009, 41, 929, for example]. For monodisperse linear PI, recent modeling [Glomann et al. Macromolecules 2011, 44, 7430] and single-chain slip-link simulation [Pilyugina et al. Macromolecules 2012, 45, 5728] suggest that the constraint release (CR) mechanism has negligible influence on the dielectric relaxation time τe in the entangled regime, which appears to disagree with the previous data. Thus, we revisited the classical problem: CR contribution to the dielectric relaxation of PI. Specifically, we made dielectric and viscoelastic measurements f...

One dimensional iron molybdophosphate anionic chains with different structural arrangements reflecting a flexibility character

Structural comparison of a new compound [(bpp)3H6]Fe2 IIIFe2 IIMo24 V(H2PO4)8(HPO4)4(PO4)4O48(OH)12· (H2O)4·2H2O(1)[bpp=1,3-di(4-pyridyl)propane] with our previously reported two compounds [(bpy)3FeII]3sdFe2 IIIFe2 IIMo24 V(H2PO4)8(HPO4)4(PO4)4O48(OH)12(H2O)4·12H2O(2) and [(bpy)3FeII]2FeIIFeIIIMo12 V(H2PO4)2(H2−x PO4)·(H1+x PO4)(HPO4)2(PO4)2O24(OH)6(H2O)2·9H2O(x=0-21)(3)(bpy=2,2′-bipyridine), which all exhibit one-dimensional mixed-valence iron molybdophosphate anionic chains constructed by alternating connection of FeIII ions and magic [FeII(Mo6P4O31)2] units, reveals that the non-hydrogen atomic ratios of Mo:Fe:P:O within the polymeric anionic chains are the same for all the three compounds, while the polymeric anionic chains of the different compounds bear different numbers of negative charges. And therefore there exist different numbers of counter cations per {Fe2 III[Fe2 II(P16Mo24 VO124)]} unit found in the titled compounds. It discloses that not only are the spatial assembling of counter cations and polymeric inorganic chains of three compounds quite different, but also the O—FeIII—O bond angles and FeIII—O bond lengths of the three different inorganic chains exhibit small differences. What is more important is that such small changes in bond length and bond angle in the assemblage of FeIII—O bonds lead to the considerable fluctuations of inorganic chains in their structural conformation within the three compounds, reflecting an interesting phenomenon of “flexibility” in the pure inorganic one dimensional mixed-valence iron molybdophosphate chains.

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments [B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential.

TRAPP: A Tool for Analysis ofTransient BindingPockets inProteins

We present TRAPP (TRAnsient Pockets in Proteins), a new automated software platform for tracking, analysis, and visualization of binding pocket variations along a protein motion trajectory or within an ensemble of protein structures that may encompass conformational changes ranging from local side chain fluctuations to global backbone motions. TRAPP performs accurate grid-based calculations of the shape and physicochemical characteristics of a binding pocket for each structure and detects the conserved and transient regions of the pocket in an ensemble of protein conformations. It also provides tools for tracing the opening of a particular subpocket and residues that contribute to the binding site. TRAPP thus enables an assessment of the druggability of a disease-related target protein taking its flexibility into account.

Spin Density Wave Fluctuations andp-Wave Pairing inSr2RuO4

Recently, a debate has arisen over which of the two distinct parts of the Fermi surface of Sr(2)RuO(4) is the active part for the chiral p-wave superconductivity exhibited. Early theories proposed p-wave pairing on the two-dimensional γ band, whereas a recent proposal focuses on the one-dimensional (α, β) bands whose nesting pockets are the source of the strong incommensurate spin density wave (SDW) fluctuations. We apply a renormalization group theory to study quasi-one-dimensional repulsive Hubbard chains and explain the form of SDW fluctuations, reconciling the absence of long-range order with their nesting Fermi surface. The mutual exclusion of p-wave pairing and SDW fluctuations in repulsive Hubbard chains favors the assignment of the two-dimensional γ band as the source of p-wave pairing.

Entropic Fluctuations in XY Chains and Reflectionless Jacobi Matrices

We study the entropic fluctuations of a general XY spin chain where initially the left(x<0)/right(x>0) part of the chain is in thermal equilibrium at inverse temperature Tl/Tr. The temperature differential results in a non-trivial energy/entropy flux across the chain. The Evans-Searles (ES) entropic functional describes fluctuations of the flux observable with respect to the initial state while the Gallavotti-Cohen (GC) functional describes these fluctuations with respect to the steady state (NESS) the chain reaches in the large time limit. We also consider the full counting statistics (FCS) of the energy/entropy flux associated to a repeated measurement protocol, the variational entropic functional (VAR) that arises as the quantization of the variational characterization of the classical Evans-Searles functional and a natural class of entropic functionals that interpolate between FCS and VAR. We compute these functionals in closed form in terms of the scattering data of the Jacobi matrix h canonically associated to the XY chain. We show that all these functionals are identical if and only if h is reflectionless (we call this phenomenon entropic identity). If h is not reflectionless, then the ES and GC functionals remain equal but differ from the FCS, VAR and interpolating functionals. Furthermore, in the non-reflectionless case, the ES/GC functional does not vanish at 1 (i.e., the Kawasaki identity fails) and does not have the celebrated ES/GC symmetry. The FCS, VAR and interpolating functionals always have this symmetry. In the cases where h is a Schr\"odinger operator, the entropic identity leads to some unexpected open problems in the spectral theory of one-dimensional discrete Schr\"odinger operators.

Conductance Fluctuations in Chains of Particles Arising from Conformational Changes of Stabilizer Molecules

We have bridged a pair of gold electrodes with various arrangements of gold nanoparticles stabilized with citrate molecules. The resulting devices exhibited current fluctuations at a constant bias voltage and fluctuations of the differential conductance as a function of the bias voltage. These fluctuations were attributed to the interplay of molecular conformation, charge switching, and breaking of the links at the interface molecules-electrode. We found that, for all investigated samples, the contact resistance at the interface molecules-electrode was by about one order of magnitude larger than that between nanoparticles coupled by citrate molecules. We conclude that the mechanism of charge transport can be viewed as a series of discrete steps involving initial hopping (injection) of the charge from the left-hand-side gold electrode to the molecules, tunnelling of the charge through the molecules-nanoparticle-molecules (MNM) unit, hopping to the next MNM unit, etc., and finally hopping (extraction) of the charge to the right-hand-side gold electrode.

Molecular Recognition through Concerted Ubiquitin Backbone and Side Chain Motion Determined from NMR and MD Simulations

Motion is involved in a large number of protein functions. For ubiquitin, residual dipolar coupling (RDC) derived ensembles have suggested it recognizes binding partners via conformational selection through motions occurring on the supra tau-c (>4 ns) timescale [1]. Subsequent relaxation dispersion (RD) studies identified microsecond fluctuations for six backbone atoms [2,3]. However, it has not been clear if these motions are independent or collective, and what role side chains play. To address those questions, we have conducted an in-depth RD analysis of the backbone and side chain methyl groups. This survey showed a large number of atoms (>30) with microsecond fluctuations. These atoms are distributed throughout the structure and nearly all show the same exchange rate, which suggests that ubiquitin undergoes collective motion involving both the backbone and side chains. The presence of microsecond side chain motion agrees with previous RDC measurements of methyl groups within ubiquitin [4]. Furthermore, comparison of different methyl nuclei indicates that the nature of the side chain fluctuations is almost entirely due to changes in rotamer populations. This is borne out in molecular dynamics simulations of ubiquitin trapped in different conformational states by binding partners [5]. Residues showing RD were significantly more likely to show changes in rotamer populations in the simulations. Put together, this leads to a model where collective microsecond backbone motion is coupled to redistribution of side chain rotamer populations. The correlation with binding partner simulations implicates this motion in conformational selection.1. Lange et al. Science. 320:1471-1475 (2008)2. Ban et al. Angew Chem Int Ed. 50:11437-1144 (2011)3. Ban et al. J Magn Reson. 221:1-4 (2012)4. Fares et al. J Biomol NMR. 45:23-44 (2009)5. Peters et al. PLoS Comput Biol. Accepted (2012)

Impedance and power fluctuations in linear chains of coupled wave chaotic cavities

The flow of electromagnetic wave energy through a chain of coupled cavities is considered. The cavities are assumed to be of sufficiently irregular shape that their eigenmodes are described by random matrix theory. The cavities are coupled by electrically short single mode transmission lines. Approximate expressions for the power coupled into successive cavities are derived, and the predictions are compared with Monte Carlo simulations. The analytic formulas separate into a product of factors. Consequently, the distribution of power in the last cavity of a very long chain approaches lognormal. For lossless cavities, signatures of Anderson localization, similar to those of the conductances of quantum wires, are observed.

Microrheological consequences of attractive colloid-colloid potentials in a two-dimensional Brownian fluid

By using microrheological methods commonly employed in videomicroscopy experiments, we study the rheology of a two-dimensional computational fluid formed by Brownian disks with the aim of exploring the influence of some effective colloid-colloid attractive interactions. The model of fluid is developed by Brownian dynamics simulations without hydrodynamical interactions, and it is characterized by calculating its equation of state from the pair distribution function. Micromechanical properties, relative and intrinsic viscosity and freezing are discussed. Then, we include attractive forces such a Asakura-Oosawa depletion force or an empiric expression proposed by Grier and Hal (GH) for an anomalous electrostatic potential observed in confined and charged colloids. By using both potentials, viscosity is clearly increased, but when the GH potential is included, viscoelastic gel state is reached for intermediate values of surface concentration. Finally, we analyse the influence of the attractive potentials in the breaking-up by thermal fluctuations of linear chains formed by 2D particles, finding that the GH potential reduces the characteristical time at which the disks can be considered as disaggregated. In this work, we employ an experimental-like methodology for the study of a Brownian hard-disk fluid, providing a very useful link with experimental procedures.

Distribution of transverse chain fluctuations in harmonically confined semiflexible polymers

Two different experimental studies of polymer dynamics based on single-molecule fluorescence imaging have recently found evidence of heterogeneities in the widths of the putative tubes that surround filaments of F-actin during their motion in concentrated solution. In one [J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchesner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)], the observations were explained in terms of the statistics of a worm-like chain confined to a potential determined self-consistently by a binary collision approximation, and in the other [B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010)], they were explained in terms of the scaling properties of a random fluid of thin rods. In this paper, we show, using an exact path integral calculation, that the distribution of the length-averaged transverse fluctuations of a harmonically confined weakly bendable rod (one possible realization of a semiflexible chain in a tube), is in good qualitative agreement with the experimental data, although it is qualitatively different in analytic structure from the earlier theoretical predictions. We also show that similar path integral techniques can be used to obtain an exact expression for the time correlation function of fluctuations in the tube cross section.

Frequency Distribution of the Amide-I Vibration Sorted by Residues in Amyloid Fibrils Revealed by 2D-IR Measurements and Simulations

The infrared optical response of amyloid fibrils Aβ(1-40) is investigated. Simulations of two models corresponding to different protonation states are compared with experiment. The simulations reveal that vibrational frequency distributions inside the fibrils are dominated by side chain fluctuations. We further confirm earlier suggestions based on 2D-IR measurements that water molecules can be trapped inside the fibrils.

Bovine pancreatic trypsin inhibitor crystals with different morphologies: a molecular dynamics simulation study

A molecular dynamics simulation study is reported for three polymorphic protein crystals (4PTI, 5PTI and 6PTI) of bovine pancreatic trypsin inhibitor (BPTI). The simulated lattice constants are in good agreement with experimental data, indicating the reliability of force field used. The fluctuation patterns of peptide chains in the three crystals are similar, and the protein structures are fairly well maintained during simulation. We observe that water forms a pronounced hydration layer near the protein surface. The diffusion coefficients of water in the three crystals are smaller than in bulk phase, and thus, the activation energies are higher. The porosity, fluctuation of peptide chains and solvent-accessible surface area as well as the diffusion coefficients of water and counterion in 5PTI are the largest among the three crystals. The diffusion of water and counterion is anisotropic, and the degree of anisotropy increases in the order of 4PTI < 5PTI < 6PTI. Despite a slight difference, the structural and diffusion properties in the three BPTI crystals are generally close. This simulation study reveals that crystal polymorphism does not significantly affect microscopic properties in the BPTI crystals with different morphologies.

Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments despite the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.

The guest ordering and dynamics in urea inclusion compounds studied by solid-state 1H and 13C MAS NMR spectroscopy

Urea inclusion compounds with different guest species were studied by 13C CP MAS and 1H MAS NMR spectroscopy. It is possible to arrange the asymmetric guest species in three different ways: head–head, head–tail and tail–tail. 13C CP MAS NMR studies indicate that the preference arrangement is determined by the interaction strength of the end functional groups. 13C relaxation experiments are used to study the dynamic properties of urea inclusion compounds. 13C relaxation studies on urea inclusion compounds with n-alkane or decanoic acid show that the 13C T1 and 13C T1ρ values exhibit the position dependence towards the center of the chain, indicating internal chain mobility. The analysis of variable-temperature 13C T1ρ experiments on urea inclusion compounds with hexadecane and pentadecane, for the first time, suggests that chain fluctuations and lateral motion of n-alkane guests may contribute to the 13C T1ρ relaxation.

Characteristic Times of Polymer Tumbling Under Shear Flow

AbstractThe tumbling dynamics of flexible chains in shear flow, analysed by Brownian Dynamics simulations, are found to be ruled by three characteristic times τtumb, τdif and τlag. The average tumbling time τtumb scales with the shear rate with a robust exponent against excluded volume (EV) or hydrodynamic interactions, $\tau _{{\rm tumb}} \approx {\dot {\gamma }}^{{-} 2/3} $. The chain extensions in the flow plane decorrelate in a time τdif determined by the diffusion of the chain configuration in gradient direction, $\tau _{{\rm dif}} \approx Y^{2} /D$. The chain keeps memory of its configuration over a number of tumblings events given by the ratio τdif/τtumb. While for ideal chains $\tau _{{\rm dif}} /\tau _{{\rm tumb}} \approx O(1)$, for expanded (EV) chains we find $\tau _{{\rm dif}} /\tau _{{\rm tumb}} \approx {\dot {\gamma }}^{0.2} $. Hence, EV chains tumble in a more deterministic way as ${\dot {\gamma }}$ is increased. As a consequence, contrary to previous assumptions, the exponential tail of the tumbling time distribution $P(\tau )\approx {\exp} ({-} \nu \tau )$ presents a non‐Poissonian exponent. This exponent ν is found to be determined by a new characteristic time τlag measuring how fast the chain in‐flow elongation X responses to the drag force induced by chain fluctuations in gradient direction Y. PSCS numbers.magnified image

Crystal structure of the sweet-tasting protein thaumatin II at 1.27 Å

Thaumatin, an intensely sweet-tasting protein, elicits a sweet taste sensation at 50 nM. Here the X-ray crystallographic structure of one of its variants, thaumatin II, was determined at a resolution of 1.27 Å. Overall structure of thaumatin II is similar to thaumatin I, but a slight shift of the Cα atom of G96 in thaumatin II was observed. Furthermore, the side chain of residue 67 in thaumatin II is highly disordered. Since residue 67 is one of two residues critical to the sweetness of thaumatin, the present results suggested that the critical positive charges at positions 67 and 82 are disordered and the flexibility and fluctuation of these side chains would be suitable for interaction of thaumatin molecules with sweet receptors.

Compression of polyelectrolyte brushes in a salt-free theta solvent

This paper examines the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. It focuses on the special case of semi-dilute brushes in a salt-free theta solvent, for which Zhulina and Borisov (J. Chem. Phys. 107, 5952 (1997)) have derived analytical predictions using the classical strong-stretching theory (SST). Interestingly, SST predicts that the brushes contract as they are compressed together maintaining a polymer-free gap, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Abstract Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.

Molecular Simulations Distinguish Rhodopsin Counterion Models by Retinal Polyene Fluctuations

We investigated retinal conformational changes within the binding cavity of rhodopsin through all-atom molecular dynamics (MD) simulations on the microsecond time scale. Two distinct pathways involving post-isomerization release of retinal conformational strain were tested. The MD trajectories for the counterion-switch and complex-counterion mechanisms [1] show that retinal experiences completely distinct geometrical rearrangements, yielding differences in its orientation and conformation. In the counterion-switch simulation the dihedral angle C11=C12-C13=C14 fluctuates, and is correlated with changes in the C5-, C9-, and C13-methyl group orientations with respect to the membrane normal. For the complex-counterion simulation, changes in the dihedral angle C7=C8-C9=C10 allow the methyl group orientation to remain relatively unaffected (∼60° for the C5-, C9-, and C13-methyl groups), consistent with 2H NMR data [2,3]. The C5=C6-C7=C8 and C9=C10-C11=C12 torsion angles also experience significant fluctuations, but at different times in each counterion simulation and not in conjunction with retinal methyl re-orientation. In addition to retinal polyene chain analysis, the calculated 2H NMR spectra from each simulation clearly demonstrate that the retinal methyl orientations for the complex-counterion mechanism accurately reproduce experimental 2H NMR data for Meta I [2,3], whereas the counterion simulation does not. Rhodopsin simulations on the microsecond time scale are essential for modeling rhodopsin activation up to the Meta I photointermediate, because retinal polyene chain fluctuations occur as late as ∼1500 ns into each simulation. This work builds on our previous computational studies examining rhodopsin in the dark and Meta I states [1,4] and provides valuable insights into the rhodopsin activation process. [1] K. Martínez-Mayorga et al. (2006) JACS128, 16502-16503. [2] G.F.J. Salgado et al. (2006) JACS128, 11067-11071. [3] A.V. Struts et al. (2007) JMB372, 50-66. [4] P.-W. Lau et al. (2007) JMB372, 906-917.