Experimental Order Parameters Research Articles

Cooperative freezing of the L12 ordered domains at the critical cooling temperature of Ni3Fe alloy

It is well known that Ni3Fe transforms from a disordered solid solution to an ordered intermetallic with L12 superstructure when the alloy is cooled slowly. Here we elucidate the underlying cooperative phenomenon and the atomistic mechanism of this ordering process based on simulations using embedded atom potentials. As the simulated alloy is cooled from the disordered state to the critical cooling temperature (T c), Ni atoms with L12 order [denoted as Ni(L12 ⩾ 1) atoms] increase significantly along with Ni atoms having the least deviation from L12 local order (denoted as Ni([IP]3) atoms). The ordering (up to T c) occurs predominantly through random increase in Ni(L12 ⩾ 1) atoms throughout the system, as indicated by absence of long-range order. At T c, L12 ordered domains formed by Ni(L12 ⩾ 1) atoms ‘freeze’, i.e. these domains, collectively, achieve a threshold strength against thermal fluctuations. This is indicated by (i) dissipation of large-scale fluctuations of Ni(L12 ⩾ 1) atoms at T c and (ii) the growth of the L12 domains through propagation (at the expense of atoms with non-L12 local environment) as the alloy is cooled below T c. The stability threshold of the L12 ordered domains at T c is qualitatively consistent with (i) the critical slowing down, i.e. a significant increase in annealing time (to about 41 days) at 497 °C close to T c (∼500 °C) and (ii) sharp changes in bulk properties (due to loss of stability of the domains) when the alloy is heated across T c to about 550 °C. Further, the experimental long-range order parameter values as a function of reduced temperature are in reasonable agreement with the corresponding values of the simulated alloys. The contribution of Ni([IP]3) atoms to ordering in the actual alloy is potentially significant since such atoms together with nearest neighbours constitute about 75% of the total atoms in the simulated alloys at T c.

Effect of monovalent ion binding on molecular dynamics of the S100-family calcium-binding protein calbindin D9k.

Calbindin D9k is a member of the S100 subfamily of EF-hand calcium binding proteins, and has served as an important model system for biophysical studies. The fast timescale dynamics of the calcium-free (apo) state is characterized using molecular dynamics simulations. Order parameters for the backbone NH bond vectors are determined from the simulations and compared with experimentally derived values, with a focus on the dynamics of calcium-binding site I. There is a significant discrepancy between simulated and experimental order parameters for site I residues in the case of no ion bound in site I. However, it was found in the simulations that a Na+ ion can bind in site I, and the resulting order parameters determined from the simulations are in excellent agreement with experiment. Comparisons are made to X-ray structures of other S100 family members in which Na+ ions were observed or suggested to be bound in site I. © 2019 Wiley Periodicals, Inc.

Probing (UN)Folding Transition Paths of Fast-Folding Proteins by Single-Molecule Fluorescence: Exploring the Role of Secondary Structure, Fold Topology and Sequence

Protein folding involves formation of secondary structural elements and their collapse into well-defined 3-dimensional structure. Attempts to study how these processes cooperate to form the native structure and determine folding mechanisms has been focus of research for decades. Addressing these questions require looking at the distributions of behaviors of individual molecules, which has been successfully attained by theory and computer simulations. Experimentally, the problem must be approached by single-molecule spectroscopic methods, which have not had the required time-resolution. We are investigating protein folding at the single-molecule level combining advanced custom-built fluorescence-based SM-FRET techniques optimized for high-count rates and a maximum likelihood analysis (MLA) of photon arrival times that we developed for the detection of (un)folding transition paths of microsecond folding proteins. To investigate the roles of secondary structure, fold topology, and amino acid sequence we are performing these experiments on three fast-folding protein models, all consisting of three secondary structure elements in an antiparallel arrangement: En-HD (three α-helices), and Nedd4-WW3 and FBP11WW2, which fold onto homologous 3-stranded β-sheets but with different amino acid sequence. We are investigating their folding transition paths by 2-color SM-FRET using variants labeled with FRET pairs at the two ends in free diffusion experiments. Because these proteins fold-unfold in microseconds, free diffusion offers the opportunity to catch folding transitions during the diffusive trajectories without immobilization and thus without significantly perturbing folding landscape. Our analysis of these data using MLA of photon trajectories (rather than binning) provides the free energy landscape as a function of the experimental order parameter (FRET-pair distance) and the intramolecular diffusion coefficient. Subsequent reconstruction of the molecular trajectories from the photon trajectories using stochastic methods provide a direct glimpse of barrier crossing events.

Molecular properties of a bent-core nematic liquid crystal A131 by multi-level theory simulations

ABSTRACTMulti-level theory simulations have been performed to model a number of important molecular properties of a bent-core nematic liquid crystal (LC) A131. These important properties include molecular conformations, molecular Raman spectra, differential polarisability ratios, molecular crystals packing, atomic LC structures, order parameters, and Raman depolarisation spectra. The simulations contain four theory levels, involving molecular quantum chemistry, molecular crystal packing, super cell density functional based tight binding optimisation, and super cell molecular dynamics calculations. To heat initial optimised super cell structures, molecular dynamics simulations reveal phase transitions to uniaxial and biaxial nematic phases from molecular crystals. LC atomic structures result in direct calculations on order parameters, which can be further applied to computations on Raman depolarisation spectra with differential polarisability ratios, obtained in the molecular quantum chemistry theory level. The good agreement of simulated Raman depolarisation spectra with the experiment provides a detailed analysis on the unusually low values of experimental uniaxial order parameters.

Comparative Study of REDOR and CPPI Derived Order Parameters by 1H-Detected MAS NMR and MD Simulations.

The measurement of dipolar couplings among directly bonded nuclei yields direct information on the amplitude of dynamic processes in the solid-state. For a reliable motional analysis using, e.g., the model-free approach, a correct quantification of the absolute values of these order parameters is absolutely essential. In the absence of a reference value for the rigid limit, too low dipolar coupling values might be misinterpreted as motion. Therefore, a detailed understanding of the effects that influence the quantification of the experimental order parameters is necessary. We compare here REDOR and CPPI derived order parameters assessed in 1H-detected experiments, and discuss the influence of remote protons and rf inhomogeneity on the extracted dipolar coupling constant for MAS rotation frequencies in the range 20-100 kHz. Experimental results are furthermore compared with the order parameter obtained from a molecular dynamics simulation. We find that fast magic-angle spinning up to 100 kHz can yield artifact-free REDOR based 1H,15N order parameters for perdeuterated and 100% amide back-exchanged proteins, and potentially even in uniformly protonated samples. We believe that awareness of systematic errors introduced by the measurement and in the analysis of order parameters will yield a better understanding of the dynamic properties of a protein derived from solid-state NMR observables.

Drude Polarizable Force Field for Molecular Dynamics Simulations of Saturated and Unsaturated Zwitterionic Lipids.

Additive force fields are designed to account for induced electronic polarization in a mean-field average way, using effective empirical fixed charges. The limitation of this approximation is cause for serious concerns, particularly in the case of lipid membranes, where the molecular environment undergoes dramatic variations over microscopic length scales. A polarizable force field based on the classical Drude oscillator offers a practical and computationally efficient framework for an improved representation of electrostatic interactions in molecular simulations. Building on the first-generation Drude polarizable force field for the dipalmitoylphosphatidylcholine 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecule, the present effort was undertaken to improve this initial model and expand the force field to a wider range of phospholipid molecules. New lipids parametrized include dimyristoylphosphatidylcholine (DMPC), dilauroylphosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), dipalmitoylphosphatidylethanolamine (DPPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE). The iterative optimization protocol employed in this effort led to lipid models that achieve a good balance between reproducing quantum mechanical data on model compound representative of phospholipids and reproducing a range of experimental condensed phase properties of bilayers. A parametrization strategy based on a restrained ensemble-maximum entropy methodology was used to help accurately match the experimental NMR order parameters in the polar headgroup region. All the parameters were developed to be compatible with the remainder of the Drude polarizable force field, which includes water, ions, proteins, DNA, and selected carbohydrates.

Examination of Mixtures Containing Sphingomyelin and Cholesterol by Molecular Dynamics Simulations.

The all-atom CHARMM36 (C36) force field is used to simulate bilayers of pure palmitoylsphingomyelin (PSM) as well as binary mixtures of PSM and stearoylsphingomyelin (SSM) at various cholesterol concentrations (XC) and temperatures. C36 simulation data is in good agreement with experimental deuterium order parameters and previous computational results, providing evidence of the utility of the force field for potentially studying more complex membranes. The area compressibility modulus is shown to achieve a large value of 2.82 ± 0.08 N/m in cholesterol-rich membranes (XC = 0.50). Surface area per lipid (SA/lip), tilt angle, membrane thicknesses, and acyl chain ordering are shown to have strong dependencies on cholesterol concentration. Relaxation times also indicate cholesterol dependence and show a strong preference for rotational axial motion over wobbling motion. Radial distribution functions and lipid clustering indicate strong relationships between lateral ordering and hydrogen bonding, which is long lived in SM membranes. These interactions lead to strong self-association of cholesterol at high concentrations, causing shielding from further SM-cholesterol interactions. The importance of a ternary component on SM-SM hydrogen bonds is revealed in light of previous results and is consequential in the modeling of lipid rafts.

Acyl Chain Disorder and Azelaoyl Orientation in Lipid Membranes Containing Oxidized Lipids.

Oxidized phospholipids occur naturally in conditions of oxidative stress and have been suggested to play an important role in a number of pathological conditions due to their effects on a lipid membrane acyl chain orientation, ordering, and permeability. Here we investigate the effect of the oxidized phospholipid 1-palmitoyl-2-azelaoyl-sn-glycero-3-phosphocholine (PazePC) on a model membrane of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) using a combination of (13)C-(1)H dipolar-recoupling nuclear magnetic resonance (NMR) experiments and united-atom molecular dynamics (MD) simulations. The obtained experimental order parameter SCH profiles show that the presence of 30 mol % PazePC in the bilayer significantly increases the gauche content of the POPC acyl chains, therefore decreasing the thickness of the bilayer, although with no stable bilayer pore formation. The MD simulations reproduce the disordering effect and indicate that the orientation of the azelaoyl chain is highly dependent on its protonation state with acyl chain reversal for fully deprotonated states and a parallel orientation along the interfacial plane for fully protonated states, deprotonated and protonated azelaoyl chains having negative and positive SCH profiles, respectively. Only fully or nearly fully protonated azelaoyl chain are observed in the (13)C-(1)H dipolar-recoupling NMR experiments. The experiments show positive SCH values for the azelaoyl segments confirming for the first time that oxidized chains with polar termini adopt a parallel orientation to the bilayer plane as predicted in MD simulations.

Local Ordering at Mobile Sites in Proteins from Nuclear Magnetic Resonance Relaxation: The Role of Site Symmetry.

Restricted motions in proteins (e.g., N-H bond dynamics) are studied effectively with NMR. By analogy with restricted motions in liquid crystals (LC), the local ordering has in the past been primarily represented by potentials comprising the L = 2, |K| = 0, 2 spherical harmonics. However, probes dissolved in LCs experience nonpolar ordering, often referred to as alignment, while protein-anchored probes experience polar ordering, often referred to as orientation. In this study we investigate the role of local (site) symmetry in the context of the polarity of the local ordering. We find that potentials comprising the L = 1, |K| = 0, 1 spherical harmonics represent adequately polar ordering. It is useful to characterize potential symmetry in terms of the irreducible representations of D2h point group, which is already implicit in the definition of the rotational diffusion tensor. Thus, the relevant rhombic L = 1 potentials have B1u and B3u symmetry whereas the relevant rhombic L = 2 potentials have Ag symmetry. A comprehensive scheme where local potentials and corresponding probability density functions (PDFs) are represented in Cartesian and spherical coordinates clarifies how they are affected by polar and nonpolar ordering. The Cartesian coordinates are chosen so that the principal axis of polar axial PDF is pointing along the z-axis, whereas the principal axis of the nonpolar axial PDF is pointing along ±z. Two-term axial potentials with 1 ≤ L ≤ 3 exhibit substantial diversity; they are expected to be useful in NMR-relaxation-data-fitting. It is shown how potential coefficients are reflected in the experimental order parameters. The comprehensive scheme representing local potentials and PDFs is exemplified for the L = 2 case using experimental data from (15)N-labeled plexin-B1 and thioredoxin, (2)H-, and (13)C-labeled benzenehexa-n-alkanoates, and nitroxide-labeled T4 lysozyme. Future prospects for improved ordering analysis based on combined atomistic and mesoscopic approaches are delineated.

Dynamic allostery governs cyclophilin A–HIV capsid interplay

Host factor protein Cyclophilin A (CypA) regulates HIV-1 viral infectivity through direct interactions with the viral capsid, by an unknown mechanism. CypA can either promote or inhibit viral infection, depending on host cell type and HIV-1 capsid (CA) protein sequence. We have examined the role of conformational dynamics on the nanosecond to millisecond timescale in HIV-1 CA assemblies in the escape from CypA dependence, by magic-angle spinning (MAS) NMR and molecular dynamics (MD). Through the analysis of backbone (1)H-(15)N and (1)H-(13)C dipolar tensors and peak intensities from 3D MAS NMR spectra of wild-type and the A92E and G94D CypA escape mutants, we demonstrate that assembled CA is dynamic, particularly in loop regions. The CypA loop in assembled wild-type CA from two strains exhibits unprecedented mobility on the nanosecond to microsecond timescales, and the experimental NMR dipolar order parameters are in quantitative agreement with those calculated from MD trajectories. Remarkably, the CypA loop dynamics of wild-type CA HXB2 assembly is significantly attenuated upon CypA binding, and the dynamics profiles of the A92E and G94D CypA escape mutants closely resemble that of wild-type CA assembly in complex with CypA. These results suggest that CypA loop dynamics is a determining factor in HIV-1's escape from CypA dependence.

Access to Cα backbone dynamics of biological solids by 13C T1 relaxation and molecular dynamics simulation.

We introduce a labeling scheme for magic angle spinning (MAS) solid-state NMR that is based on deuteration in combination with dilution of the carbon spin system. The labeling strategy achieves spectral editing by simplification of the HαCα and aliphatic side chain spectral region. A reduction in both proton and carbon spin density in combination with fast spinning (≥50 kHz) is essential to retrieve artifact-free (13)C-R1 relaxation data for aliphatic carbons. We obtain good agreement between the NMR experimental data and order parameters extracted from a molecular dynamics (MD) trajectory, which indicates that carbon based relaxation parameters can yield complementary information on protein backbone as well as side chain dynamics.

From Classical to Quantum Glasses with Ultracold Polar Molecules

We study the dynamics of a bilayer system of ultracold polar molecules, which exhibits classical and quantum glassy behavior, characterized by long tails in the relaxation time and dynamical heterogeneity. In the proposed setup, quantum fluctuations are of the order of thermal fluctuations and the degree of frustration can be tuned by the interlayer distance. We discuss the possible observation of a glassy anomalous diffusion and dynamical heterogeneity in experiment using internal degrees of freedom of the molecules in combination with optical detection.

Simulations of Anionic Lipid Membranes: Development of Interaction-Specific Ion Parameters and Validation Using NMR Data

Overbinding of ions to lipid head groups is a potentially serious artifact in simulations of charged lipid bilayers. In this study, the Lennard-Jones radii in the CHARMM force field for interactions of Na(+) and lipid oxygen atoms of carboxyl, phosphate, and ester groups were revised to match osmotic pressure data on sodium acetate and electrophoresis data on palmitoyloleoyl phosphatidylcholine (POPC) vesicles. The new parameters were then validated by successfully reproducing previously published experimental NMR deuterium order parameters for dimyristoyl phosphatidylglycerol (DMPG) and newly obtained values for palmitoyloleoyl phosphatidylserine (POPS). Although the increases in Lennard-Jones diameters are only 0.02-0.12 Å, they are sufficient to reduce Na+ binding, and thereby increase surface areas per lipid by 5-10% compared with the unmodified parameters.

Molecular Dynamics Simulations Support the use of Methyl Generalized Order Parameters in the “Entropy Meter”

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Unfortunately, conformational entropy has been difficult to measure experimentally. We have been working towards using measures of fast internal motion as a proxy for conformational entropy. Implementation of this approach has been impeded by the apparent need to employ a model-dependent interpretation of the obtained generalized order parameters. We have recently proposed that the quantitative relationship between generalized order parameters and conformational entropy could be determined empirically and effectively create an ‘entropy meter’ (Marlow et al. Nat. Chem. Biol. 6, 353). This approach has initially employed methyl symmetry axis order parameters that can be obtained relatively easily. The approach then rests on the coupling between motion of the methyl bearing side chains and the rest of the amino acids being sufficient to report on the whole protein. Here, we examine the generality of this assumption using molecular dynamics simulations of a number of proteins. The MD simulations performed with the NAMD suite showed excellent agreement between the calculated and experimental side chain order parameters for all the proteins, a marked improvement from previous studies. We find a general correlation between the internal dynamics of protein and the protein conformational entropy. The calculated protein conformational entropy showed excellent linear correlation to both the calculated NMR order parameter of methyl groups as well as the experimentally measured NMR methyl order parameters. Supported by NIH grant GM102447 and a grant from the Mathers Foundation.

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Induced Smectic Phase in a Binary Mixture of Nematogens

The phase diagram of binary system of nematogenic compounds 4-n-pentyl phenyl 4-n′-hexyloxy benzoate (ME6O.5) and 4-cyanophenyl 4-heptyl benzoate (CPHB) shows the presence of induced smectic phase. In the present paper, we report the results of DSC, refractive index, and density measurements of different binary mixtures of (ME6O.5 + CPHB) throughout the entire composition range. The density and refractive index values have been analyzed to obtain orientational order parameters. We have fitted the experimental order parameters with the theoretical values from McMillan's theory for mixtures having smectic phase, and Maier–Saupe theory for others having nematic phase only.

Density, Optical and Static Dielectric Studies of a Nematogenic Tolan Compound

We report here temperature variation of refractive indices, dielectric permittivities and densities of a nematogenic tolan compound (4-n-butyl-4′-ethoxytolan). The sample exhibits high birefringence. The refractive indices and density values have been analyzed to obtain the orientational order parameters. Experimental order parameters are compared with theoretical Maier-Saupe values. The variation of dielectric permittivities with temperature has been determined for the sample at frequency 1 kHz. The sample shows very low dielectric anisotropy. The molecular dipole moment and the angle of inclination β of the molecular dipole moment with the director are also calculated.

Landau theory description of observed isotropic to anisotropic phase transition in mixed clay gels

A characteristic new cooperative dehydration transition, in 1:1 Laponite-MMT cogel, was observed at T(c) ≈ 60 °C, a temperature at which the storage modulus (G(')) and depolarization ratio (D(p)) showed sharp increase, and the isotropic cogel turned into an anisotropic one. The dehydration dynamics could be described through power-law relations: G(') ∼ (T(c)-T)(-γ) and D(p) ∼ (T(c)-T)(-β) with γ ≈ β = 0.40 ± 0.05. The x-ray diffraction data revealed that the crystallite size decreased from 17 nm (at 20 °C) to 10 nm (at 80 °C) implying loss of free and inter-planar water. When this cogel was spontaneously cooled below T(c), it exhibited much larger storage modulii values which implied the existence of several metastable states in this system. This phase transition could be modeled through Landau theory, where the depolarization ratio was used as experimental order parameter (ψ). This parameter was found to scale with temperature, as ψ ∼ (T(c)-T)(-α), with power-law exponent α = 0.40 ± 0.05; interestingly, we found α ≈ β ≈ γ.

Lipid Membranes with a Majority of Cholesterol: Applications to the Ocular Lens and Aquaporin 0

Using molecular dynamics (MD) simulations, we studied the structure and dynamics of two dimyristoylphosphatidylcholine (DMPC):cholesterol bilayers at concentrations representative of the ocular lens (ratios of 1:1 and 1:2). These MD simulations agree well with experimental deuterium order parameters and bilayer peak-to-peak distances. Although it is known that the average surface area per lipid rapidly decreases from low to moderate levels of cholesterol, our simulations indicate that there is a relatively small change in the average lipid area from 50 to 66.7% cholesterol (40.5 ± 0.2 and 39.5 ± 0.1 Å(2)/lipid, respectively). Radial distribution functions for the hydroxyl group on cholesterol indicate the formation of cholesterol-only nanoscale domains for the membrane with 66.7% cholesterol but a uniform distribution of cholesterol and DMPC for the membrane with 50% cholesterol. These small domains form a single shell of hexagonally packed cholesterols that are interconnected in a web-like structure of cholesterol. Calculations of internal DMPC dynamics show that the relaxation times for carbon-hydrogen reorientation of choline decrease with an increase in cholesterol, but the main body (carbonyl-glycerol to C11) is independent of cholesterol concentration. MD simulations of the aquaporin 0 tetramer show stabilization in its interactions with lipid membranes containing cholesterol by forming ring-ring stacking between surface aromatic residues of the protein and the rings of cholesterol. Moreover, there is an increase in hydrogen bonds with longer lifetimes in a mixed bilayer of DMPC and cholesterol.

Comparison of Simulated and Experimental Order Parameters in FePt—II

Eight FePt thin film specimens of various thicknesses, compositions, and order parameters have been analyzed to determine the robustness and fidelity of multislice simulations in determining the chemical order parameter via electron diffraction (ED). The shape of the simulated curves depends significantly on the orientation and thickness of the specimen. The ED results are compared to kinematical scattering order parameters, from the same films, acquired from synchrotron X-ray diffraction (XRD). For the specimens analyzed with convergent beam electron diffraction conditions, the order parameter closely matched the order parameter as determined by the XRD methodology. However, the specimens analyzed by selected area electron diffraction conditions did not show good agreement. This has been attributed to substrate effects that hindered the ability to accurately quantify the intensity values of the superlattice and fundamental reflections.