Secondary structure prediction of beta-hairpin peptide tryptophan zipper-I

We have investigated the folding properties of tryptophan zipper-I molecule which folds into a stable β-hairpin motif in aqueous solution as suggested by nuclear magnetic resonance (NMR) experiments. An all-atom presentation, including hydrogen, was used with an implicit solvent. As a simulation technique, simulated tempering algorithm was used to obtain equilibrium conformations of the molecule at ten distinct temperatures. Our minimum energy configuration obtained from simulated tempering algorithm is a β-hairpin motif with 1.30 Å backbone root-mean-square deviation from the reference PDB structure (1le0.pdb). Several quantities and exhaustive folding free energy landscapes were determined and discussed in order to clarify the folding behavior.     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Cytochrome c: the effect of temperature and pressure from molecular dynamics simulations

Cytochrome c has been extensively investigated due to its role in the process of electron transfer in the mitochondrial system. The effect of temperature and pressure on horse cytochrome c was investigated using normal mode analysis and Molecular Dynamics simulations. The conformational space of the molecule and the anharmonic component of oscillations were obtained further by molecular dynamics simulations for 1.5 ns in solvent environment. The simulated root means square fluctuations, radii of gyration, hydrogen bond arrangements and atomic packing densities reveal that the protein remains compact for the duration of the simulation; high temperature induced partial unfolding at surface regions was observed. The covalent bonding arrangement of the Fe (heme) was investigated during the simulation. These results provide insight into the stability of electron transport by cytochrome c under various pressures and temperatures and provide the regions that could be mutated to enhance the stability and electron transfer properties of the protein.     

Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I: Dependence on native structures and amino acid sequences

The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a1, a2, b1, and b2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a1 and a2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b1 and b2, but their native conformation is different from that of proteins a1 and a2. However, the chevron plots of proteins a1 and a2 are very similar to each other, and those of proteins b1 and b2 differ considerably. Since the contact orders of proteins b1 and b2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.     

Coupled oscillator models with no scale separation

We consider a class of spatially discrete wave equations that describe the motion of a system of linearly coupled oscillators perturbed by a nonlinear potential. We show that the dynamical behavior of this system cannot be understood by considering the slowest modes only: there is an “inverse cascade” in which the effects of changes in small scales are felt by the largest scales and the mean-field closure does not work. Despite this, a one and a half degree of freedom model is derived that includes the influence of the small-scale dynamics and predicts global conformational changes accurately. Thus, we provide a reduced model for a system in which there is no separation of scales. We analyze a specific coupled-oscillator system that models global conformation change in biomolecules, introduced in [I. Mezi?, On the dynamics of molecular conformation, Proc. Natl. Acad. Sci. 103 (20) (2006) 7542-7547]. In this model, the conformational states are stable to random perturbations, yet global conformation change can be quickly and robustly induced by the action of a targeted control. We study the efficiency of small-scale perturbations on conformational change and show that “zipper” traveling wave perturbations provide an efficient means for inducing such change. A visualization method for the transport barriers in the reduced model yields insight into the mechanism by which the conformation change occurs.     

Folding kinetics of two-state proteins based on the model of general random walk in native contact number space

We investigated the folding kinetics of a series of two-state proteins by using the model of general random walk in native contact number space, and derive the observed linear relationship between the logarithms of the folding rate constants and the numbers of native contacts from “kinetic viewpoint”. The protein folding speed limit and stability in this model are consistent with experimental observations.     

Gas-phase conformational and energetic properties of deprotonated dinucleotides

Ion mobility experiments and molecular modeling calculations were used to investigate the gas-phase conformations and folding energetics of 16 deprotonated dinucleotides. [M-H]^- ions were formed by MALDI and their collision cross-sections measured in helium using ion mobility based techniques. Cross-sections of theoretical structures, generated by molecular mechanics/dynamics calculations, were compared to the experimental values for conformational identification of the dinucleotides. Temperature dependent measurements and kinetic theory were also used to obtain energetic and dynamic data concerning the folding properties of the dinucleotides. Three distinct families of conformations, with significantly different collision cross-sections, were identified: a “stacked” family in which the two nucleobases stack; an “H-bonded” family in which the two nucleobases stay in the same plane and are hydrogen-bonded to each other; and an “open” family in which the two nucleobases are separated from each other. At temperatures ≥ 300 K these conformers rapidly interconvert in most systems, but they can be separated and individually observed in the lower temperature (80-200 K) experiments. The types and relative amounts of each conformer observed, and the temperature at which they can be separated, are base and sequence dependent. Theoretical modeling of the temperature-dependent data was used to determine isomerization barrier heights between the various conformers and yielded values between 0.8-12.9 kcal/mol, depending on the dinucleotide. Received 17 May 2002 Published online 13 September 2002     

Overlap distribution in random and designed heteropolymers

We study the overlap between low-energy states in lattice models of heteropolymers with contact interactions. The overlap distribution gives information on the degree of correlation in the energy landscape. Designed sequences have rather correlated energy landscapes, which favor fast folding kinetics. Chains with random interactions have much less correlated energy landscapes. It is indeed believed that the mean-field theory for this model coincides with the Random Energy Model, whose different low-energy states are completely unrelated. This picture has been supported by numerical studies of maximally compact configurations. Without applying this constraint, we find that the overlap distribution is indeed bimodal as expected, but it has a broad peak at large overlap, indicating a non-vanishing width for the valleys of low-energy states. This feature probably plays an important role in the kinetics of the model. It is not evident that the range of such correlations shrinks to zero for large systems. The range of the correlations seems to be influenced by the number of contacts per residue in the ground state: the smaller this quantity, the larger the correlations. Received 16 August 2000     

Heat capacity of ZnO with cubic structure at high temperatures

The heat capacities at constant pressure and constant volume, and thermal expansivity are calculated for ZnO with rocksalt-type and zinc-blende-type cubic structures over a wide range of temperatures using molecular dynamics simulations with interactions due to effective pair-wise potentials which consist of the Coulomb, dispersion, and repulsion interaction. It is shown that the calculated structural and thermodynamic parameters including lattice constant, thermal-expansion coefficient, isothermal bulk modulus and its pressure derivative at ambient condition are in good agreement with the available experimental data and the latest theoretical results. At extended pressure and temperature ranges, lattice constant and heat capacity have also been predicted. The structural and thermodynamic properties of ZnO with cubic structure are summarized in the 300-1500 K temperature ranges and up to 100 kbar pressure.     

Modeling the temperature-dependent peptide vibrational spectra based on implicit-solvent model and enhance sampling technique

We herein review our studies on simulating the thermal unfolding Fourier transform infrared and two-dimensional infrared spectra of peptides. The peptide–water configuration ensembles, required forspectrum modeling, aregenerated at a series of temperatures using the GBOBCimplicit solvent model and the integrated tempering sampling technique.The fluctuating vibrational Hamiltonians of the amide I vibrational band are constructed using the Frenkel exciton model.The signals are calculated using nonlinear exciton propagation. The simulated spectral features such as the intensity and ellipticity are consistent with the experimental observations. Comparing the signals for two beta-hairpin polypeptides with similar structures suggests that this technique is sensitive to peptide folding landscapes.     

Counterion vibrations in the DNA low-frequency spectra

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na⁺ , K⁺ , Rb⁺ and Cs⁺ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na⁺ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs⁺ have effect on the internal vibrations of the DNA structural elements.     

Synthesis and physical properties of negative thermal expansion materials Zr1−xMxW2O8−y (M=Sc, In, Y) substituted for Zr(IV) sites by M(III) ions

Zr_1−xM_xW₂O_8−y (M=Sc, In and Y) solid solutions substituted up to x=0.04 for Zr(IV) sites by M(III) ions were synthesized by a solid-state reaction. X-ray diffraction experiments from 90 to 560 K revealed that all solid solutions had a cubic crystal structure and showed negative thermal expansion coefficients. The lattice parameters of Zr_1−xM_xW₂O_8−y were smaller than that of ZrW₂O₈ probably due to oxygen defects, though the ionic radii of substituted M³⁺ ions were larger than that of Zr⁴⁺. Order-disorder phase transition temperatures of the substituted samples drastically decreased in the order of Y, In and Sc compared to the percolation theory, and decreased with increasing M content.     

First-principles calculations of structural and thermodynamic properties of Y 3Al5O12

The pseudo-potential plane-wave method using the generalized gradient approximation (GGA) within the framework of the density functional theory is applied to study the structural and thermodynamic properties of Y ₃Al₅O₁₂. The lattice constants and bulk modulus are calculated. They keep in good agreement with other theoretical data and experimental results. The quasi-harmonic Debye model, in which the phononic effects are considered, is applied to the study of the thermodynamic properties. The temperature effect on the structural parameters, bulk modulus, thermal expansion coefficient, specific heats and Debye temperatures in the whole range from 0 to 20 GPa and temperature range from 0 to 1500 K.     

Phase diagram of uniaxial antiferromagnetic particles: Field perpendicular to the easy axis

We consider a spherical uniaxial antiferromagnetic particle in the presence of an external magnetic field perpendicular to its easy axis. The model is described by a classical Heisenberg Hamiltonian including a single-ion uniaxial anisotropy, where the magnetic moments of the particle are represented by continuous spin vectors. We employ mean-field calculations and Monte Carlo simulations to determine the phase diagram of the system. The phase diagram in the plane field versus temperature is obtained for particles with radii ranging from three up to twelve spacing lattice units. We have seen that a particle with more than nine shells behaves as a true thermodynamic system. We find the explicit dependence of the zero temperature critical field and the Néel temperature on the diameter of the particle. At low temperatures, we have also shown that, for particles with three or more shells, the critical field follows a T² law, which is in agreement with the predictions of the spin-wave theory, when the field is perpendicular to the easy axis.     

Tea saponin additive to extract eleutheroside B and E from Eleutherococcus senticosus by ultrasonic mediation and its application in a semi-pilot scale

The safety of ethanol in operations and its effects on human health are gradually being questioned. Under this premise, we attempted to use the natural surfactant tea saponin, which originates from the processing residues of camellia oil, as the additive of the extraction solvent and to extract eleutheroside B and eleutheroside E in the roots and rhizomes of E. senticosus by ultrasonic mediation. After a single-factor experiment, extraction kinetics at different powers and reaction temperatures, and Box–Behnken design optimization, the optimal conditions obtained were 0.3% tea saponin solution as the extraction solvent, 20 mL/g liquid–solid ratio, 250 W ultrasonic irradiation power (43.4 mW/g ultrasonic power density) and 40 min ultrasonic irradiation time. Under optimal conditions, satisfactory yields of eleutheroside B (1.06 ± 0.04 mg/g) and eleutheroside E (2.65 ± 0.12 mg/g) were obtained with semi pilot scale ultrasonic extraction equipment. The experiments showed that compared with the traditional thermal extraction process, the extraction time is significantly reduced at lower operating temperatures.     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation

In order to investigate the effect of pulse width and solvent on the nonlinear properties of metal nanostructures, silver nanowires were fabricated in a direct current electric field (DCEF) using a solid-state ionic method and characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). The nonlinear refractive index (γ) of silver nanowires suspended in ethanol was measured using the Z-scan technique and laser radiation of various (femto-, pico-, and nanosecond) pulse durations. Experimental results indicated that silver nanowires have obvious positive refractive nonlinearities and γ (the Kerr-induced self-focusing) increases as the pulse duration increases from 7.4×10⁻⁸ cm²/GW at 110 fs to 1.6×10⁻⁴ cm²/GW at 8 ns, due to the additional influence of the atomic reorientational Kerr effect in the case of longer pulses. Due to the solvent dependence of the nonlinear behavior of the silver nanowires, the nonlinear absorption and refraction of silver nanowires suspended in de-ionized water are smaller than those of silver samples suspended in ethanol. The thermal nonlinearities are insignificant in our experimental conditions.     

Theoretical simulations of magnetic nanotubes using Monte Carlo method

We present the results of the Monte Carlo simulations of magnetic nanotubes, which are based on the plane structures with the square unit cell at low temperatures. The spin configurations, thermal equilibrium magnetization, magnetic susceptibility and the specific heat are investigated for the nanotubes of different diameters, using armchair or zigzag edges. The dipolar interaction, Heisenberg model interaction and also their combination are considered for both ferromagnetic and anti-ferromagnetic cases. It turns out that the magnetic properties of the nanotubes strongly depend on the form of the rolling up (armchair or zigzag). The effect of dipolar interaction component strongly manifests itself for the small radius nanotubes, while for the larger radius nanotubes the Heisenberg interaction is always dominating. In the thermodynamic part, we have found that the specific heat is always smaller for the nanotubes with smaller radii.