Harmonic Bond Research Articles

Coarse-Grained Modeling of the Actin Filament Derived from Atomistic-Scale Simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.

Polyion Adsorption onto Catanionic Surfaces. A Monte Carlo Study

The adsorption of a single and negatively charged polyion with varying flexibility onto a surface carrying both negative and positive charges representing a charged membrane surface has been investigated by using a simple model employing Monte Carlo simulations. The polyion was represented by a sequence of negatively charged hard spheres connected with harmonic bonds. The charged surface groups were also represented by charged hard spheres, and they were positioned on a hard surface slightly protruding into the solution. The surface charges were either frozen in a liquidlike structure or laterally mobile. With a large excess of positive surface charges, the classical picture of a strongly adsorbed polyion with an extended and flat configuration emerged. However, adsorption also appeared at a net neutral surface or at a weakly negatively charged surface, and at these conditions the adsorption was stronger with a flexible polyion as compared to a semiflexible one, two features not appearing in simpler models containing homogeneously charged surfaces. The presence of charged surface patches (frozen surface charges) and the ability of polarization of the surface charges (mobile surface charges) are the main reasons for the enhanced adsorption. The stronger adsorption with the flexible chain is caused by its greater ability to spatially correlate with the surface charges.

Artifacts in dynamical simulations of coarse-grained model lipid bilayers

With special focus on dissipative particle dynamics simulations of anisotropic and complex soft matter, such as lipid bilayers in water, we have investigated the occurrence of artifacts in the results obtained from dynamical simulations of coarse-grained particle-based models. The particles are modeled by beads that interact via soft repulsive conservative forces (as defined in dissipative particle dynamics simulations), harmonic bond potentials, as well as bending potentials imparting stiffness to the lipid tails. Two different update schemes are investigated: dissipative particle dynamics with a velocity-Verlet-like integration scheme [G. Besold, I. Vattulainen, M. Karttunen, and J. M. Polson, Phys. Rev. E 63, R7611 (2000)] and Lowe-Andersen thermostatting [C. P. Lowe, Europhys. Lett. 47, 145 (1999)] with the standard velocity-Verlet integration algorithm. By varying the integration time step, we examine various physical quantities, in particular pressure profiles and kinetic bead temperatures, for their sensitivity to artifacts caused by the specific combination of integration technique and the thermostat. We then propose a simple fingerprint method that allows monitoring the presence of simulation artifacts.

Reactivity of Atomic Cobalt with Molecular Oxygen: A Combined IR Matrix Isolation and Theoretical Study of the Formation and Structure of CoO2

The reactivity of atomic cobalt toward molecular oxygen in rare gas matrices has been reinvestigated. Experiments confirm that Co atoms in their a(4)F ground state are inert toward O(2) in solid argon and neon but reactive in the b(4)F first excited state, in agreement with the previous gas-phase study of Honma and co-workers. The formation of CoO(2) starting from effusive beams of Co and O(2) has been followed by IR absorption spectroscopy, both in neon and argon matrices. Our observations show that only the dioxo form, OCoO, is stabilized in the matrix and that IR absorptions previously assigned to the peroxo and superoxo forms are due to other, larger species. The present data strongly support the linear geometry in rare gas matrices proposed by Weltner and co-workers. We report on measurements on all IR-active fundamental modes for (16)OCo(16)O, (18)OCo(18)O, and (16)OCo(18)O with additional combination transitions supplying anharmonicity correction. This allows for a 5.93 +/- 0.02 mdyne/A CoO harmonic bond force constant in solid neon. Using the empirical relationship previously optimized for the CoO diatomics, an approximate value for the CoO internuclear bond distance is proposed (1.615 +/- 0.01A). In light of recent theoretical studies predicting (2)A(1) or (6)A(1) electronic ground states, the geometry and electronic structure of the OCoO molecule has also been reconsidered. Calculations carried out at the CCSD(T)/6-311G(3df) level indicate a linear structure with an r(e) = 1.62 A bond distance, consistent with the experimental estimate. For later studies of larger systems, where CCSD(T) calculations become too time-consuming, an effective DFT-based method is proposed which reproduces the basic electronic and geometrical properties of cobalt dioxide. Quantitative results are compared to the experimental data and high-level results regarding bond length and frequencies. This DFT method is used to propose a reaction pathway.

A coarse grain model for n-alkanes parameterized from surface tension data

Molecular dynamics simulations are carried out in a systematic manner to develop a coarse grain model for multiple-of-three carbon n-alkanes. The procedure involves optimizing harmonic bond and bend parameters, and Lennard-Jones nonbonded parameters, to match observables taken from fully atomistic simulations and from experiment. The experimental values used consist of surface tension and bulk density data. Scaling relations are introduced to allow for the representation of the remaining n-alkanes. As n increases these relations converge to the multiple-of-three carbon values. The model is assessed by comparing it to both fully atomistic simulation and experimental data which was not used in the fitting procedure.

Anharmonicity in mineral physics: A physical interpretation

Mineral physicists often refer to the quasi‐harmonic approximation. This approximation accepts the intrinsically anharmonic effects of positive thermal expansion coefficient, α, and pressure‐dependent bulk modulus, KT. However, for insulators at high temperatures, the classical specific heat, CV, and the product αKT are assumed to be independent of temperature at constant volume. Departures from this approximation are termed anharmonicity. We interpret this distinction using derivatives of the atomic potential function, ϕ(r), with atomic spacing, r. CV and KT are reasonably explained by harmonic bonds, that is, ϕ ∝ (r − a)2, where a is the equilibrium value of r, so that ϕ″ = d2ϕ/dr2 is the only derivative considered. Thermal pressure or expansion and pressure dependence of KT depend on ϕ‴ (referred to as first‐order anharmonic effects). Temperature dependence of CV requires ϕiv and is a second‐order anharmonic effect. The temperature variation of αKT arises from ϕv, a third‐order effect. By calculating the Grüneisen parameter, γ, as the ratio of thermal pressure to thermal energy, we relate its anharmonicity to a ratio of derivatives of ϕ. For all commonly used finite strain theories, this gives a temperature variation of γ at high temperature and constant volume systematically less than that of CV. Anharmonicity of CV, which has been more comprehensively studied, may be a few percent at 2000 K, but decreases strongly with compression, so that anharmonicity of both γ and CV is negligible (less than 1% in the case of γ under deep‐Earth conditions).

The pure rotational spectra of the lanthanum monohalides, LaF, LaCl, LaBr, LaI

Pure rotational spectra have been measured for all the major isotopomers of the lanthanum monohalides, LaF, LaCl, LaBr, and LaI, in their ground and (except for La 81 Br ) excited vibrational states. The spectra were observed with a cavity pulsed jet Fourier transform microwave spectrometer in the frequency range 5–24 GHz. The molecules were prepared by laser ablation of La metal and allowing the resulting plasma to react with SF 6, Cl 2, Br 2, or CH 3I precursor in an Ar carrier gas of the pulsed jet. For LaBr this is the first reported spectrum of any kind. Rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants, and nuclear spin–rotation constants have been determined for all the molecules. Accurate equilibrium ( r e ) internuclear distances have given an indication of where the Born–Oppenheimer approximation is beginning to fail. From the centrifugal distortion constants and vibration–rotation ( α e ) constants good estimates of the harmonic vibration frequencies and bond dissociation energies have been obtained. The halogen nuclear quadrupole coupling constants indicate the molecules to be highly ionic.

Analytical Potential Energy Function for the Ground State X1Σ+ of Lanthanum Monofluoride**The project supported by National Natural Science Foundation of China under Grant No. 10074037

The equilibrium geometry, harmonic frequency and bond dissociation energy of lanthanum monofluoride have been calculated using Density-Functional Theory (DFT), post-HF methods MP2 and CCSD(T) with the energy-consistent relativistic effective core potentials. The possible electronic state and reasonable dissociation limit of the ground state of LaF are determined based on atomic and molecular reaction statics. Potential energy curve scans for the ground state X1Σ+ have been performed at B3LYP and CCSD(T) levels, due to their better results of harmonic frequency and bond dissociation energy. We find that the potential energy calculated with CCSD(T) is about 0.6 eV larger than the bond dissociation energy, when the internuclear distance is as large as 0.8 nm. The problem that single-reference ab initio methods do not meet dissociation limit during calculations of lanthanide heavy-metal elements is analyzed. We propose the calculation scheme to derive the analytical Murrell-Sorbie potential energy function. Vibrotational spectroscopic constants Be, ωe, ωeχe, αe, βe, De and He obtained by the standard Dunham treatment coincide well with the results of rotational analyses on spectroscopic experiments.

Equilibrium polymerization of cyclic carbonate oligomers. II. Role of multiple active sites

Ring opening polymerization of bisphenol A polycarbonate is studied by Monte Carlo simulations of a model comprising a fixed number of Lennard-Jones particles and harmonic bonds [J. Chem. Phys. 115, 3895 (2001)]. Bond interchanges produced by a low concentration (0.10%⩽ca⩽0.36%) of chemically active particles lead to equilibrium polymerization. There is a continuous transition in both 2D and 3D from unpolymerized cyclic oligomers at low density to a system of linear chains at high density, and the polymeric phase is much more stable in three dimensions than in two. The steepness of the polymerization transition increases rapidly as ca decreases, suggesting that it is discontinuous in the limit ca→0. The transition is entropy driven, since the average potential energy increases systematically upon polymerization, and there is a steady decline in the degree of polymerization as the temperature is lowered. The mass distribution functions for open chains and for rings are unimodal, with exponentially decaying tails that can be fitted by Zimm–Schulz functions and simpler exponential forms.

Rigid-body formalism for simulating macromolecules

Abstract In our work we aim at developing a model where macromolecules are represented on a mesoscopic level as an assembly of rigid bodies which interact via arbitrary bonded and non-bonded interactions. For the non-bonded interactions we use a variant of the Gay–Berne potential, while the bonded interactions are split into an orientational part and a harmonic bond between two arbitrary points in the respective material frames.

Time-Trimming Tricks for Dynamic Simulations: Splitting Force Updates to Reduce Computational Work

Time-Trimming Tricks for Dynamic Simulations: Splitting Force Updates to Reduce Computational Work

An ab initio two-component relativistic method including spin–orbit coupling using the regular approximation

In this paper we present the implementation of the two-component scaled zeroth-order regular approximation (ZORA) method in the molecular electronic structure package GAMESS-UK. It is the first application of this method, which was earlier investigated in the context of density functional theory, in molecular ab initio basis set calculations. The performance of the method is tested in atomic calculations, which we can compare with numerical results, on xenon and radon and in molecular calculations on the molecules AgH, HI, I2, AuH, TlH, and Bi2. In calculations on the I2 molecule we investigated the effect of the different approaches regarding the internal Coulomb matrix used in the ZORA method. For the remaining molecules we computed harmonic frequencies and bond lengths. It is shown that the scaled ZORA approach is a cost-effective alternative to the Dirac–Fock method.

Molecular modeling of dimetal systems: Part 4. Dirhenium bonds

The relationship between bond order ( N), harmonic force constant ( k r ) and characteristic bond length free of strain ( r 0) for dirhenium bonds has been studied by molecular-mechanics simulation of suitable structures well characterized by X-ray diffraction. It follows the same trend, N= ak r = abr 0 −5, found before for dimolybdenum and dichromium bonds.

Simulations of the Effect of Diblock Surfactant Spacer Molecules on Micelle Structure and Function

A simple model for surfactants in solution is used to investigate the effect of diblock spacer molecules on the structure of micellar systems. The solvent is modeled by a simple Lennard-Jones fluid and the surfactants and spacer molecules are modeled by chains of Lennard-Hones sites connected by simple harmonic bonds. The surfactant is modeled as a solventphobic tail attached to a single solventphilic head site; the spacer is modeled as a solventphobic tail attached to a chain of solventphilic head sites. Molecular dynamics simulations on large systems ({approximately}40 000 particles) are performed to investigate the properties of the model. The strength of the interaction between the solventphilic portion of the spacer and the solvent and the effect of the length of both the solventphobic and the solventphilic portions of the spacer on the structure of the micelle solution are investigated. The simulations suggest that for the spacer to keep micelles apart, the interaction between the solvent and solventphilic portion of the spacer must be fairly strong. Weak interactions between the solventphilic portion of the spacer and the solvent cause the spacer to collapse on the surface of the micelle.

Structure and Dynamics of Dilute Polymer Solutions under Shear Flow via Nonequilibrium Molecular Dynamics

We present and discuss results obtained by an extensive nonequilibrium molecular dynamics computer simulation study of polymer solutions under shear, where the chain consists of N beads connected by a finitely extendable nonlinear elastic (FENE) spring force and the solvent is explicitly taken into account. Various scaling laws are extracted from the data which allow one to predict the qualitativeand to certain extent also quantitativestructural and rheological behavior of polymer solutions under good solvent conditions. For most quantities, the results drawn from simulation are compared with experimental data and theoretical predictions which are based on similar models (e.g., harmonic bond potentials or Brownian dynamics methods). Specifically, and in contrast to common theoretical approaches, the simulation yield information about a set of different but characteristic relaxation times, which determine the rheological and structural behavior (for example, flow birefringence, structure factor, rotational dynamics) separately, the difference either resulting from the underlying static or dynamic nature or from relaxation processes which act on different length scales.

Molecular Modeling of Dimetal Systems. Part 2. Low-Order Dimolybdenum

Through molecular modeling of the available structures containing dimolybdenum bonds of orders 3.5 and 3, solution pairs of harmonic force constant (kr) and bond length (ro) have been obtained as (3.63 mdyne/A, 2.07 A) and (3.37 mdyne/A, 2.10 A), respectively. Together with the known solution pair for MoMo, this sufficed to establish a general relationship between kr, ro and bond order, N, as N = 0.9537kr = 131.8ro-5. Using this relationship as a sampling curve, we extended the analysis to include Mo2 bonds of orders 2 and 1. The relationship was accordingly shown to apply to the entire {N, kr} space.

Development of an All-Atom Force Field for Heterocycles. Properties of Liquid Pyrrole, Furan, Diazoles, and Oxazoles

The approach to the extension of the optimized potentials for liquid simulations all-atom (OPLS-AA) force field, which was tested for pyridine and the diazenes in the first paper of this series, has been extended to pyrrole, pyrazole, imidazole, furan, isoxazole, and oxazole. Standard OPLS Lennard-Jones parameters are used for the nonbonded interactions in conjunction with partial charges obtained from fitting to RHF/6-31G* electrostatic potential surfaces. The harmonic bond stretching and angle bending terms are adopted mostly from the AMBER force field, although the addition of two new atom types was required. The resultant force field was tested by computing the gas-phase structures of the heterocycles, heterocycle−water interaction energies, properties of the pure liquids, and the relative free energies of hydration for pyrrole and imidazole.

Synthesis and Spectroscopic Identification of Ethylidyne Adsorbed on Ni(111)

The interaction of ethylene adsorbed on Ni(111) with gas-phase H atoms has been investigated. The major adsorbed reaction product is identified by high-resolution electron energy loss spectroscopy to be ethylidyne (C−CH3). This study is the first direct spectroscopic observation of a C−CH3 species adsorbed on Ni in an ultrahigh-vacuum environment. Spectra of four isotopomers, C−CH3, 13C−13CH3, C−CD3, and 13C−13CD3, are reported, and a complete and consistent vibrational assignment of their fundamental modes is presented. Based on this assignment, a force field is derived from the measured vibrational frequencies using a normal-modes analysis and is found to be in good agreement with that deduced from IR spectra of an ethylidyne species in an organometallic complex. Inspection of the eigenvectors of the normal-mode displacements reveals that substantial mixing of harmonic bond motions is the origin of the unusual upshift in frequency of the C−C stretching mode upon deuteration. A quantitative determination of the relative dynamic bond dipole moments demonstrates that the changes in intensity and dipole activity of the C−C stretching and symmetric CH3 deformation modes upon deuteration, phenomena common to all C−CD3 spectra, also arise from extensive mixing of bond motions. A detailed analysis of the spectra strongly suggests a C3v or C3 local environment for ethylidyne and a 3-fold hollow adsorption site.

Scaling and scale breaking in polyelectrolytes

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest-neighbor interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behavior is well reproduced by the analytical high-T expansions even for fairly low temperatures and system sizes. In addition, results from low-T expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for conformational as well as thermodynamical properties. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behavior, which is verified by Monte Carlo results, is, for the end-to-end distance, consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-T expansion is inaccurate at realistic temperatures.

Kinetics of homopolymer collapse

Langevin-equation simulation is used to study the dynamics of a simple model of homopolymer collapse at infinite dilution for polymers of lengths N=100, 200, 300, 500, and 1024 units. Lennard-Jones potentials are chosen to represent the bead–bead interactions and a harmonic potential bonds nearest-neighbor beads. The Flory coil-to-collapsed globule transition is brought about by an adjustment of the Lennard-Jones potential interactions. The average cluster size and distribution, along with the radius of gyration are used to characterize the collapse dynamics. Our results indicate that there are several kinetic mechanisms that lead to a collapsed polymer. At early times the dominant mechanisms involve cluster creation and growth by adsorption of slack polymer, whereas for later times the mechanism involves cluster coarsening. For this latter mechanism we find that the average cluster size 〈s〉 grows as 〈s〉=Atz, where z is dependent on u3, the third virial coefficient. Depending on the value of u3 we determine two values for z, first, z=0.60±0.02 for u3 not equal to zero and second z=0.66±0.03 for u3 equal to zero, both representing a departure from Lifshitz–Slyozov theory.