Determination of the number of degrees of freedom of the trapeziometacarpal joint–An in vitro study

ObjectiveMost of the studies about trapeziometacarpal joint assume that it exhibits only two independent degrees of freedom, but the experimental or theoretical support for considering a two-degrees of freedom model is not always clear.Materials and methodsTherefore, an in vitro kinematic study has been designed to demonstrate, from experimental data, that only two of the trapeziometacarpal degrees of freedom (i.e., flexion/extension and adduction/abduction) are non-null and independent. Several movements of maximal amplitude in flexion, abduction and circumduction have been realized and the relative position and orientation of the segment coordinate system embedded on the first metacarpal with respect to that embedded on the trapezium have been collected using electromagnetic sensors. The trapeziometacarpal rotations have been described using a joint coordinate system and the joint displacements have been evaluated on the axes of this coordinate system.ResultsThe root mean square (RMS) values of the joint displacement components have been found small enough to assume that the trapeziometacarpal joint has no translation degrees of freedom. A paraboloid coupling equation has been found between the internal/external rotation angle and the two other, flexion/extension and adduction/abduction, angles.ConclusionThus, this study demonstrates that the trapeziometacarpal joint has only two independent rotational degrees of freedom, and further, the described methodology could also be used to determine the coupling laws between degrees of freedom of various joints.     

Ad hoc continuum-atomistic thermostat for modeling heat flow in molecular dynamics simulations

An ad hoc thermostating procedure that couples a molecular dynamics (MD) simulation and a numerical solution to the continuum heat flow equation is presented. The method allows experimental thermal transport properties to be modeled without explicitly including electronic degrees of freedom in a MD simulation. The method is demonstrated using two examples, heat flow from a constant temperature silver surface into a single crystal bulk, and a tip sliding along a silver surface. For the former it is shown that frictional forces based on the Hoover thermostat applied locally to grid regions of the simulation are needed for effective feedback between the atomistic and continuum equations. For fast tip sliding the thermostat results in less surface heating, and higher frictional and normal forces compared to the same simulation without the thermostat.     

An Application of Classical Molecular Dynamics Simulation and AB Initio Density-Functional Calculation in Surface Physics

Abstract

Classical molecular dynamics simulation and ab initio mixed basis Car-Parrinello methods are discussed and applied to the investigation of the results of a recently performed STM-based experiment involving the adsorption of C₆₀ molecules on the dimerized Si surface. We show that these methods are capable of providing the theoretical basis for this experiment and test the validity of the associated conjectures.

A mixed-basis all-electron formalism for the Car-Parrinello method is proposed to obtain the detailed understanding of the electronic states and dynamics of surface structure. A band structure calculation using this formalism is performed for the c(4 × 3) structure of C₆₀ adsorbed on Si (100) surface and is compared with the experimental results.     

A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations

A hybrid atomistic-continuum method is presented for incorporating Joule heating into large-scale molecular dynamics (MD) simulations. When coupled to a continuum thermostat, the method allows resistive heating and heat transport in metals to be modeled without explicitly including electronic degrees of freedom. Atomic kinetic energies in a MD simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity, atomic density, and average kinetic energy in the MD simulation. A network of resistors is established from which the potential at every FDG region is calculated given an applied voltage. The potential differences and the resistance between connected FDG regions are used to calculate the current between the two points and the heat generated from that current. This information is then added back into the atomic simulation. The method is demonstrated by simulating Joule heating and melting, along with associated changes in current, of single and bundles of metal nanowires, as well as a “pinched” wire under applied strain.     

A simple two-dimensional representation for the common secondary structural elements of polypeptides and proteins

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C^αatoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudo-dihedral involving four sequential C^αatoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple ϕ,ψ pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor. © 1997 Wiley-Liss, Inc.     

Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium

The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)₅₀, (AlaGly)₂₅, and (AlaGly)₇₅ polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.     

Molecular dynamics simulation of protein folding by essential dynamics sampling: folding landscape of horse heart cytochrome c

A new method for simulating the folding process of a protein is reported. The method is based on the essential dynamics sampling technique. In essential dynamics sampling, a usual molecular dynamics simulation is performed, but only those steps, not increasing the distance from a target structure, are accepted. The distance is calculated in a configurational subspace defined by a set of generalized coordinates obtained by an essential dynamics analysis of an equilibrated trajectory. The method was applied to the folding process of horse heart cytochrome c, a protein with approximately 3000 degrees of freedom. Starting from structures, with a root-mean-square deviation of approximately 20 A from the crystal structure, the correct folding was obtained, by utilizing only 106 generalized degrees of freedom, chosen among those accounting for the backbone carbon atoms motions, hence not containing any information on the side chains. The folding pathways found are in agreement with experimental data on the same molecule.     

Two- and Higher Point Correlation Functions in Proteins

Abstract

A method is presented for a more efficient sampling of the configurational space of proteins as compared to conventional sampling techniques such as molecular dynamics. The method is based on the large conformational changes in proteins revealed by the “essential dynamics” analysis. A form of constrained dynamics is performed, forcing the system to move along some of the essential coordinates. This results in a broader sampling of the essential subspace than in a comparable conventional molecular dynamics simulation without constraints. The new sampling method (essential dynamics sampling) was applied to the histidine-containing phosphocarrier protein HPr. The results indicate that the essential dynamics sampling method produces physically allowed structures, as estimated by the evaluation of many geometrical properties. In addition, a study of the motions in the essential subspace reveals a diffusion-like behavior.     

Investigation of the influence of external factors on the conformational dynamics of rhodopsin-like receptors by means of molecular dynamics simulation

Abstract

The study reports about the influence of binding of orthosteric ligands on the conformational dynamics of β-2-adrenoreceptor. Using molecular dynamics (MD) simulation, we found that there was a little fraction of active states of the receptor in its apo (ligand-free) ensemble. Analysis of MD trajectories indicated that such spontaneous activation of the receptor is accompanied by the motion in intracellular part of its alpha-helices. Thus, receptor’s constitutive activity directly results from its conformational dynamics. On the other hand, the binding of a full agonist resulted in a significant shift of the initial equilibrium towards its active state. Finally, the binding of the inverse agonist stabilized the receptor in its inactive state. It is likely that the binding of inverse agonists might be a universal way of constitutive activity inhibition in vivo. Our results indicate that ligand binding redistribute pre-existing conformational degrees of freedom (in accordance to the Monod–Wyman–Changeux Model) of the receptor rather than cause induced fit in it. Therefore, the ensemble of biologically relevant receptor conformations is encoded in its spatial structure, and individual conformations from that ensemble might be used by the cell in conformity with the physiological behavior.     

Investigations of Nematic-Isotropic Transition by Means of Constant Pressure Molecular Dynamics Simulations

Abstract

Constant pressure molecular dynamics simulations, which secure the system to be under hydrostatic pressure, are used to simulate the behavior of liquid crystals consisting of anisotropic molecules with both translational and orientational freedom. In order to investigate to what extent can the properties known to real liquid crystalline phases be explained by the anisotropy of the shape of the molecules alone, the molecular dynamic (MD) simulation uses purely repulsive short-range pair potentials representing soft spherocylinders. A clear change in the microscopic as well as the macroscopic physical properties are observed near the phase transition from nematic liquid crystal to isotropic liquid.     

An Adiabatic Molecular Dynamics Method for the Calculation of Free Energy Profiles

A new molecular dynamics method for calculating free energy profiles for rare events is presented. The new method is based on the creation of an adiabatic separation between the reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass, thereby allowing the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profiles are obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, require no postprocessing of the output data. The new method is applied to a variety of model problems and its performance tested against free energy calculations using the "bluemoon ensemble" approach. The comparison shows that free energy profiles can be calculated with greater ease and efficiency using the new method.     

Molecular dynamics of oligopeptides 6. A comparative study of poincare cross-section of monopeptide frames in media with different hydrophobicity

A comparative study of the molecular dynamics of natural amino acid residues and their closest homologues and isomers was carried out. Molecular dynamics protocols not interfering with the principle of equidistribution of energy with respect to degrees of freedom were used. Poincare cross-sections, auto- and cross-correlation of complex exponential curves as a function of dihedrons were considered. The classification of dynamic properties of conformational degrees of freedom in the series of amino acid residues was carried out.     

Ionisation of fullerenes and fullerene clusters using ultrashort laser pulses.

We give a brief review of the literature concerning the ultra-short pulse ionisation of fullerenes in the gas phase. Emphasis is placed on the excitation time dependence of different ionisation regimes as manifested by photoelectron spectroscopy. The ionisation rates are modelled for the intermediate situation where the excitation energy is equilibrated between electronic degrees of freedom but not yet coupled to vibrational degrees of freedom. The model is shown to describe many aspects of the experiments. New results are presented on the intra-cluster molecular fusion of fullerene molecules when van der Waals bound clusters of fullerenes are exposed to ultra-short laser pulses. Pump-probe measurements give a decay time constant for the intra-cluster fusion reaction of 520 +/- 55 fs. A comparison with monomer ionisation results suggests that the time window for the fusion reaction is influenced by the coupling of the electronic excitation energy to vibrational degrees of freedom of the molecules in the cluster.     

A Comparison Between Elastic Network Interpolation and MD Simulation of 16S Ribosomal RNA

Abstract

In this paper a coarse-grained method called elastic network interpolation (ENI) is used to generate feasible transition pathways between two given conformations of the core central domain of 16S Ribosomal RNA (16S rRNA). The two given conformations are the extremes generated by a molecular dynamics (MD) simulation, which differ from each other by 10Å in root-mean-square deviation (RMSD). It takes only several hours to build an ENI pathway on a 1.5GHz Pentium with 512 MB memory, while the MD takes several weeks on high-performance multi-processor servers such as the SGI ORIGIN 2000/2100. It is shown that multiple ENI pathways capture the essential anharmonic motions of millions of timesteps in a particular MD simulation. A coarse-grained normal mode analysis (NMA) is performed on each intermediate ENI conformation, and the lowest 1% of the normal modes (representing about 40 degrees of freedom (DOF)) are used to parameterize fluctuations. This combined ENI/NMA method captures all intermediate conformations in the MD run with 1.5Å RMSD on average. In addition, if we restrict attention to the time interval of the MD run between the two extreme conformations, the RMSD between the closest ENI/NMA pathway and the MD results is about 1Å. These results may serve as a paradigm for reducedDOF dynamic simulations of large biological macromolecules as well as a method for the reduced-parameter interpretation of massive amounts of MD data.     

Mesoscale Modeling of Amphiphilic Fluid Dynamics

Abstract

So-called “vector models”, in which surfactant molecules retain only translational and orientational degrees of freedom, have been used to study the equilibrium properties of amphiphilic fluids for nearly a decade now. We demonstrate that hydrodynamic lattice-gas automata provide an effective means of coupling the Hamiltonian of such vector models to hydrodynamic flow with conserved momentum, thereby providing a self-consistent treatment of the hydrodynamics of amphiphilic fluids. In this “talk”, we describe these hydrodynamic lattice-gas models in two and three dimensions, and present their application to problems of amphiphilic-fluid hydrodynamics, including the dynamics of phase separation and the shear-induced sponge-to-lamellar phase transition.     

The Implementation of the Iterative Diagonalization Scheme and ab initio Molecular Dynamics Simulation with the LAPW Method

Abstract

A new ab initio molecular dynamics method based on the full-potential linearized-augmented-plane-wave (LAPW) basis set has been implemented. The LAPW basis set has been successfully employed for systems containing localized electrons such as first row atoms and transition metals. In our implementation of the LAPW-MD scheme, iterative residual minimization algorithm is used to solve the electronic states problem. The atoms are moved according to forces derived from the Hellman–Feynman theorem and incomplete basis set correction terms. The performance of the program is further enhanced by parallelization. We will discuss technical details of the program implementation and present results obtained from this code to the equilibrium structures and vibrational properties of simple diatomic molecules.     

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract

Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nosé-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox associated with steady-state statistical mechanics: the Gibbs entropy of a nonequilibrium steady state decreases continuously to minus infinity.     

Investigation of the mechanism for rapid heating of nitrogen and air in gas discharges

A rapid heating of nitrogen-oxygen mixtures excited by gas discharges is investigated numerically with allowance for the following main processes: the reactions of predissociation of highly excited electronic states of oxygen molecules (which are populated via electron impact or via the quenching of the excited states of N₂ molecules), the reactions of quenching of the excited atoms O(¹ D) by nitrogen molecules, the VT relaxation reactions, etc. The calculated results adequately describe available experimental data on the dynamics of air heating in gas-discharge plasmas. It is shown that, over a broad range of values of the reduced electric field E/N, gas heating is maintained by a fixed fraction of the discharge power that is expended on the excitation of the electronic degrees of freedom of molecules (for discharges in air, η_E?28%). The lower the oxygen content of the mixture, the smaller the quantity η_E. The question of a rapid heating of nitrogen with a small admixture of oxygen is discussed.     

Multishelled Gold Nanowires

Abstract

The current miniaturization of electronic devices raises many questions about the properties of various materials at nanometre-scales. Recent molecular dynamics computer simulations have shown that small finite nanowires of gold exist as multishelled structures of lasting stability. These classical simulations are based on a well-tested embedded atom potential. Molecular dynamics simulation studies of metallic nanowires should help in developing methods for their fabrication, such as electron-beam litography and scanning tunneling microscopy.