Types Of Potential Functions Research Articles

Potential Function Describing the Folding of the 30 nm Fiber

Most of the DNA in a eucaryotic cell nucleus is accurately described as an extremely long thin fiber which is smoothly folded by histones into a thicker fiber called the 30 nm fiber. For the DNA to remain biologically functional, the 30 nm fiber must be only marginally stable. Therefore, we assume that the 30 nm fiber has fluidlike properties under physiologic conditions. It does not possess a single well-defined structure, but rather at any given instant it will possess a structure that lies within specified limits in an energy landscape. We predict an energy landscape for the 30 nm fiber by modeling the fiber as an elastic rod (DNA) subjected to an external potential (histones). For this purpose, closed-form helix-on-a-linear-helix solutions for the equilibrium configuration of an elastic rod are parametrized to fit the dimensions of the so-called solenoid model of the 30 nm fiber. We introduce a method of including a Lennard-Jones type potential function into the elastic rod model that represents histone-DNA interactions, and we parametrize the potential according to known thermodynamic data. The resulting energy landscape for the 30 nm fiber allows for structural irregularities under physiologic conditions and for unfolding of the fiber when the DNA is sufficiently overor underwound. Our model predicts that forcing a change in the amount of twist in DNA of -6.5% or +4.5% from an intrinsic twist of 10.5 base pairs per turn is sufficient to unfold the 30 nm fiber. These results describe a self-activating mechanism which enables RNA polymerase to unfold chromatin during transcription. According to our model, formation of the open complex itself is sufficient to unfold over 200 base pairs of DNA.

Robust control for planar manipulators with image feature parameter potential

In this paper, we deal with a planar manipulator control problem using camera information. We derive two types of the controller to compensate the full Lagrangian manipulator dynamics using the Lyapunov stability theory. One controller uses the image Jacobian, and the other controller requires the manipulator Jacobian and the direct kinematics. Hence these controllers are expected to have real-time computational advantages, and a robustness against the miscalibration of the camera intrinsic parameters, focal length, etc. In order to analyze the stability of the latter controller, we exploit the property of the rotational matrix and propose a new type of potential function of the image feature parameter space. The controller based on the image feature parameter potential has a nonlinear saturated potential term. Experimental results are presented to illustrate the controllers performance.

Molecular dynamics study of infinitely dilute aqueous solutions of small biological molecules. Calculation of the static and dynamic properties of formaldehyde

A molecular dynamics calculation of a dilute aqueous solution of formaldehyde was carried out using the MCY potential for the water-water interaction and an ab initio potential, a fit by a 12-6-1 type potential function, for the formaldehyde-water interaction. Several static and dynamic properties (thermodynamic functions, radial distribution functions, coordination numbers, velocity and dipole autocorrelation functions, mean square displacements, diffusion coefficients and reorientational correlation times) were calculated for this system. The results show the hydrophilic nature of the CH 2 group, and a strong interaction between the solute and solvent molecules that dydrate the carbonyl group, which hinders the translational and rotational movement of formaldehyde in this medium. The comparison of dynamical properties for pure water and in solution show how the presence of this solute leads to a smooth stabilization of the system, an enhancement of the “cage” effect in the structure of the solvent, a decrease of the translational diffusion coefficient and an increase of the reorientation time.

Application of Heuristic Asymmetric Mapping for mobile robot navigation using ultrasonic sensors

In this paper, an experimental study of a navigation system that allows a mobile robot to travel in an environment about which it has no prior knowledge is described. Data from multiple ultrasonic range sensors are fused into a representation called Heuristic Asymmetric Mapping to deal with the problem of uncertainties in the raw sensory data caused mainly by the transducer's beam-opening angle and specular reflections. It features a fast data-refresh rate to handle a dynamic environment. Potential-field method is used for on-line path planning based on the constructed gridtype sonar map. The mobile robot can therefore learn to find a safe path according to its self-built sonar map. To solve the problem of local minima in conventional potential field method, a new type of potential function is formulated. This new method is simple and fast in execution using the concept from distance-transform path-finding algorithms. The developed navigation system has been tested on our experimental mobile robot to demonstrate its possible application in practical situations. Several interesting simulation and experimental results are presented.

Structural features for hydrated CN − clusters at room temperature

Monte Carlo simulations have been carried out for CN −(H 2O) n ( n = 1–8) at room temperature using bond-bond type potential functions. The radial distribution functions and the corresponding running coordination numbers revealed the mean pictures of the gas phase hydration of CN − ion. The analysis of the quenched structures for n = 1–4 revealed that entropy effect plays important roles in these clusters. The picture of the hydration behavior shows that the CN − ion cannot be simply classified a ‘structure breaker’ in aqueous systems: the N-side of this ion is a ‘structure maker’ rather than a ‘structure breaker’ and the C-side is a real ‘structure breaker’.

Polarization effect on the static and dynamic properties of molten lithium iodide

We present how to treat the polarization effect on the static and dynamic properties in molten lithium iodide (LiI). Iodide anion has the biggest polarizability among all the halogen anions and lithium cation has the smallest polarizability among all the alkaline metal cations. The mass ratio of I to Li is 18.3 and the ion size ratio is 3.6, so we expect the most drastic characteristic motion of ions is observed. The softness of the iodide ion was examined by modifying the repulsive term in the Born-Mayer-Huggins type potential function in the previous work. In the present work we consider the polarizability of iodide ion with the dipole rod method in which the dipole rod is put at the center of mass and we solve the Euler-Lagrange equation. This method is one type of Car-Parrinello method.

Applicability of commonly used atom-atom type potential energy functions in structural analysis of nucleic acids. The role of electrostatic interactions

Applicability of five popular force fields (AMBER, CFF91, CVFF CHARMM and GROMOS) to the structural analysis of nucleic acids without explicit solvent has been examined. Structures of nine deoxyoligonucleotides in the A- and B-forms were optimized by energy minimization and compared with well-refined crystallographic data. Several models for electrostatic interactions were tested including constant and distance dependent dielectric functions in combination with varied effective charges of the phosphate groups. Similarity tests of the theoretical and experimental structures were based on a distance analysis in a conformational parameter space of the DNA molecules and on a proposed scoring scheme.

Two classes of dynamical systems all of whose bounded trajectories are closed

According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, other dynamical systems having such a closed orbit property are found on T*(R3−{0}). Consider a natural dynamical system on T*(R4−{0}) whose Hamiltonian function is composed of kinetic and potential energies, and invariant under a SO(2) action. Then one can reduce the system to a Hamiltonian system on T*(R3−{0}) by the use of the Kustaanheimo–Stiefel transformation. If the original potential on R4−{0} is a central one, Bertrand’s method is applicable to the reduced system for determining the potential so that any bounded motions may be periodic. As a result, two types of potential functions will be found; one is linear in the radial variable and the other proportional to the inverse square root of that. The dynamical systems obtained are capable of physical interpretation. In particular, the dynamical system with the inverse square root potential may be called the twofold Kepler system, whose bounded trajectories have a self-intersection point.

Supersonic jet spectroscopy of floppy molecules

The application of supersonic jet spectroscopy to the study of low-frequency, large-amplitude, anharmonic motions in the excited states of floppy molecules has been discussed. In particular, our work on inversion and torsional vibrations of 9, 10-dihydroanthracene and dihydrophenanthrene by laser-induced fluorescence excitation technique has been reviewed. The inversion of dihydroanthracene is nicely fitted with a quadratic Gaussian type potential function and the height of the barrier in the S1 state is calculated to be 94 cm−1. The inter-ring torsional frequencies of dihydrophenanthrene appear as a prominent progression and Frank-Condon analysis shows that the S1 state of the molecule is planar in contrast to a skew configuration in the ground state. A peculiar alternation of band gaps has been noticed.

A solution algorithm for the finite element analysis of creep problems

A solution algorithm for the transient analysis of bodies undergoing creep under constant or time varying loads is presented. The constitutive equation adopted is of the form: έc=γσm. The finite element formulation is carried out in terms of displacements and creep strains as internal variables. The time discretization is achieved with a trapezoidal time integration scheme. The creep strains are condensed out to give an equation for displacement increments involving a modified stiffness matrix and force vector. A Newton—Raphson iterative scheme is used for the non‐linear creep strain rate‐stress relation, and creep strains are updated at the end of the time step. The algorithm has been implemented in NOSTRUM for two‐dimensional structural and plane continuum problems, with a von Mises type potential function governing the multiaxial creep constitutive relationship. Numerical results are presented.

An empirical potential function for metal centers: Application to molecular mechanics calculations on metalloproteins

AbstractAt present, most molecular mechanics programs that model metalloproteins do not allow for specific geometric requirements at metal centers. An analysis of small‐molecule crystal structures containing four‐, five‐, and six‐coordinated zinc, retrieved from the Cambridge Structural Database (CSD), leads to a new metal‐center potential function for use in molecular mechanisc programs. This potential function includes as variables the metal‐ligand separations and the angles subtended at the metal and allows specifically for distortions from frequently occurring types of coordination geometries (e.g. tetrahedron square pyramid, trigonal bipyramid, and octahedron). The combination of such a metal‐center potential function and one for hydrogen bonds allowing for Ione‐pair directionality makes monopole electrostatic contributions to the force‐field energy superfluous, thus circumventing many problems associated with the assignment to the force‐field energy superfluous, thus circumventing many problems associated with the assignment of atomic apartial charges and a dielectric constant. The molecular mechanics program ‘YETI’, containing both types of potential functions, has been used to refine details of substrate binding of 16 complexes of human carbonic anhydrase II with small molecules. The stereochemistry of the refined complexes is in good agreement with data retrived from the CSD and hence allows realistic structure activity relationships.

Computer experiments on aqueous solutions. VI. Potential energy function for tert-butyl alcohol dimer and molecular dynamics calculation of 3 mol % aqueous solution of tert-butyl alcohol

Molecular dynamics (MD) calculation has been carried out for a dilute aqueous solution of tert-butyl alcohol (TBA) at 298.15 K and with experimental density value by the use of constant temperature technique developed previously. The total number of molecule is 216, seven of which are TBA. The mole fraction of TBA is thus 0.032. For water–water and TBA–water interactions, the MCY (Matsuoka–Clementi–Yoshimine) potential and previously reported potential determined by MO calculation are used. A new potential for TBA–TBA is determined by ab initio LCAO SCF calculations for more than 500 different configurations with an STO-3G basis set and subsequent multiparameter fitting of the MO data to a 12-6-3-1 type potential energy function. The MD calculation is extended up to 84 000 time steps (26 ps) and final 60 000 time steps are used to calculate both static and dynamic properties of the system. Both hydrophobic hydration and interaction due to TBA molecules are proved to be stronger than those of methanol studied previously. Structural promotion of water is clearly observed in radial distribution functions and trajectories of each molecule. The configuration and trajectory of all the molecules in solution indicate clearly the association of TBA molecules. It is also found from pair interaction distribution functions that no hydrogen bonding interaction occurs between two TBA molecules. The self-diffusion coefficient of water in the solution is appreciably smaller than that in pure water.

Lennard‐Jones (12,6) Parameters for the Non‐Ionic Contributions to Interionic Pairpotentials of Alkali Cations and Halide Anions from Crystal Data

AbstractLennard‐Jones (12,6) parameters for the pair interaction potentials of the alkali cations and halide anions were calculated on the basis of different alkali halide crystal data. Averaged values ϱ¯ and ϵ¯ were obtained by fitting the Buckingham type potential functions of Sangster and Dixon [15] for each individual alkali halide crystal. It was demonstrated, that these values can be used to predict unknown interaction potentials between unlike particles using the combination rules of Lorentz‐Berthelot [24] or those of Kong [18]. In particular it was shown, that the averaged parameters ϱ¯ and ϵ¯ lead to better results than the corresponding values originating from noble gas atoms.

Ab-initio refinement of an orbital-centred force field for biomolecules. test cases including peptides, a sulphonamide and modelling of DNA helices

The application of the Oribital-centred Force Field (OFF) to the calculation of the conformational behaviour of biomolecules is further considered. This method includes classical type potential functions between atom centres, but also specifies the location of non-core orbital lobes and their strength of electrostatic interaction with other lobes or atom centres. It is shown that the OFF method is not particularly advantageous for peptide systems, since although non-core orbital lobes are present with typical electrostatic strength, they do not dominate the potential surface. For other systems, however, of which sulphonamide is used as an example, the interactions between non-core orbitals are the major contribution, as was earlier shown to be the case for the nucleic acid backbone. An interesting test case is the dioxy system OXO, for which a priori the OFF approach may be inadequate because of an anomeric effect discussed by other authors interested in saccharide systems. The possibility that an intrinsic rotational potential may be required is considered but remains by no means obvious (the need for such potentials is normally absent when the OFF approach is used). Finally, the applications of the OFF approach are illustrated and tested by reference to the conformational analysis of 5′-AMP and to the computer-aided model building of DNA helices.

Vibrational assignment and potential function for t r a n s-diazene (diimide): Predictions for c i s-diazene

A revised assignment of vibrational fundamentals is developed for trans-diazene (HN=NH) and its −d1 and −d2 modifications that is consistent with all of the published spectra. The fundamental frequencies (in cm−1) for trans-diazene are: (Ag) 3128, 1583, 1529; (Au) 1286; (Bu) 3120, 1322. A seven-parameter, general valence type potential function is fit to the 18 observed frequencies of the three isotopic species with an average frequency error of 6.6 cm−1. When transformed into internal coordinate space, the theoretical potential function calculated by Perić, Buenker, and Peyerimhoff compares favorably with the empirical function. From empirical potential functions of trans-methyldiazene, trans-diazene, and cis-methyldiazene, a potential function for cis-diazene is constructed and used to predict the vibrational frequencies of this elusive substance.

The energetics of diatom/solid dissociative adsorption

The generalized Langevin method for gas-solid scattering is combined with a London-Eyring-Polanyi-Sato type potential function in order to allow calculation of collisions and simple reactions at the gas-solid interface. Energy transfer and dissociative adsorption for selected collission configurations for a diatomic molecule scattering off a Cu(100) single crystal face have been studied by integrating the classical trajectories. Special emphasis is placed on determining the relative importance of the macroscopic parameters of the collision system on the microscopic mechanisms of these processes. Energy accommodation and dissociative adsorption were found to be greatly effected by the Debye temperature of the solid.

Conformational studies on 1,1-bis(methylthio)ethylene

Energy calculations are performed for several conformations of the title compound with Lennard-Jones type potential function, EH, CNDO/2 and ab initio methods. Energy maps are built up and used to discuss the possibility of the existence of several conformers. General qualitative agreement is obtained with previous experimental findings.

Theoretical radiative lifetime of the metastable c3Πu state of H2

Magnetic dipole and electric quadrupole interactions are considered here as the mechanism for the forbidden radiative transition from the metastable c3Πu state of H2 to the dissociative b3Σu+ state. The discrete vibrational wavefuncion for the c3Πu state is generated from Browne’s potential. The continuum vibrational wavefunction for the b3Σu+ state is generated from an exponential type pontential function, which fits closely with Kolos and Wolniewicz’s potential. By virtue of this exponential type potential function, the phase integral and the exponential integral of the continuum vibrational wavefunction become integrable and an analytical expression is given for the vibrational wavefunction of b3Σu+. The electronic wavefunctions, used here to calculate the transition moments, are two-center wavefunctions previously derived by Chiu (for c3Πu) and by Hirschfelder and Linnett (for b3Σu+). It is found that the translational expansion of the magnetic dipole operator (originally at the center of mass) at the atomic centers generates an additional gradient operator, which contributes significantly towards the magnetic dipole transition probability. From the total transition probability which is a sum of that due to magnetic dipole transition and that due to electric quadrupole transition, a lifetime of τ=1.76 msec is calculated for the lowest vibrational level of the c3Πu state. For a comparison, the δ-function approximation is used for the continuum vibrational wavefunction. This approximation gives rather good agreement with the accurate calculation.

Intermolecular forces and thermodynamical functions of orthorhombic polyethylene lattice

Infrared and Raman data which are related to the intermolecular forces of the orthorhombic polyethylene lattice, the lattice mode frequencies, and the correlation field splittings of the methylene rocking and scissoring modes have been summarized through the temperature range of room to liquid helium temperature. The normal mode frequencies have been calculated for the three-dimensional crystal lattice with the dimensions measured at various temperatures, two values of the setting angle, 48.8° and 42°, being adopted for the calculation. A pairwise intermolecular force field has been assumed and the Buckingham type potential functions V (r) =B exp(−Cr)−Ar−6 (r is the interatomic distance) have been taken into account for the atomic pairs of H–H and C–H with r<4.0 Å. The potential parameters for both kinds of atomic pair have been determined by the least-squares method so as to reproduce the observed frequency data through the wide temperature range, and compared with the values reported previously. The errors involved in the intermolecular force constants thus determined and also in the calculated frequencies due to the uncertainty in the value of the setting angle assumed in the calculation have been estimated by the error-transfer method. For the temperature dependence of the lattice mode frequencies an appreciable amount of discrepancy has still been recognized even after repetition of least-squares fittings. This may be due to the approximation of the pairwise intermolecular potential and also to the anharmonic character of the lattice vibrations. The observed B1u–B2u correlation field splitting of the CH2 rocking, as well as the νa–νb splitting for the ν8 (the CH2 rocking–twisting) branch has been reproduced fairly well by the present calculation. Using the potential functions thus obtained, the thermodynamical functions, the internal energy, the entropy, the Helmholtz free energy, and the heat capacity of the orthorhombic polyethylene lattice have been calculated in the quasiharmonic approximation, giving a good agreement with the experimental results obtained by thermal measurements.

Vibrational spectra and intermolecular forces of 1,3,5,-trioxane and 1,3,5,7-tetroxocane crystals

Polarized infrared and Raman spectra of 1,3,5-trioxane (CH2O)3 and 1,3,5,7-tetroxocane (CH2O)4 crystals have been measured. The correlation field splittings for the E vibrations of the trigonal cell of trioxane have been detected by measuring polarized Raman spectra on a single-crystal specimen. The observed polarization properties of the infrared and Raman bands of tetroxocane single crystal have been interpreted by the crystal structure. The optically active lattice vibrations of the two crystals have been detected in the far-infrared and/or Raman spectra. The normal mode calculations have been performed for the three-dimensional crystal lattices by using the valence-force-field intramolecular forces and the van der Waals intermolecular interactions for the atomic pairs of H⋅⋅⋅H, O⋅⋅⋅H, C⋅⋅⋅H, O⋅⋅⋅O, C⋅⋅⋅O, and C⋅⋅⋅C. The parameters of the Lennard-Jones type potential functions have been adjusted so as to reproduce the observed lattice mode frequencies by the least-squares method and compared with the values permitted empirically by previous workers.