N-body Interactions Research Articles

Modeling salt-mediated electrostatics of macromolecules: The discrete surface charge optimization algorithm and its application to the nucleosome

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.

Theory of Coulomb scattering in particle beams using Markov’s method

An analytic theory of Coulomb scattering in particle beams is derived. It rests on the assumption that the N-body interaction can be well approximated by the vector superposition of all individual two-body interactions on a single, randomly chosen particle. This is the only assumption or approximation needed. A direct mathematical correspondence exists with the general problem of random flights, which was solved by Markov. The theoretical prediction agrees with Monte Carlo simulation to within a few percent for the lateral trajectory displacement for a particular case. The computation time required for the analytical result is at least an order of magnitude smaller than that required for Monte Carlo simulation.

N-body study of anisotropic membrane inclusions: Membrane mediated interactions and ordered aggregation

We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes.

Polymer Gas Approach to N-Body Lattice Systems

We give a simple proof, based only on combinatorial arguments, of the Kotecký–Preiss condition for the convergence of the cluster expansion. Then we consider spin systems with long-range N-body interactions. We prove directly, using the polymer gas representation, that the pressure may be written in terms of an absolutely convergent series uniformly in the volume when the interaction is summable in a suitable sense. We also give an estimate of this radius of convergence. In order to get the proof we use a method introduced by Cassandro and Olivieri in the early 1980s. We apply this method to various concrete examples.

N-fermion ground state of Calogero-Sutherland type models in two and higher dimensions

I obtain the exact ground state of N fermions in D dimensions ( D ≥ 2) in the case that the N particles are interacting via long-ranged two-body and three-body interactions and further they are also interacting via the harmonic oscillator potential. I also obtain the N-fermion ground state in the case that the oscillator potential is replaced by an N-body Coulomb-like interaction.

Fragmentation of Molecular Clouds: The Initial Phase of a Stellar Cluster

The isothermal gravitational collapse and fragmentation of a region within a molecular cloud and the subsequent formation of a protostellar cluster are investigated numerically. The clump mass spectrum that forms during the fragmentation phase can be well approximated by a power-law distribution dN/dM∝M−1.5. In contrast, the mass spectrum of protostellar cores that form in the centers of Jeans-unstable clumps and that evolve through accretion and N-body interactions is described by a lognormal distribution with a width that is in excellent agreement with observations of multiple stellar systems.

Theoretical study of the n-body interaction energies of the ring, cage and prism forms of (H 2O) 6

The MP2 method is used together with basis sets as large as aug-cc-pVQZ to calculate the binding energies and the various n-body interaction energies of the ring, cage and prism forms of (H 2O) 6. It is found that nearly all of the energy changes due to adoption of basis sets more flexible than aug-cc-pVDZ and to the inclusion of electron correlation effects are due to the 2-body interactions.

Fractional Quantum Hall Effect States as Exact Ground States

We construct many particle Hamiltonians for which the Laughlin and Jain wavefunctions are exact ground states. The Hamiltonians involve fermions in a magnetic field and with inter-particle interactions. For the Laughlin wave-functions, the interactions involve two- and three-body correlations similar to the Chern–Simons interactions, whereas for the projected Jain wave-functions, N-body interactions (which cannot be explicitly written down in general) are involved.

HKT and OKT geometries on soliton black hole moduli spaces

We consider Shiraishi's metrics on the moduli space of extreme black holes. We interpret the simplification in the pattern of N-body interactions that he observed in terms of the recent picture of black holes in four and five dimensions as composites, made up of intersecting branes. We then show that the geometry of the moduli space of a class of black holes in five and nine dimensions is hyper-Kahler with torsion, and octonionic-Kähler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersymmetry and show that both of the above geometries arise naturally in this context. In addition, we construct a large class of hyper-Kahler with torsion and octonionic-Kähler with torsion geometries in various dimensions. We also present a brane interpretation of our results.

Comparisons between statistics of low energy collision cascades generated by full molecular dynamics and by its binary collision approximation

Collision cascades in Cu, Au and Cu3Au are generated by full molecular dynamics (MD) and by its binary collision approximation (BCA) with the Marlowe program. Cu and Au primaries have 1 keV initial energy. The same Molière repulsive potential is used in both models for close encounters. In the MD model, this potential is carefully splined to the pair component of the N-body potential developed by Ackland and Vitek. In the BCA, this N-body interaction is roughly modeled by a constant isotropic 4 eV binding energy of the target atoms to their rest positions. Time distributions of the number of atoms moving with a total energy higher than a threshold value E d are compared and discussed. Recoil range distributions during the cascade development are discussed as well. The agreement between MD and BCA is fairly good in all cases for E d larger than about 3 eV. In the case of smaller E d-values, the BCA may result in an overestimate of the number of moving atoms in the late development of the cascades. This discrepancy is suggested to originate in the lack of attractive forces between the moving particles and the surrounding atoms in the BCA.

Structural and vibrational analysis of amorphous Au55 clusters.

We present a structural and vibrational analysis of several amorphous (disordered) and ordered isomers of a 55-atom gold cluster. A Gupta n-body potential, with parameters fitted to gold clusters, was used to model the metallic bonding in the ${\mathrm{Au}}_{55}$ cluster. The molecular-dynamics method combined with simulated annealing and quenching techniques were used to perform the cluster structure optimization. Our results show that several nonequivalent and nearly degenerate in energy amorphous cluster structures are more stable than those with high symmetry like the 55-atom Mackay icosahedron and the fcc cuboctahedron. The calculated distribution of normal frequencies clearly discriminates between amorphous and ordered cluster configurations and confirms their stability. A common-neighbor analysis was implemented to characterize the disordered cluster structures, identifying the short-range order of the amorphous phase, according to the local environment of each atom pair in the cluster. Distorted multilayer icosahedral order was found to be the more representative of the amorphous clusters with the lowest energies. At higher energies, the amorphous structures are characterized by the presence of distorted local icosahedral order. The origin of the higher stability of amorphous vs ordered isomers in ${\mathrm{Au}}_{55}$ is in the short range of the n-body interaction existing in the metal cluster bonding. \textcopyright{} 1996 The American Physical Society.

Fast adaptive multipole method for computation of electrostatic energy in simulations of polyelectrolyte DNA

This article presents a fast adaptive method for the computation of long-range electrostatic interactions in computer simulations of polyelectrolyte DNA. Classically, the computation of electrostatic energy involves a direct summation of all pairwise in teractions due to the charged phosphate groups in the molecule. This results in an N-body interaction problem with an asymptotic time complexity of O(N2) which is computationally very expensive and limits the number of phosphate groups that can be used in computer simulations of polyelectrolyte DNA to at most several hundred. We describe an effort to speed up computer simulations of polyelectrolyte DNA with the use of a fast adaptive hierarchical algorithm for the computation of electrostatic energy (i.e., modified Debye–Hückel energy). The asymptotic time complexity is reduced to O(N) with the implementation of the fast hierarchical algorithm on serial computers. This is achieved by grouping phosphate groups into an adaptive hierarchical data structure and computing the interactions between groups using low order multipole and Taylor series expansions expressed in Cartesian coordinates. We first examine the accuracy and speed enhancements of the fast hierarchical method in the computation of the electrostatic energy of circular DNA at zero and high salt concentrations. The fast hierarchical method is further tested in a one-step Monte Carlo (MC) simulated annealing algorithm for closed circular supercoiled DNA. In all cases, we observe order of magnitude reductions in the computation time with negligible loss of numerical accuracy in the electrostatic energy computation. © 1996 by John Wiley & Sons, Inc.

Microstructural analysis of simulated liquid and amorphous Ni.

Molecular dynamics simulations and a systematic analysis of the local atomic structure have been done to investigate the microstructure of liquid and amorphous Ni. The n-body Gupta potential, based on the second moment approximation of a tight-binding Hamiltonian, was used to model the metallic bonding of the system. The calculated pair distribution function (PDF) of liquid and amorphous Ni are in agreement with experimental measurements. A decomposition of the first and second peaks of the PDF into components according to the local environment of the pairs shows that the atomic coordination of the liquid phase contains a high abundance of icosahedral and distorted icosahedral structures. Crystalline and icosahedral (regular and distorted) atomic configurations contribute in approximately the same proportion to the short-range order of the amorphous phase. These results indicate that n-body interactions favor the formation of crystalline order in amorphous metals. \textcopyright{} 1996 The American Physical Society.

`Smart' self-avoiding trails and the collapse of chain polymers in three dimensions

Recently, it was shown that certain `smart' self-avoiding trails have end-to-end distances in three dimensions. Also, the corrections to scaling of and the specific heat are qualitatively very similar to those for polymers exactly at the point. The question was thus posed whether they are in the same universality class as linear polymers at the temperature. We show that this is not the case since these trails show a first-order transition, instead of the second-order transition at the usual point. We argue that this is due to the fact that the `smartness' of these trails implies that the renormalized n-body interactions vanish identically for any finite . We conjecture that the qualitative similarity with recent simulations of polymers indicates that for n-body interactions the renormalized three-body interaction is small in real polymers.

Spectral Theory of Physical and Chemical Binding,

A spectral method which provides unified quantum mechanical descriptions of both physical and chemical binding phenomena is reported for constructing the adiabatic electronic potential energy surfaces of aggregates of atoms or other interacting fragments. The formal development, based on use of a direct product of complete sets of atomic spectral eigenstates and the pairwise-additive nature of the total Hamiltonian matrix in this basis, is seen to be exact when properly implemented and to provide a separation theorem for N-body interaction energies in terms of response matrices which can be calculated once and for all for atoms and other fragments of interest. Its perturbation theory expansion provides a generalization of familiar (Casimir−Polder) second-order pairwise-additive and (Axilrod−Teller) third-order nonadditive interaction energies, expressions which are recovered explicitly in the long-range-dipole expansion limit. A program of ab initio computational implementation of the formal development i...

The problem of flame propagation in a random velocity field: weak turbulence limit

The problem of thin flame front propagation with curvature-dependent speed in a weak turbulent flow has been considered, and its connection with classical problems in the physics of disordered systems such as polymers in a random medium, growing interfaces and n-body interaction problems has been discussed. By a path-integral approach, an explicit formula for the randomly moving flame front in terms of the fluctuating velocity field has been derived. The steepest-descent approximation has been used to find the random configuration of the flame surface in the limit of small Markstein diffusivity. New expressions for the turbulent burning velocity (the overall propagation rate of a flame surface subject to a random velocity field) involving the random velocity field along the Lagrangian trajectories have been derived.

MONTE CARLO STUDY OF THE ORDER OF PHASE TRANSITION OF A MULTISPIN INTERACTIONS ISING MODEL

The order of phase transition of a two-dimensional Ising model with m-body interactions in the horizontal direction and n-body interactions in the vertical direction in the m = 3, n = 3 case is of the first-order which is determined by our Monte Carlo algorithm, while in the m= 3,n=2 case the transition is of the second order.

Nonlinear effect of atomic displacements and created defects in irradiation cascades

The effects of cascade interaction on the atomic mixing and the created defects were studied by molecular dynamics simulations. The simulations were carried out with the Gibson II potential, chosen for the purpose of comparison with previous MD results in the literature. Preliminary simulations were also carried out with N-body interactions represented by a semi-empirical RGL potential. It is shown that the mixing observed from two simultaneous and nearby cascades of energy in the range of 500 eV to 1.5 keV is increased by a factor of 3 to 4 when compared to the mixing from a single spike of the same energy.

Classical spin lattice systems with vacuum

We present cluster properties for the lattice spin systems with general n-body interaction and we apply it to find the asymptotic expansion of the logarithm of the partition function in powers of the volume as well as a local limit theorem for the particle number.

Path integral approach for fermi systems with N-body interactions

The path integral formulation of many-body systems in terms of collective fields, previously developed for two-body forces, is extended to arbitrary many-body interactions. In particular, the time-dependent mean-field approximation to quantum transition amplitudes is derived for such intrractions. Furthermore the problem of how to incorporate properly the exchange terms in lowest order mean-field approximation is solved.