Monte-Carlo Search Algorithm Research Articles

Monte Carlo maximum likelihood circle fitting using circular density functions

Finding the "best-fitting" circle to describe a set of points in two dimensions is discussed in terms of maximum likelihood estimation. Several combinations of distributions are proposed to describe the stochastic nature of points in the plane, as the points are considered to have a common, typically unknown center, a random radius, and random angular orientation. A Monte Carlo search algorithm over part of the parameter space is suggested for finding the maximum likelihood parameter estimates. Examples are presented, and comparisons are drawn between circles fit by this proposed method, least squares, and other maximum likelihood methods found in the literature.

CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts, residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low-cost global protein fold determination. Here, we present CABS-NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C-Alpha-Beta-Side-group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge-based force field. Its versatile structure enables a variety of protein-modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS-NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low-energy structures obtained from chemical shifts by CABS-NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl-methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post-experiment processing of various kinds of NMR data or fast and low-cost structural analysis in the still challenging field of new fold predictions.

A ground state phase diagram of a spinless, extended Falicov–Kimball model on thetriangular lattice

Correlated systems with hexagonal layered structures have come to thefore with renewed interest in cobaltates, transition metal dichalcogenides andGdI2. While superconductivity, unusual metal and possible exotic states (prevented fromlong-range order by strong local fluctuations) appear to come from frustration andcorrelation working in tandem in such systems, they freeze at a lower temperature tocrystalline states. The underlying effective Hamiltonian in some of these systems is believedto be the Falicov–Kimball model and therefore, a thorough study of the ground state ofthis model and its extended version on a non-bipartite lattice is important. Using a MonteCarlo search algorithm, we identify a large number of different possible ground states withcharge order as well as valence and metal–insulator transitions. Such competing states,close in energy, give rise to complex charge order and other broken symmetry structures aswell as the phase segregations observed in the ground state of these systems.

PERIOD VARIATIONS IN THE CLOSE BINARY BM UMa

We present the results of analysing of the light curve and O-C variations in the eclipsing sys- tem BM UMa, based on V-band observations which cover the period from JD 2454933 to 2454961 using two robotic remotely-controlled telescopes of Tzec Maun Observatory (USA) along with observations made with the RK-600 telescope of Odessa Astronomical Obser- vatory. The full light curve displays a total primary eclipse with a duration 0.06 of the period, or 24 min- utes, and a partial secondary eclipse, with both max- ima of equal magnitude. For our obesrvations, we determined the sta- tistically optimal values of the initial epoch of T0 = 2454944.2814 ± 0.0001 and orbital period of P =0 . d 271226 ± 0.000002. The depths of primary and secondary minima are nearly equal, 0. m 838 ± 0.006 and 0. m 748 ± 0.006, respectively. The physical pa- rameters of the system were calculated using the Wilson-Devinney code, appended with the Monte Carlo search algorithm. The result establishes BM UMa as a contact system (fillout factor 10.7%) with parameters: mass ratio 0.538 ± 0.001, inclination 86. ◦ 815 ± 0.005, and temperatures of components 4700 ± 20 K and 4510 ± 10 K. The more massive component is larger and cooler. The 72 archival and 11 newly-obtained times of light minimum cover the interval 1961-2010 and allowed us to exclude possible systematic period variations in BM UMa and to determine an initial epoch of HJD 2447927.382 and orbital period of P =0 . d 2712209 ± 0.0000006.

The Crystal Structure of Progesterone 5β-Reductase from Digitalis lanata Defines a Novel Class of Short Chain Dehydrogenases/Reductases

Progesterone 5beta-reductase (5beta-POR) catalyzes the stereospecific reduction of progesterone to 5beta-pregnane-3,20-dione and is a key enzyme in the biosynthetic pathway of cardenolides in Digitalis (foxglove) plants. Sequence considerations suggested that 5beta-POR is a member of the short chain dehydrogenase/reductase (SDR) family of proteins but at the same time revealed that the sequence motifs that in standard SDRs contain the catalytically important residues are missing. Here we present crystal structures of 5beta-POR from Digitalis lanata in complex with NADP(+) at 2.3A and without cofactor bound at 2.4A resolution together with a model of a ternary complex consisting of 5beta-POR, NADP(+), and progesterone. Indeed, 5beta-POR displays the fold of an extended SDR. The architecture of the active site is, however, unprecedented because none of the standard catalytic residues are structurally conserved. A tyrosine (Tyr-179) and a lysine residue (Lys-147) are present in the active site, but they are displayed from novel positions and are part of novel sequence motifs. Mutating Tyr-179 to either alanine or phenylalanine completely abolishes the enzymatic activity. We propose that the distinct topology reflects the fact that 5beta-POR reduces a conjugated double bond in a steroid substrate via a 1-4 addition mechanism and that this requires a repositioning of the catalytically important residues. Our observation that the sequence motifs that line the active site are conserved in a number of bacterial and plant enzymes of yet unknown function leads us to the proposition that 5beta-POR defines a novel class of SDRs.

Tuning Selectivity in Adsorption on Composite Chiral Surfaces

Designing the structure of enantioselective adsorbents is a difficult task. In this work we propose a simple theoretical method of optimization of selectivity in adsorption on a model chiral surface composed of inert and active sites. Our approach is based on using the molecular footprints of the adsorbing enantiomers to find the optimal arrangement of active sites on the surface. In particular, we use a Monte Carlo search algorithm to predict the spatial distribution of active sites leading to the highest enantioselectivity. Additionally, we present the results of grand canonical Monte Carlo simulations performed for the equilibrium adsorption of enantiomers from a racemic mixture on the surfaces obtained using the MC approach. The optimal pattern of the active sites is dependent on the footprint of the chiral molecule as well as on the pressure under which the separation is performed.

Characterization of a hybrid Monte Carlo search algorithm for structure determination

A hybrid Monte Carlo (HMC) search algorithm has recently been shown to be a promising method for structure determination from powder diffraction data [Johnston, David, Markvardsen & Shankland (2002).Acta Cryst.A58, 441–447]. Here, the performance of the algorithm on a number of different crystal structures is investigated as a function of its control parameters. This detailed analysis required the use of a system for distributed computing in order to keep the calculation times within a reasonable time frame. The results obtained confirm previous findings and a detailed discussion of the effect of the control parameters on the efficiency of the HMC method is provided. The results suggest a method for setting these parameters automatically, which is an essential step if HMC is to find routine use in the determination of crystal structures.

Spectroscopy of polycyclic aromatic hydrocarbons and very small grains in photodissociation regions

We have coupled a singular value decomposition method with a Monte Carlo search algorithm to analyse the mid- infrared ISOCAMspectral maps of photodissociation regions (PDRs) in NGC 7023 and ρ Oph-SR3.Three different spectra and their associated spatial distribution were extracted from this analysis. It is shown that they can be associated with polycyclic aromatic hydrocarbons (PAHs) in their cationic and neutral forms and a third population of carbonaceous very small grains (VSGs). The method allows for the first time (i) to separate the contribution of neutral PAHs to the interstellar emission spectrum from that of cationic PAHs; (ii) to show that the 7.8 µm component of the "7.7 µm" broad feature is carried by VSGs, whereas the 7.6 µm component is due to PAHs; and (iii) to give evidence that free-flying PAHs are produced in PDRs by photoevaporation of VSGs. It is proposed that these carbonaceous VSGs are indeed PAH clusters. We derived a minimal size of 400 carbon atoms per cluster and estimated a UV absorption power of the order of 10 −24 WC −1 for their dissociation.

Assessing search strategies for flexible docking

We assess the efficiency of molecular dynamics (MD), Monte Carlo (MC), and genetic algorithms (GA) for docking five representative ligand–receptor complexes. All three algorithms employ a modified CHARMM-based energy function. The algorithms are also compared with an established docking algorithm, AutoDock. The receptors are kept rigid while flexibility of ligands is permitted. To test the efficiency of the algorithms, two search spaces are used: an 11-Å-radius sphere and a 2.5-Å-radius sphere, both centered on the active site. We find MD is most efficient in the case of the large search space, and GA outperforms the other methods in the small search space. We also find that MD provides structures that are, on average, lower in energy and closer to the crystallographic conformation. The GA obtains good solutions over the course of the fewest energy evaluations. However, due to the nature of the nonbonded interaction calculations, the GA requires the longest time for a single energy evaluation, which results in a decreased efficiency. The GA and MC search algorithms are implemented in the CHARMM macromolecular package. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1623–1631, 1998

A parallel Monte Carlo search algorithm for the conformational analysis of polypeptides

In recent years several approaches have been proposed to overcome the multiple-minima problem associated with nonlinear optimization techniques used in the analysis of molecular conformations. One such technique based on a parallel Monte Carlo search algorithm is analyzed. Experiments on the Intel iPSC/2 confirm that the attainable parallelism is limited by the underlying acceptance rate in the Monte Carlo search. It is proposed that optimal performance can be achieved in combination with vector processing. Tests on both the IBM 3090 and Intel iPSC/2-VX indicate that vector performance is related to molecule size and vector pipeline latency.

Determination of Protein Structures in Solution Using Nmr Data and Impact

A new procedure for generating and refining protein structures that satisfy constraints derived from two-di mensional data includes an internal coordinate Monte Carlo search algorithm for conformational sampling and a simple target function with terms for describing the structural information contained in 2-D NMR spectra. Solution structures of the peptide neutrophil defensin NP-5, generated with a metric matrix distance geometry algorithm, are refined with the Monte Carlo procedure, leading to structures with interproton distances that are closer to the bounds observed in the NMR data and have improved local geometry. In model studies, an α- helical peptide is rapidly folded from an extended chain when NMR distance constraints corresponding to an α- helix are used as input parameters. The ab initio folding of NP-5 from an extended chain and possible application to studying protein folding pathways are discussed. Cal culations were carried out with the program package IMPACT (Integrated Modeling Program Using Applied Chemical Theory), under development. An overview of IMPACT is presented.