Practical modeling of molecular systems with symmetries

A new method for efficient modeling of macromolecular systems with symmetries is presented. The method is based on a hierarchical representation of the molecular system and a novel fast binary tree‐based neighbor list construction algorithm. The method supports all types of molecular symmetry, including crystallographic symmetry. Testing the proposed neighbor list construction algorithm on a number of different macromolecular systems containing up to about 200,000 of atoms shows that (1) the current binary tree‐based neighbor list construction algorithm scales linearly in the number of atoms for the central subunit, and sublinearly for its replicas, (2) the overall computational overhead of the method for a system with symmetry with respect to the same system without symmetry scales linearly with the cutoff value and does not exceed 50% for all but one tested macromolecules at the cutoff distance of 12 Å. (3) the method may help produce optimized molecular structures that are much closer to experimentally determined structures when compared with the optimization without symmetry, (4) the method can be applied to models of macromolecules with still unknown detailed structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ion Selective Electrode Array Analysis Using Variable Step-Size Generalized Simulated Annealing

A global optimum location algorithm called Variable Step-Size Generalized Simulated Annealing(VSGSA) was applied to treating the data obtained by using an array of ion-electrodes in solutions containing mixtures of Na+, K+, Ca2+. Unlike traditional optimization algorithms such as simplex procedure, VSGSA can be used to determine the model parameters without any priori information about the analytical system under investigation and overcome the disadvantage of simplex method which might converge to local extrema depending on the starting positions. The algorithm was applied to po-tentiometric determination of ions in mixture solutions.     

The atom assignment problem in automated de novo drug design. 3. Algorithms for optimization of fragment placement onto 3D molecular graphs

Summary Atom assignment onto 3D molecular graphs is a combinatoric problem in discrete space. If atoms are to be placed efficiently on molecular graphs produced in drug binding sites, the assignment must be optimized. An algorithm, based on simulated annealing, is presented for efficient optimization of fragment placement. Extensive tests of the method have been performed on five ligands taken from the Protein Data Bank. The algorithm is presented with the ligand graph and the electrostatic potential as input. Self placement of molecular fragments was monitored as an objective test. A hydrogen-bond option was also included, to enable the user to highlight specific needs. The algorithm performed well in the optimization, with successful replications. In some cases, a modification was necessary to reduce the tendency to give multiple halogenated structures. This optimization procedure should prove useful for automated de novo drug design.     

Computer-Assisted Optimization of pH and Ion Concentration Selectivity in HPLC Using a Mixture Design Simplex Method

Abstract

A computer-assisted mixture design simplex method is presented for optimization of two-factor (pH and ion concentration) simultaneous selectivity for the optimal separation in reversed-phase HPLC. The method is based on two-factor selectivity rectangle concept with a special polynomial estimated from nine preliminary runs. Then connect to general simplex method for optimization. Double criteria simulation system (DCSS) is established for the measurement of chromatographic performance by this method. The validity of the optimization strategy is proved by applying it to an actual mixture and as compared with the general simplex method about thirty eight experiments can be omitted.     

An adaptive immune optimization algorithm for energy minimization problems

Based on the immune theory of biology, a novel evolutionary algorithm, adaptive immune optimization algorithm (AIOA), is proposed. In AIOA, density regulation and immune selection is adopted to control the individual diversity and the convergence adaptively. By an application of the algorithm to the optimization of test functions, it is shown that the algorithm is a highly efficient optimization method compared with other stochastic optimization methods. The algorithm was also applied to the optimization of Lennard-Jones clusters, and the results show that the method can find the optimal structure of N相似文献   

Automated flexible ligand docking method and its application for database search

We have developed a new docking program that explores ligand flexibility. This program can be applied to database searches. The program is similar in concept to earlier efforts, but it has been automated and improved. The algorithm begins by selecting an anchor fragment of a ligand. This fragment is protonated, as needed, and then placed in the receptor by the DOCK algorithm, followed by minimization using a simplex method. Finally, the conformations of the remaining parts of the putative ligands are searched by a limited backtrack method and minimized to get the most stable conformation. To test the efficiency of this method, the program was used to regenerate ten ligand–protein complex structures. In all cases, the docked ligands basically reproduced the crystallographic binding modes. The efficiency of this method was further tested by a database search. Ten percent of molecules from the Available Chemicals Directory (ACD) were docked to a dihydrofolate reductase structure. Most of the top-ranking molecules (7 of the top 13 hits) are dihydrofolate or methotrexate derivatives, which are known to be DHFR inhibitors, demonstrating the suitability of this program for screening molecular databases. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1812–1825, 1997     

Simplex optimization of the adaptive kalman filter

A method for determining concentrations from overlapped spectral data when a complete model is not available is described. This approach combines simplex optimization with the adaptive Kalman filter to yield a method in which initial guesses for the adaptive filter are generated by the simplex algorithm. The performance of the method is demonstrated by deconvoluting overlapped synthetic data and spectral data.     

Comparison of simplex algorithms

A new modification of the super-modified simplex algorithm is described. The performance of this algorithm is compared with that of the super-modified simplex algorithm and the Nelder-Mead, or modified, simplex algorithm, using both mathematical functions and experimental optimization of an inductively coupled plasma spectrometer. The modification added to the super-modified simplex algorithm increases its speed and accuracy over the original super-modified algorithm.     

An improved skmplex algorithm for dealing with boundary conditions

Two existing and one new method for dealing with boundaries in simplex optimization are tested on 2-, 3-, and 5-parameter test functions, each subject to five different boundary conditions. The performance of the new method is shown to be the most consistent over all conditions.     

Performance analysis of the double-iterated Kalman filter for molecular structure estimation

A possible application of a novel double-iterated Kalman filter (DIKF) as an algorithm for molecular structure determination is investigated in this work. Unlike traditional optimization algorithms, the DIKF does not exploit experimental nuclear magnetic resonance (NMR) constraints in a penalty function to be minimized but used them to filter the atomic coordinates. Furthermore, it is a nonlinear Bayesian estimator able to handle the uncertainty in the experimental data and in the computed structures, represented as covariance matrices. The algorithm presented applies all constraints simultaneously, in contrast with DIKF algorithms for structure determination found in literature, which apply the constraints one at a time. The performances of both paradigms are tested and compared with those obtained by a commonly used optimization algorithm (based on the conjugate gradient method). Besides providing estimates of the conformational uncertainty directly in the final covariance matrix, DIKF algorithms appear to generate structures with a better stereochemistry and be able to work with realistically imprecise constraints, while time performances are strongly affected by the heavy matricial calculations they require. © 1996 by John Wiley & Sons, Inc.     

Simplex optimization of acoustic assay for plasminogen activators

This article discusses the optimization of a newly developed method for measuring the activity of plasminogen activators using a thickness-shear-mode acoustic sensor. A variable-size simplex algorithm was used for optimization. Preliminary tests were performed to design the first simplex. A desirability function was defined to translate each performance value to a membership value of 0 to 1. If there was more than one performance variable, their membership values were translated to an aggregated membership value using another function that considers their individual influence on sensor performance. Two rounds of optimization were carried out for streptokinase followed by a single optimization for tissue-type plasminogen activator. In the last optimization, ratios of control variables were used in order to reduce the number of parameters and to formulate easily adjustable assay conditions. The results showed the usefulness of the simplex method for optimizing this type of assay, and the importance of preliminary tests and prior knowledge in providing rapid convergence using fewer experiments. The optimized plasminogen activator assay can be considered a reference method for measurement of all members of this drug class.     

Pattern recognition strategies for molecular surfaces. II. Surface complementarity

Fuzzy logic based algorithms for the quantitative treatment of complementarity of molecular surfaces are presented. Therein, the overlapping surface patches defined in article I1 of this series are used. The identification of complementary surface patches can be considered as a first step for the solution of molecular docking problems. Standard technologies can then be used for further optimization of the resulting complex structures. The algorithms are applied to 33 biomolecular complexes. After the optimization with a downhill simplex method, for all these complexes one structure was found, which is in very good agreement with the experimental results.     

Controlled-advancement rigid-body optimization of nanosystems

In this study, we propose a novel optimization algorithm, with application to the refinement of molecular complexes. Particularly, we consider optimization problem as the calculation of quasi-static trajectories of rigid bodies influenced by the inverse-inertia-weighted energy gradient and introduce the concept of advancement region that guarantees displacement of a molecule strictly within a relevant region of conformational space. The advancement region helps to avoid typical energy minimization pitfalls, thus, the algorithm is suitable to work with arbitrary energy functions and arbitrary types of molecular complexes without necessary tuning of its hyper-parameters. Our method, called controlled-advancement rigid-body optimization of nanosystems (Carbon), is particularly useful for the large-scale molecular refinement, as for example, the putative binding candidates obtained with protein–protein docking pipelines. Implementation of Carbon with user-friendly interface is available in the SAMSON platform for molecular modeling at https://www.samson-connect.net . © 2019 Wiley Periodicals, Inc.     

Simplex optimization of response-time-limited systems : A Study with a Spectrophotometric Determination of Aluminium and Mathematical Test Functions

A two-part modification to the standard simplex optimization is used to speed up the optimization of systems limited by response time. The modications are tested on a slow spectrophotometric procedure for aluminium, and on 2-, 3- and 5-parameter test functions. The modifications are shown to work for the aluminium method, with substantial time-savings, and to be statistically valid when used on the test functions. The best combination of the new modifications and the standard method are discussed.     

Fully quantum mechanical energy optimization for protein-ligand structure

We present a quantum mechanical approach to study protein-ligand binding structure with application to a Adipocyte lipid-binding protein complexed with Propanoic Acid. The present approach employs a recently develop molecular fractionation with a conjugate caps (MFCC) method to compute protein-ligand interaction energy and performs energy optimization using the quasi-Newton method. The MFCC method enables us to compute fully quantum mechanical ab initio protein-ligand interaction energy and its gradients that are used in energy minimization. This quantum optimization approach is applied to study the Adipocyte lipid-binding protein complexed with Propanoic Acid system, a complex system consisting of a 2057-atom protein and a 10-atom ligand. The MFCC calculation is carried out at the Hartree-Fock level with a 3-21G basis set. The quantum optimized structure of this complex is in good agreement with the experimental crystal structure. The quantum energy calculation is implemented in a parallel program that dramatically speeds up the MFCC calculation for the protein-ligand system. Similarly good agreement between MFCC optimized structure and the experimental structure is also obtained for the streptavidin-biotin complex. Due to heavy computational cost, the quantum energy minimization is carried out in a six-dimensional space that corresponds to the rigid-body protein-ligand interaction.     

Optimization of gradient profiles in ion-exchange chromatography using computer simulation programs

Optimization procedure of gradient separations in ion-exchange chromatography using simplex optimization method in combination with the computer simulation program for ion-exchange chromatography is presented. The optimization of parameters describing gradient profile for the separation in ion chromatography is based on the optimization criterion obtained from calculated chromatograms. The optimization criterion depends on the parameters used for calculations and thus exhibits the quality of gradient conditions for the separation of the analytes. Simplex method is used to calculate new gradient profiles in order to reach optimum separations for the selected set of analytes. The Simplex algorithm works stepwise, for each new combination of parameters that describe the gradient profile a new calculation is performed and from the calculated chromatogram the optimization criterion is determined. The proposed method is efficient and may reduce the time and cost of analyses of complex samples with ion-exchange chromatography.     

Simplex optimization of a nitrogen-cooled argon inductively coupled plasma for multi-element analysis

A medium power (5 kW) nitrogen-cooled argon inductively coupled plasma (ICP) system was used in an investigation of the basic and modified simplex methods of optimization. The optimum operating conditions for the ICP system were established for 23 commonly determined elements covering a wavelength range from 180 to 340 nm and including an approximately equal number of atomic and ionic lines.Initially the optimization was carried out for individual elements on the basis of two responses: net signal-to-background ratio (SBR) and ionization interference (II).The simplex technique indicated a need to improve the nebulization system.In achievement of maximum SBR, interesting correlations were found between the optimum power required, on the one hand, and the difficulty of excitation of the elements and the optimum intermediate-gas flowrate, on the other.Finally a method for optimization of the conditions for the plasma in multi-element analysis, based on the sequential use of maximum SBR and minimum ionization interference (MII) responses, was devised and successfully tested against several routine analytical methods. Application of the conditions established during these optimizations result in an analytically useful plasma giving good detection limits as well as minimum ionization interference effects.     

A New Method for Molecular Mechanics

A promising new method for optimizing molecular structures is described. In place of the terms involving bond angles and torsion angles, used in the force fields of conventional molecular mechanics, two-body central forces between atoms are used exclusively, resulting in a considerable computational advantage. The program STRFIT, using this method has been tested by comparing geometries obtained with those found using the popular molecular mechanics program MM2 (Allinger) for a variety of cyclic and acyclic molecules. For unstrained molecules, the difference in steric energy between geometries refined by STRFIT and MM2 is only a few tenths of a kilocalorie and up to about a kilocalorie for strained molecules. Geometry optimization with STRFIT, to a structure that is slightly higher in energy than the structure arrived at by MM2 starting from the same initial starting geometry, is three to eight times faster. A complete new package of programs for conveniently and rapidly doing molecular mechanics calculations is described. It includes a convenient algorithm for the input of approximate molecular structures, a rapid structure-optimizing module using a pure Central force-field approach, and a drawing program designed for use with a dot-matrix printer or a laser printer.     

Rotation in simplex optimization

A modification of the modified simplex method of optimization was tested. This modification involves rotation of the simplex when the standard simplex motion by reflection, expansion and contraction, fails to lead to continued progress of the simplex. Two other methods and several kinds of rotation are compared for four response surfaces. Certain rotations are shown to be superior to others and to two previously reported operations that do not involve rotation.     

Application of a modified simplex method to the multivariable optimization of a new FIA system for the determination of osmium

A methodology based on the coupling of experimental design and a modified simplex method is proposed for the optimization of a new flow injection-kinetic system for the spectrophotometric determination of Os (IV) with m-acetylchlorophosphonazo, which has for the first time been used as chromogenic reagent in the quantitative analysis of this element. An orthogonal array design is utilized to design the experimental protocol, in which six variables are varied simultaneously, and obtain the initial simplex using 25 experiments. A modified simplex method is applied to continuously optimize the data of the orthogonal array design; the search for optimum conditions of ¶6 variables using the modified simplex method required only 25 experiments. The efficiency and simplicity of the coupling of the experimental design and the modified simplex method are attractive for the development of new analytical methods. The method has been applied to the determination of Os (IV) in a refined ore as well as in a secondary alloy and provided satisfactory results.