Stochastic molecular optimization using generalized simulated annealing

We propose a stochastic optimization technique based on a generalized simulated annealing (GSA) method for mapping minima points of molecular conformational energy surfaces. The energy maps are obtained by coupling a classical molecular force field (THOR package) with a GSA procedure. Unlike the usual molecular dynamics (MD) method, the method proposed in this study is force independent; that is, we obtain the optimized conformation without calculating the force, and only potential energy is involved. Therefore, we do not need to know the conformational energy gradient to arrive at equilibrium conformations. Its utility in molecular mechanics is illustrated by applying it to examples of simple molecules (H₂O and H₂O₃) and to polypeptides. The results obtained for H₂O and H₂O₃ using Tsallis thermostatistics suggest that the GSA approach is faster than the other two conventional methods (Boltzmann and Cauchy machines). The results for polypeptides show that pentalanine does not form a stable α-helix structure, probably because the number of hydrogen bonds is insufficient to maintain the helical array. On the contrary, the icoalanine molecule forms an α-helix structure. We obtain this structure simulating all Φ, Ψ pairs using only a few steps, as compared with conventional methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 647–657, 1998     

Global optimization of atomic and molecular clusters using the space-fixed modified genetic algorithm method

A modified genetic algorithm approach has been applied to atomic Ar clusters and molecular water clusters up to (H₂O)₁₃. Several genetic operators are discussed which are suitable for real-valued space-fixed atomic coordinates and Euler angles. The performance of these operators has been systematically investigated. For atomic systems, it is found that a mix of operators containing a coordinate-averaging operator is optimal. For angular coordinates, the situation is less clear. It appears that inversion and two-point crossover operators are the best choice. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1233–1244     

Standing wave optimization of SMB using a hybrid simulated annealing and genetic algorithm (SAGA)

In this paper we draw on two stochastic optimization techniques, Simulated Annealing and Genetic Algorithm (SAGA), to create a hybrid to determine the optimal design of nonlinear Simulated Moving Bed (SMB) systems. A mathematical programming model based on the Standing Wave Design (SWD) offers a significant advantage in optimizing SMB systems. SAGA builds upon the strength of SA and GA to optimize the 16 variables of the mixed-integer nonlinear programming model for single- and multi-objective optimizations. The SAGA procedure is shown to be robust with computational time in minutes for single-objective optimization and in a few hours for a multi-objective optimization, which is comprised of more than one hundred points.     

A genetic algorithm for flexible molecular overlay and pharmacophore elucidation

Summary A genetic algorithm (GA) has been developed for the superimposition of sets of flexible molecules. Molecules are represented by a chromosome that encodes angles of rotation about flexible bonds and mappings between hydrogen-bond donor proton, acceptor lone pair and ring centre features in pairs of molecules. The molecule with the smallest number of features in the data set is used as a template, onto which the remaining molecules are fitted with the objective of maximising structural equivalences. The fitness function of the GA is a weighted combination of: (i) the number and the similarity of the features that have been overlaid in this way; (ii) the volume integral of the overlay; and (iii) the van der Waals energy of the molecular conformations defined by the torsion angles encoded in the chromosomes. The algorithm has been applied to a number of pharmacophore elucidation problems, i.e., angiotensin II receptor antagonists, Leu-enkephalin and a hybrid morphine molecule, 5-HT_1D agonists, benzodiazepine receptor ligands, 5-HT₃ antagonists, dopamine D₂ antagonists, dopamine reuptake blockers and FKBP12 ligands. The resulting pharmacophores are generated rapidly and are in good agreement with those derived from alternative means.     

A geometry optimization benchmark using highly correlated wavefunctions (FCI and MRD-CI)

Summary Full configuration interaction (FCI) geometry optimizations have been performed for the X³B₁, a¹A₁, b¹B₁ and c¹A₁ electronic states of CH₂, the X²B₁ and A²A₁ electronic states of NH₂ and the X¹A₁ electronic state of BH₃ using a DZP basis set. The results are compared with those obtained using the MRD-CI method at different levels of theoretical treatment. The agreement between the geometrical parameters optimized with the FCI and MRD-CI methods is very good.     

Geometry optimizations of benzene clusters using a modified genetic algorithm

A modified genetic algorithm with real-number coding, non-uniform mutation and arithmetical crossover operators was described in this paper. A local minimization was used to improve the final solution obtained by the genetic algorithm. Using the exp-6-1 interatomic energy function, the modified genetic algorithm with local minimization (MGALM) was applied to the geometry optimization problem of small benzene clusters (C6H6)N(N = 2-7) to obtain the global minimum energy structures. MGALM is simple but the structures optimized are comparable to the published results obtained by parallel genetic algorithms.     

Cofolga: a genetic algorithm for finding the common folding of two RNAs

In order to predict non-coding RNA genes and functions on the basis of genome sequences, accurate secondary structure prediction is useful. Although single-sequence folding programs such as mfold have been successful, it is of great importance to develop a novel approach for further improvement of the prediction performance. In the present paper, a secondary structure prediction method based on genetic algorithm, Cofolga, is proposed. The program developed performs folding and alignment of two homologous RNAs simultaneously. Cofolga was tested with a dataset composed of 13 tRNAs, seven 5S rRNAs, five RNase P RNAs, and five SRP RNAs; as a result, it turned out that the average prediction accuracies for the tRNAs, 5S rRNAs, RNase P RNAs, and SRP RNAs obtained by Cofolga with an optimal weight factor and default parameters were 83.6, 81.8, 73.5, and 67.7%, respectively. These results were superior to those obtained by a single-sequence folding based on free-energy minimization in which corresponding average prediction accuracies were 52.4, 47.4, 57.7, and 52.3%, respectively. Cofolga has a post-processing in which a single-sequence folding is performed after fixation of a predicted common structure; this post-processing enables Cofolga to predict a structure that is present in one of two RNAs alone. The executable files of Cofolga (for Windows/Unix/Mac) can be obtained by an e-mail request.     

Evaluation of a method for controlling molecular scaffold diversity in de novo ligand design

We describe an algorithm for the automated generation of molecular structures subject to geometric and connectivity constraints. The method relies on simulated annealing and simplex optimization of a penalty function that contains a variety of conditions and can be useful in structure-based drug design projects. The procedure controls the diversity and complexity of the generated molecules. Structure selection filters are an integral part and drive the algorithm. Several procedures have been developed to achieve reliable control. A number of template sets can be defined and combined to control the range of molecules which are searched. Ring systems are predefined. Normally, the ring-system complexity is one of the most elusive and difficult factors to control when fusion-, bridge- and spiro-structures are built by joining templates. Here this is not an issue; the decision about which systems are acceptable, and which are not, is made before the run is initiated. Queries for inclusion and exclusion spheres are incorporated into the objective function, and, by using a flexible notation, the structure generation can be directed and more focused. Simulated annealing is a reliable optimizer and converges asymptotically to the global minimum. The objective functions used here are degenerate, so it is likely that each run will produce a different set of good solutions.     

A novel conformation optimization model and algorithm for structure-based drug design

In this paper, we present a multi-scale optimization model and an entropy-based genetic algorithm for molecular docking. In this model, we introduce to the refined docking design a concept of residue groups based on induced-fit and adopt a combination of conformations in different scales. A new iteration scheme, in conjunction with multi-population evolution strategy, entropy-based searching technique with narrowing down space and the quasi-exact penalty function, is developed to address the optimization problem for molecular docking. A new docking program that accounts for protein flexibility has also been developed. The docking results indicate that the method can be efficiently employed in structure-based drug design.     

Multiobjective optimization of simulated moving bed and Varicol processes using a genetic algorithm

The size of the packing material, the total number of columns and the total feed concentration have significant impacts on the economics of a preparative chromatographic separation, through their effects on column pressure drop, column efficiency and thermodynamics. In this work, the role of these parameters on the performances of a simulated moving bed and a Varicol process is investigated on a chiral separation system from literature, using an equilibrium stage model. A multiple objective optimization technique based on a genetic algorithm is adopted, which allows to maximize simultaneously the purity of the extract and productivity of the unit. In this way, it is possible to optimize and compare the performances of both processes in a wide range of parameter values, so as to assess their relative potential under equally optimized conditions. The optimization results, i.e. the so-called Pareto sets, have been discussed in the frame of equilibrium theory and the roles of these three parameters have been clarified.     

Topological study of a hypothetical molecular sieve MCR-16 with extra-large open pores

The topology of the framework of a novel zeolite, named MCR-16, with cylindrical channels spanned by the 16-membered ring, is constructed, in which the sigma transformation is a conceptual device for inter-relating the known zeolite mordenite and the hypothetical MCR-16. The consistent molecular mechanics force field is used as the foundation for the discussion on the steric energy of the structure. The configuration energy is minimized by the simulated annealing method. The consequent Si–O, Si–Si and O–O distances and Si–O–Si and O–Si–O angles of the designed MCR-16 structure are all within the limits of the reasonable ranges.     

Continuous optimization methods for ground-state searches of spin clusters

Computational methods were developed for ground-state searches of Heisenberg model spin clusters in which spin sites were represented by classical spin vectors. Simulated annealing, continuous genetic algorithm, and particle swarm optimization methods were applied for solving the problems. Because the results of these calculations were influenced by the settings of optimization parameters, effective parameter settings were also investigated. The results indicated that a continuous genetic algorithm is the most effective method for ground-state searches of Heisenberg model spin clusters, and that a mutation operator plays an important role in this genetic algorithm. These results provide useful information for solving physically or chemically important continuous optimization problems.     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Development and optimisation of a novel genetic algorithm for studying model protein folding

Determination of the native state of a protein from its amino acid sequence is the goal of protein folding simulations, with potential applications in gene therapy and drug design. Location of the global minimum structure for a given sequence, however, is a difficult optimisation problem. In this paper, we describe the development and application of a genetic algorithm (GA) to find the lowest-energy conformations for the 2D HP lattice bead protein model. Optimisation of the parameters of our standard GA program reveals that the GA is most successful (at finding the lowest-energy conformations) for high rates of mating and mutation and relatively high elitism. We have also introduced a number of new genetic operators: a duplicate predator—which maintains population diversity by eliminating duplicate structures; brood selection—where two parent structures undergo crossover and give rise to a brood of (not just two) offspring; and a Monte Carlo based local search algorithm—to explore the neighbourhood of all members of the population. It is shown that these operators lead to significant improvements in the success and efficiency of the GA, both compared with our standard GA and with previously published GA studies for benchmark HP sequences with up to 50 beads.     

Peak alignment of NMR signals by means of a genetic algorithm

Nuclear magnetic resonance (NMR) analysis of complex samples, such as biofluid samples is accompanied by variations in peak position and peak shape not directly related to the sample. This is due to variations in the background matrix of the sample and to instrumental instabilities. These variations complicate and limit the interpretation and analysis of NMR data by multivariate methods. Alignment of the NMR signals may circumvent these limitations and is an important preprocessing step prior to multivariate analysis. Previous aligning methods reduce the spectral resolution, are very computer-intensive for this kind of data (65k data points in one spectrum), or rely on peak detection. The method presented in this work requires neither data reduction nor preprocessing, e.g. peak detection. The alignment is achieved by taking each segment of the spectrum individually, shifting it sidewise, and linearly interpolating it to stretch or shrink until the best correlation with a corresponding reference spectrum segment is obtained. The segments are automatically picked out with a routine, which avoids cutting in a peak, and the optimization process is accomplished by means of a genetic algorithm (GA). The peak alignment routine is applied to NMR metabonomic data.¹     

Flexible ligand docking using a genetic algorithm

Summary Two computational techniques have been developed to explore the orientational and conformational space of a flexible ligand within an enzyme. Both methods use the Genetic Algorithm (GA) to generate conformationally flexible ligands in conjunction with algorithms from the DOCK suite of programs to characterize the receptor site. The methods are applied to three enzyme-ligand complexes: dihydrofolate reductase-methotrexate, thymidylate synthase-phenolpthalein and HIV protease-thioketal haloperidol. Conformations and orientations close to the crystallographically determined structures are obtained, as well as alternative structures with low energy. The potential for the GA method to screen a database of compounds is also examined. A collection of ligands is evaluated simultaneously, rather than docking the ligands individually into the enzyme.Abbreviations GA genetic algorithm; dhfr, dihydrofolate reductase - mtx methotrexate - ts thymidylate synthase - fen phenolphalein - HIV human immune deficiency virus - hivp HIV protease - thk thioketal haloperidol     

Energy minimization of mixed argon–xenon microclusters using a genetic algorithm

This article describes a parallel real-coded genetic algorithm implemented to find global minimum energy structures of microclusters of non-bonded argon and xenon atoms. Using appropriate genetic operators, the genetic algorithm was able to find minimum energy structures for microclusters of two to twenty atoms, in all possible combinations of argon and xenon. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 :1096–1111, 1997     

Determining molecular structures and conformations directly from electron diffraction using a genetic algorithm.

A global optimization strategy, based upon application of a genetic algorithm (GA), is demonstrated as an approach for determining the structures of molecules possessing significant conformational flexibility directly from gas-phase electron diffraction data. In contrast to the common approach to molecular structure determination, based on trial-and-error assessment of structures available from quantum chemical calculations, the GA approach described here does not require expensive quantum mechanical calculations or manual searching of the potential energy surface of the sample molecule, relying instead upon simple comparison between the experimental and calculated diffraction pattern derived from a proposed trial molecular structure. Structures as complex as all-trans retinal and p-coumaric acid, both important chromophores in photosensing processes, may be determined by this approach. In the examples presented here, we find that the GA approach can determine the correct conformation of a flexible molecule described by 11 independent torsion angles. We also demonstrate applications to samples comprising a mixture of two distinct molecular conformations. With these results we conclude that applications of this approach are very promising in elucidating the structures of large molecules directly from electron diffraction data.     

FT-IR, FT-Raman spectra, density functional computations of the vibrational spectra and molecular geometry of biomolecule 5-aminouracil

FT-IR and FT-Raman spectra of the biomolecule 5-aminouracil were recorded in the regions 400–4000 cm⁻¹ and 10–3500 cm⁻¹, respectively. The observed vibrational wavenumbers were analyzed and assigned to different normal modes of vibration of the molecule. Density functional calculations were performed to support wavenumber assignments of the observed bands. A comparison with the molecule of uracil was made, and specific scale factors were employed in the predicted wavenumbers of 5-aminouracil. With the purpose of study the important molecule 5-aminouracil, its equilibrium geometry and harmonic wavenumbers were calculated for the first time by the B3LYP DFT method. The vibrational wavenumbers were compared with IR and Raman experimental data. Also good reproduction of the experimental wavenumbers is obtained and the % error is very small. All the tautomeric forms of 5-aminouracil were determined and optimized. The dimer forms were also simulated. The energy, atomic charges and dipole moments were discussed and several general conclusions were underlined.