Combinatorial library design using a multiobjective genetic algorithm

Early results from screening combinatorial libraries have been disappointing with libraries either failing to deliver the improved hit rates that were expected or resulting in hits with characteristics that make them undesirable as lead compounds. Consequently, the focus in library design has shifted toward designing libraries that are optimized on multiple properties simultaneously, for example, diversity and "druglike" physicochemical properties. Here we describe the program MoSELECT that is based on a multiobjective genetic algorithm and which is able to suggest a family of solutions to multiobjective library design where all the solutions are equally valid and each represents a different compromise between the objectives. MoSELECT also allows the relationships between the different objectives to be explored with competing objectives easily identified. The library designer can then make an informed choice on which solution(s) to explore. Various performance characteristics of MoSELECT are reported based on a number of different combinatorial libraries.     

A novel frequency distribution selection method for efficient plate layout of a diverse combinatorial library.

A deterministic method (frequency distribution method) for selecting compounds from a partitioned virtual combinatorial library for efficient synthesis is presented here. The method is based on reagent frequency analysis and can be applied to any library of molecules distributed in any given partitioned chemical space (cluster, cell-based, etc.). Compound selection by reagent frequency distribution can produce a unique, diverse set of molecules that adequately represents the library while requiring the least amount of compounds to be synthesized and minimizing the number of different reagents that must be used. This method also provides a practical solution to the configuration of plate layout. Because the method essentially identifies "expensive" regions in the chemical space to synthesize for a desired diversity or similarity coverage, decisions concerning the necessity to synthesize these compounds can be addressed. Minimum compound generation and efficient plate layout results in savings both in time of synthesis and cost of materials. This method always results in a discrete solution, which can be used for any given library size as well as any combination of reagents and is also readily adaptable to robotic automation.     

GLARE: a new approach for filtering large reagent lists in combinatorial library design using product properties

We present a novel computer algorithm, called GLARE (Global Library Assessment of REagents), that addresses the issue of optimal reagent selection in combinatorial library design. This program reduces or eliminates the time a medicinal chemist spends examining reagents which a priori cannot be part of a "good" library. Our approach takes the large reagent sets returned by standard chemical database queries and produces often considerably reduced reagent sets that are well-behaved with respect to a specific template. The pruning enforces "goodness" constraints such as the Lipinski rule of five on the product properties such that any reagent selection from the resulting sets produces only "good" products. The algorithm we implemented has three important features: (i) As opposed to genetic algorithms or other stochastic algorithms, GLARE uses a deterministic greedy procedure that smoothly filters out nonviable reagents. (ii) The pruning method can be biased to produce reagent sets with a balanced size, conserving proportionally more reagents in smaller sets. (iii) For very large combinatorial libraries, a partitioning scheme allows libraries as large as 10(12) to be evaluated in 0.25 s on an IBM AMD Opteron processor. This algorithm is validated on a diverse set of 12 libraries. The results that we obtained show an excellent compliance to the product property requirements and very fast timings.     

Cytotoxicity Induction by the Oxidative Reactivity of Nanoparticles Revealed by a Combinatorial GNP Library with Diverse Redox Properties

It is crucial to establish relationship between nanoparticle structures (or properties) and nanotoxicity. Previous investigations have shown that a nanoparticle’s size, shape, surface and core materials all impact its toxicity. However, the relationship between the redox property of nanoparticles and their toxicity has not been established when all other nanoparticle properties are identical. Here, by synthesizing an 80-membered combinatorial gold nanoparticle (GNP) library with diverse redox properties, we systematically explored this causal relationship. The compelling results revealed that the oxidative reactivity of GNPs, rather than their other physicochemical properties, directly caused cytotoxicity via induction of cellular oxidative stress. Our results show that the redox diversity of nanoparticles is regulated by GNPs modified with redox reactive ligands.     

Contemporary Synthesis of Ultrasmall (sub-10 nm) Upconverting Nanomaterials

Due to their unique photophysical properties, upconverting nanoparticles (UCNPs), i. e. particles capable of converting near-infrared (NIR) photons into tunable emissions in the range of ultraviolet (UV) to NIR, have great potential for use in various biomedical fields such as bioimaging, photodynamic therapy and bioanalytical applications. As far as biomedical applications are concerned, these materials have a number of advantageous properties such as brilliant luminescence and exceptional photostability. Very small “stealth” particles (sub-10 nm), which can circulate in the body largely undetected by the immune system, are particularly important for in vivo use. The fabrication of such particles, which simultaneously have a defined (ultrasmall) size and the required optical properties, is a great challenge and an area that is in its infancy. This minireview provides a concise overview of recent developments on appropriate synthetic methodologies to produce such UCNPs. Particular attention was given to the influence of both surfactants and dopants used to precisely adjust size, crystalline phase and optical properties of UCNPs.     

Agonists of the follicle stimulating hormone receptor from an encoded thiazolidinone library

The design, synthesis, characterization, and screening of a large, encoded thiazolidinone library are described. Three sets of 35 building blocks were combined by encoded split-pool synthesis to give a library containing more than 42 000 members. Building block selection was based in part on a novel small molecule follicle stimulating hormone receptor agonist hit and in part for diversity. HPLC/MS techniques were applied at the single-bead level to build confidence in the reliability of library construction. Application of two distinct screening strategies resulted in the identification of compounds with significantly improved potency over the initial hit. This work demonstrates the versatility of encoded libraries for preparing a large number of analogues of a given hit while simultaneously generating a large collection of compounds for screening against other targets.     

Synthesis of steroid-biaryl ether hybrid macrocycles with high skeletal and side chain variability by multiple multicomponent macrocyclization including bifunctional building blocks

Utilizing the multiple multicomponent macrocyclization including bifunctional building blocks (MiB) strategy, a library of nonracemic, nonrepetitive peptoid-containing steroid-biaryl ether hybrid macrocycles was built. Up to 16 new bonds, including those of the macrocyclization, can be formed in one pot simultaneously while introducing varied elements of diversity. Functional diversity is generated primarily by choosing Ugi-reactive functional building blocks, bearing the respective recognition or catalytic motifs. These appear attached to the peptoid backbone of the macrocyclic cavity, similar to side chains of amino acids found in enzyme active sites. Likewise, skeletal diversity is based on the variation of defined bifunctional building blocks which allow the parallel formation of macrocyclic cavities that are highly diverse in shape and size and thus perspectively in function. This straightforward approach is suitable to generate multifunctional macrocycles for applications in catalysis, supramolecular, or biological chemistry.     

Optimal control determination of MMA polymerization in non-isothermal batch reactor using bifunctional initiator

In this work, we determine the optimal control for free-radical methyl methacrylate polymerization using a bifunctional initiator in a non-isothermal batch reactor. A detailed unsteady-state model of the process is employed. Four different optimal control objectives are realized, each of which optimizes a given variable simultaneously with the specification of another. The first two objectives involve the maximization of monomer conversion in a specified operation time, and the minimization of operation time for a specified, final monomer conversion. The last two objectives involve the maximization of monomer conversion for specified, final number and weight average polymer molecular weights. The temperature of heat-exchange fluid inside reactor jacket is considered as a control function of an independent variable. To meet the specification of an optimization variable other than time, the differential model of batch process is derived in the range of specified variable. Equations are provided for Jacobian evaluations to help in the accurate solution of process model. A genetic algorithms-based optimal control method is applied to realize the four optimal control objectives. The results show that optimal control can significantly enhance the performance of the batch polymerization process.     

Multi objective SNP selection using pareto optimality

Biomarker discovery is a challenging task of bioinformatics especially when targeting high dimensional problems such as SNP (single nucleotide polymorphism) datasets. Various types of feature selection methods can be applied to accomplish this task. Typically, using features versus class labels of samples in the training dataset, these methods aim at selecting feature subsets with maximal classification accuracies. Although finding such class-discriminative features is crucial, selection of relevant SNPs for maximizing other properties that exist in the nature of population genetics such as the correlation between genetic diversity and geographical distance of ethnic groups can also be equally important. In this work, a methodology using a multi objective optimization technique called Pareto Optimal is utilized for selecting SNP subsets offering both high classification accuracy and correlation between genomic and geographical distances. In this method, discriminatory power of an SNP is determined using mutual information and its contribution to the genomic–geographical correlation is estimated using its loadings on principal components. Combining these objectives, the proposed method identifies SNP subsets that can better discriminate ethnic groups than those obtained with sole mutual information and yield higher correlation than those obtained with sole principal components on the Human Genome Diversity Project (HGDP) SNP dataset.     

Solid-phase synthesis of a 6-phenylquinolin-2(1H)-one library directed toward nuclear hormone receptors

A library of 6-phenylquinolin-2(1H)-ones with diversity at position 1 and the ortho, meta, and para positions of the pendant phenyl ring has been synthesized using solid-phase parallel synthetic techniques. A key step in the synthesis of the library is a tandem alkylation cleavage in which diversity can be introduced at position 1 simultaneously to the cleavage from the resin. The yields of this step were significantly improved over what has previously been reported by addition of cesium carbonate to scavenge the acid that is formed during the reaction. Furthermore, we have shown that the solid support linkage is tolerant to Suzuki coupling and etherification reaction conditions and that selective cleavage of the linkage can take place in the presence of esters. The resulting 6-phenylquinolin-2(1H)-one library was screened against a panel of nuclear hormone receptors (androgen, estrogen alpha and beta isoforms, glucocorticoid, mineralocorticoid, and progesterone). Certain members of this library display moderate affinity for several of these receptors, and consequently, the 6-phenylquinolin-2(1H)-one core of the library may be considered a privileged structure for nuclear hormone receptors. In contrast, other members of the library display high selectivity for a particular receptor. The highest affinity ligand (9{2,1,1}) possesses an affinity of 330 nM for the androgen receptor, whereas the most selective ligand (9{2,4,1}) displays an affinity of 900 nM for the androgen receptor and a selectivity of 140-fold over the next highest affinity receptor.     

PLUMS: a program for the rapid optimization of focused libraries

PLUMS is a new method to perform rational monomer selection for combinatorial chemistry libraries. The algorithm has been developed to optimize focused libraries with specific two-dimensional and/or three-dimensional properties. A preliminary step is the identification of those molecules in the initial virtual library which satisfy the imposed property constraints; we define these molecules as the virtual hits. From the virtual hits, PLUMS generates a starting library, which is the true combinatorial library that includes all the virtual hits. Monomers are then removed in an iterative fashion, thus reducing the size of the library. At each iteration, the worst monomer is removed. Each sublibrary is selected using a global scoring function, which balances effectiveness and efficiency. The iterative process continues until one is left with a library that consists entirely of virtual hits. The optimal library, which is the best compromise between effectiveness and efficiency, can then be selected according to the score. During the iterative process, equivalent solutions may well occur and are taken into account by the algorithm, according to a user-defined parameter. The number of monomers for each substitution site and the size of the library are parameters that can be either optimized or used to constrain the selection. The results obtained on two test libraries are presented. PLUMS was compared with genetic algorithms (GA) and monomer frequency analysis (MFA), which are widely used for monomer selection. For the two test libraries, PLUMS and GA gave equivalent results. MFA is the fastest method, but it can give misleading solutions. Possible advantages and disadvantages of the different methods are discussed.     

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Mo̸ller-Plesset perturbation theory

Many approximations have been developed to help deal with the O(N(4)) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be carried out in O(N(4)) operations. This should be compared to the usual scaling behavior of O(N(5)) and O(N(6)) for MP2 and MP3, respectively. The THC-DF technique can also be applied to other methods in electronic structure theory, such as coupled-cluster and configuration interaction, promising significant gains in computational efficiency and storage reduction.     

Desirability-based methods of multiobjective optimization and ranking for global QSAR studies. Filtering safe and potent drug candidates from combinatorial libraries

Up to now, very few applications of multiobjective optimization (MOOP) techniques to quantitative structure-activity relationship (QSAR) studies have been reported in the literature. However, none of them report the optimization of objectives related directly to the final pharmaceutical profile of a drug. In this paper, a MOOP method based on Derringer's desirability function that allows conducting global QSAR studies, simultaneously considering the potency, bioavailability, and safety of a set of drug candidates, is introduced. The results of the desirability-based MOOP (the levels of the predictor variables concurrently producing the best possible compromise between the properties determining an optimal drug candidate) are used for the implementation of a ranking method that is also based on the application of desirability functions. This method allows ranking drug candidates with unknown pharmaceutical properties from combinatorial libraries according to the degree of similarity with the previously determined optimal candidate. Application of this method will make it possible to filter the most promising drug candidates of a library (the best-ranked candidates), which should have the best pharmaceutical profile (the best compromise between potency, safety and bioavailability). In addition, a validation method of the ranking process, as well as a quantitative measure of the quality of a ranking, the ranking quality index (Psi), is proposed. The usefulness of the desirability-based methods of MOOP and ranking is demonstrated by its application to a library of 95 fluoroquinolones, reporting their gram-negative antibacterial activity and mammalian cell cytotoxicity. Finally, the combined use of the desirability-based methods of MOOP and ranking proposed here seems to be a valuable tool for rational drug discovery and development.     

Multiobjective optimization of combinatorial libraries

Combinatorial chemistry and high-throughput screening have caused a fundamental shift in the way chemists contemplate experiments. Designing a combinatorial library is a controversial art that involves a heterogeneous mix of chemistry, mathematics, economics, experience, and intuition. Although there seems to be little agreement as to what constitutes an ideal library, one thing is certain: only one property or measure seldom defines the quality of the design. In most real-world applications, a good experiment requires the simultaneous optimization of several, often conflicting, design objectives, some of which may be vague and uncertain. In this paper, we discuss a class of algorithms for subset selection rooted in the principles of multiobjective optimization. Our approach is to employ an objective function that encodes all of the desired selection criteria, and then use a simulated annealing or evolutionary approach to identify the optimal (or a nearly optimal) subset from among the vast number of possibilities. Many design criteria can be accommodated, including diversity, similarity to known actives, predicted activity and/or selectivity determined by quantitative structure-activity relationship (QSAR) models or receptor binding models, enforcement of certain property distributions, reagent cost and availability, and many others. The method is robust, convergent, and extensible, offers the user full control over the relative significance of the various objectives in the final design, and permits the simultaneous selection of compounds from multiple libraries in full- or sparse-array format.     

Assessing the scaffold diversity of screening libraries

Medicinal chemists have traditionally realized assessments of chemical diversity and subsequent compound acquisition, although a recent study suggests that experts are usually inconsistent in reviewing large data sets. To analyze the scaffold diversity of commercially available screening collections, we have developed a general workflow aimed at (1) identifying druglike compounds, (2) clustering them by maximum common substructures (scaffolds), (3) measuring the scaffold diversity encoded by each screening collection independently of its size, and finally (4) merging all common substructures in a nonredundant scaffold library that can easily be browsed by structural and topological queries. Starting from 2.4 million compounds out of 12 commercial sources, four categories of libraries could be identified: large- and medium-sized combinatorial libraries (low scaffold diversity), diverse libraries (medium diversity, medium size), and highly diverse libraries (high diversity, low size). The chemical space covered by the scaffold library can be searched to prioritize scaffold-focused libraries.     

Simulated molecular evolution in a full combinatorial library

BACKGROUND: The Darwinian concept of 'survival of the fittest' has inspired the development of evolutionary optimization methods to find molecules with desired properties in iterative feedback cycles of synthesis and testing. These methods have recently been applied to the computer-guided heuristic selection of molecules that bind with high affinity to a given biological target. We describe the optimization behavior and performance of genetic algorithms (GAs) that select molecules from a combinatorial library of potential thrombin inhibitors in 'artificial molecular evolution' experiments, on the basis of biological screening results. RESULTS: A full combinatorial library of 15,360 members structurally biased towards the serine protease thrombin was synthesized, and all were tested for their ability to inhibit the protease activity of thrombin. Using the resulting large structure-activity landscape, we simulated the evolutionary selection of potent thrombin inhibitors from this library using GAs. Optimal parameter sets were found (encoding strategy, population size, mutation and cross-over rate) for this artificial molecular evolution. CONCLUSIONS: A GA-based evolutionary selection is a valuable combinatorial optimization strategy to discover compounds with desired properties without needing to synthesize and test all possible combinations (i.e. all molecules). GAs are especially powerful when dealing with very large combinatorial libraries for which synthesis and screening of all members is not possible and/or when only a small number of compounds compared with the library size can be synthesized or tested. The optimization gradient or 'learning' per individual increases when using smaller population sizes and decreases for higher mutation rates.     

Combinatorial solid-phase synthesis of 6-hydroxy-1,2,3,4-tetrahydro-beta-carbolines from l-5-hydroxytryptophan

A library of biologically relevant 6-hydroxy-tetrahydro-beta-carbolines (6-OH-THBCs) based on the L-5-OH-tryptophan scaffold was prepared. A solid-phase synthesis was developed, utilizing aminomethyl polystyrene resin and solid-phase-optimized reactions, such as Pictet-Spengler condensation. The library was designed such that three points of diversity would be readily introduced, making the strategy potentially suitable for generation of a large number of compounds.     

Directed evolution of oxygenases: screening systems, success stories and challenges

The field of directed evolution of oxygenases (mono-, di- and epoxygenases) is rapidly advancing as an increasing number of success stories indicate. A significant number of screening systems have been developed to specifically improve oxygenase properties. Oxygenases will become very valuable biocatalysts for synthetic applications in industry when stability, cofactor and activity properties match industrial demands. This review summarizes screening systems and principles of screening systems that have been used for directed evolution of oxygenases. Sections on mutagenic conditions, mutant library size and property improvements provide a comprehensive picture on performance and limitations of current directed evolution methodologies for oxygenases. A discussion of challenges in the directed evolution of oxygenases for industrial exploitation concludes this review.     

Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO2, H2CO, and C6H6

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode-mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO2 and H2CO that are subject to the strongest anharmonic mode-mode coupling within 10 cm(-1) of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C6H6 in the CH stretching (nu12) frequency region, in which combination tones nu13nu16 and nu2nu13nu18 appear on account of an intensity borrowing from nu12via the anharmonic coupling.     

Machine learning based pattern recognition applied to microarray data

Motivation: Microarrays have allowed the expression level of thousands of genes or proteins to be measured simultaneously. Data sets generated by these arrays consist of a small number of observations (e.g., 20-100 samples) on a very large number of variables (e.g., 10,000 genes or proteins). The observations in these data sets often have other attributes associated with them such as a class label denoting the pathology of the subject. Finding the genes or proteins that are correlated to these attributes is often a difficult task since most of the variables do not contain information about the pathology and as such can mask the identity of the relevant features. We describe a genetic algorithm (GA) that employs both supervised and unsupervised learning to mine gene expression and proteomic data. The pattern recognition GA selects features that increase clustering, while simultaneously searching for features that optimize the separation of the classes in a plot of the two or three largest principal components of the data. Because the largest principal components capture the bulk of the variance in the data, the features chosen by the GA contain information primarily about differences between classes in the data set. The principal component analysis routine embedded in the fitness function of the GA acts as an information filter, significantly reducing the size of the search space since it restricts the search to feature sets whose principal component plots show clustering on the basis of class. The algorithm integrates aspects of artificial intelligence and evolutionary computations to yield a smart one pass procedure for feature selection, clustering, classification, and prediction.