Hai Du

A planning module for performing grid search, factorial design, and related combinatorial studies on an automated chemistry workstation

Abstract The investigation of combinations of factors in a defined search space has broad application in chemistry experimentation. The factors can involve continuous variables such as concentration and temperature, or discrete variables such as chemical reactants or reagents. The number of data points rapidly becomes quite large in such factorial experimentation, which can be adequately handled through the use of an automated chemistry workstation. The automated chemistry workstation utilizes experiment templates for implementation of factorial designs. Experimental templates represent generic plans that are used repetitively with slight variation of designated parameters for the chemical system under investigation. A linkage is established between the dimensions of the search space and the variables in the experimental template. Various patterns of points can be selected, enabling the composition of full factorial or partial factorial designs. The search space points are inscribed in the experimental template, giving rise to one experimental plan per point in the search space. The experimental plans are assessed for resource availability and those for which resources are sufficient are then scheduled for parallel implementation on a microscale automated chemistry workstation. An adaptive feature allows unproductive experiments to be terminated early, de-allocating resources for use in other experiments. Experimental plans can be readily composed and implemented for fundamental studies of chemical reactions, generating response surfaces, performing parallel screening procedures, and creating indexed combinatorial chemical libraries.

A parallel simplex search method for use with an automated chemistry workstation

The Simplex method, an inherently serial means of optimization, can be used to search for improved conditions for chemical reactions. We have developed an automated chemistry workstation equipped for parallel adaptive experimentation. To exploit the capabilities of the workstation and thereby optimize reaction conditions in a more expedient manner, we have developed an experiment-planning module for performing Simplex searches in parallel. The parallel Simplex search (PSS) module enables multiple composite modified Simplex (CMS) searches to be performed in a concurrent manner. Features have been incorporated for two applications. (1) Multiple concurrent simplex searches in one search space, enabling optimization of conditions for one reaction. The use of Simplex searches starting from several points in a search space reduces the possibility of falsely concluding that a local maximum is the global maximum. (2) Concurrent investigation of multiple search spaces with one Simplex search per space, enabling optimization of conditions for each member of a set of catalysts or set of reactants for a given reaction. This latter feature is useful for combinatorial chemistry applications. All individual Simplex searches in a PSS study must employ the same experimental template. The PSS module includes options to define conditions for simplex moves as well as specifying initial points in the search space. Provisions are included for stop criteria, termination of an individual Simplex search, and global termination of multiple Simplex searches. The PSS method provides a parallel yet adaptive means for identifying improved conditions for chemical reactions.

Virtual libraries of tetrapyrrole macrocycles. Combinatorics, isomers, product distributions, and data mining.

A software program (PorphyrinViLiGe) has been developed to enumerate the type and relative amounts of substituted tetrapyrrole macrocycles in a virtual library formed by one of four different classes of reactions. The classes include (1) 4-fold reaction of n disubstituted heterocycles (e.g., pyrroles or diiminoisoindolines) to form β-substituted porphyrins, β-substituted tetraazaporphyrins, or α- or β-substituted phthalocyanines; (2) combination of m aminoketones and n diones to form m × n pyrroles, which upon 4-fold reaction give β-substituted porphyrins; (3) derivatization of an 8-point tetrapyrrole scaffold with n reagents, and (4) 4-fold reaction of n aldehydes and pyrrole to form meso-substituted porphyrins. The program accommodates variable ratios of reactants, reversible or irreversible reaction (reaction classes 1 and 2), and degenerate modes of formation. Pólyas theorem (for enumeration of cyclic entities) has also been implemented and provides validation for reaction classes 3 and 4. The output includes the number and identity of distinct reaction-accessible substituent combinations, the number and identity of isomers thereof, and the theoretical mass spectrum. Provisions for data mining enable assessment of the number of products having a chosen pattern of substituents. Examples include derivatization of an octa-substituted phthalocyanine with eight reagents to afford a library of 2,099,728 members (yet only 6435 distinct substituent combinations) and reversible reaction of six distinct disubstituted pyrroles to afford 2649 members (yet only 126 distinct substituent combinations). In general, libraries of substituted tetrapyrrole macrocycles occupy a synthetically accessible region of chemical space that is rich in isomers (>99% or 95% for the two examples, respectively).

Implementation of the multidirectional search algorithm on an automated chemistry workstation. A parallel yet adaptive approach for reaction optimization

Abstract We have developed an experiment-planning module for applying a powerful new pattern search algorithm toward the problems of reaction investigation and optimization. The experiment planner works in conjunction with a closed-loop automated chemistry workstation equipped for parallel experimentation. The new algorithm, developed by Torczon for parallel computation of mathematical functions, achieves a focused yet parallel approach to finding regions of improved response. Like a full factorial design, the search space involves a regular grid of points. Like the Simplex algorithm, the multidirectional search (MDS) algorithm uses the movement of a simplex through a search space. However, with each movement all points except the single best are discarded, whereas the Simplex algorithm discards only the one worst point. Thus, in an n-dimensional space, the MDS algorithm projects n mandatory points at every cycle (beyond the initial). In addition, a larger number of exploratory points are identified by look-ahead projection of possible future simplices. Such exploratory points lie on multiple independent lines of search. The responses for the mandatory and exploratory points are acquired via parallel experimentation, with the latter points examined to the extent that the workstation has available capacity during the same schedule. The data from such exploratory points can be used in later cycles of experimentation, accelerating convergence on the region of optimal response. In the case of unlimited parallel experimentation capacity, all possible points in the space are projected, as in a full factorial design. The MDS algorithm thus adapts to the available parallel capacity of the workstation. The MDS planning module includes options for specifying initial points, stop criteria, and early-termination processes. Provisions are included for parallel scheduling of batches of experiments, convergence of the search, and movement at the boundaries of the search space. An MDS investigation can thus be implemented with global decision-making concerning movements through a search space, and local decision-making concerning termination of individual experiments. The MDS algorithm enables directed evolutionary searches in a parallel mode and is ideally suited for rapid optimization of chemical reactions using a microscale automated chemistry workstation.

Decision-tree programs for an adaptive automated chemistry workstation. Application to catalyst screening experiments

Abstract Automated chemistry workstations with the capability of altering the course of experimentation based on acquired data are essential for performing strategic searches. Such adaptive experimentation requires the ability to compose experimental plans for initiating, monitoring, evaluating, and making decisions about experiments. We have developed a decision-tree (DT) experiment-planning module that includes a complete command set for adaptive operation of the workstation. Functions for dialog prompts are included, enabling generic programs to be tailored for specific applications by various users. The DT experiment-planning module is one component of an experiment planner for an automated microscale chemistry workstation. The DT functions are also used to compose early-termination programs and describe objective functions for use in the companion factorial design, composite-modified simplex, and multidirectional search experiment-planning modules. The features of the DT experiment-planning module are illustrated with a program that screens a list of candidate compounds for catalytic activity. A set of dialog boxes at the beginning of the program prompts the user for information. Based on this information, the candidates are examined automatically (in a serial process) in exhaustive or hill-climbing searching strategies. A yield vs. time pattern-matching procedure is performed dynamically in order to assess whether monitoring should be continued. Decisions also are made concerning examination of the candidate at higher or lower concentrations. Higher concentrations are achieved by addition of aliquots of the candidate to the ongoing reaction, while lower concentrations are achieved by spawning a new reaction. When a user-defined yield threshold is reached or the entire user-specified concentration range has been spanned, catalysts and their effective concentration ranges are identified. This experiment-planning module enables composition of flexible programs for adaptive experimentation that can be used as stand-alone programs or as decision-making components of other searching programs.

An experiment planner for performing successive focused grid searches with an automated chemistry workstation

Abstract Automated chemistry workstations equipped for parallel and adaptive experimentation can provide a significant impact in chemistry research, particularly for exploring search spaces as part of optimization studies. A traditional method of investigating a search space involves generation of a response surface upon examination of a regular grid of points (e.g., as in a full factorial design). Such experimental approaches are compatible with parallel experimentation but are not adaptive in directing the search toward favorable regions of the search space. We have developed an algorithm wherein a succession of grid searches is performed in a search space. The location of the optimal response obtained in one search cycle constitutes the location about which a subsequent more fine-grained search is performed. In this manner, a sequential iterative optimization can be achieved: one cycle is comprised of a set of parallel reactions followed by data evaluation, and multiple cycles occur until one of several user-defined termination criteria is satisfied. In successive cycles, the number of levels on each dimension can be decremented and the range of each dimension can be decreased by a defined “shrinkage” factor. The resulting successive focused grid search (SFGS) affords a breadth-first then in-depth study. We have developed an experimental planner that enables the SFGS algorithm to be implemented on an automated chemistry workstation. Options are available for adjusting the scope of experimentation to conserve material resources (e.g., solvent, reagents, reactants) or to curtail the duration of experimentation. Collectively, the SFGS module enables parallel adaptive experimentation and affords a comprehensive response surface that is fine-grained in the region of optimal response.

An approach for parallel and adaptive screening of discrete compounds followed by reaction optimization using an automated chemistry workstation

The challenge of finding appropriate reagents, catalysts, or cocatalysts for chemical reactions is typically met with a strategy of surveying broadly to identify a good starting point (i.e., a hit) from which an in-depth optimization can be performed. We have developed an approach for experiment planning that enables this two-tiered strategy to be implemented on an automated chemistry workstation. One experiment-planning module (Parascreen) for screening discrete substances to identify hits is linked to a second module (Multidirectional search, MDS) for optimization of each hit compound. The screening module has been constructed through modification of an experiment-planning module for performing grid searches. Each candidate is examined over a range of concentrations. Two levels of decision-making are performed. (1) Local evaluation: Yield-versus-time data from a given reaction are examined in a pattern-matching procedure to assess whether monitoring should be continued or terminated. (2) Global evaluation: When a user-defined threshold (e.g., yield) is reached, the candidate is flagged as a hit; any experiments at higher concentration of the same candidate are deleted. Each of the hit compounds is subjected to identification of refined conditions by means of an MDS optimization. Each module alone enables parallel adaptive experimentation. Several issues for automated use of two different modules in succession have been addressed. This two-tiered approach of breadth-first screening followed by in-depth optimization of hits enables autonomous experimentation using an automated chemistry workstation.

A two-tiered strategy for simplex and multidirectional optimization of reactions with an automated chemistry workstation

A two-tiered strategy for optimizing reaction conditions has been developed for use with an automated chemistry workstation capable of parallel adaptive experimentation. In tier one, a broad survey of conditions is performed in parallel. In tier two, the promising region identified in the first tier is used as the starting point for in-depth searches. The search strategies employed in tier two include the composite-modified Simplex (CMS), multidirectional search (MDS), and parallel Simplex search (PSS) methods. Accordingly, this two-tiered strategy has been integrated into the CMS, MDS, and PSS experiment-planning modules. Each of these methods requires an initial user-defined simplex to explore reaction conditions. The breadth-first survey avoids the lengthy experimentation that occurs when the initial simplex is located far from the optimal region, and also diminishes the possibility of trapping in local maxima. Thus, the two-tiered strategy (breadth-first, depth-second) enables the optimal region to be reached rapidly.

Enumeration of Virtual Libraries of Combinatorial Modular Macrocyclic (Bracelet, Necklace) Architectures and Their Linear Counterparts

A wide variety of cyclic molecular architectures are built of modular subunits and can be formed combinatorially. The mathematics for enumeration of such objects is well-developed yet lacks key features of importance in chemistry, such as specifying (i) the structures of individual members among a set of isomers, (ii) the distribution (i.e., relative amounts) of products, and (iii) the effect of nonequal ratios of reacting monomers on the product distribution. Here, a software program (Cyclaplex) has been developed to determine the number, identity (including isomers), and relative amounts of linear and cyclic architectures from a given number and ratio of reacting monomers. The program includes both mathematical formulas and generative algorithms for enumeration; the latter go beyond the former to provide desired molecular-relevant information and data-mining features. The program is equipped to enumerate four types of architectures: (i) linear architectures with directionality (macroscopic equivalent = electrical extension cords), (ii) linear architectures without directionality (batons), (iii) cyclic architectures with directionality (necklaces), and (iv) cyclic architectures without directionality (bracelets). The program can be applied to cyclic peptides, cycloveratrylenes, cyclens, calixarenes, cyclodextrins, crown ethers, cucurbiturils, annulenes, expanded meso-substituted porphyrin(ogen)s, and diverse supramolecular (e.g., protein) assemblies. The size of accessible architectures encompasses up to 12 modular subunits derived from 12 reacting monomers or larger architectures (e.g. 13-17 subunits) from fewer types of monomers (e.g. 2-4). A particular application concerns understanding the possible heterogeneity of (natural or biohybrid) photosynthetic light-harvesting oligomers (cyclic, linear) formed from distinct peptide subunits.

PhotochemCAD 3: Diverse Modules for Photophysical Calculations with Multiple Spectral Databases

The PhotochemCAD program, developed over 30 years, is described comprehensively with focus on features of the most recent version (PhotochemCAD 3). The program is equipped with a streamlined user interface and provisions for handling multiple spectral databases. Eight modules enable calculations to be performed on the basis of the spectra in the databases. The calculational modules provide results concerning properties of individual compounds (oscillator strength, transition dipole moment, natural radiative lifetime), interactions of multiple compounds (Förster energy transfer, Dexter energy transfer, analysis of energy transfer among an array of chromophores) and composition of mixtures (multicomponent analysis). Synthetic spectra (blackbody radiator, Gaussian and Lorentzian curves, delta functions) also can be generated. For comparison and calculation, synthetic and experimental spectra can be shifted along both coordinate axes and combined by addition, subtraction and use of multiplicative factors. The core databases (described in the companion paper) have been expanded to 339 compounds for which absorption spectra (including molar absorption coefficient, ε), fluorescence spectra (including fluorescence quantum yield, Φf) and references to the primary literature have been included where available (552 spectra altogether). A database of 31 solar spectra also is included. Each calculational module is described along with illustrative examples.