Machine-enabled inverse design of inorganic solid materials: promises and challenges

Developing high-performance advanced materials requires a deeper insight and search into the chemical space. Until recently, exploration of materials space using chemical intuitions built upon existing materials has been the general strategy, but this direct design approach is often time and resource consuming and poses a significant bottleneck to solve the materials challenges of future sustainability in a timely manner. To accelerate this conventional design process, inverse design, which outputs materials with pre-defined target properties, has emerged as a significant materials informatics platform in recent years by leveraging hidden knowledge obtained from materials data. Here, we summarize the latest progress in machine-enabled inverse materials design categorized into three strategies: high-throughput virtual screening, global optimization, and generative models. We analyze challenges for each approach and discuss gaps to be bridged for further accelerated and rational data-driven materials design.

The grand challenge of materials science, discovery of novel materials with target properties, can be greatly accelerated by machine-learned inverse design strategies.     

Beyond generative models: superfast traversal,optimization, novelty,exploration and discovery (STONED) algorithm for molecules using SELFIES

Inverse design allows the generation of molecules with desirable physical quantities using property optimization. Deep generative models have recently been applied to tackle inverse design, as they possess the ability to optimize molecular properties directly through structure modification using gradients. While the ability to carry out direct property optimizations is promising, the use of generative deep learning models to solve practical problems requires large amounts of data and is very time-consuming. In this work, we propose STONED – a simple and efficient algorithm to perform interpolation and exploration in the chemical space, comparable to deep generative models. STONED bypasses the need for large amounts of data and training times by using string modifications in the SELFIES molecular representation. First, we achieve non-trivial performance on typical benchmarks for generative models without any training. Additionally, we demonstrate applications in high-throughput virtual screening for the design of drugs, photovoltaics, and the construction of chemical paths, allowing for both property and structure-based interpolation in the chemical space. Overall, we anticipate our results to be a stepping stone for developing more sophisticated inverse design models and benchmarking tools, ultimately helping generative models achieve wider adoption.

Interpolation and exploration within the chemical space for inverse design.     

Molecular Property Optimizations with Boundary Conditions through the Best First Search Scheme

There is an increasing interest in applying quantum chemistry to rationally design novel compounds with some desired characteristics. Furthermore, many applications require more than one property to be optimal. In this Concept, several inverse design strategies, based on the discrete best first search scheme, are introduced that allow for the simultaneous optimization of multiple properties or the optimization of the most vital target property with constraints for secondary properties. A detailed assessment of the different optimization techniques is carried out, and special attention is paid to improve the cost efficacy and performance by tuning the process parameters. Our suggested protocol allows for a more successful optimization routine when additional boundary conditions are desired.     

Inverse molecular design in a tight-binding framework

The number of chemical species of modest molecular weight that can be accessed with known synthetic methods is astronomical. An open challenge is to explore this space in a manner that will enable the discovery of molecular species and materials with optimized properties. Recently, an inverse molecular design strategy, the linear combination of atomic potentials (LCAP) approach [J. Am. Chem. Soc. 128, 3228 (2006)] was developed to optimize electronic polarizabilities and first hyperpolarizabilities. Here, using a simple tight-binding (TB) approach, we show that continuous optimization can be carried out on the LCAP surface successfully to explore vast chemical libraries of 10(2) to 10(16) extended aromatic compounds. We show that the TB-LCAP optimization is not only effective in locating globally optimal structures based on their electronic polarizabilities and first hyperpolarizabilities, but also is straightforwardly extended to optimize transition dipole moments and HOMO-LUMO energy gaps. This approach finds optimal structures among 10(4) candidates with about 40 individual molecular property calculations. As such, for structurally similar molecular candidates, the TB-LCAP approach may provide an effective means to identify structures with optimal properties.     

Designing electrostatic interactions in biological systems via charge optimization or combinatorial approaches: insights and challenges with a continuum electrostatic framework

Electrostatic interactions between biological molecules are crucially influenced by their aqueous environment, with efficient and accurate models of solvent effects required for robust molecular design strategies. Continuum electrostatic models provide a reasonable balance between computational efficiency and accurate system representation. In this article, I review two specific molecular design strategies, charge optimization and combinatorial design, paying particular attention to how the continuum framework (also briefly described herein) successfully enables both theoretical insights and molecular designs and presents a challenge in design applications due to what I call “the isostericity constraint.” Efforts to work around the isostericity constraint and other challenges are discussed. Additionally, particular emphasis is placed on using such models in the rational design of particularly tight, specific, or promiscuous interactions, in keeping with the increased sophistication of current molecular design applications.     

Designing molecules with optimal properties using the linear combination of atomic potentials approach in an AM1 semiempirical framework

The linear combination of atomic potentials (LCAP) approach is implemented in the AM1 semiempirical framework and is used to design molecular structures with optimized properties. The optimization procedure uses property derivative information to search molecular space and thus avoid direct enumeration and evaluation of each molecule in a library. Two tests are described: the optimization of first hyperpolarizabilities of substituted aromatics and the optimization of a figure of merit for n-type organic semiconductors.     

Inverse design and synthesis of acac-coumarin anchors for robust TiO2 sensitization

An inverse design methodology suitable to assist the synthesis and optimization of molecular sensitizers for dye-sensitized solar cells is introduced. The method searches for molecular adsorbates with suitable photoabsorption properties through continuous optimization of "alchemical" structures in the vicinity of a reference molecular framework. The approach is illustrated as applied to the design and optimization of linker chromophores for TiO(2) sensitization, using the recently developed phenyl-acetylacetonate (i.e., phenyl-acac) anchor [McNamara et al. J. Am. Chem. Soc.2008, 130, 14329-14338] as a reference framework. A novel anchor (3-acac-pyran-2-one) is found to be a local optimum, with improved sensitization properties when compared to phenyl-acac. Its molecular structure is related to known coumarin dyes that could be used as lead chromophore anchors for practical applications in dye-sensitized solar cells. Synthesis and spectroscopic characterization confirms that the linker provides robust attachment to TiO(2), even in aqueous conditions, yielding improved sensitization to solar light and ultrafast interfacial electron injection. The findings are particularly relevant to the design of sensitizers for dye-sensitized solar cells because of the wide variety of structures that are possible but they should be equally useful for other applications such as ligand design for homogeneous catalysis.     

Calibration of forcefields for molecular simulation: Sequential design of computer experiments for building cost‐efficient kriging metamodels

We present a global strategy for molecular simulation forcefield optimization, using recent advances in Efficient Global Optimization algorithms. During the course of the optimization process, probabilistic kriging metamodels are used, that predict molecular simulation results for a given set of forcefield parameter values. This enables a thorough investigation of parameter space, and a global search for the minimum of a score function by properly integrating relevant uncertainty sources. Additional information about the forcefield parameters are obtained that are inaccessible with standard optimization strategies. In particular, uncertainty on the optimal forcefield parameters can be estimated, and transferred to simulation predictions. This global optimization strategy is benchmarked on the TIP4P water model. © 2013 Wiley Periodicals, Inc.     

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.     

Designing molecules by optimizing potentials

The astronomical number of accessible discrete chemical structures makes rational molecular design extremely challenging. We formulate the design of molecules with specific tailored properties as performing a continuous optimization in the space of electron-nuclear attraction potentials. The optimization is facilitated by using a linear combination of atomic potentials (LCAP), a general framework that creates a continuous property landscape from an otherwise unlinked set of discrete molecular-property values. A demonstration of this approach is given for the optimization of molecular electronic polarizability and hyperpolarizability. We show that the optimal structures can be determined without enumerating and separately evaluating the characteristics of the combinatorial number of possible structures, a process that would be much slower. The LCAP approach may be used with quantum or classical Hamiltonians, suggesting possible applications to drug design and new materials discovery.     

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.     

Identification of hits and lead structure candidates with limited resources by adaptive optimization

Three stochastic optimization algorithms (Simulated Annealing (SA), Evolution Strategy (ES), and Particle Swarm Optimization (PSO)) and a Random Search were assessed for their ability to generate small activity-enriched subsets of molecular compound libraries. The optimization algorithms were employed to perform an "intelligent" iterative sampling of library molecules avoiding the biological testing of the full library. This study was performed to find a suitable optimization algorithm along with suitable parametrization. Particularly, the optimal number of iterations and population size were of interest. Optimizations were performed with limited resources as the maximal number of compound evaluations was restricted to 300. Results show that all three optimization algorithms are able to produce comparably good results, clearly outperforming a Random Search. While ES was able to come up with good solutions after a few optimization cycles, SA favored high numbers of iterations and was therefore less suited for library design. We introduce PSOs as an alternative approach to focused library design. PSO was able to produce high quality solutions while exhibiting marked autoadaptivity. Its implicit step size control makes it a straightforward out-of-the-box optimization algorithm. We further demonstrate that a nearest neighbor algorithm can successfully be applied to map from continuous search space to discrete chemical space.     

Coarse-graining errors and numerical optimization using a relative entropy framework

The ability to generate accurate coarse-grained models from reference fully atomic (or otherwise "first-principles") ones has become an important component in modeling the behavior of complex molecular systems with large length and time scales. We recently proposed a novel coarse-graining approach based upon variational minimization of a configuration-space functional called the relative entropy, S(rel), that measures the information lost upon coarse-graining. Here, we develop a broad theoretical framework for this methodology and numerical strategies for its use in practical coarse-graining settings. In particular, we show that the relative entropy offers tight control over the errors due to coarse-graining in arbitrary microscopic properties, and suggests a systematic approach to reducing them. We also describe fundamental connections between this optimization methodology and other coarse-graining strategies like inverse Monte Carlo, force matching, energy matching, and variational mean-field theory. We suggest several new numerical approaches to its minimization that provide new coarse-graining strategies. Finally, we demonstrate the application of these theoretical considerations and algorithms to a simple, instructive system and characterize convergence and errors within the relative entropy framework.     

Gradient‐driven molecule construction: An inverse approach applied to the design of small‐molecule fixating catalysts

Rational design of molecules and materials usually requires extensive screening of molecular structures for the desired property. The inverse approach to deduce a structure for a predefined property would be highly desirable, but is, unfortunately, not well defined. However, feasible strategies for such an inverse design process may be successfully developed for specific purposes. We discuss options for calculating “jacket” potentials that fulfill a predefined target requirement—a concept that we recently introduced (Weymuth and Reiher, MRS Proceedings 2013, 1524, DOI:10.1557/opl.2012.1764). We consider the case of small‐molecule activating transition metal catalysts. As a target requirement we choose the vanishing geometry gradients on all atoms of a subsystem consisting of a metal center binding the small molecule to be activated. The jacket potential can be represented within a full quantum model or by a sequence of approximations of which a field of electrostatic point charges is the simplest. In a second step, the jacket potential needs to be replaced by a chemically viable chelate‐ligand structure for which the geometry gradients on all of its atoms are also required to vanish. To analyze the feasibility of this approach, we dissect a known dinitrogen‐fixating catalyst to study possible design strategies that must eventually produce the known catalyst. © 2014 Wiley Periodicals, Inc.     

Library design practices for success in lead generation with small molecule libraries

The generation of novel structures amenable to rapid and efficient lead optimization comprises an emerging strategy for success in modern drug discovery. Small molecule libraries of sufficient size and diversity to increase the chances of discovery of novel structures make the high throughput synthesis approach the method of choice for lead generation. Despite an industry trend for smaller, more focused libraries, the need to generate novel lead structures makes larger libraries a necessary strategy. For libraries of a several thousand or more members, solid phase synthesis approaches are the most suitable. While the technology and chemistry necessary for small molecule library synthesis continue to advance, success in lead generation requires rigorous consideration in the library design process to ensure the synthesis of molecules possessing the proper characteristics for subsequent lead optimization. Without proper selection of library templates and building blocks, solid phase synthesis methods often generate molecules which are too heavy, too lipophilic and too complex to be useful for lead optimization. The appropriate filtering of virtual library designs with multiple computational tools allows the generation of information-rich libraries within a drug-like molecular property space. An understanding of the hit-to-lead process provides a practical guide to molecular design characteristics. Examples of leads generated from library approaches also provide a benchmarking of successes as well as aspects for continued development of library design practices.     

A gradient-directed Monte Carlo approach to molecular design

The recently developed linear combination of atomic potentials (LCAP) approach [M. Wang et al., J. Am. Chem. Soc. 128, 3228 (2006)] allows continuous optimization in a discrete chemical space, and thus is useful in the design of molecules for targeted properties. To address further challenges arising from the rugged, continuous property surfaces in the LCAP approach, we develop a gradient-directed Monte Carlo (GDMC) strategy as an augmentation to the original LCAP optimization method. The GDMC method retains the power of exploring molecular space by utilizing local gradient information computed from the LCAP approach to jump between discrete molecular structures. It also allows random MC moves to overcome barriers between local optima on property surfaces. The combined GDMC-LCAP approach is demonstrated here for optimizing nonlinear optical properties in a class of donor-acceptor substituted benzene and porphyrin frameworks. Specifically, one molecule with four nitrogen atoms in the porphyrin ring was found to have a larger first hyperpolarizability than structures with the conventional porphyrin motif.     

The integrated multivariate approach for the development of dry reagent strips for quantitative clinical analysis

Summary The paper describes the development and the optimization of a visually and metrically evaluable dry reagent strip for quantitative clinical analysis of blood glucose based upon an enzymatic oxidation connected with a following colour coupling reaction. In contrast to classical experimental strategies, multivariate statistical methods were used to design a complex biochemical system with optimal properties. Former experiments were evaluated by means of factor analysis and the relations between the 12 biochemical variables and the 6 strip properties were studied. The mathematical discrimination between biochemically more and less relevant variables allowed a reduction of the number of experiments by a statistically reasonable design of additional selected experiments. By application of a pattern recognition technique and multivariate linear regression the data space and the variables' space were analysed. A following multivariate prediction using the partial least-squares technique yielded a glucose test strip with high reproducibility and long-term thermal stability.     

Design Strategies for Diradical Boron/Nitrogen Doped Carbon-Based Materials

New heterocyclic diradicaloids based on boron and nitrogen-doped polycyclic systems with open-shell ground-states are obtained via concomitant structural and quinoidal extensions, thus allowing to merge the best of both design strategies. A combination of experimental characterization and theoretical calculations have helped disclose their electronic structure, as well as rationalize their associated magnetic and photophysical properties, spanning the chemical space of available molecular templates for cutting-edge applications in organic electronics and spintronics.     

Artificial Intelligence for Autonomous Molecular Design: A Perspective

Domain-aware artificial intelligence has been increasingly adopted in recent years to expedite molecular design in various applications, including drug design and discovery. Recent advances in areas such as physics-informed machine learning and reasoning, software engineering, high-end hardware development, and computing infrastructures are providing opportunities to build scalable and explainable AI molecular discovery systems. This could improve a design hypothesis through feedback analysis, data integration that can provide a basis for the introduction of end-to-end automation for compound discovery and optimization, and enable more intelligent searches of chemical space. Several state-of-the-art ML architectures are predominantly and independently used for predicting the properties of small molecules, their high throughput synthesis, and screening, iteratively identifying and optimizing lead therapeutic candidates. However, such deep learning and ML approaches also raise considerable conceptual, technical, scalability, and end-to-end error quantification challenges, as well as skepticism about the current AI hype to build automated tools. To this end, synergistically and intelligently using these individual components along with robust quantum physics-based molecular representation and data generation tools in a closed-loop holds enormous promise for accelerated therapeutic design to critically analyze the opportunities and challenges for their more widespread application. This article aims to identify the most recent technology and breakthrough achieved by each of the components and discusses how such autonomous AI and ML workflows can be integrated to radically accelerate the protein target or disease model-based probe design that can be iteratively validated experimentally. Taken together, this could significantly reduce the timeline for end-to-end therapeutic discovery and optimization upon the arrival of any novel zoonotic transmission event. Our article serves as a guide for medicinal, computational chemistry and biology, analytical chemistry, and the ML community to practice autonomous molecular design in precision medicine and drug discovery.