Efficient Crystal Structure Prediction for Structurally Related Molecules with Accurate and Transferable Tailor-Made Force Fields

Solid-State Evaluation of a Newly Emerged Polymorph for Early-Stage Pharmaceutical Development

This work presents the solid-state evaluation of a new polymorph (Form M) discovered during the early-stage pharmaceutical development of a new chemical entity GDC-6599. Form screening and active pharmaceutical ingredient (API) crystallization development identified Form A of GDC-6599 as the experimentally most stable polymorph, although more stable polymorphs were predicted by crystal structure prediction (CSP). Later, a new polymorph, Form M, was discovered in the crystallization of a kilogram-scale API batch. The powder X-ray diffraction (PXRD) pattern of Form M was consistent with the calculated pattern of the predicted most stable polymorph (Rank 1) by CSP. Form A and Form M were subsequently speculated as enantiotropic polymorphs according to their melting temperatures and enthalpies. Slurry competition (SC) experimentally confirmed Form M as the more stable polymorph at temperatures relevant to pharmaceutical development. To support API manufacturing, a quantitative PXRD method was successfully developed for controlling the Form A percentage during the API crystallization process. To understand the impact of Form M on the drug product performance, pharmaceutical and biopharmaceutical evaluations were carried out. The intrinsic solubility of Form M was found to be 56% of the intrinsic solubility of Form A, consistent with their calculated solubility ratio based on the Gibbs free energy difference predicted by CSP. Biopharmaceutical assessment further suggested that the observed solubility reduction would not impact the biopharmaceutical performance of GDC-6599 at doses relevant for the proposed clinical studies, providing form selection flexibility for clinical formulation development. Accordingly, Form M was recommended for future API manufacturing and solid dosage form development. Meanwhile, Form A was confirmed to be physically stable in a suspension formulation for extemporaneous preparation and was recommended to support the early cohorts of Phase I clinical studies.

Accurate Lattice Free Energies of Packing Polymorphs from Probabilistic Generative Models

Finite-temperature lattice free energy differences between polymorphs of molecular crystals are fundamental to understanding and predicting the relative stability relationships underpinning polymorphism, yet are computationally expensive to obtain. Here, we implement and critically assess machine-learning-enabled targeted free energy calculations derived from flow-based generative models to compute the free energy difference between two ice crystal polymorphs (Ice XI and Ic), modeled with a fully flexible empirical classical force field. We demonstrate that even when remapping from an analytical reference distribution, such methods enable a cost-effective and accurate calculation of free energy differences between disconnected metastable ensembles when trained on locally ergodic data sampled exclusively from the ensembles of interest. Unlike classical free energy perturbation methods, such as the Einstein crystal method, the targeted approach analyzed in this work requires no additional sampling of intermediate perturbed Hamiltonians, offering significant computational savings. To systematically assess the accuracy of the method, we monitored the convergence of free energy estimates during training by implementing an overfitting-aware weighted averaging strategy. By comparing our results with ground-truth free energy differences computed with the Einstein crystal method, we assess the accuracy and efficiency of two different model architectures, employing two different representations of the supercell degrees of freedom (Cartesian vs quaternion-based). We conduct our assessment by comparing free energy differences between crystal supercells of different sizes and temperatures and assessing the accuracy in extrapolating lattice free energies to the thermodynamic limit. While at low temperatures and in small system sizes, the models perform with similar accuracy. We note that for larger systems and high temperatures, the choice of representation is key to obtaining generalizable results of quality comparable to that obtained from the Einstein crystal method. We believe this work to be a stepping stone toward efficient free energy calculations in larger, more complex molecular crystals.

The seventh blind test of crystal structure prediction: structure ranking methods

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol-1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

Crystal Structure Prediction Using Generative Adversarial Network with Data-Driven Latent Space Fusion Strategy

Crystal structure prediction (CSP) is an important field of material design. Herein, we propose a novel generative adversarial network model, guided by a data-driven approach and incorporating the real physical structure of crystals, to address the complexity of high-dimensional data and improve prediction accuracy in materials science. The model, termed GAN-DDLSF, introduces a novel sampling method called data-driven latent space fusion (DDLSF), which aims to optimize the latent space of generative adversarial networks (GANs) by combining the statistical properties of real data with a standard Gaussian distribution, effectively mitigating the "mode collapse" problem prevalent in GANs. Our approach introduces a more refined generation mechanism specifically for binary crystal structures such as gallium nitride (GaN). By optimizing for the specific crystallographic features of GaN while maintaining structural rationality, we achieve higher precision and efficiency in predicting and designing structures for this particular material system. The model generates 9321 GaN binary crystal structures, with 16.59% reaching a stable state and 24.21% found to be metastable. These results can significantly enhance the accuracy of crystal structure predictions and provide valuable insights into the potential of the GAN-DDLSF approach for the discovery and design of binary, ternary, and multinary materials, offering new perspectives and methods for materials science research and applications.

Discovery of a Series of Macrocycles as Potent Inhibitors of Leishmania Infantum

Macrocycles are prominent among drugs for treatment of infectious disease, with many originating from natural products. Herein we report on the discovery of a series of macrocycles structurally related to the natural product hymenocardine. Members of this series were found to inhibit the growth of Plasmodium falciparum, the parasite responsible for most malaria cases, and of four kinetoplastid parasites. Notably, macrocycles more potent than miltefosine, the only oral drug used for the treatment of the neglected tropical disease visceral leishmaniasis, were identified in a phenotypic screen of Leishmania infantum. In vitro profiling highlighted that potent inhibitors had satisfactory cell permeability with a low efflux ratio, indicating their potential for oral administration, but low solubility and metabolic stability. Analysis of predicted crystal structures suggests that optimization should focus on the reduction of π-π crystal packing interactions to reduce the strong crystalline interactions and improve the solubility of the most potent lead.

Unprecedented Packing Polymorphism of Oxindole: An Exploration Inspired by Crystal Structure Prediction

Crystal polymorphism, characterized by different packing arrangements of the same compound, strongly ties to the physical properties of a molecule. Determining the polymorphic landscape is complex and time-consuming, with the number of experimentally observed polymorphs varying widely from molecule to molecule. Furthermore, disappearing polymorphs, the phenomenon whereby experimentally observed forms cannot be reproduced, pose a significant challenge for the pharmaceutical industry. Herein, we focused on oxindole (OX), a small rigid molecule with four known polymorphs, including a reported disappearing form. Using crystal structure prediction (CSP), we assessed OX solid-state landscape and thermodynamic stability by comparing predicted structures with experimentally known forms. We then performed melt and solution crystallization in bulk and nanoconfinement to validate our predictions. These experiments successfully reproduced the known forms and led to the discovery of four novel polymorphs. Our approach provided insights into reconstructing disappearing polymorphs and building more comprehensive polymorph landscapes. These results also establish a new record of packing polymorphism for rigid molecules.

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

Free Energy Perturbation Approach for Accurate Crystalline Aqueous Solubility Predictions

Early assessment of crystalline thermodynamic solubility continues to be elusive for drug discovery and development despite its critical importance, especially for the ever-increasing fraction of poorly soluble drug candidates. Here we present a detailed evaluation of a physics-based free energy perturbation (FEP+) approach for computing the thermodynamic aqueous solubility. The predictive power of this approach is assessed across diverse chemical spaces, spanning pharmaceutically relevant literature compounds and more complex AbbVie compounds. Our approach achieves predictive (RMSE = 0.86) and differentiating power (R2 = 0.69) and therefore provides notably improved correlations to experimental solubility compared to state-of-the-art machine learning approaches that utilize quantum mechanics-based descriptors. The importance of explicit considerations of crystalline packing in predicting solubility by the FEP+ approach is also highlighted in this study. Finally, we show how computed energetics, including hydration and sublimation free energies, can provide further insights into molecule design to feed the medicinal chemistry DMTA cycle.

Continuous chiral distances for two-dimensional lattices

Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two-dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic-style coordinates. The four non-oblique Bravais classes of two-dimensional lattices form low-dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real-valued distances satisfying metric axioms. This article analyzes these and newer G-chiral distances for millions of two-dimensional lattices that are extracted from thousands of available two-dimensional materials and real crystal structures in the Cambridge Structural Database.

Predicting crystal form stability under real-world conditions

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

Solid Form Screenings in Pharmaceutical Development: a Perspective on Current Practices

Solid form screening is a crucial step in new drug development because solid forms of a drug substance significantly affect stability, dissolution and manufacturing processes of its drug products. This perspective introduces solid-state science from a practical standpoint, aiming to reduce knowledge gaps and promote communications among scientists with diverse background. This perspective starts with a concise overview that followed by discussion on timeline and goals of solid form screening. Techniques for solid from identification and characterization are then discussed. Subsequently, the perspective presents commonly used methods in solid form screening and introduces criteria and strategies to effectively select a favorable solid form based on screening results. The last section summarizes current practices in pharmaceutical industries and suggests potential opportunities for future research and development.

A data-driven and topological mapping approach for the a priori prediction of stable molecular crystalline hydrates

Predictions of the structures of stoichiometric, fractional, or nonstoichiometric hydrates of organic molecular crystals are immensely challenging due to the extensive search space of different water contents, host molecular placements throughout the crystal, and internal molecular conformations. However, the dry frameworks of these hydrates, especially for nonstoichiometric or isostructural dehydrates, can often be predicted from a standard anhydrous crystal structure prediction (CSP) protocol. Inspired by developments in the field of drug binding, we introduce an efficient data-driven and topologically aware approach for predicting organic molecular crystal hydrate structures through a mapping of water positions within the crystal structure. The method does not require a priori specification of water content and can, therefore, predict stoichiometric, fractional, and nonstoichiometric hydrate structures. This approach, which we term a mapping approach for crystal hydrates (MACH), establishes a set of rules for systematic determination of favorable positions for water insertion within predicted or experimental crystal structures based on considerations of the chemical features of local environments and void regions. The proposed approach is tested on hydrates of three pharmaceutically relevant compounds that exhibit diverse crystal packing motifs and void environments characteristic of hydrate structures. Overall, we show that our mapping approach introduces an advance in the efficient performance of hydrate CSP through generation of stable hydrate stoichiometries at low cost and should be considered an integral component for CSP workflows.