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Multi-Dimensional Structural Fingerprinting for Quantitative Polymorph Comparison: A Comprehensive Topological Analysis of Sulfathiazole, Galunisertib and Aripiprazole Polymorphs

This paper introduces a robust, unit-cell-independent multi-dimensional topological fingerprinting framework that quantitatively compares organic crystal polymorphs across five structural categories, demonstrating its effectiveness in classifying and ranking sulfathiazole, galunisertib, and aripiprazole forms with superior correlation to COMPACK cluster matching compared to existing invariant descriptors.

Original authors: Nikolaos Galanakis, David Hughes, Mark Tuckerman

Published 2026-10-23

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CC BY 4.0

Original authors: Nikolaos Galanakis, David Hughes, Mark Tuckerman

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of solid materials, a single chemical substance can exist in more than one way. Just as a set of bricks can be stacked to build a wall, a tower, or a bridge, the same molecules can arrange themselves into different three-dimensional patterns when they crystallize. These different arrangements are called polymorphs. While the chemical recipe remains identical, the physical structure changes, and with it, the material's behavior. For medicines, this difference is critical; one arrangement might dissolve quickly in the body to cure an illness, while another might remain inert, or worse, become unstable and lose its potency. Pharmaceutical companies must identify and control every possible form a drug can take, but telling these subtle variations apart is notoriously difficult. Traditional methods often rely on comparing the patterns of X-rays bouncing off the crystals, which can be like trying to identify a person by their shadow: it gives a clue, but it misses the details of the face.

A team of researchers has developed a new way to look inside these crystal structures, moving beyond simple shadows to measure the actual relationships between molecules. Instead of asking if two crystals look the same, their method asks how they are different and in exactly which ways. By breaking a crystal down into five distinct layers of organization—how the molecules pack together, how they touch and bond, how they twist and bend, how their parts are oriented, and how they are spaced in 3D space—they created a detailed "fingerprint" for each form. This approach was tested on three different drug molecules: sulfathiazole, an antibiotic; galunisertib, a cancer treatment; and aripiprazole, an antipsychotic. The researchers found that while some aspects of a crystal's structure remain stubbornly consistent across different forms, others change dramatically, and the specific pattern of change depends entirely on the molecule itself.

The core of this new method is a shift in perspective. Rather than trying to force two crystal structures to line up perfectly, which often fails when the molecules have twisted into different shapes, the researchers treated the crystal as a collection of repeating patterns. They examined the entire crystal, not just a small snapshot, and measured the distances and angles between molecules in a way that does not depend on how the crystal was oriented in space or how it was labeled in a database. This ensures that the comparison is fair and consistent, regardless of who measured it or where it was stored. The team then compared these measurements using a mathematical tool that calculates the "work" required to turn one distribution of distances into another, providing a precise score of similarity.

When applied to sulfathiazole, which has five known forms, the method revealed that the spatial arrangement of the molecules—their neighbors and how they are spaced—was the most consistent feature across all forms. However, the way the molecules themselves twisted and the specific patterns of their hydrogen bonds varied enough to clearly separate the forms into two distinct groups. This matched what other established methods had found, but the new approach explained why they were different, breaking the similarity down into its component parts. For the cancer drug galunisertib, which has ten different forms, the story was different. Here, the internal shape of the molecule and the spatial arrangement were the most stable features, while the way the molecules packed together and bonded changed the most. This high degree of variety made it difficult for older methods to tell the forms apart, but the new fingerprinting technique successfully navigated the complexity, identifying subtle differences that other tools missed.

The most challenging test came with aripiprazole, a flexible drug molecule that can twist and turn in many ways. In this case, the spatial arrangement of the molecules was the least consistent feature, varying wildly between forms. The method successfully distinguished between forms that shared the same packing but had different molecular shapes, and those that shared the same shape but were packed differently. This ability to separate "packing polymorphs" from "conformational polymorphs" is a significant advance, as it allows scientists to understand exactly what is changing when a drug shifts from one form to another. The researchers confirmed that their method is robust, meaning it gives the same results even if the atomic positions are slightly shifted by experimental noise, and it is fast enough to screen thousands of structures in seconds.

By providing a clear, multi-dimensional map of how crystal structures relate to one another, this work offers a powerful new tool for the pharmaceutical industry. It does not replace the need to understand a drug's stability or how well it dissolves, but it provides a fast and reliable way to flag new forms that are structurally distinct from known ones. The study demonstrates that by looking at crystals through multiple lenses simultaneously, scientists can move past vague similarities and see the precise structural relationships that define a material. This clarity is essential for ensuring that medicines are safe, effective, and consistent, turning the complex puzzle of crystal forms into a solvable problem.

Technical Summary: Multi-Dimensional Structural Fingerprinting for Quantitative Polymorph Comparison

Problem Statement
Polymorphism in organic molecular crystals presents a significant challenge for pharmaceutical and materials science, as different crystalline forms of the same molecule can exhibit drastically different physical, chemical, and bioavailability properties. Traditional methods for comparing polymorphs, such as powder X-ray diffraction (PXRD) pattern matching, unit cell parameter comparisons, or subjective visual inspection, often fail to capture the full complexity of structural relationships. While computational methods like COMPACK (cluster overlay) and invariant descriptors (e.g., SOAP, PDD, AMD) have advanced the field, they typically provide a single aggregate similarity score or focus on specific aspects (e.g., geometric overlay or local atomic environments) without decomposing why two structures differ. There is a need for a robust, quantitative method that can systematically distinguish between different sources of structural variation—such as conformational changes, symmetry shifts, and packing rearrangements—while remaining invariant to unit cell settings and Cartesian frames.

Methodology
The authors present a multi-dimensional topological fingerprinting approach that quantifies structural relationships through five independent yet complementary categories. The framework is implemented in Python and processes crystallographic information files (CIF) to generate descriptors on the full periodic crystal, ensuring invariance to unit cell choice, space-group setting, and Cartesian frame.

The five structural categories are:

Crystal Packing: Analyzes unit cell-level organization via packing efficiency, density, Niggli-reduced cell geometry, symmetry operations (Jaccard similarity of space-group types), and molecular multiplicity ( $Z$ and $Z'$ ).
Intermolecular Interaction Networks: Characterizes contact length distributions, contact directionality (in molecule-fixed frames), and hydrogen bond geometry (distances and angles) using the Wasserstein distance to compare distributions.
Molecular Conformation: Focuses on internal geometry by comparing matched torsion angles (bond-by-bond via graph isomorphism), bond angles at rotatable vertices, improper angles, and intramolecular contact networks.
Fragment Orientation: Describes the relative spatial arrangement of molecular fragments using inertia tensor analysis (shape anisotropy) and comprehensive $\pi$ - $\pi$ stacking interactions (classifying motifs as face-to-face, edge-to-face, or tilted).
Spatial Geometry: Captures multi-scale ordering from the first coordination shell to intermediate-range order via fragment distance distributions, radial distribution functions (RDF), coordination numbers, and first-shell anisotropy.

Similarity metrics are derived primarily using the Wasserstein distance, converted to bounded similarity scores ( $s = \exp(-W/\sigma)$ ). The overall similarity is a weighted sum of the five category scores (default equal weighting of $w=0.20$ per category), producing a five-component similarity vector that reveals the specific structural dimensions in which polymorphs differ.

Key Contributions

Decomposition of Similarity: Unlike methods that return a single score, this approach resolves structural similarity into five physically distinct components, allowing researchers to identify whether differences arise from packing, conformation, or interaction networks.
Invariance: All descriptors are constructed to be invariant to the unit cell, space-group setting, and Cartesian frame, verified numerically to within $4 \times 10^{-9}$ .
Modular Architecture: The framework employs specialized comparator classes for each category, facilitating independent validation and extension to new descriptor types.
Distribution-Based Metrics: By utilizing the Wasserstein distance, the method handles varying sample sizes and captures the full shape of geometric distributions rather than relying on simple means or variances.

Results
The method was validated on three pharmaceutical polymorph families:

Sulfathiazole (5 DFT-optimized forms): Spatial geometry was the most consistent category (0.78–0.86), while conformation and interaction networks varied most, effectively separating Forms II, III, and IV from Forms I and V. The overall similarity showed a strong correlation with COMPACK cluster matching (Spearman $\rho = -0.89$ with RMSD).
Galunisertib (10 experimental forms): Spatial geometry and conformation were the most consistent categories, while crystal packing varied the most. The method demonstrated that COMPACK's cluster-based overlay finds few matching molecules for this diverse dataset, whereas the fingerprint captures a broader multi-dimensional picture.
Aripiprazole (9 experimental forms): This flexible molecule showed less conserved spatial geometry (0.41–0.74). The decomposition successfully distinguished forms that share packing but not conformation (Forms I and X) from those that share conformation but not lattice (Forms III, IV, and V). The overall similarity correlated well with the number of molecules matched by COMPACK ( $\rho = 0.67$ ).

In benchmark tests against invariant descriptors (AMD, PDD, SOAP), the fingerprint identified the form of CSD depositions as reliably as PDD and SOAP. For distinct polymorphs, the fingerprint followed COMPACK cluster matching more closely than the invariant descriptors, particularly for aripiprazole. The method is computationally efficient, processing a full polymorph family in under 3 seconds on a standard workstation.

Significance
The paper claims that this framework provides a fast, interpretable, and quantitative tool for solid-form screening and crystal structure prediction. By separating structural variation into independent dimensions, it offers insights that geometric overlay methods (like COMPACK) and invariant descriptors cannot provide individually. The authors state that the method is suitable for high-throughput applications, such as flagging new forms that are structurally distinct from known ones, validating crystal structure predictions, and analyzing structural relationships in polymorphic families. The work positions the fingerprint as a complementary tool to energy-based methods and geometric overlays, advancing quantitative methods for solid-state chemistry without requiring expensive energy calculations.

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