Persistent Homology for Virtual Screening

Keller, Bryn; Lesnick, Michael; Willke, Theodore L.

doi:10.26434/chemrxiv.6969260.v3

Cited by 4 publications

(4 citation statements)

References 46 publications

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“…Persistent homology already has several interesting chemistry applications. In the analysis of point cloud data (e.g., Cartesian coordinates of atoms) it has helped characterize different conformations of molecules, 19,20 solution phase organization [21][22][23] , and to identify chemical reactivity 24 using filtration values based upon Euclidean distance. In the case of manifolds, sublevelset persistent homology has been applied to the probability surfaces of activated processes 25 and in the characterization of energy landscapes.…”

Section: Sublevelset Persistent Homologymentioning

confidence: 99%

Additive energy functions have predictable landscape topologies

Story

Sadhu

Adams

et al. 2023

The Journal of Chemical Physics

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Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features—such as the number of sublevelset persistence bars—could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

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Section: Sublevelset Persistent Homologymentioning

confidence: 99%

Additive energy functions have predictable landscape topologies

Story

Sadhu

Adams

et al. 2023

The Journal of Chemical Physics

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“…In [16, 15, 14], the authors obtained successful results by integrating single persistent homology outputs with various ML models. Furthermore, in [50], the authors used multipersistence homology with fibered barcode approach in the 3 D setting and obtained promising results. In the past few years, TDA tools were also successfully combined with various deep learning models for SBVS and property prediction [71, 72].…”

Section: Related Workmentioning

confidence: 99%

“…In particular„ we compare our methods against the well-known 3 D -methods Ultrafast Shape Recognition (USR) [8], shape-based, ligand-centric method (ROCS) [38], PatchSurfer (PS) [42], Zernike (GZD) [92] and PH_VS [50] in Cleves-Jain dataset. In Table 1, we report the performances of all these 3 D methods with 50 conformations [84] except PH_VS with 1 conformation [50]. In Table 2, we compare our models against other state-of-the-art VS methods on DUD-E Diverse dataset.…”

Section: Figurementioning

confidence: 99%

“…We compare our methods against the 23 state-of-the-art baselines including USR [8], ROCS [38], PS [42], GZD [92], PH_VS [50], USR + GZD [84], USR + PS [84], USR + ROCS [84], GZD + PS [84], GZD + ROCS [84], PS + ROCS [84], Findsite [101], Fragsite [102], Gnina [87], GOLD-EATL [96], Glide-EATL [96], CompM [96], CompScore [75], CNN [77], DenseFS [44], SIEVE-Score [98], DeepScore [94], and RF-Score-VSv3 [98].…”

Section: Figurementioning

confidence: 99%

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ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery

Demir

Coskunuzer²,

Segovia-Domínguez

et al. 2022

Preprint

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In computer-aided drug discovery (CADD), virtual screening (VS) is used for identifying the drug candidates that are most likely to bind to a molecular target in a large library of compounds. Most VS methods to date have focused on using canonical compound representations (e.g., SMILES strings, Morgan fingerprints) or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. Our primary contribution is framing the VS process as a new topology-based graph ranking problem by partitioning a compound into chemical substructures informed by the periodic properties of its atoms and extracting their persistent homology features at multiple resolution levels. We show that the margin loss fine-tuning of pretrained Triplet networks attains highly competitive results in differentiating between compounds in the embedding space and ranking their likelihood of becoming effective drug candidates. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin (e.g., 93% gain for Cleves-Jain and 54% gain for DUD-E Diverse dataset).

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Bigraded Betti numbers and generalized persistence diagrams

Kim,

Moore

2024

J Appl. and Comput. Topology

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Commutative diagrams of vector spaces and linear maps over $$\mathbb {Z}^2$$ Z 2 are objects of interest in topological data analysis (TDA) where this type of diagrams are called 2-parameter persistence modules. Given that quiver representation theory tells us that such diagrams are of wild type, studying informative invariants of a 2-parameter persistence module M is of central importance in TDA. One of such invariants is the generalized rank invariant, recently introduced by Kim and Mémoli. Via the Möbius inversion of the generalized rank invariant of M, we obtain a collection of connected subsets $$I\subset \mathbb {Z}^2$$ I ⊂ Z 2 with signed multiplicities. This collection generalizes the well known notion of persistence barcode of a persistence module over $$\mathbb {R}$$ R from TDA. In this paper we show that the bigraded Betti numbers of M, a classical algebraic invariant of M, are obtained by counting the corner points of these subsets Is. Along the way, we verify that an invariant of 2-parameter persistence modules called the interval decomposable approximation (introduced by Asashiba et al.) also encodes the bigraded Betti numbers in a similar fashion. We also show that the aforementioned results are optimal in the sense that they cannot be extended to d-parameter persistence modules for $$d \ge 3$$ d ≥ 3 .

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Persistent Homology for Virtual Screening

Cited by 4 publications

References 46 publications

Additive energy functions have predictable landscape topologies

Additive energy functions have predictable landscape topologies

ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery

Bigraded Betti numbers and generalized persistence diagrams

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