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Abstract Motivation:Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds. Results:We put forward a differential geometry‐based geometric learning (DG‐GL) hypothesis that the intrinsic physics of three‐dimensional (3D) molecular structures lies on a family of low‐dimensional manifolds embedded in a high‐dimensional data space. We encode crucial chemical, physical, and biological information into 2D element interactive manifolds, extracted from a high‐dimensional structural data space via a multiscale discrete‐to‐continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures in analytical forms for certain analytically differentiable density estimators. These low‐dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse, and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrate that the proposed DG‐GL strategy outperforms other advanced methods in the predictions of drug discovery‐related protein‐ligand binding affinity, drug toxicity, and molecular solvation free energy. Availability and implementation:http://weilab.math.msu.edu/DG‐GL/ Contact:wei@math.msu.edu
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This content will become publicly available on March 15, 2026
Multiscale Differential Geometry Learning for Protein Flexibility Analysis
ABSTRACT Protein structural fluctuations, measured by Debye‐Waller factors or B‐factors, are known to be closely associated with protein flexibility and function. Theoretical approaches have also been developed to predict B‐factor values, which reflect protein flexibility. Previous models have made significant strides in analyzing B‐factors by fitting experimental data. In this study, we propose a novel approach for B‐factor prediction using differential geometry theory, based on the assumption that the intrinsic properties of proteins reside on a family of low‐dimensional manifolds embedded within the high‐dimensional space of protein structures. By analyzing the mean and Gaussian curvatures of a set of low‐dimensional manifolds defined by kernel functions, we develop effective and robust multiscale differential geometry (mDG) models. Our mDG model demonstrates a 27% increase in accuracy compared to the classical Gaussian network model (GNM) in predicting B‐factors for a dataset of 364 proteins. Additionally, by incorporating both global and local protein features, we construct a highly effective machine‐learning model for the blind prediction of B‐factors. Extensive least‐squares approximations and machine learning‐based blind predictions validate the effectiveness of the mDG modeling approach for B‐factor predictions.
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- Award ID(s):
- 2052983
- PAR ID:
- 10616125
- Publisher / Repository:
- Journal of Computational Chemistry
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 46
- Issue:
- 7
- ISSN:
- 0192-8651
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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