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Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of biomolecular datasets obstruct the efficient application of ML algorithms in the field. In addition to data and algorithm, an efficient ML machinery for biomolecular predictions must include structural representation as an indispensable component. Mathematical representations that simplify the biomolecular structural complexity and reduce ML dimensionality have emerged as a prime winner in D3R Grand Challenges. This review is devoted to the recent advances in developing low-dimensional and scalable mathematical representations of biomolecules in our laboratory. We discuss three classes of mathematical approaches, including algebraic topology, differential geometry, and graph theory. We elucidate how the physical and biological challenges have guided the evolution and development of these mathematical apparatuses for massive and diverse biomolecular data. We focus the performance analysis on protein–ligand binding predictions in this review although these methods have had tremendous success in many other applications, such as protein classification, virtual screening, and the predictions of solubility, solvation free energies, toxicity, partition coefficients, protein folding stability changes upon mutation, etc.
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DG‐GL: Differential geometry‐based geometric learning of molecular datasets
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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- PAR ID:
- 10453264
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Biomedical Engineering
- Volume:
- 35
- Issue:
- 3
- ISSN:
- 2040-7939
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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