Duc Duy Nguyen

Duc D. Nguyen, Bao Wang, Guo-wei Wei

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, $ΔG_{\text{el}}$, and binding free energy, $ΔΔG_{\text{el}}$, is of tremendous significance to computational biophysics and biochemistry. Recently, it has been warned in the literature (Journal of Chemical Theory and Computation 2013, 9, 3677-3685) that the widely used grid spacing of $0.5$ Å$ $ produces unacceptable errors in $ΔΔG_{\text{el}}$ estimation with the solvent exclude surface (SES). In this work, we investigate the grid dependence of our PB solver (MIBPB) with SESs for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of $ΔG_{\text{el}}$ obtained at the grid spacing of $1.0$ Å$ $ compared to $ΔG_{\text{el}}$ at $0.2$ Å$ $ averaged over 153 molecules is less than 0.2\%. Our results indicate that the use of grid spacing $0.6$ Å$ $ ensures accuracy and reliability in $ΔΔG_{\text{el}}$ calculation. In fact, the grid spacing of $1.1$ Å$ $ appears to deliver adequate accuracy for high throughput screening.

Ekaterina Merkurjev, Duc DUy Nguyen, Guo-Wei Wei

Machine learning methods have greatly changed science, engineering, finance, business, and other fields. Despite the tremendous accomplishments of machine learning and deep learning methods, many challenges still remain. In particular, the performance of machine learning methods is often severely affected in case of diverse data, usually associated with smaller data sets or data related to areas of study where the size of the data sets is constrained by the complexity and/or high cost of experiments. Moreover, data with limited labeled samples is a challenge to most learning approaches. In this paper, the aforementioned challenges are addressed by integrating graph-based frameworks, multiscale structure, modified and adapted optimization procedures and semi-supervised techniques. This results in two innovative multiscale Laplacian learning (MLL) approaches for machine learning tasks, such as data classification, and for tackling diverse data, data with limited samples and smaller data sets. The first approach, called multikernel manifold learning (MML), integrates manifold learning with multikernel information and solves a regularization problem consisting of a loss function and a warped kernel regularizer using multiscale graph Laplacians. The second approach, called the multiscale MBO (MMBO) method, introduces multiscale Laplacians to a modification of the famous classical Merriman-Bence-Osher (MBO) scheme, and makes use of fast solvers for finding the approximations to the extremal eigenvectors of the graph Laplacian. We demonstrate the performance of our methods experimentally on a variety of data sets, such as biological, text and image data, and compare them favorably to existing approaches.

Bao Wang, Zhixiong Zhao, Duc D. Nguyen et al.

We present a feature functional theory - binding predictor (FFT-BP) for the protein-ligand binding affinity prediction. The underpinning assumptions of FFT-BP are as follows: i) representability: there exists a microscopic feature vector that can uniquely characterize and distinguish one protein-ligand complex from another; ii) feature-function relationship: the macroscopic features, including binding free energy, of a complex is a functional of microscopic feature vectors; and iii) similarity: molecules with similar microscopic features have similar macroscopic features, such as binding affinity. Physical models, such as implicit solvent models and quantum theory, are utilized to extract microscopic features, while machine learning algorithms are employed to rank the similarity among protein-ligand complexes. A large variety of numerical validations and tests confirms the accuracy and robustness of the proposed FFT-BP model. The root mean square errors (RMSEs) of FFT-BP blind predictions of a benchmark set of 100 complexes, the PDBBind v2007 core set of 195 complexes and the PDBBind v2015 core set of 195 complexes are 1.99, 2.02 and 1.92 kcal/mol, respectively. Their corresponding Pearson correlation coefficients are 0.75, 0.80, and 0.78, respectively.