We present a new Matched Interface and Boundary (MIB) regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the Poisson–Boltzmann (PB) equation. In a regularization method, by decomposing the potential function into two or three components, the singular component can be analytically represented by the Green’s function, while other components possess a higher regularity. Our new regularization combines the efficiency of two-component schemes with the accuracy of the three-component schemes. Based on this regularization, a new MIB finite difference algorithm is developed for solving both linear and nonlinear PB equations, where the nonlinearity is handled by using the inexact-Newton’s method. Compared with the existing MIB PB solver based on a three-component regularization, the present algorithm is simpler to implement by circumventing the work to solve a boundary value Poisson equation inside the molecular interface and to compute related interface jump conditions numerically. Moreover, the new MIB algorithm becomes computationally less expensive, while maintains the same second order accuracy. This is numerically verified by calculating the electrostatic potential and solvation energy on the Kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes.

Randomness often plays an important role in the spatial and temporal dynamics of biological systems. General stochastic simulation methods may lead to excessive computational cost for a system in which a large number of molecules involved. Therefore, multi-scale hybrid simulation methods become important for stochastic simulations. Here we build a spatially hybrid method which couples two approaches: discrete stochastic simulation and continuous stochastic differential equations. In our method, the locations of the interfaces between the two approaches are changing according to the distribution of molecules in a one-dimensional domain. To balance the accuracy and efficiency, the time step of the numerical method for the continuous stochastic differential equations is adapted to the dynamics of the molecules near the adaptive interfaces. The simulation results for a linear system and two nonlinear biological systems in different one-dimensional domains demonstrate the effectiveness and advantage of our new hybrid method with the adaptive time step control.

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable (“dry” and “wet”) hydration states. The resulting dry-wet transition rates are then used in a spatially-dependent multi-state continuous-time Markov chain Brownian dynamics simulations, and the related Fokker–Planck equation calculations, of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semi-quantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of non-equilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding versus unbinding. Our study thus provides a significant step forward towards efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

HIV-1 is the most common and pathogenic strain of human immunodeficiency virus consisting of many subtypes. To study the difference among HIV-1 subtypes in infection, diagnosis and drug design, it is important to identify HIV-1 subtypes from clinical HIV-1 samples. In this work, we propose an effective numeric representation called Subsequence Natural Vector (SNV) to encode HIV-1 sequences. Using the representation, we introduce an improved linear discriminant analysis method to classify HIV-1 viruses correctly. SNV is based on distribution of nucleotides in HIV-1 viral sequences. It not only computes the number of nucleotides, but also describes the position and variance of nucleotides in viruses. To validate our alignment-free method, 6902 complete genomes and 11,668 pol gene sequences of HIV-1 subtypes were collected from the up-to-date Los Alamos HIV database. SNV outperforms the three popular methods, Kameris, Comet and REGA, with almost 100% Sensitivity and Specificity, also with much less time. Our subtyping algorithm especially works better for circulating recombinant forms (CRFs) consisting of a few sequences. Our approach is also powerful to separate unique recombinant forms (URFs) from other subtypes with 100% Sensitivity and Specificity. Moreover, phylogenetic trees based on SNV representation are constructed using full-length HIV-1 genomes and pol genes respectively, where viruses from the same subtype are clustered together correctly.

Classification of DNA sequences is an important issue in the bioinformatics study, yet most existing methods for phylogenetic analysis including Multiple Sequence Alignment (MSA) are time-consuming and computationally expensive. The alignment-free methods are popular nowadays, whereas the manual intervention in those methods usually decreases the accuracy. Also, the interactions among nucleotides are neglected in most methods. Here we propose a new Accumulated Natural Vector (ANV) method which represents each DNA sequence by a point in R18. By calculating the Accumulated Indicator Functions of nucleotides, we can further find an Accumulated Natural Vector for each sequence. This new Accumulated Natural Vector not only can capture the distribution of each nucleotide, but also provide the covariance among nucleotides. Thus global comparison of DNA sequences or genomes can be done easily in R18. The tests of ANV of datasets of different sizes and types have proved the accuracy and time-efficiency of the new proposed ANV method.