Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity, and geometric complexity associated with the PB equation.
View Article and Find Full Text PDFThe Poisson-Boltzmann (PB) model is a widely used electrostatic model for biomolecular solvation analysis. Formulated as an elliptic interface problem, the PB model can be numerically solved on either Eulerian meshes using finite difference/finite element methods or Lagrangian meshes using boundary element methods. Molecular surface generators, which produce the discretized dielectric interfaces between solutes and solvents, are critical factors in determining the accuracy and efficiency of the PB solvers.
View Article and Find Full Text PDFThis work describes TABI-PB 2.0, an improved version of the treecode-accelerated boundary integral Poisson-Boltzmann solver. The code computes the electrostatic potential on the molecular surface of a solvated biomolecule, and further processing yields the electrostatic solvation energy.
View Article and Find Full Text PDFMonte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule.
View Article and Find Full Text PDFThe Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that have provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses the three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001.
View Article and Find Full Text PDFBiological rhythms, generated by feedback loops containing interacting genes, proteins and/or cells, time physiological processes in many organisms. While many of the components of the systems that generate biological rhythms have been identified, much less is known about the details of their interactions. Using examples from the circadian (daily) clock in three organisms, Neurospora, Drosophila and mouse, we show, with mathematical models of varying complexity, how interactions among (i) promoter sites, (ii) proteins forming complexes, and (iii) cells can have a drastic effect on timekeeping.
View Article and Find Full Text PDFJ Comput Phys
January 2011
The Poisson-Boltzmann (PB) equation is an established multiscale model for electrostatic analysis of biomolecules and other dielectric systems. PB based molecular dynamics (MD) approach has a potential to tackle large biological systems. Obstacles that hinder the current development of PB based MD methods are concerns in accuracy, stability, efficiency and reliability.
View Article and Find Full Text PDFThe Poisson-Boltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)-based PBE software package, the MIBPB solver, for electrostatic analysis.
View Article and Find Full Text PDFThis paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur.
View Article and Find Full Text PDFGeometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces.
View Article and Find Full Text PDFThe discrete wavelet transform may be used as a signal-processing tool for visualization and analysis of nonstationary, time-sampled waveforms. The highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity, and accepting a least-squares inverse (pseudoinverse) in place of a true inverse. A new algorithm for the pseudoinverse of the shift-invariant transform that is easier to implement in array-oriented scripting languages than existing algorithms is presented together with self-contained proofs.
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