Homologous recombination (HR) is a major pathway for the repair of double strand breaks, which is of primary importance for genomic stability and survival of all organisms. The crucial step in HR is the formation of the nucleoprotein filament composed by a single stranded DNA chain surrounded by the recombinases protein. The filament leads the search for an undamaged homologue, a sister-chromat...

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fas...

We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras when the Rmatrices act properly. When this construction is applied to quantum groups, we get examples of quantum groupoids, which are semi-classical limits o...

End-point free energy calculations using MM-GBSA and MM-PBSA provide a detailed understanding of molecular recognition in protein-ligand interactions. The binding free energy can be used to rank-order protein-ligand structures in virtual screening for compound or target identification. Here, we carry out free energy calculations for a diverse set of 11 proteins bound to 14 small molecules using...

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the...

Computer simulations have been demonstrated to be important for unraveling atomic mechanisms in biological systems. In this study, we show how combining unbiased molecular dynamic simulations with appropriate analysis tools can successfully describe metal-based drug interactions with DNA. To elucidate the noncovalent affinity of cisplatin's family to DNA, we performed extensive all-atom molecul...

Many important protein-protein interactions are mediated by peptide recognition modular domains, such as the Src homology 3 (SH3), SH2, PDZ, and WW domains. Characterizing the interaction interface of domain-peptide complexes and predicting binding specificity for modular domains are critical for deciphering protein-protein interaction networks. Here, we propose the use of an energetic decompos...

The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson-Boltzmann equation in the limit of zero-size ...

<p style='text-indent:20px;'>In this note, we propose a slightly different proof of Gallavotti's theorem ["Statistical Mechanics: A Short Treatise", Springer, 1999, pp. 48-55] on the derivation linear Boltzmann equation for Lorentz gas with Poisson distribution obstacles in Boltzmann-Grad limit.</p>

We present a derivation of Boltzmann principle SB = kB lnW based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth century with the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a modern, self-contained and accessible form....