Derivatives of molecular surface area and volume: Simple and exact analytical formulas

Abstract

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.

Accurate single-sequence prediction of solvent accessible surface area using local and global features

“…In this approach a computational ball is rolled on the surface of the protein coordinates and probes for which and how much of the residues are accessible, i.e., in contact with the ball. Recently Klenin et al introduced a fast analytical method to calculate the ASA using power diagrams [15]. Other efforts in characterizing the surface of proteins were also carried out [16, 17, 18, 19, 20, 21, 22].…”

Recent Advances and Future Trend on the Emerging Role of GPUs as Platforms for Virtual Screening-Based Drug Discovery

“…In order to check the accuracy of our method, we check MURCIA calculations with previous POWERSASA results (Klenin 2011). Figure 15 shows an overall good concordance between both methods.…”

“…There have been several efforts to develop a fast method for the SASA calculation. To the best of our knowledge, the fastest method nowadays is POWERSASA (Klenin et al, 2011). Its running time depends linearly on the number of atoms of the molecule.…”

Computational characterization and prediction of metal–organic framework properties

“…[73] Other sampling methods exist, however, for the determination of both accessible surface area and accessible pore volume, such as the use of ray casting [74] and analytical calculations. [75,76] Another tool at our disposal for geometric characterization of pore space is the pore size distribution (PSD), as illustrated on Figure 7 in the case of metal-organic framework HKUST-1 (also known as Cu3(btc) 2 ). Experimentally, pore size distributions can be obtained by numerical analysis of experimental low-temperature nitrogen or argon adsorption isotherms, [78,79] given the choice of a reference pore geometry (slit-like, cylindrical, spherical) and of an approximate chemical composition (though no kernels are available specifically for MOF materials).…”