Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications

Abstract

Continuum solvent treatments based on the Poisson–Boltzmann equation have been widely accepted for energetic analysis of biomolecular systems. In these approaches, the molecular solute is treated as a low dielectric region and the solvent is treated as a high dielectric continuum. The existence of a sharp dielectric jump at the solute–solvent interface poses a challenge to model the solvation energetics accurately with such a simple mathematical model. In this study, we explored and evaluated a strategy based on the “induced surface charge” to eliminate the dielectric jump within the finite-difference discretization scheme. In addition to the use of the induced surface charges in solving the equation, the second-order accurate immersed interface method is also incorporated to discretize the equation. The resultant linear system is solved with the GMRES algorithm to explicitly impose the flux conservation condition across the solvent–solute interface. The new strategy was evaluated on both analytical and realistic biomolecular systems. The numerical tests demonstrate the feasibility of utilizing induced surface charge in the finite-difference solution of the Poisson–Boltzmann equation. The analysis data further show that the strategy is consistent with theory and the classical finite-difference method on the tested systems. Limitations of the current implementations and further improvements are also analyzed and discussed to fully bring out its potential of achieving higher numerical accuracy.

Compositional segregation, structural transformation and property-temperature relationship of high-Curie temperature Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystals

“…T phase transition anomalies (T M-T ) based on Refs. [22,23], and [35]. Only one sharp peak at 218°C can be observed in sample 12#, which confirms that this crystal sample is T phase at room temperature.…”

“…M A ? T as reported in previous studies [22,23,44]. High value of S m for crystal sample 9# was achieved (*0.95 % at room temperature), and then dropped to *0.8 % at 90°C at which the crystal is in M A phase and the phenomenon of bifurcated S-E curve disappears.…”

“…cubic (C) phase transition. However, recent research has shown the existence of lowsymmetry orthorhombic (O) or monoclinic (M) phases bridging between the high-symmetry R and T phases, which are generally regarded as the origin of high piezoelectricity of Pb-based perovskites near the MPB composition [21][22][23]. For example, Wang et al [22] summarized the phase transformation sequence and phase stabilities of PIN-PMN-PT single crystals with various thermal and electric histories and proposed a stable monoclinic M A phase after poling along the [001] direction, while Li et al [23] found that crystals exhibiting ultrahigh piezoelectric properties undergo a phase transition sequence of M A ?…”

Exploring the regeneration process of ruthenium(II) dyes by cobalt mediator in dye-sensitized solar cells from first-principle calculations

“…To further improve the performance of the device, great efforts have been devoted to optimizing ruthenium dyes to match with cobalt mediators [19e23]. By using octadecylphosphonic acid as a co-adsorbent, Liu et al reported a PCE of up to 8.5% for DSSC employing Z907 and [Co(bpy) 3 ] 2þ/3þ [24]. Moreover, a PCE of 8.6% was achieved by tuning the highest occupied molecular orbital (HOMO) of dye and introducing the alkoxy substituents to insulate the TiO 2 surface [25].…”

Acceleration of Linear Finite-Difference Poisson–Boltzmann Methods on Graphics Processing Units

“…1 Due to the high dimensionalities of typical biomolecular systems, it is extremely important to increase the accuracy and efficiency of PBE models. 2 …”