Finite difference Poisson-Boltzmann

Fig. 11.28 Focusing can improve the accuracy of finite difference Poisson-Boltzmann calculations.

Applications of Finite Difference Poisson-Boltzmann Calculations... 

Rocchia W, Sridharan S, Nicholls A, Alexov E, Chiabrera A, Honig B (2002) Rapid grid-based construction of the molecular surface for both molecules and geometric objects applications to the finite difference Poisson-Boltzmann method, J Comp Chem, 23 128-137... 

K. Sharp,/. Comput. Chem., 12, 454 (1991). Incorporating Solvent and Ion Screening into Molecular Dynamics Using the Finite-Difference Poisson-Boltzmann Method. 

Numerical strategies for computing both the electronic and nuclear components of the ET rate are now rather advanced (see the chapter by Newton). For example, in both proteins and small molecules, finite-difference Poisson-Boltzmann methods are widely used for computing the outer-sphere component of the solvent reorganization energy Aq [9, 10, 11, 12] ... 

Vizcarra CL, Zhang NG, Marshall SA, Wingreen NS, Zeng C, Mayo SL (2008) An improved pairwise decomposable finite-difference Poisson-Boltzmann method for computational protein design. J Comput Chem 29 1153-1162... 

CHARMM + finite difference Poisson Boltzmann electrostatics... 

To solve the PB equation for arbitrary geometries requires some type of discretization, to convert the partial differential equation into a set of difference equations. Finite difference methods divide space into a cubic lattice, with the potential, charge density, and ion accessibility defined at the lattice points (or grid points ) and the permittivity defined on the branches (or grid lines ). Equation [1] becomes a system of simultaneous equations referred to as the finite difference Poisson-Boltzmann (FDPB) equation ... 

Table 1 Free Energies of Hydration (kcal/mol) for Organic Molecules Calculated with the Finite Difference Poisson-Boltzmann (FDPB) Method and Experimental Results...

Sharp KA (1998) Calculation of electron transfer reorganization energies using the finite difference Poisson-Boltzmann model. Biophys J 73 1241-1250... 

Prabhu, N.V., Zhu, P., Sharp, K.A. Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method. J. Comput. Chem. 2004,25(16), 2049-64, December. 

Relative to finite-difference Poisson-Boltzmann approaches, such methods have the advantage that only the two-dimensional cavity surface must be discretized. 

An issue with all of these discretization schemes—except possibly the genuine isodensity surface that is not considered in this work—is the fact that the solvation energy is a discontinuous function of the atomic coordinates, because discretization points appear and disappear as the overlap between atomic spheres changes. (In principle, the energy also loses rotational invariance upon discretization, but we fund that this problem is not serious [42]). The discontinuity problem, which is shared by finite-difference Poisson-Boltzmann solvers, has recently been resolved in the context of PCMs, with the development of intrinsically smooth discretization algorithms [42, 70, 76, 87]. These are discussed in Section 11.4.1. 

An issue with the PCM formalism introduced in Section 11.2.2.1 is that the electrostatic energy is in general a discontinuous function as the solute atoms are displaced, because the number and size of the surface tesserae may change as a function of solute geometry. A similar problem is suffered by finite-difference Poisson-Boltzmann solvers, and the "solution" in those cases (in order to achieve stable forces for MD simulations, for example) is tight thresholding and/or some kind of interpolation between grid points [80-83]. 

Wang, J., Cai, Q., Xiang, Y., and Luo, R. (2012). Reducing grid dependence in finite-difference Poisson-Boltzmann calculations,. Chem. Theory Comput. 8, pp. 2741-2751. 

Wang, J. U. N., and R. A. Y. Luo. 2010. Assessment of linear finite-difference Poisson-Boltzmann solvers. Journal of Computational Chemistry 31, no. 8 1689-1698. 

Laberge, M., Vanderkooi, J.M., Sharp, K.A. Effect of a protein electric field on the CO stretch fi equency. Finite difference Poisson-Boltzmann calculations on carbonmonoxycy-tochromes c. J. Phys. Chem. 100, 10793-10801 (1996)... 

Use of the finite difference Poisson-Boltzmann method to calculate the self-and interaction energies of the ionizable groups in water and in the protein. 

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