FDPB

Use of the finite-difference PB (FDPB) method to calculate the self- and interaction-energies of the ionizable groups in the protein and solvent. 

The procedure is computationally efficient. For example, for the catalytic subunit of the mammalian cAMP-dependent protein kinase and its inhibitor, with 370 residues and 131 titratable groups, an entire calculation requires 10 hours on an SGI 02 workstation with a 175 MHz MIPS RIOOOO processor. The bulk of the computer time is spent on the FDPB calculations. The speed of the procedure is important, because it makes it possible to collect results on many systems and with many different sets of parameters in a reasonable amount of time. Thus, improvements to the method can be made based on a broad sampling of systems. 

FDPB methods have been extensively applied to the study of static protein structures (for reviews see refs [1,61]), but their use in MD simulations is more recent. To our knowledge, Davis and McCammon [62] were the first to obtain solvation forces by analytical... 

While in most applications the GB model works remarkably well, some problems were found when computing the binding of aliphatic cyclic ureas to HIV-1 protease [56]. The GB model failed to reproduce both experimental data and the results of FDPB calculations. This is not surprising. It is common for a parameterized model to fail sometimes. The problem is that it is impossible to predict for which... 

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...

Solvation energies computed ° with the FDPB method agree well with experiment as seen in Table 1 and Figure 2. Additional results are reported elsewhere. 2 where the PB methods break down is not clear. There is the question of whether disagreements are due to the method or to poor parameters. Research to answer this question is under way in several groups. 

Figure 2 Agreement of computed (FDPB) and experimental free energies of hydration = 0.9997 for eight compounds.

Another local dielectric constant model described by Sharp et al., should also be noted to our knowledge, however it has not yet been used in the FDPB pfCg calculations. 

The first computations of ionization constants of residues in proteins for structures derived from molecular dynamics trajectories were described by Wendoloski and Matthew for tuna cytochrome c. In that study, conformers were generated using molecular dynamics simulations with a range of solvents, simulating macroscopic dielectric formalisms, and one solvent model that explicitly included solvent water molecules. The authors calculated individual pR values, overall titration curves, and electrostatic potential surfaces for average structures and structures along each simulation trajectory. However, the computational scheme for predicting electrostatic interactions in proteins used by Wendoloski and Matthew was not based on a FDPB model but on the modified Tanford-Kirkwood approach, which is not discussed in this chapter. 

There are several examples of application of the FDPB model in theoretical analysis of protein stability. " Fiere we discuss experimental and theoreticaP results for the pFi dependence of barnase stability. Barnase is a ribonuclease from Bacillus amyloliquefaciens, a small (110 residues), monomeric, single-domain enzyme that lacks disulfide bonds and undergoes reversible unfolding by a two-state process. ... 

These FDPB-based methods might be further improved by using a position-dependent dielectric function that treats distinct regions of the protein differently (e.g., surface, interior, polar, nonpolar, charged, flexible, rigid, etc.), as has been mentioned by Warshel and others. These methods, as they mature, can be applied to questions of protein stability versus pH, the pH-dependent binding of inhibitors, and so on. The availability of these fast and automated methods makes the finite difference Poisson-Boltzmann method a useful predictive tool for the computational chemist. 

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