Implicit solvent model

Suppose that we were to average out the effects of all of the solvent molecules, effectively integrating over the coordinates describing the solvent molecules. This would dramatically simplify the description of the solvent molecules, and thereby simplify the computation of the energy of the solute-solvent system. This is the general principle behind the implicit solvent models. The solvent is described by a single term, its dielectric constant, and we just need to treat the interaction of the solute with this field. 

The Poisson eqnation (Eq. (1.63)) describes the electrostatics of a dielectric medium with an embedded charged species  

Note that the solute charge distribution (from its wavefunction) enters into the definition of the potential V, and so this equation must be solved iteratively, thus giving rise to the term self-consistent reaction field (SCRF). 

The shape of the cavity affects the difficulty in solving the Poisson equation. If the cavity is a sphere, then an analytical solution is obtained. If the solute is an ion with charge q, we get the Bom equation 

The Kirwood-Onsager model can be readily extended to using higher order multipole moments. 

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As a first step, it is important to estabUsh implicit solvent models on fundamental principles. For the sake of concreteness, let us consider a solute u immersed in a bulk solution V. The configuration of the solute is represented by the vector X = xj, Xo,.... All other degrees of freedom of the bulk solution surrounding the solute, which may include solvent... 

In the following sections, we describe an implicit solvent model based on this free energy decomposition that is widely used in biophysics. It consists in representing the nonpolar free energy contributions on the basis of the solvent-accessible surface area... 

SASA), a concept introduced by Lee and Richards [9], and the electrostatic free energy contribution on the basis of the Poisson-Boltzmann (PB) equation of macroscopic electrostatics, an idea that goes back to Born [10], Debye and Htickel [11], Kirkwood [12], and Onsager [13]. The combination of these two approximations forms the SASA/PB implicit solvent model. In the next section we analyze the microscopic significance of the nonpolar and electrostatic free energy contributions and describe the SASA/PB implicit solvent model. 

In Section III we described an approximation to the nonpolar free energy contribution based on the concept of the solvent-accessible surface area (SASA) [see Eq. (15)]. In the SASA/PB implicit solvent model, the nonpolar free energy contribution is complemented by a macroscopic continuum electrostatic calculation based on the PB equation, thus yielding an approximation to the total free energy, AVP = A different implicit... 

B Roux, T Simonson, eds. Implicit Solvent Models for Biomolecular Simulations. Special Issue of Biophys Chem Amsterdam Elsevier, 1999. 

Another advantage of PB based pKa calculations is that effects of electrolytes are readily accounted for in the PB equation. The Coulombic contribution in conjunction with salt dependence to the abnormally depressed pAVs of histidine in staphylococcal nuclease has been experimentally tested [56], Recently, the methodology used in the PB calculations (Eqs. 10-11 and 10-12) has been combined with the generalized Born (GB) implicit solvent model [94] to offer pKa predictions at a reduced computational cost [52],... 

The discrete protonation states methods employing implicit solvent models in both MD and MC steps have significantly lower computational cost. Dlugosz and... 

The titration coordinates evolve along with the dynamics of the conformational degrees of freedom, r, in simulations with GB implicit solvent models [37, 57], An extended Hamiltonian formalism, in analogy to the A dynamics technique developed for free energy calculations [50], is used to propagate the titration coordinates. The deprotonated and protonated states are those, for which the A value is approximately 1 or 0 (end-point states), respectively. Thus, in contrast to the acidostat method, where A represents the extent of deprotonation, is estimated from the relative occupancy of the states with A 1 (see later discussions). The extended Hamiltonian in the CPHMD method is a sum of the following terms [42],... 

Im W, Chen J, Brooks CL III (2006) Peptide and protein folding and conformational equilibria Theoretical treatment of electrostatics and hydrogen bonding with implicit solvent models. Adv Protein Chem 72 173-198. 

Simonson T, Carlsson J, Case DA (2004) Proton binding to proteins pKa calculations with explicit and implicit solvent models. J Am Chem Soc 126 4167-4180. 

Pratt, L. R., and Rempe, S. B. (1999). Quasi-chemical theory and implicit solvent models for simulations. In Simulation and Theory of Electrostatic Interactions in Solution. Computational Chemistry, Biophysics, and Aqueous Solutions (L. R. Pratt and G. Hummer, eds.), vol. 492 of AIP Conference Proceedings, pp. 172-201. American Institute of Physics, Melville, NY... 

Bursulaya, B. D., and Brooks, C. L. (2000). Comparative study of the folding free energy landscape of a three-stranded /i-sheet protein with explicit and implicit solvent models./. Phys. Chem. B 104, 12378-12383. 

A key element of many simplified free energy methods is the use of an implicit description of the solvent. Implicit solvent models are based on the concept of a PMF, presented briefly in this section see [11] for a detailed review see Chap. 4 for applications of the PMF concept that are not related to implicit solvation. 

It is interesting to consider another approximate derivation, which uses the implicit solvent models discussed earlier (Sect. 12.4). Indeed, we can decompose the binding reaction into the steps shown in Fig. 12.5 [94] first, the ligand charges are switched off in pure solvent, leaving a nonpolar solute second, the attractive... 

Roux, B. Simonson, T., Implicit solvent models, Biophys. Chem. 1999, 78, 1-20... 

The weakest point of our approach is the treatment of the bulk solvent. The energies derived from an implicit solvent model like IPCM are mainly based on energy calculations on gas-phase structures and effects of explicit solvent molecules are not included. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

Desolvation free energies are computed using either explicit solvent or an implicit solvent model. While explicit solvent simulations are usually considered more accurate or at least more representative of the true molecular environment, simulations using implicit solvent are often chosen... 

Solvent effects can be incorporated into two kinds of solvation models, either those that consider each solvent molecule as an individual molecular species (explicit models), or those that deal with the averaged effect of the solvent molecules through use of a coarse-grained description of solvent (e.g., dielectric models, implicit solvent models, etc.). 

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