PMC:4264129 / 50967-59445 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4264129","sourcedb":"PMC","sourceid":"4264129","source_url":"http://www.ncbi.nlm.nih.gov/pmc/4264129","text":"2.3. Free Energy Calculations\nThe focus of this subsection is the free energy calculation for explicit solvent models. The continuum-solvent calculations characterized above can provide free energies for individual solutes in any conformation, protonation state and tautomeric form. The method is not well suited, however, to the problem under investigation in the present survey pertaining to the possible disruption of intramolecular H-bonds in protic solvents. Since calculation of relative free energies is satisfactory for finding the more stable conformation, a perturbation method can be utilized in simulations where large solvent boxes including a solute and explicit solvent molecules are considered. The perturbation procedure is based on the work of Zwanzig and Jorgensen [93,94] and is widely used as the “free energy perturbation (FEP) method”.\nWhen the FEP method is applied, the atoms of solute and solvent molecules are characterized as sets of point charges with assigned van der Waals parameters. Locations of the solute charges symbolize those for atomic nuclei in the molecule. The combined effect of the accepted net solute charges should reproduce the in-solution molecular electrostatic potential nearly within and out of the van der Waals surface. To achieve this, it is useful to obtain the values of the point charges and determine their locations for the involved conformers/tautomers of the solute by geometry optimizations followed by the fit of charges to the in-solution MEP. In the applications of FEP below, the geometry of the solute with an intramolecular H-bond is converted into another structure without this bond. The atomic charges are also converted gradually and simultaneously from the starting set to final set, characterizing the corresponding conformations. The free energy is a state function, thus even if the intermediate states do not exist physically (when, e.g., the proton annihilation/proton development path is traveled) the sum of the perturbed free energy increments are theoretically correct. The molar free energy increment in the “i”th step, ΔGi is calculated as −RT ln[exp(−(Epi − Eri)/RT)]av, where the average of the exponential expression has to be calculated through a long simulation. Eri and Epi and are the total energies of the system per mole in a given configuration with parameters applied for the reference and perturbed solutes, respectively. The FEP in this case is led through controlled conformations or states. The constancy of the charge and geometry parameters is maintained only for a perturbation step. The actual parameters for the reference and perturbed states can be determined by a linear transformation of their values between the starting and the end structures. For example, conformations with and without an intramolecular H-bond correspond to perturbation parameters λ = 0 and λ = 1, respectively. In order to keep the free energy increments below about 4 kJ/mol, Δλ may be as small as about one hundredth.\nThe models used for water as solvent are generally TIP3P or TIP4P [20]. Some rigid, united atom CHn (n = 1–3) models also are available for small organic solvents such as CCl4, CHCl3, CH2Cl2, CH3CN, CH3OH [95] when the BOSS program (Biochemical and Organic Simulation System) [96] is used for Monte Carlo simulations [97,98,99]. The solvent models were parameterized for producing good density and heat of vaporization for the neat solvent, thus the accepted model implicitly accounts for the solvent-solvent interactions, including mutual polarizations of these molecules. Recently, however, one can create solvent boxes with all-atom solvent models by using the OPLS-AA 12–6–1 force field parameters [85,86].\nFigure 4 The free energy perturbation (FEP) curves for the transformations of conformers with an intramolecular H-bond to structures without H-bonds. Shown are 1,2-ethanediol (1) to (2), salicylic acid (3) to (4), and β-alanine zwitterion (5) to (6) where structure numbering is taken from Figure 2. Figure 4 is an illustration of the course of three FEP curves for conformational changes of the same molecules schematically compared in Figure 2. It is clear that the FEP, provided as the percent transformation, is not necessarily monotonic. For the two neutral molecules the most favorable hydration can be expected at about 20% and 60% transformations between the starting and finishing local energy minimum structures. For the gauche zwitterionic β-alanine, the ionic sites are less open for hydration and the solvation free energy the less favorable (5 is the trans, 6 is the gauche conformation).\nIn MD simulations, the solute geometry can change under the forces acting on each solute atom. Determination of bond stretching, bond bending and torsion parameters for every special molecule with possible intramolecular H-bond(s) is a very time consuming procedure. On the other hand, application of some average reference geometric parameters, stretching, bending force constants, and acceptance of average torsion potentials for these rather special molecules may lead to unreliably distorted structures in a flexible solute model. Thus use of the rigid optimized geometry could be favored from energy point of view and the computer time must be shorter if the energies of the solution configurations are to be averaged for a model with all rigid elements as compared with a slower convergence in case of a flexible solute. This option is not available for MD simulations, where individual molecular mechanics parameterization is desirable for high quality simulations. In some applications of the software, the lengths of the σ-bonds with hydrogen can be kept at fixed values although the problem of the critical torsion flexibility still remains.\nA further problem related to the use of the flexible solute model is that the MEP-fitted-charges characterize only the given optimized geometry. If the solute leaves this structure even temporarily, the charges are not relevant for the new geometry. Common in most MD and MC programs used in the past twenty years, however, is that the atomic point charges do not change through the simulation. In MD simulations with flexible solute geometry, the atomic charges are kept constant even if the structure changes among quite different conformational states.\nThis problem may be overcome by the use of the fluctuating charge (FC) model [100,101]. This approach introduces a polarizable force field, where the atomic point charges are allowed to fluctuate in response to the environment. Accordingly, this approach can account for the conformation dependence of the charges through the calculation of the solute-solvent interaction energies relevant to the actual solute geometry. The computation time increases by only about 10%, thus the method is applicable for simulations of large systems [102,103]. Nonetheless, MD/FEP calculation using the FC model has not been found even for small molecules in the surveyed literature.\nThe present review concentrates on results obtained with the described methods, although more recent simulation programs allow consideration of polarization charges on the solute and induced dipoles on the solvent [104]. The QM/MM (quantum mechanics/molecular mechanics) method [105,106] corresponds to the state-of-the-art level, but no article has been found where the QM/MM procedure was used for resolving the problem addressed in the title of this paper. The Car-Parinello molecular dynamics procedure (CPMD) [107] is another high-level theoretical method that could be applied as a state-of the-art procedure. The method applies pseudopotentials and the plane-wave basis set with periodic boundary conditions. The primary advantage of CPMD in comparison with ab initio molecular dynamics methods is that by introducing the extended variable Lagrangian formalism, CPMD can avoid the time demanding self-consistent matrix diagonalization at every step in the trajectory. Despite the attractive features of the method, the treatment of the electronic structure allows the application of CPMD only for systems that are remarkably smaller than those which can be easily considered in classical simulations. Although the possible disruption of the intramolecular H-bond in solution has been investigated only for small solutes below, the need to consider several hundred solvent molecules must have prevented applying CPMD because no such study has been found in the literature search.","divisions":[{"label":"Title","span":{"begin":0,"end":29}},{"label":"Figure caption","span":{"begin":3711,"end":4013}}],"tracks":[{"project":"2_test","denotations":[{"id":"25353178-14634989-52044444","span":{"begin":6860,"end":6863},"obj":"14634989"},{"id":"25353178-15224394-52044445","span":{"begin":6864,"end":6867},"obj":"15224394"},{"id":"25353178-20136072-52044446","span":{"begin":7208,"end":7211},"obj":"20136072"},{"id":"25353178-18190187-52044447","span":{"begin":7272,"end":7275},"obj":"18190187"},{"id":"25353178-10032153-52044448","span":{"begin":7508,"end":7511},"obj":"10032153"},{"id":"T85984","span":{"begin":6860,"end":6863},"obj":"14634989"},{"id":"T49409","span":{"begin":6864,"end":6867},"obj":"15224394"},{"id":"T92061","span":{"begin":7208,"end":7211},"obj":"20136072"},{"id":"T30576","span":{"begin":7272,"end":7275},"obj":"18190187"},{"id":"T54844","span":{"begin":7508,"end":7511},"obj":"10032153"}],"attributes":[{"subj":"25353178-14634989-52044444","pred":"source","obj":"2_test"},{"subj":"25353178-15224394-52044445","pred":"source","obj":"2_test"},{"subj":"25353178-20136072-52044446","pred":"source","obj":"2_test"},{"subj":"25353178-18190187-52044447","pred":"source","obj":"2_test"},{"subj":"25353178-10032153-52044448","pred":"source","obj":"2_test"},{"subj":"T85984","pred":"source","obj":"2_test"},{"subj":"T49409","pred":"source","obj":"2_test"},{"subj":"T92061","pred":"source","obj":"2_test"},{"subj":"T30576","pred":"source","obj":"2_test"},{"subj":"T54844","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#93eccb","default":true}]}]}}