Computational biochemistry ferenc Bogár György Ferency
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- 2.4. Charges
- 2.5. Parametrization
- 2.6. Thermochemistry in Molecular Mechanics
- 3. Non-Traditional (Polarizable) Molecular Mechanics Methods
| Ei is the the electric field.
A non-periodic simulation of aqueaus (implicit) solvation effect can be handled by means of the modification of the Coulomb interaction to Eq. 2.22:
The first part is the responsible for the polar part of the solvation free energy, the second part is the non-polar contribution which depends on the atomic suface areas of the solvent accessible surface. σi is the atomic solvation free energy increment. The force field is implemented in AMBER molecular mechanics/molecular dynamics package and in the package for preparation the input files (AMBERTOOLS) [21]. 2.4. Charges Charges int he traditional force fields were developed as point charges. In AMBER force field [11-14,21] the effective charges were obtained by fitting the gas phase electrostatic potential of small peptides calculated by HF/6-31G* and used RESP (Restrained Electrostatic Potential) or RESP-like charges were developed [22]. The charges means that how many electrons are shared between atoms. The calculation is not simple. The calculation is based on the following equation.
A least square minimization of the potential at a point and the calculated potential with weighting factors for the points give the point charges. The Nth charge can be calculated
Another algorithm is also applied (Charges from Electrostatic Potentials using a Grid based method, CHELPG [23]). The potential map can be calculated by ab initio method. Point charges with the same quality can be generated by semiempirical quantum chemical method AM1 with afitting function (AM1-BCC charges [24]). 2.5. Parametrization The parametrization of the traditional force fields based on two approaches: (i) evaluation of experimental data and (ii) evaluation of theoretical calculations [19]. The parameters must be consistent in a force field. The experimental and theoretical data is fitted by the functioons applied int he force field. 2.6. Thermochemistry in Molecular Mechanics It is very important to obtain the heat of formation of the molecules. The simplest calculation is related to alkanes. The heat of formation for an alkane can be given by Eq. 2.25.
The ΔHsteric is calculated by molecular mechanics. ΔHconf
where Ni is the mole fraction of the conformers, ΔHi is the enthalpy difference between conformers. ΔH10, ΔH20, ΔH30 and ΔH40 are the corrections for primary, secondary, tertiary and quaternary carbon atoms. ΔHbond is the sum of the bond enthalpies for C-C and C-H bonds. The heat of formation of alkanes is important, because the experimental values are very precise in calorimetric measurements. The molecules with sighly strained structure are good examples for the parametrization. The angle deformation and the torsion function can be refined on the basis of the experimental results [25]. The heat of formation of molecules with heteroatoms at one conformation is given in Eq. 2.27:
A similar expression without the steric contribution is available for the entropy estimation. 3. Non-Traditional (Polarizable) Molecular Mechanics Methods The non-traditional molecular mechanics methods consider the polarizability of the atoms/groups int he molecules. We describe two of these methods: Ponder et al. [26 ] and Gresh et al. [27] developed AMOEBA [26] and SIBFA (Sum of Interactions between Fragments Ab Initio calculated) [27], respectively. 3.1. AMOEBA The method AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) expand the classical force field expressions by the permanent electrostatic interaction between the point charges and multipoles and the induces electrostatic interactions considering polarizability (see Eq. 2.21). The expression contains the bond deformations, the bond-angle cross term, a formal Wilson-Decius-Cross decomposition of angle bending into in-plane (Vangle) and out-of-plane (Voop) terms. The van der Waals expression is a Lennard-Jones potential modified to 14-7. The electrostatics decomposed into permenant and induced potential.
The bond deformations are calculated by Eq. 2.27, which is a modified/refined Hooke’s law with third and forth order polynom. bonds
(2.22) out-of-plane
The van der Waals potential van der Waals
The 14-7 function provide a softer repulsive character than the Lennard-Jones 6-12 function. It fits better the ab initio quantum chemical results and the liquid propertis in noble gases. In the expression all of the atom pairs are considered but the X-H bond distance is reduced (reduction factor) ont he basis of X-ray structural analysis.
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