Computational biochemistry ferenc Bogár György Ferency
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- 2.2. The MM force fields
- 2.3. The AMBER force field
| 2.1. Non-bonded interactions
The non-covalent interactions include the Coulomb interactions between point charges and the van der Waals interactions with 12-6 Lennard-Jones potential (at systems with a lot of H-bonds 10-6 Lennard-Jones potential). The functions are described in Eq. 2.16 and Eq. 2.17.
rij is the distance between atoms i and j. qi and qj are the point charges of the atoms. ε is the effective dielectric constant.
rij is the distance between atoms i and j. εij is expressed by the arithmetic or geometric average of the van der Waals constants of the two atoms in the atom-pairs (εij = (εi εj)1/2 or εij = (εi +εj)/2), which depends ont he type of the force field). R0,ij is expressed similarly by deriving the parameters from the van der Waals parameters of i and j atoms (by the arithmetic or geometric average). The potential energy of the van der Waals interaction vs. distance of atoms is described in Figure 2.6. (12-6 Lennard-Jones potential, curve is black). In some cases r-9 is the repulsive function. There is a possibility to express the van der Waals interactions by a Buckingham exponential-r-6 potential Eq. 2.18.
Figure 2.6. The potential energy vs. distance of atoms calculated by 12-6 Lennard-Jones function There are many functional forms of the force fields. There are force fields for general organic compounds (MM2 [6], MM3 [7], MM4 [8], UFF (Universal Force Field) [9], MMFF [10].A lot of other force fields were developed for biomolecules (peptides, proteins, DNA, RNA): AMBER ( AMBER94 [11], AMBER98 [12], AMBER99 [13], AMBER2002 [14] ), CHARMM (CHARMM19 [15], CHARMM22 [16], GROMOS [17], OPLSAA, OPLSUA [18]. 2.2. The MM force fields The first generally used force field was developed by Allinger et al. [6-8]. A detailed description of the functions in MM2 and MM3 is summerized e.g. in Lit. [19]. The potential function is the same as Eq. 2.2. The electrostatic interactions are considered in a molecule the interactions between bond dipoles defined by Eq. 2.19 obtained by statistical mechanics.
where ε is the effective dielectric constant in the solution. The angles are defined in Figure 2.7. The dipoles are modified by the electronegativity of the two heavy atoms. The MM2 force field is modified in MMX by Gilbert implemented in PCMODEL [20] which is useful for metal complexes, transition states, ions, too. 
Figure 2.7. The interactions between two dipoles with the geometric parameters. The function is defined in Eq. 2.19. 2.3. The AMBER force field Assisted Model Building with Energy Refinement (AMBER) based ont he following equation which is suitable for the biomolecules (peptides, proteins, DNA) [11-14]:
Force fields based on atom-centered dipole polarizabilities can be applied by using the polarization term Eq. 2.21 polarization
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