Empirical force fields for biological macromolecules: Overview and issues

Abstract

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

Comparison of multiple Amber force fields and development of improved protein backbone parameters

“…For example, if we optimized the absolute difference of QM and MM energies for glycine tetrapeptide (Gly 3 ), we would minimize the absolute error (ae) between the MM and QM energies (Equation 1): (1) where E QM (i) and E MM (i) correspond to the QM and MM energies respectively for i-th glycine tetrapeptide conformer and N is the number of all glycine conformers. In our case, MM energy for a given conformer is given by the AMBER energy function (see ff94 5 ): (2) where the dihedral energy term is: (3) V n is dihedral force constant (amplitude), n is dihedral periodicity, and γ n is a phase of the dihedral angle θ (which would be either φ or ψ for backbone dihedral terms). The Fourier series in E dihedral is approximated using a small number of terms.…”

“…Therefore the function we optimized was calculated as an average of QM and MM energy differences with each conformer's energy set as a reference in turn. This gives an average absolute error (aae) defined as follows: (4) where is the QM energy of conformer j with conformer i as a reference, and is the MM energy of conformer j with conformer i as a reference, N is number of conformers, which is 28 for Gly 3 . Another possibility to define a function for optimization is to concentrate on what the maximum absolute error (mae) might be when we consider all individual QM and MM differences and, again, take into account that any conformer may serve as a reference "zero energy".…”

“…All molecular dynamics simulations for Gly 3 and Ala 3 tetrapeptides were carried out with the sander module in AMBER8 7 using several different force fields as discussed in the main text: ff94 5 , ff99 11 , Garcia's modification of ff94 13 with C-N-C α -C and N-C α -C-N terms zeroed (denoted ff94gs in the text), Pande's modified ff99 19 with C-N-C α -C term replaced by the one from ff94 (denoted ff99ϕ), ff03 24 (as present in AMBER8 distribution) and ff99SB developed as described above. The time step was 2 fs, and all bonds involving hydrogen were constrained by SHAKE with a tolerance of 10 −4 Å. Glycine and alanine tetrapeptide systems were solvated by approximately 520 TIP3P 33 water molecules in a periodic box.…”

“…We first discuss the plots for Gly 3 . The plots obtained from the Gly 3 simulations are symmetric with respect to the origin, while alanine plots are not due to the presence of the chiral center on the alanine α-carbon.…”

“…For a more in-depth overview of current force fields and trends in force field development, the reader is referred to recent review articles [2][3][4] . In this report, we focus on the existing AMBER fixed charge additive force fields.…”