Ammm:MM/PBSA with amber: theory and application
Introduction
MM-PBSA method implemented in AMBER is to calculate the binding free energy for the association of two proteins or protein-ligand interation. It represents the postprocessing method to evaluate free energies of binding or to calculate absolute or relative free energies of molecules in solution.The sets of structures are usually collected with molecular dynamics or Monte Carlo methods. The first application of this model in its present form was to study the stability of the A- and B-forms of RNA and DNA by Srinivasan et al. in 1998 [1] You can also check the review [2].
MM/PB(GB)SA
The overall objective of the MM-PBSA method (molecular mechanics/Poisson-Boltzmann surface area) and it's complementary MM-GBSA method (molecular mechanics/generalized Born surface area ) is to calculate the free energy difference between two states which most often represent the bound and unbound state of two solvated molecules or alternatively to compare the free energy of two different solvated conformations of the same molecule.
- This method is to divide up the calculation according to the following thermodynamic cycle:
- Protocol for MM-PBSA and MM-GBSA Calculations
- The values of the free energy of binding (ΔGbind) were calculated according to the equation:
where com, rec, and lig stand for complex, receptor, and ligand, respectively. The free energy of each of these was estimated as a sum of the four terms
where ΔGb is the binding free energy in solution, ΔEMM is the molecular mechanics energy, comprised of a van der Waals and an electrostatic contribution; ΔGpol is the electrostatic/polar interation and ΔGpol stand for nonpolar interactions. The electrostatic solvation energy is determined using the finite difference Poisson-Boltzmann [3]. or generalized Born method [4]., and the nonpolar contribution is estimated by the solvent-accessibility surface method. ΔEMM was calculated by the following equation:
The hydrophobic contribution to the solvation free energy (ΔGnonpol) was determined with a function of the solvent-accessible surface-area:
where A is the solvent-accessible surface area and γ and b, the empirical parameters
Computational Alanine Scanning
Why do we need to do Alanine mutagenesis？
As an extension of the MM-PBSA, the application of computational alanine-scanning methodology is particularly impressive since further understanding of the nature of binding in complexes, in terms of the diverse biophysical features of the process, is essential to a phenomenological interpretation of the results. The reliable prediction of key residues in the interface of the protein-ligand/protein-protein has immediate applications in protein-ligand/protein-protein interaction. The major advantage of this method is that it enables estimation of the contribution of each residue to the overall protein-ligand/protein binding; thereby identifying mutations that can enhance the binding affinities of the complex.Crystallographic structures and alanine scanning mutagenesis of protein-protein/ligand interfacial residues have generated a large amount of information that allowed the discovery of energetically important determinants of specificity at intermolecular protein interfaces.
Protocol for alanine scanning
The binding free energy difference between the mutant and wild-type complexes is defined as
ΔΔGbinding = ΔGbinding_mutant－ΔGbinding_wild type
The binding free energy of two molecules is the difference between the free energy of the complex and the respective monomers (the receptor and the ligand):
ΔGbinding = Gcomplex－(Greceptor + Gligand)
The free energy of the complex and respective monomers can be calculated by summing the internal energy (bond, angle. And dihedral), the electrostatic and the van der Waals interactions, the free energy of polar solvation, the free energy of nonpolar solvation, and the entropic contribution for the molecule free energy:
Gmolecule = Einternal + Eelectrostatic+ Evdw +Gpolar solvation + Gnonpolar solvation－TS
The first three terms were calculated using the Cornell force field with no cutoff. The electrostatic solvation free energy (ΔGpolar solvation) was calculated using the finite difference Poisson-Boltzmann [5]. or generalized Born method [6]. The nonpolar contribution to solvation free energy due to van der Waals interactions between the solute and the solvent and cavity formation was modeled as a term that is dependent on the solvent-accessible surface area of the molecule. It was estimated using an empirical relation, ∆Gnonpolar solvation = γA + b, where A is the solvent-accessible surface area that was estimated using the molsurf program, which is based on the idea primarily developed by Connolly. γ and b are empirical constants
Binding Free Energy Decomposition
In order to obtain a detailed view of the protein inhibitor binding, the interaction energies were further decomposed to contributions from each protein residue and inhibitor segment. Moreover, contributions from protein main chains and side chains were separated. These decompositions were possible for molecular mechanics and solvation energies and not for entropies.
- The binding interaction of each inhibitor-residue pair includes three terms: van der Waals contribution (ΔGvdw), electrostatic contribution (ΔGele) and solvation contribution (ΔGGB):
ΔGinhibitor_residue =ΔGvdw + ΔGele+ ΔGGB
where ΔGvdw and ΔGele are nonbonded van der Waal interaction and electrostatic interaction between inhibitor and each protein residue.
Application
- Protein/DNA/RNA-ligand interaction
1.Shin-ichi Fujiwara and Takashi Amisaki. Identification of High Affinity Fatty Acid Binding Sites on Human Serum Albumin by MM-PBSA Method. Biophysical Journal. 94, 2008,95–103.
- Protein-nucleic acid interaction
2.John Eargle1 et al. Dynamics of Recognition between tRNA and Elongation Factor Tu.J. Mol. Biol. (2008) 377, 1382–1405.
- Protein-protein interaction
3.Vincent Zoete et al. Study of the Insulin Dimerization: Binding Free Energy Calculations and Per-Residue Free Energy Decomposition. Proteins 2005;61:79–93.
- Nucleic acid interaction
- High throughput screening using MM/PBSA
4. Scott P. Brown and Steven W. Muchmore. Large-Scale Application of High-Throughput Molecular Mechanics with Poisson-Boltzmann Surface Area for Routine Physics-Based Scoring of Protein-Ligand Complexes. J. Med. Chem. 2009, 52, 3159–3165.
Example: procedures performing MM/PBSA in AMBER
Protein-ligand preparation
- Ligand: see Antechamber (http://water.bme.utexas.edu/wiki/index.php/ABS:ff_amber_ligand_parameter)
- Protein: checking the structure like missing atoms and missing residues (How to model them, you can use modeller or other softwares, http://salilab.org/modeller/), nonstandard amino acid, ions, adding correct hydrogen and so on.
Molecular dynamics simulation
minimise ras-raf &cntrl imin=1,maxcyc=1000,ncyc=500, cut=8.0,ntb=1, ntc=2,ntf=2, ntpr=100, ntr=1, restraintmask=':1-242', restraint_wt=2.0 / heat ras-raf &cntrl imin=0,irest=0,ntx=1, nstlim=25000,dt=0.002, ntc=2,ntf=2, cut=8.0, ntb=1, ntpr=500, ntwx=500, ntt=3, gamma_ln=2.0, tempi=0.0, temp0=300.0, ntr=1, restraintmask=':1-242', restraint_wt=2.0, nmropt=1 / heat ras-raf &cntrl imin=0,irest=1,ntx=5, nstlim=25000,dt=0.002, ntc=2,ntf=2, cut=8.0, ntb=2, ntp=1, taup=1.0, ntpr=500, ntwx=500, ntt=3, gamma_ln=2.0, temp0=300.0, ntr=1, restraintmask=':1-242', restraint_wt=2.0, / heat ras-raf &cntrl imin=0,irest=1,ntx=5, nstlim=250000,dt=0.002, ntc=2,ntf=2, cut=8.0, ntb=2, ntp=1, taup=2.0, ntpr=1000, ntwx=1000, ntt=3, gamma_ln=2.0, temp0=300.0, /
Generate snapshots
Calculate free energy
Firstly, you must generate top files for complex, receptor and ligand (delete waters) using tleap or xleap (Please check leap module in amber) Run
mm_pbsa.pl mm_pbsa.in > mm_pbsa.log *** Abbreviations for mm_pbsa output *** ELE - non-bonded electrostatic energy + 1,4-electrostatic energy VDW - non-bonded van der Waals energy + 1,4-van der Waals energy INT - bond, angle, dihedral energies GAS - ELE + VDW + INT PBSUR - hydrophobic contrib. to solv. free energy for PB calculations PBCAL - reaction field energy calculated by PB PBSOL - PBSUR + PBCAL PBELE - PBCAL + ELE PBTOT - PBSOL + GAS GBSUR - hydrophobic contrib. to solv. free energy for GB calculations GB - reaction field energy calculated by GB GBSOL - GBSUR + GB GBELE - GB + ELE GBTOT - GBSOL + GAS TSTRA - translational entropy (as calculated by nmode) times temperature TSROT - rotational entropy (as calculated by nmode) times temperature TSVIB - vibrational entropy (as calculated by nmode) times temperature *** Prefixes in front of abbreviations for energy decomposition *** "T" - energy part due to _T_otal residue "S" - energy part due to _S_idechain atoms "B" - energy part due to _B_ackbone atoms
Preparing the input file
http://biomol.bme.utexas.edu/~smile1/mm_pbsa/
Some softwares to be used
Support MM/PBSA calculation
Amber (http://ambermd.org/)
Charmm (http://www.charmm.org/)
sietraj (http://www2.bri.nrc.ca/ccb/pub/sietraj_main.php)
For nonpolar/surface area calculation
molsurf (http://www2.chemie.uni-erlangen.de/services/molsurf/)
MSMS (http://mgl.scripps.edu/people/sanner/html/msms_home.html)
LCPO (Weiser J, Shenkin PS, Still WC. Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO). J Comput Chem 1999;20:217–230)
For polar/electrostatic interaction
- http://honiglab.cpmc.columbia.edu/ (for DELPHI)
- http://www.scripps.edu/bashford (for MEAD)
- http://adrik.bchs.uh.edu/uhbd.html (for UHBD)
- pbsa within amber
Some error information
References
- ↑ J. Srinivasan, T.E. Cheatham, III, P. Kollman and D.A. Case. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate--DNA helices. 1998. J. Am. Chem. Soc.. 120, 9401-9409
- ↑ P.A. Kollman, I. Massova, C. Reyes, B. Kuhn, S. Huo, L. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D.A. Case and T.E. Cheatham, III.Calculating structures and free energies of complex molecules: Combining molecular mechanics and continuum models. 2000. Accts. Chem. Res.. 33: p. 889-897.
- ↑ Honig B, Nicholls A. Classical electrostatics in biology and chemistry. Science 1995. Science. 268: p. 1144–1149.
- ↑ Onufriev A, Bashford D, Case DA. Exploring protein native states and large-scale conformational changes with a modified generalized born model. 2004 Proteins. 55: p. 383–394.
- ↑ Honig B, Nicholls A. Classical electrostatics in biology and chemistry. Science 1995. Science. 268: p. 1144–1149.
- ↑ Onufriev A, Bashford D, Case DA. Exploring protein native states and large-scale conformational changes with a modified generalized born model. 2004 Proteins. 55: p. 383–394.