A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-Phase Quantum Mechanical Calculations
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A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-Phase Quantum Mechanical Calculations YONG DUAN,1 CHUN WU,1 SHIBASISH CHOWDHURY,1 MATHEW C. LEE,1 GUOMING XIONG,1 WEI ZHANG,1 RONG YANG,1 PIOTR CIEPLAK,2,3 RAY LUO,2 TAISUNG LEE,2,3 JAMES CALDWELL,2 JUNMEI WANG,2 PETER KOLLMAN2,† 1Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716 2Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143 3Accelrys Inc., 9685 Scranton Rd, San Diego, California 92121 Received 7 April 2003; Accepted 1 July 2003 Abstract: Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc- pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of ϭ 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1999–2012, 2003 Key words: point-charge force field; quantum mechanical calculations; molecular mechanics simulations Introduction efficient force field that can represent macromolecules in the condensed phase is becoming more critical. Advancements in the field of molecular mechanics simulations In molecular mechanics-based molecular dynamics simula- have concentrated in the areas of simulation methodologies in tions, the molecular systems are represented by molecular mechan- the past. Some highlights of these include accurate treatment of electrostatics,1 efficient conformational sampling methods,2,3 methods for massively parallel simulations,4,5 and continuum solvent models.6,7 These developments have enabled long-time Correspondence to: Y. Duan; e-mail: [email protected] simulations close to the folding time of small proteins,4 and †Deceased several successful folding simulations of miniproteins have Contract/grant sponsor: NIH Research Source; contract/grant number: been reported recently.8–11 Thus, the conformational sampling CRR-15588 ability of all-atom models has reached an important threshold at Contract/grant sponsor: National Institute of General Medical Sciences; which simulations of many biologically relevant processes are contract/grant numbers: GM-64458 and GM-67168 (to Y.D.), and GM- increasingly routine; however, the development of force fields 29072 (to P.A.K.) has lagged behind. With the growing interest in ever more Contract/grant sponsor: The State of Delaware and University of realistic simulations, the need for a reasonably accurate and Delaware Research Fund (to Y.D.) © 2003 Wiley Periodicals, Inc. 2000 Duan et al. • Vol. 24, No. 16 • Journal of Computational Chemistry ics models in which the parameters are developed based on fun- able force field, its application to Monte Carlo simulations is far damental physical principles. The accuracy of a simulation is from being straightforward. largely determined by two factors: conformation sampling, and In contrast to the polarizable formulation, the traditional all- model accuracy. In the past, the conformational sampling ability of atom representation of force fields strikes a balance between molecular dynamics simulation was viewed as the primary bottle- performance and accuracy. However, until recently, all-atom force neck.12,13 With the advancements in simulation methodolo- fields have been developed based on gas-phase quantum mechan- gies14,15 and the increase in computer speed, this limitation is ical calculations of small peptides. One major deficiency in this gradually diminishing. Increasingly, accuracy of the underlying approach is that such a force field lacks proper representation of models becomes the dominant factor in the outcome of a simula- the polarization effect in condensed phase. For example, the dipole tion. For example, with current simulation methodologies and fast moment of alanine-dipeptide in extended conformation is 1.51 computers one can readily reach the folding time scales of small Debye in the gas phase and 1.74 Debye in organic solvent ( ϭ 4), peptides using continuum solvent models,16 and in some cases, differing by more than 15%. Consequently, force fields developed using all-atom solvent models4; however, whether the simulations based on gas-phase quantum mechanical calculations underesti- can accurately reflect physical reality now depend on the force mate the electrostatic interactions when applied to the study of field parameters used to represent the physical interactions. proteins. In reality, they are more suited for small peptides in the An important characteristic of the current molecular mechanics gas phase rather than proteins in the condensed phase. In the rest models is that their parameters are obtained through high-level of this article, we will describe our new atom-centered point quantum mechanical calculations on short peptide fragments. Such charge all-atom force field that was design to address this defi- an approach has several advantages. It assures generality and ciency. allows further refinement upon the availability of more accurate quantum mechanical methods. Because the parameters are integral components of a molecular mechanics model that describes the Methods interacting molecular forces, they are often referred to as the “force field” parameters. Among the early all-atom force field developers, In keeping with our previous minimalist approach, this model is an Weiner et al. successfully adopted this approach17 and developed effective two-body additive model. The potential function describ- one of the first-generation molecular mechanics force fields based ing interactions among particles comprises electrostatic, van der primarily on quantum mechanical data. Due to the inadequate Waals, bond, bond angle, and dihedral terms [eq. (1)] computing power of the time, much of the applications of this force field were limited to in vaccuo simulations.18 A decade later, ϭ ͑ Ϫ ͒2 ϩ ͑ Ϫ ͒2 Etotal Kb b beq K eq 19 after considerable accumulation of simulation data, Cornell et al. bonds angle developed one of the second-generation force fields based on V A B q q improved quantum mechanical calculations. Since then, the Cor- ϩ n ͓ ϩ ͑ Ϫ ␥͔͒ ϩ ͫ ij Ϫ ij ϩ i j ͬ 1 cos n 12 6 (1) 2 Rij Rij Rij nell et al. force field has enjoyed a wide range of applications in dihedrals iϽj simulating both nucleic acids and proteins. One remarkable early success of Cornell et al. force field was that it demonstrated the where, Kb and K are the force constants for the bond and bond ability to move incorrect conformations to the correct ones when 20,21 angles, respectively; b and are bond length and bond angle; beq combined with accurate calculation of electrostatic forces. and are the equilibrium bond length and bond angle; is the Despite their successes, the existing “second-generation” force eq dihedral angle and Vn is the corresponding force constant; the fields are still based on gas-phase quantum mechanical calcula- phase angle ␥ takes values of either 0° or 180°. The nonbonded tions, simulations of small molecules, and typically nanosecond part of the potential is represented by van der Waals ( Aij) and time-scale simulations of proteins. Recent developments in force London dispersion terms (Bij) and interactions between partial fields include the fully polarizable force fields from Kollman atomic charges (q and q ). is the dielectric constant that takes 22 23 i j group and from Friesner group. These force fields can poten- into account of the effect of the medium that is not explicitly tially provide accurate representations in both the gas phase and represented and usually equals to 1.0 in a typical solvated envi- the condensed phase, and is suited for simulations in a variety of ronment where solvent is represented explicitly. The nonbonded solvent environments (e.g., membrane proteins). On the other terms are calculated for all atom pairs that are either separated by hand, these force fields all tend to sacrifice computational effi- more than three bonds or are not bonded. Interactions between ciency for accuracy. This factor alone may discourage their wide- atoms separated by three bonds account for the one to four inter- spread use. An even serious drawback for the inclusion of polar- actions in which the electrostatic and van der Waals parts are izability is the reduced integration stability. Although the reduced by 20–50%, depending on the specific implementation of computational overhead can be minimized to 30–50%, our tests the force field. In this version, the one to four electrostatic inter- show that a 0.5-fs integration time step is required to obtain a actions are divided by a factor of 1.20 and the Lennard–Jones stable trajectory (Duan, unpublished results).