The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO)

The polarizable continuum model (PCM) for the description of solvent effects is combined with the fragment molecular orbital (FMO) method at several levels of theory, using a many‐body expansion of the electron density and the corresponding electrostatic potential, thereby determining solute (FMO)–solvent (PCM) interactions. The resulting method, denoted FMO/PCM, is applied to a set of model systems, including α‐helices and β‐strands of alanine consisting of 10, 20, and 40 residues and their mutants to charged arginine and glutamate residues. The FMO/PCM error in reproducing the PCM solvation energy for a full system is found to be below 1 kcal/mol in all cases if a two‐body expansion of the electron density is used in the PCM potential calculation and two residues are assigned to each fragment. The scaling of the FMO/PCM method is demonstrated to be nearly linear at all levels for polyalanine systems. A study of the relative stabilities of α‐helices and β‐strands is performed, and the magnitude of the contributing factors is determined. The method is applied to three proteins consisting of 20, 129, and 245 residues, and the solvation energy and computational efficiency are discussed. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 976–985, 2006

[1]  Donald G. Truhlar,et al.  Universal reaction field model based on ab initio Hartree–Fock theory , 1998 .

[2]  Rodney J Bartlett,et al.  A natural linear scaling coupled-cluster method. , 2004, The Journal of chemical physics.

[3]  Yuji Mochizuki,et al.  Configuration interaction singles method with multilayer fragment molecular orbital scheme , 2005 .

[4]  R. Huber,et al.  Bovine chymotrypsinogen A X-ray crystal structure analysis and refinement of a new crystal form at 1.8 A resolution. , 1985, Journal of molecular biology.

[5]  Fumitoshi Sato,et al.  Calculation of all-electron wavefunction of hemoprotein cytochrome c by density functional theory , 2001 .

[6]  Giovanni Scalmani,et al.  Energies, structures, and electronic properties of molecules in solution with the C‐PCM solvation model , 2003, J. Comput. Chem..

[7]  Kazuo Kitaura,et al.  Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method. , 2005, The Journal of chemical physics.

[8]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[9]  Kotoko Nakata,et al.  Ab initio quantum mechanical study of the binding energies of human estrogen receptor α with its ligands: An application of fragment molecular orbital method , 2005, J. Comput. Chem..

[10]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[11]  K. Kitaura,et al.  Multilayer formulation of the fragment molecular orbital method (FMO). , 2005, The journal of physical chemistry. A.

[12]  Beate Paulus,et al.  Ab initio incremental correlation treatment with non-orthogonal localized orbitals , 2003 .

[13]  Kazuo Kitaura,et al.  Second order Møller-Plesset perturbation theory based upon the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[14]  J. W. Neidigh,et al.  Designing a 20-residue protein , 2002, Nature Structural Biology.

[15]  G. Scuseria,et al.  Achieving linear-scaling computational cost for the polarizable continuum model of solvation , 2004 .

[16]  Kazuo Kitaura,et al.  The importance of three-body terms in the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[17]  Hui Li,et al.  Improving the efficiency and convergence of geometry optimization with the polarizable continuum model: New energy gradients and molecular surface tessellation , 2004, J. Comput. Chem..

[18]  A. Klamt,et al.  COSMO : a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient , 1993 .

[19]  D. Chipman Reaction field treatment of charge penetration , 2000 .

[20]  Roberto Improta,et al.  Computation of protein pK’s values by an integrated density functional theory/Polarizable Continuum Model approach , 2004 .

[21]  Mark S. Gordon,et al.  A new hierarchical parallelization scheme: Generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method (FMO) , 2004, J. Comput. Chem..

[22]  Jacopo Tomasi,et al.  Evaluation of the dispersion contribution to the solvation energy. A simple computational model in the continuum approximation , 1989 .

[23]  Florent Cipriani,et al.  Neutron Laue diffractometry with an imaging plate provides an effective data collection regime for neutron protein crystallography , 1997, Nature Structural Biology.

[24]  Christian Silvio Pomelli,et al.  An improved iterative solution to solve the electrostatic problem in the polarizable continuum model , 2001 .

[25]  Jacopo Tomasi,et al.  A new definition of cavities for the computation of solvation free energies by the polarizable continuum model , 1997 .

[26]  Fumio Hirata,et al.  A hybrid approach for the solvent effect on the electronic structure of a solute based on the RISM and Hartree-Fock equations , 1993 .

[27]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[28]  Jacopo Tomasi,et al.  Remarks on the use of the apparent surface charges (ASC) methods in solvation problems: Iterative versus matrix‐inversion procedures and the renormalization of the apparent charges , 1995, J. Comput. Chem..

[29]  J. Tomasi,et al.  Quantum mechanical continuum solvation models. , 2005, Chemical reviews.

[30]  P. Claverie,et al.  Improvements of the continuum model. 1. Application to the calculation of the vaporization thermodynamic quantities of nonassociated liquids , 1988 .

[31]  Jan H. Jensen,et al.  Continuum solvation of large molecules described by QM/MM: a semi-iterative implementation of the PCM/EFP interface , 2003 .

[32]  Kazuo Kitaura,et al.  On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory , 2004 .

[33]  Jacopo Tomasi,et al.  A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics , 1997 .

[34]  Kazuo Kitaura,et al.  Coupled-cluster theory based upon the fragment molecular-orbital method. , 2005, The Journal of chemical physics.