An approximate DFT method for QM/MM simulations of biological structures and processes

In the last years, we have developed a computationally efficient approximation to density functional theory, the so called self-consistent charge density functional tight-binding scheme (SCC-DFTB). To extend its applicability to biomolecular structures, this method has been implemented into quantum mechanical/molecular mechanics (QM/MM) and linear scaling schemes and augmented with an empirical treatment of the dispersion forces. We review here applications of the SCC-DFTB QM/MM method to proton transfer (PT) reactions in enzymes like liver alcohol dehydrogenase and triosephosphate isomerase. The computational speed of SCC-DFTB allows not only to compute minimum energy pathways for the PT but also the potential of mean force. Further applications concern the dynamics of polypeptides in solution and of ligands in their biological environment. The developments reviewed allowed for the first time realistic QM simulations of polypeptides, a protein and a DNA dodecamer in the nanosecond time scale.

[1]  Weitao Yang,et al.  Linear Scaling Methods for Electronic Structure Calculations , 2002 .

[2]  U. Gerstmann,et al.  Approximate density-functional calculations of spin densities in large molecular systems and complex solids , 2001 .

[3]  Andrey A. Bliznyuk,et al.  A combined quantum chemical/molecular mechanical study of hydrogen-bonded systems , 1992 .

[4]  Carlo Adamo,et al.  Predicting proton transfer barriers with density functional methods , 1999 .

[5]  J. Gao,et al.  A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations. , 1992, Science.

[6]  Thomas Frauenheim,et al.  Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment , 2001 .

[7]  Martin Karplus,et al.  A Theoretical Analysis of the Proton and Hydride Transfer in Liver Alcohol Dehydrogenase (LADH) , 2002 .

[8]  Thomas Frauenheim,et al.  Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB, AM1 and PM3 methods in comparison with DFT, HF and MP2 calculations , 2001 .

[9]  J. Gready,et al.  Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules , 1999, J. Comput. Chem..

[10]  John A. Board,et al.  The Sigma MD Program and a Generic Interface Applicable to Multi-Functional Programs with Complex, Hierarchical Command Structure , 2002 .

[11]  R A Friesner,et al.  Quantum mechanical calculations on biological systems. , 1998, Current opinion in structural biology.

[12]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[13]  S. Suhai,et al.  Application of an approximate density-functional method to sulfur containing compounds , 2001 .

[14]  Giacinto Scoles,et al.  Intermolecular forces in simple systems , 1977 .

[15]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[16]  Sándor Suhai,et al.  Theoretical Study of Aqueous N-Acetyl-l-alanine N‘-Methylamide: Structures and Raman, VCD, and ROA Spectra , 1998 .

[17]  Qiang Cui,et al.  Functional specificities of methylglyoxal synthase and triosephosphate isomerase: a combined QM/MM analysis. , 2002, Journal of the American Chemical Society.

[18]  C. Mijoule,et al.  Density functional theory applied to proton-transfer systems. A numerical test , 1993 .

[19]  Thomas Frauenheim,et al.  Hybrid SCC-DFTB/molecular mechanical studies of H-bonded systems and ofN-acetyl-(L-Ala)nN?-methylamide helices in water solution , 2000 .

[20]  J. Gready,et al.  Coupled semiempirical molecular orbital and molecular mechanics model (QM/MM) for organic molecules in aqueous solution , 1997, J. Comput. Chem..

[21]  S. Scheiner,et al.  Comparison of methods for calculating the properties of intramolecular hydrogen bonds. Excited state proton transfer , 1999 .

[22]  Tai-Sung Lee,et al.  A pseudobond approach to combining quantum mechanical and molecular mechanical methods , 1999 .

[23]  C. Reynolds,et al.  Semiempirical MO methods: the middle ground in molecular modeling , 1997 .

[24]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[25]  S. Goedecker Linear scaling electronic structure methods , 1999 .

[26]  J. Hermans,et al.  Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine “dipeptides” (Ace‐Ala‐Nme and Ace‐Gly‐Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution , 2003, Proteins.

[27]  Thomas Frauenheim,et al.  Modeling zinc in biomolecules with the self consistent charge‐density functional tight binding (SCC‐DFTB) method: Applications to structural and energetic analysis , 2003, J. Comput. Chem..

[28]  V. Barone,et al.  Proton transfer in model hydrogen-bonded systems by a density functional approach , 1994 .

[29]  K. Merz,et al.  Density functional study of symmetric proton transfers , 1994 .

[30]  Kenneth M. Merz,et al.  Quantum mechanical/quantum mechanical methods. I. A divide and conquer strategy for solving the Schrödinger equation for large molecular systems using a composite density functional–semiempirical Hamiltonian , 2000 .

[31]  Thomas Frauenheim,et al.  Atomistic simulations of complex materials: ground-state and excited-state properties , 2002 .

[32]  Manuel F. Ruiz-López,et al.  An iterative procedure to determine Lennard-Jones parameters for their use in quantum mechanics/molecular mechanics liquid state simulations , 2002 .

[33]  P. Schleyer Encyclopedia of computational chemistry , 1998 .

[34]  Pavel Hobza,et al.  Intercalators. 1. Nature of Stacking Interactions between Intercalators (Ethidium, Daunomycin, Ellipticine, and 4‘,6-Diaminide-2-phenylindole) and DNA Base Pairs. Ab Initio Quantum Chemical, Density Functional Theory, and Empirical Potential Study , 2002 .

[35]  J. Stewart Optimization of parameters for semiempirical methods I. Method , 1989 .

[36]  M Elstner,et al.  Quantum mechanics simulation of protein dynamics on long timescale , 2001, Proteins.

[37]  Sándor Suhai,et al.  A Self‐Consistent Charge Density‐Functional Based Tight‐Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology , 2000 .

[38]  Jiali Gao,et al.  Optimization of the Lennard‐Jones parameters for a combined ab initio quantum mechanical and molecular mechanical potential using the 3‐21G basis set , 1996 .

[39]  Pavel Hobza,et al.  Performance of empirical potentials (AMBER, CFF95, CVFF, CHARMM, OPLS, POLTEV), semiempirical quantum chemical methods (AM1, MNDO/M, PM3), and ab initio Hartree–Fock method for interaction of DNA bases: Comparison with nonempirical beyond Hartree–Fock results , 1997 .

[40]  U. Singh,et al.  A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl− exchange reaction and gas phase protonation of polyethers , 1986 .

[41]  Pavel Hobza,et al.  Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations. , 2002, Journal of the American Chemical Society.

[42]  Efthimios Kaxiras,et al.  A QM/MM Implementation of the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) Method , 2001 .

[43]  M. Karplus,et al.  Combining ab initio and density functional theories with semiempirical methods , 2002 .

[44]  M. Karplus,et al.  Substrate conformational transitions in the active site of chorismate mutase: Their role in the catalytic mechanism , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[45]  S. Scheiner Theoretical Studies of Excited State Proton Transfer in Small Model Systems , 2000 .

[46]  Alistair P. Rendell,et al.  Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods applied to enzyme reactions , 2000 .

[47]  J. Ponder,et al.  An efficient newton‐like method for molecular mechanics energy minimization of large molecules , 1987 .

[48]  Xiaodong Zhang,et al.  CALCULATING ACCURATE REDOX POTENTIALS IN ENZYMES WITH A COMBINED QM/MM FREE ENERGY PERTURBATION APPROACH , 2002 .

[49]  M. Karplus,et al.  A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations , 1990 .

[50]  Timothy Clark,et al.  Quo Vadis semiempirical MO-theory? , 2000 .

[51]  Walter Thiel,et al.  Description of peptide and protein secondary structures employing semiempirical methods , 2001 .

[52]  Efthimios Kaxiras,et al.  A Self-Consistent Charge Density-Functional Based Tight-Binding Scheme for Large Biomolecules , 2000 .

[53]  Robert G. Bell,et al.  AB INITIO AND DENSITY FUNCTIONAL THEORY STUDIES OF PROTON TRANSFER REACTIONS IN MULTIPLE HYDROGEN BOND SYSTEMS , 1995 .

[54]  Walter Thiel,et al.  Enzymatic reactions of triosephosphate isomerase: A theoretical calibration study , 2002 .

[55]  Sándor Suhai,et al.  DFT studies on helix formation in N-acetyl-(L-alanyl)n-N′-methylamide for n=1–20 , 2000 .

[56]  György G. Ferenczy,et al.  Quantum mechanical computations on very large molecular systems: The local self‐consistent field method , 1994, J. Comput. Chem..

[57]  P. Lugli,et al.  A simple tight-binding approach to Time-Dependent Density-Functional Response-Theory , 2001 .

[58]  K. Morokuma,et al.  A NEW ONIOM IMPLEMENTATION IN GAUSSIAN98. PART I. THE CALCULATION OF ENERGIES, GRADIENTS, VIBRATIONAL FREQUENCIES AND ELECTRIC FIELD DERIVATIVES , 1999 .

[59]  Qin Wu,et al.  Empirical correction to density functional theory for van der Waals interactions , 2002 .

[60]  Sándor Suhai,et al.  A comparative study of MP2, B3LYP, RHF and SCC-DFTB force fields in predicting the vibrational spectra of N-acetyl-L-alanine-N'-methyl amide: VA and VCD spectra , 1999 .

[61]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[62]  Alexander D. MacKerell,et al.  PROTON AND HYDRIDE TRANSFERS IN SOLUTION : HYBRID QM/MM FREE ENERGY PERTURBATION STUDY , 1996 .

[63]  K. Morokuma,et al.  ONIOM: A Multilayered Integrated MO + MM Method for Geometry Optimizations and Single Point Energy Predictions. A Test for Diels−Alder Reactions and Pt(P(t-Bu)3)2 + H2 Oxidative Addition , 1996 .

[64]  Markus Meuwly,et al.  Simulation of proton transfer along ammonia wires: An “ab initio” and semiempirical density functional comparison of potentials and classical molecular dynamics , 2002 .

[65]  Giulia Galli,et al.  Large‐Scale Electronic Structure Calculations Using Linear Scaling Methods , 2000 .

[66]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.