Geometry optimization and transition state search in enzymes: Different options in the microiterative method

In the current article we present a systematic analysis of the different options in the so-called "microiterative method" used to locate minima and transition- state (TS) structures of big systems on quantum mechanics/molecular mechanics potential energy surfaces. The method splits the system in two parts: a core zone in which accurate second-order search is carried out, and an environment that is kept minimized with a cheap first-order algorithm. The different options studied here are: the alternating frequency between the environment minimization and the TS search in the core, the number of atoms included in each zone, and two alternative ways to reduce the computational cost in the calculation of core- environment interactions. The tests have been done at two different steps of the enzymatic mechanism of mandelate racemase: a proton transfer and a carbon configuration inversion step. The two selected TS structures differ in the number of atoms involved in their associated transition vectors; the proton transfer TS is an example of a local motion, whereas the carbon configuration inversion TS corresponds to a more global movement of several groups and residues, including an important number of atoms. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem 98: 367-377, 2004

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

[2]  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.

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

[4]  Emili Besalú,et al.  On the automatic restricted-step rational-function-optimization method , 1998 .

[5]  G. Monard,et al.  Determination of Enzymatic Reaction Pathways Using QM/MM Methods , 2003 .

[6]  Feliu Maseras,et al.  IMOMM: A new integrated ab initio + molecular mechanics geometry optimization scheme of equilibrium structures and transition states , 1995, J. Comput. Chem..

[7]  P. Kollman,et al.  Atomic charges derived from semiempirical methods , 1990 .

[8]  José M. Lluch,et al.  The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface , 2002 .

[9]  F. Javier Luque,et al.  Perturbation approach to combined QM/MM simulation of solute-solvent interactions in solution , 2003 .

[10]  Jiali Gao,et al.  Absolute free energy of solvation from Monte Carlo simulations using combined quantum and molecular mechanical potentials , 1992 .

[11]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[12]  Optimizing efficiency of perturbative Monte Carlo method , 1998 .

[13]  Emili Besalú,et al.  Another way to implement the Powell formula for updating Hessian matrices related to transition structures , 1999 .

[14]  Richard J. Hall,et al.  Aspects of hybrid QM/MM calculations: The treatment of the QM/MM interface region and geometry optimization with an application to chorismate mutase , 2000 .

[15]  Peter A. Kollman,et al.  AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules , 1995 .

[16]  X. Prat-Resina,et al.  How important is the refinement of transition state structures in enzymatic reactions , 2003 .

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

[18]  Laxmikant V. Kale,et al.  Algorithmic Challenges in Computational Molecular Biophysics , 1999 .

[19]  Tamar Schlick,et al.  A truncated Newton minimizer adapted for CHARMM and biomolecular applications , 1994, J. Comput. Chem..

[20]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[21]  Walter Thiel,et al.  Linear scaling geometry optimisation and transition state search in hybrid delocalised internal coordinates , 2000 .

[22]  Martin J. Field,et al.  A temperature-dependent nudged-elastic-band algorithm , 2003 .

[23]  J. M. Lluch,et al.  A QM/MM study of the racemization of vinylglycolate catalyzed by mandelate racemase enzyme. , 2001, Journal of the American Chemical Society.

[24]  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 .

[25]  Ajit Banerjee,et al.  Search for stationary points on surfaces , 1985 .

[26]  H. Bernhard Schlegel,et al.  Exploring potential energy surfaces for chemical reactions: An overview of some practical methods , 2003, J. Comput. Chem..

[27]  Roger Fletcher,et al.  A new efficient method for locating saddle points , 1981 .

[28]  Thom Vreven,et al.  Geometry optimization with QM/MM, ONIOM, and other combined methods. I. Microiterations and constraints , 2003, J. Comput. Chem..

[29]  Weitao Yang,et al.  Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface , 2000 .

[30]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[31]  Ron Elber,et al.  Temperature dependent reaction coordinates , 2000 .

[32]  Alistair P. Rendell,et al.  Comparison of linear‐scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions. II. An energy decomposition analysis , 2002, J. Comput. Chem..

[33]  Thanh N. Truong,et al.  Development of a perturbative approach for Monte Carlo simulations using a hybrid ab initio QM/MM method , 1996 .

[34]  X. Prat-Resina,et al.  On the modulation of the substrate activity for the racemization catalyzed by mandelate racemase enzyme. A QM/MM study , 2002 .

[35]  Ionel Michael Navon,et al.  Performance of hybrid methods for large‐scale unconstrained optimization as applied to models of proteins , 2003, J. Comput. Chem..

[36]  Ian H. Williams,et al.  Transition-state structural refinement with GRACE and CHARMM: Flexible QM/MM modelling for lactate dehydrogenase , 1999 .

[37]  Claude Millot,et al.  A coupled density functional‐molecular mechanics Monte Carlo simulation method: The water molecule in liquid water , 1996 .

[38]  R. Friesner,et al.  Frozen orbital QM/MM methods for density functional theory , 2000 .

[39]  Ron Elber,et al.  Long time dynamics of complex systems. , 2002, Accounts of chemical research.

[40]  Peter Pulay,et al.  Ab initio geometry optimization for large molecules , 1997, J. Comput. Chem..