Next-generation DFT-based quantum models for simulations of biocatalysis Darrin M. York University of Minnesota Minneapolis, Minnesota USA

Outline AM1/d-PhoT model for RNA catalysisAM1/d-PhoT model for RNA catalysis Efficient treatment of long-range electrostatics in semiempirical calculationsEfficient treatment of long-range electrostatics in semiempirical calculations Improved charge-dependant response propertiesImproved charge-dependant response properties Selected applicationsSelected applications

Study phosphate reactivity comprehensively (using small models) with high-level quantum models (ab initio and DFT)Study phosphate reactivity comprehensively (using small models) with high-level quantum models (ab initio and DFT) Construct accurate semiempirical quantum models capable of being used in linear-scaling electronic structure and QM/MM simulationsConstruct accurate semiempirical quantum models capable of being used in linear-scaling electronic structure and QM/MM simulations Develop improved (accurate, fast and general) models for electrostatics, solvation and generalized solvent boundary potentials.Develop improved (accurate, fast and general) models for electrostatics, solvation and generalized solvent boundary potentials. Investigate how to improve next-generation semiempirical quantum models to account for charge-dependent response properties without significant sacrifice of efficiency.Investigate how to improve next-generation semiempirical quantum models to account for charge-dependent response properties without significant sacrifice of efficiency. Validate methods with respect to known reactions in solution, then apply them to the important problem of RNA catalysis in a realistic system consisting of many thousands of particles, and simulated for many tens of nanoseconds.Validate methods with respect to known reactions in solution, then apply them to the important problem of RNA catalysis in a realistic system consisting of many thousands of particles, and simulated for many tens of nanoseconds. …in words

Phosphates and phosphoranes

Mechanisms for phosphoryl transfer Dissociative D N Concerted A N D N Associative A N +D N

QCRNA – Online! Molecule (2000+) Reaction Mechanism (300+) Giese et al., J. Mol. Graph. Model. 25, 423 (2006).

Potential Energy Surface Reaction Tables Graphical Interface QCRNA – Online! Giese et al., J. Mol. Graph. Model. 25, 423 (2006).

Phosphate isomerization (Migration) Liu et al., J. Phys. Chem. B,.109, (2005); Chem. Commun., 31, 3909 (2005). Silva-Lopez et al., Chem. Eur. J., 11, 2081 (2005); Mayaan et al., J. Biol. Inorg. Chem., 9, 807 (2004). Range et al., J. Am. Chem. Soc., 126, 1654 (2004). Chem. Commun.Chem. Eur. J. Biol. Inorg. Chem.J. Am. Chem. Soc.Chem. Commun.Chem. Eur. J. Biol. Inorg. Chem.J. Am. Chem. Soc. movie

Parameter Optimization: AM1/d Methods Training set included a wide variety of biological phosphates and phosphoranes, hydrogen bonded complexes, proton affinities and reaction paths of associative and dissociative mechanisms in different charge states. Nam et al., J. Chem. Theory Comput., submitted.

Why use a semiempirical model? It is important to note that for the ribozyme systems of interest, the details of the mechanisms remain topics of considerable debate. Hence the goal is to test multiple mechanisms with a model that is sufficiently predictive to discern the most probable path. A consensus has emerged that, in certain ribozymes such as HHR and HDV, a large scale conformational change either precedes or is concomitant with the chemical step of the reaction. This necessitates the use of a quantum model that is able to be used with extensive conformational sampling (i.e., simulation) while providing an accurate description, in terms of energy, structure and charge distribution, along multiple mechanistic paths (i.e., not a single pre- determined 1-D reaction coordinate) in order to be predictive.

Modification for AM1/d-PhoT Model If G A and G B = 0,  MNDO Hamiltonian Modified Core-Core Repulsion Core-Core Repulsion MNDO AM1 and PM3 If G A and G B = 1,  AM1 and PM3 Want a d-orbital method for hypervalent species, but one that also describes reasonably hydrogen bonding interactions. Combine MNDO/d framework with a modified core-core term similar to AM1 (and retaining some AM1 parameters unmodified) to build a semiempirical model for phosphoryl transfer reactions: AM1/d-PhoT

AM1/d-PhoT Model for Phosphoryl Transfer

Reaction Energies and Barrier Heights Error* Neutral Rxn Monoanionic Rxn Dianionic Rxn Dissociative Rxn AM1/dAM1PM3AM1/dAM1PM3AM1/dAM1PM3AM1/dAM1PM3 Reaction Energy Reaction Energy No. Rxn No. Rxn5423 MSE MUE Activation Energy Activation Energy No. TS No. TS MSE MUE Relative Intermediate Energy Relative Intermediate Energy No. Int No. Int87 MSE MUE *Errors are computed against “B3LYP/ G(3df,2p) adiabatic energies”

Linear Free Energy Relations Transphosphorylation of a cyclic phosphate with enhanced leaving groups. Slope of plot is the Brønsted correlation parameter β lg often used to characterize phosphoryl transfer reactions. The logk values were calculated from DFT and are contained in QCRNA.

Gas Phase Proton Affinity I B3LYP : B3LYP/ G(3df,2p)//B3LYP/6-31++G(d,p) MoleculeRef. Error B3LYPAM1/dAM1PM3MNDO/d H3O+H3O+H3O+H3O HOH CH 3 OH CH 3 CH 2 OH C 6 H 5 OH CH 3 CO 2 H P(O)(OH)(OH)(OH) P(O)(O)(OH) P(O)(O)(OH)(OH) P(O)(O)(O)(OH) P(O)(OH)(OH)(OCH 3 ) P(O)(O)(OH)(OCH 3 ) P(O)(OH)(OCH 3 )(OCH 3 ) P(O)(OH)(OCH 2 CH 2 O) MSE MUE Range et al., Phys. Chem. Chem. Phys. 7, 3070 (2005).

Gas Phase Proton Affinity II: Phosphorane Compounds MoleculeRef. Error B3LYPAM1/dAM1PM3MNDO/d P(OH)(OH)(OH)(OH)(OH) P(OH)(OH)(OH)(OH)(OH) P(OH)(OH)(OCH 2 CH 2 O)(OH) P(OH)(OCH 2 )(OCH 2 CH 2 O)(OH) P(OH)(OH)(OCH 2 CH 2 O)(OCH 2 ) MSE MUE Range et al., Phys. Chem. Chem. Phys. 7, 3070 (2005). B3LYP : B3LYP/ G(3df,2p)//B3LYP/6-31++G(d,p)

Example: QM/MM of Di-anionic Reactions in Water q = R(P-O l ) - R(O n -P) Dejaegere and Karplus, JACS 1993 Cox and Ramsay, Chem. Rev Comparison with DFT and Expt. in kcal/mol *DFT: B3LYP/ G(3df,2p)RxnGasAquoAM1/dDFTAM1/dExpt DMP TS ~32 TS Prod EPTS ~24 Prod TMPTS ~32 Prod RxnGasAquoAM1/dDFTAM1/dExpt DMPTS ~32 TS Prod EPTS ~24 Prod TMPTS ~32 Prod

Problems Dispersion interactionsDispersion interactions Relative conformational energies: sugar puckering and pseudorotation transition statesRelative conformational energies: sugar puckering and pseudorotation transition states Proper treatment of polarizability and multiple charge statesProper treatment of polarizability and multiple charge states

Giese et al., J. Chem. Phys., 123, (2005). The Problem of Charge-dependent Response Properties with Semiempirical Methods Atoms are of course an extreme case: but typically polarizabilities of neutral molecules are typically off by 25%, and anions by significantly more…

Goal: Improve charge-dependent response properties of semiempirical methods without significantly increasing computational cost. Possible solutions: Reparameterize modelsReparameterize models Increase minimal basis-set representationIncrease minimal basis-set representation Make basis set exponents charge dependentMake basis set exponents charge dependent

DFT-based model… Giese et al., J. Chem. Phys. 123, (2005).

A Variational Electrostatic Projection (VEP) Method for QM/MM Calculations Goal: Model large-scale electrostatic effects of solvent-shielded macromolecular environment - and it’s linear response – in hybrid QM/MM calculations for a fraction of computational cost of explicit simulation Method: Green’s function approach that involves variational projection and reduced dimensional mapping of surrounding solvent-shielded macromolecular environment onto the dynamical reaction zone Gregersen and York, J. Phys. Chem. B, 109, (2005). Gregersen and York, J. Comput. Chem., 27, 103 (2006).

Reaction Region QM active site + MM surrounding (Newtonian dynamics) Buffer Region (Langevin dynamics) External potential of solute and solvent Stochastic boundary Multi-scale Quantum Models

Linear-scaling QM/MM-Ewald Method Nam et al., J. Chem. Theory Comput., 1, 2 (2005).

Applications to enzymes and ribozymes Hammerhead ribozyme Hammerhead ribozyme Best characterized ribozyme – but complicated: role of metals, chemical/conformational steps, non-inline native structure Hairpin ribozyme Hairpin ribozymeHairpin ribozymeHairpin ribozyme No metal cofactor, in-line configuration

General acid/base mechanism

Tai-Sung Lee et al., submitted. Mg 2+ ion is observed to coordinate the O2’ of G8 increasing it’s acidity in the early TS and then migrate closer to the leaving group O5’ position of the scissile phosphate in the late TS. Simulations help to explain the long-standing disconnect between available structures and biochemical data (in particular, thio effect studies).

Early TS Late TS

Other Projects… Parameters for RNA reactive intermediatesParameters for RNA reactive intermediatesParameters for RNA reactive intermediatesParameters for RNA reactive intermediates DNA bendingDNA bendingDNA bendingDNA bending Polarization-exchange couplingPolarization-exchange couplingPolarization-exchange couplingPolarization-exchange coupling Linear-scaling electronic structureLinear-scaling electronic structureLinear-scaling electronic structureLinear-scaling electronic structure

Acknowledgements George Giambasu George Giambasu Dr. Tim Giese Dr. Tim Giese Yun Liu Yun Liu Dr. Evelyn Mayaan Dr. Evelyn Mayaan Adam Moser Adam Moser Dr. Kwangho Nam Dr. Kwangho Nam Dr. Kevin Range Dr. Kevin Range Funding/Resources: University of Minnesota University of Minnesota NIH NIH ACS-PRF ACS-PRF Army High-Performance Computing Research Center Army High-Performance Computing Research Center Minnesota Supercomputing Institute Minnesota Supercomputing Institute Prof Bill Scott Prof Bill Scott Prof. Qiang Cui Prof. Qiang Cui Dhd Marcus Elstner Dhd Marcus Elstner Prof. Jiali Gao Prof. Jiali Gao Prof. Walter Thiel Prof. Walter Thiel Dr. Olalla Nieto Faza Dr. Olalla Nieto Faza Dr. Francesca Guerra Dr. Francesca Guerra Dr. Carlos Silva Lopez Dr. Carlos Silva Lopez Prof. Xabier Lopez Prof. Xabier Lopez Dr. Anguang Hu Dr. Anguang Hu