Luận án tiến sĩ: Computational investigations of long-range proton transfer: Method validation and application

COMPUTATIONAL INVESTIGATIONS OF LONG-RANGE PROTON TRANSFER: METHOD VALIDATION AND APPLICATION by Demian Riccardi A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Chemistry) at the UNIVERSITY OF WISCONSIN-MADISON 2006 UMI Number: 3245613 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

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Box 1346 Ann Arbor, Ml 48106-1346 A dissertation entitled COMPUTATIONAL INVESTIGATIONS OF LONG-RANGE PROTON TRANSFER: METHOD VALIDATION AND APPLICATION submitted to the Graduate School of the University of Wisconsin-Madison in partial fulfillment of the requirements for the Degree of Doctor of Philosophy by DEMIAN RICCARDI Date of Final Oral Examination: November 16, 2006 Month & Year Degree to be awarded: December 2006 May August eke de kee kee dee ete eke de RR RRR RRR EKER RRR KERR ERE EKER KERR EERE RR RERERER Approval Signatures of Dissertation Committee —=_ ¬ <==— .“ [_—— — /⁄~ Keck Signature, Dean of Graduate School Metin Chinlbe Jer In memory of my grandfather, William Haskins (Branpa) “Pay attention to business!” il ABSTRACT Motivated by the goal of understanding the mechanism for long-range proton transfers in bio- logical systems, a combined quantum mechanical/molecular mechanical (QM/MM) methodology is validated and then applied to the investigation of the rate-limiting proton transfer in carbonic anhydrase II. The coupling between the QM and MM regions is investigated thoroughly and sys- tematically with gas phase and condensed phase studies. Several aspects of long-range proton transfer in carbonic anhydrase II are investigated. The structural dynamics of the protein and water molecules, for relevant protonation states of the proton donor and acceptor (zinc-bound water and His 64), is highlighted.

The free energy of deprotonation (pK,) for the zinc-bound water is com- puted; good agreement with experiment is attained for the wild type but not for the E106Q mutant. The downward shift of 9 pK, units for the mutant suggests a mechanistic change that has not been realized in previous studies. The validated method is then applied to simulate long-range proton transfers in solution and car- bonic anhydrase II. These investigations emphasize that the microscopic, mechanistic details of long-range proton transfer are most sensitive to the free energy of protonation or deprotonation for all groups involved in the transfer pathway.

This naturally leads to two mechanisms for a long-range proton transfer between two groups: the most common Grotthus and the less recog- nized “proton hole” mechanisms. The latter involves the protonation of the acceptor prior to the deprotonation of the donor, thereby creating a “proton hole” in the mediating pathway. Overall, fair agreement with experiment is attained, and the “proton hole” mechanism is supported as the dominant path in carbonic anhydrase II and is found to be independent of the distance between the zinc-bound water and the His 64. iil Published Work and Work in Preparation [1] D.

Cui, “Importance of van der waals interactions in QM/MM simula- tions. Cui, “Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules,” J. Cui, “pK, calculations in solution and proteins with qm/mm free energy perturbation simulations,” J. Cui, “Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes (feature article),” J.

Cui, “proton holes” in long-range proton transfer reactions in solution and enzymes: a theoretical analysis,” J. Cui, “Insights for carbonic anhydrase Il from pk, computations for the zinc bound water” (In preparation). Cui, “Characterizing the molecular details of the rate limiting long-range transfer in carbonic anhydrase II” (In preparation). IV TABLE OF CONTENTS Page ABSTRACT.OQ ee es ii Published Work and Work in Preparation.00 ee eae 1H LIST OE TABLES.OQne Vili LIST OF FIGURES.

eee X 1 General Introducfion. CO Q Q LG Q Quy v2 I 1.1 Long range proton tranSffr. ee te te ee 1 1. ee ee ee 2 2 van der Waals Interactions in QM/MM Simulations .1 QM/MM Energy Evaluation .2 Optimization of van der Waals Parameters.1 Gas Phase Comparisons.

eee eee ee 17 2. ee 33 3 ElectrostatcsinQM/MMSimulaions. Q Q Q Q Q cv vn vn gà g v v v Và ko 36 3. Q Q Q Q Q nu nu gà kg v k V k Q ki kà 38 3.1 Ewaldsum with SCC-DFTBMM.

Generalized Solvent Boundary Potential(GSBP). HQ HQ ee ee 48 3.Ặ Q Q Q Quà 54 pK, Calculations in Solution and Proteins with QM/MM Free Energy Perturbation Simulations: A Quantitative Test of QM/MM Protocols .1 The Dual Topology Single Coordinate (DTSC) Approach to pK, Calcula- tiONS.2 Gas Phase and QM/MM Coupling Correcions.4 Simulation Set-up 2. ee eee 65 425 T4-Lysozyme. Results and Discussion.1 Small Moleculesin solution.

ee ee 100 QM/MM Simulations of Human Carbonic AnhydraselII. c c Q Q c Q ng vn ng vn v k à v kg v k kg ấ 103 5. c Q HQ HQ ng ng v V KV IV 107 5.2 Periodic Boundary Condilons. Q Q Q Q HQ Và ky kia 114 5.1 Root Mean Square Deviations for backbone atoms .3 Behavior of water in the active site.4 Weakness of GSBP: dynamic properties of the system.

2, eeee ee 129 Insights for CAII from pk, computations for the zinc-bound water .0 02 ee eee eee 133 6.1 GSBP setup for 20 and 25 Ẳ innerregions.2 pK, calculations with FEP and charge perturbations .3 Results and Discussion .2 Contrasting errors within free energy derivatives and between free energies determined from independent simulalons.4 Dissecting the pK, in terms of water and protein electrostatic contributions 141 6. eee ee et ee es 147 7 ‘Proton holes” in long-range proton transfer reactions in solution and enzymes: A theoretical analysis.2 Systems and Simulaton Methods.3 QM/MM parttioningandswichng.4 Potential of mean force (PMF) calculations and analysis .5 Electrostatic potential calculations for relevant protonation states.3 Results and Discusslons.Ặ Q Q Q Q HQ Q HQ va 157 7. es 168 8 Characterizing the molecular details of the rate limiting long-range transfer in Carbonic Anhydrase ll. ee ee ee 170 8.2 Methods: “TS-reorganized” simulations and energetic decomposition .1 “TS-reorganized” simulations .2 Harvesting water wires and determining the MEP.

Electrostatic Perturbation analysis of the PMF.3 Results and Discussion .1 Ensemble of mimnimum energy paths.2 Potential of mean force for the long-range proton transferinCAII. eee ee 191 9 Conclusions. aalaaa CD 193 vũ Page LIST OF REFERENCES. ee es 196 APPENDICES Appendix A: Analysis of error inherent in the simulation protocols.

216 Appendix B: Gas phase benchmarks forSCC-DFTB. 227 Vill LIST OF TABLES Table Page 2.1 Summary of interaction energies and bond lengths: optimization set.2 Summary of interaction energles and bond lengths: test set.3 LJ parameter sets for SCC-DFTB atoms in SCC-DFTB/MM calculatons.4 RMS errors for interaction energy and hydrogen bond length.5 Gas and condensed phase comparisons for the reductionof FAD .6 Gas and condensed phase barriers for the intramolecular proton transfer in enediolate .1 Gas phase proton affinities (in kcal/mol) calculated at the SCC-DFTB, B3LYP, and CCSD levels.2 The AG" (in kcal/mol) component (Figure 4.1) for the five small molecules studied.3 Various bulk solvation contributions (in kcal/mol) to the deprotonation free energy considered for the small molecules insolution.4 The effect of the van der Waals parameters for the acidic proton on AG” and AG@2”) for acetic acid and imidazole (n kcal/mol).5 Bonded, Zero-Point-Energy (ZPE) contributions to the free energy of deprotonation and the QM/MM free energy correction as well as the QM proton affinity correction (mkcal/mol).6 The pK, shifts (in pK, units), relative to the COOH group in glycine, and the RMS difference from experimental values for the five small molecules studied.7 The pk, for His 31 and Lys 102 in the M102K mutant of the T4-Lysozyme.1 Root mean square deviations (RMSD) of backbone atoms and a summary of the “IN” and “OUT” sampling for H64. 2c eee ee es 118 1X Table Page 5.2 Percentages of water brldge tyDp€S. Q Q Q LH HQ nu n k và kg 124 5.

pK,s calculated for H64 and the Zinc-bound water with the Linear Response Approx- imation relative to 4 methyl imidazole In soluion.1 Example of statistical analysis used to determine the free energy derivatives for the deprotonation of the zinc-bound water in the E106Q mutant of CAII with a 20 A GSBP inner region .2 Free energy of deprotonation presented for each independent run of the FEP pK, 22110010519S205 ee ee 139 6.3 pK,s of the zinc-bound water in the wild type and E106Q mutantof CAI.1 Statistics for the barrier and reaction energy (in kcal/mol) associated with minimum energy paths based on different samplings of carbonic anhydrase.2 Statistics for the contribution from protein and water to the barrier and reaction energy (in kcal/mol) associated with minimum energy paths involving two bridging water molecules in carbonic anhydrase. Contribution from protein and water to the barrier and reaction energy (in kcal/mol) associated with the potential of mean force for the proton transfer from the zinc-bound waterinCAID. Q Q Q HQ HH vn k v kg kg V KV kg 190 Appendix Table A.1_ Errors in proton affinities for SCC-DFTB relative to G3B3 calculations .2 Error analysis for the proton exchange reactions between a solute and water.! Proton affinities for models of proton donor and acceptor groupsinCAII .2 Energetics for proton transfer in a gas phase active site model forCAII. 231 LIST OF FIGURES Figure Page 2.1 Training set molecules for optimization of SCC-DFTB/MM LJ parameters .2 Additional molecules not included In the traningset.3 Schematic of FADreduction.

eeee ee ee 14 2.4 Schematic of enediolate inramolecular proton transffr.5 Comparison of interaction energies between various SCC-DFTB/MM LJ parameter schemes and BBLYP. Q Q Q Q HH HH ko 19 2.6 _ Radial distribution functions of TIP3P waters about the model RAD molecule.7 _ Radial distribution functions of TIP3P water about an enediolate.8 Examples of the free energy derivative convergence and integration for the reduction Of FAD. Q Q Q Q Q Q Q Q Quy kg ng kh v k k k k kg 27 2.9 Typical thermodynamic cycle for determining the free energy required to convert A to Binthe condensed phase.10 Plot of the temperature dependence of the free energy used to determine entropic and enthalpic contributions to the reductionof FAD.11 The potential of Mean Force for the Intramolecular Proton Transfer in an Enediolate .1 Schematic representation of the GSBP partition of a solvated biomolecule in the QM/MM framework. Q Q Q Q nu gà và kia 42 3.2 Convergence of the GSBP results versus the size of the basis set for a solvated imidazole.

Flow chart representation of a GSBP set-up for a biological molecule .1 Thermodynamtc cycle forDTSC pK„calculalons .- 59 XI Figure Page 4.2 _ The five small molecules studied here for p#<„ values in solulon.3 GSBP setups forT4Lysozyme. 2002 eee eee ee 70 4.4 Representative linear fits and convergence of the free energy derivatives for solution CASES HH.5 Effect of van der Waals parameters on the computed pK, of imidazole and acetic acid 80 4.6 Schematic plot of the RMSD for pK, shifts relative to experiment as different proto- colsareused 2.7 The structure of water and stability of the protein in the pK, calculations for His 31 in the M102K mutant of T4 Lysozyme. 2 ee ee ee 89 4.8 The average structure for the H31 protonated simulation of the M102K mutant of T4 Lysozyme overlayed with the crystal structure. ee ee ee 90 4.