Coupled Two-Dimensional Main-Chain Torsional Potential for Protein

Feb 26, 2015 - The accuracy of force fields is of utmost importance in molecular modeling of proteins. Despite successful applications of force fields...
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Coupled Two-Dimensional Main-Chain Torsional Potential for Protein Dynamics II: Performance and Validation Ya Gao,†,# Yongxiu Li,†,¶,# Lirong Mou,§ Wenxin Hu,∥ Jun Zheng,∥ John Z. H. Zhang,†,⊥ and Ye Mei*,‡,⊥ †

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China Center for Laser and Computational Biophysics, State Key Laboratory of Precision Spectroscopy, Department of Physics and Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China ¶ Key Laboratory of Catalysis and Materials Science of the State Ethnic Affairs Commission and Ministry of Education, Hubei Province, South-Central University for Nationalities, Wuhan 430074, China § Institutes for Advanced Interdisciplinary Research, East China Normal University, Shanghai 200062, China ∥ Computing Center, School of Information Science & Technology, East China Normal University, Shanghai 200062, China ⊥ NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China ‡

S Supporting Information *

ABSTRACT: The accuracy of force fields is of utmost importance in molecular modeling of proteins. Despite successful applications of force fields for about the past 30 years, some inherent flaws lying in force fields, such as biased secondary propensities and fixed atomic charges, have been observed in different aspects of biomolecular research; hence, a correction to current force fields is desirable. Because of the simplified functional form and the limited number of parameters for main chain torsion (MCT) in traditional force fields, it is not easy to propose an exquisite force field that is well-balanced among various conformations. Recently, AMBER-compatible force fields with coupled MCT term have been proposed, which show some improvement over AMBER03 and AMBER99SB force fields. In this work, further calibration of the torsional parameters has been conducted by changing the solvation model in quantum mechanical calculation and minimizing the deviation from the nuclear magnetic resonance experiments for some benchmark model systems and a folded protein. The results show that the revised force fields give excellent agreement with experiments in J coupling, chemical shifts, and secondary structure populations. In addition, the polarization effect is found to be crucial for the systems with ordered secondary structures. temperature dependent,15−17 and (iii) the neighboring effect is nonnegligible.18,19 These conflicts indicate that pairwise force fields tuned for globular proteins are not applicable to less ordered structures because the electrostatic polarization effect, which is significant in the ordered secondary structures, has been absorbed into other potential energy terms, especially the main chain torsions (MCT). Applying this potential energy to IDPs and oligopeptides biases the distribution toward the ordered structures. Our idea is to fit the main chain torsions from high-level quantum mechanical calculations instead of the tuning based on the statistics of a protein data bank. Some updates to the widely used force fields have been proposed in the past few years,20−24 including our new AMBER-compatible force field.25 In conventional force fields, the main chain torsion terms are treated individually for ϕ (C− N−Cα−C) and ψ (N−Cα−C−N) as one-dimensional Fourier

1. INTRODUCTION Molecular dynamics (MD) simulation, utilizing classical potential energy functions or “force field” to describe the interactions in atomic systems, is a powerful tool for the exploration of biological phenomena, functions, and mechanisms.1,2 Protein force fields comprise bonded (bond, angle, dihedral) and nonbonded terms (van der Waals and electrostatic interaction), which are parametrized against gas phase quantum chemical calculations and spectroscopic and thermodynamics experimental data of small model molecules.3−5 Successful applications of currently widely used force fields in computer simulations of biological macromolecules have been reported in the literature;6−9 however, some recent simulations of intrinsically disordered proteins (IDPs) have raised questions about the predictive ability of force fields.10−12 In addition, some experimental studies of model peptides have shown conflict observations against the simulations. For instance, (i) the dominant conformation adopted by the alanine dipeptide is polyproline helix type II (ppII), which is chosen by the polar solvation effect,13,14 (ii) the conformational propensity is © 2015 American Chemical Society

Received: October 9, 2014 Revised: February 26, 2015 Published: February 26, 2015 4188

DOI: 10.1021/jp510215c J. Phys. Chem. B 2015, 119, 4188−4193

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The Journal of Physical Chemistry B

1UBQ). The details of the setup for the simulations are available in the Supporting Information. J coupling was calculated via the Karplus equation:

series, which are inadequate to give an exquisite description of the subtle MCT potential energy map,13,26−30 albeit a slight decrease in computational efficiency, employing a high-order coupled MCT Fourier expansion, can give a potential energy map closer to its counterpart from a high-level quantum mechanical calculations. Improvement over AMBER0331 and AMBER99SB32 force fields has been reported in our previous work.25 This idea has also been adopted by Lwin and Luo in their ff99ci force field;33 however, deviations from the experimental measurements for oligopeptides are also seen. In this work, we further calibrate the parameters by changing the solvation model in quantum mechanical calculation and slightly modifying the MCT to minimize the deviation from the experimentally measured J coupling data for some oligopeptides and ubiquitin. In our previous work, quantum mechanical (QM) calculations for the parametrization were carried out at the M06-2X/ aug-cc-pVTZ level. Despite its accuracy for small molecules in the gas phase, its compatibility with the polarizable continuum model using the integral equation formalism variant solvation model is poor (data not shown). A more recent solvation model based on solute electron density developed in Truhlar’s group has been proved to be more promising in working with M06-2X density functional.34,35 Thus, we replaced the solvation model and recalculated the free energy of alanine dipeptide at the QM level. The free energy maps are shown in Supporting Information Figure S1 for comparison. The differences, which reside mainly on the left half of the map, include enhanced population in the ppII domain and the shrunken wells in the α, β, and C7 zones. These variations lower the populations of α, β, and C7 domains and significantly increase that of ppII. The correspondence between the predicted NMR J coupling and those from experimental measurement is remarkably improved. Nevertheless, there is still room for improvement, which summons a more rigorous solvation model in the QM framework. The new free energy map is further refined by small modifications to minimize the deviations from the experimentally measured J coupling data for some oligopeptides. The MCT terms are coupled to the side chain rotation. Therefore, different parameters are used for Ala, Gly and other residues except for Pro. The MCT torsion parameters for Pro are kept intact as in the original AMBER force fields; that is, two one-dimensional Fourier expansions. The final coupled MCT parameters are listed in the Supporting Information.

3

J(ϑ) = A cos2(ϑ + Δ) + B cos(ϑ + Δ) + C

(1)

The parameters used in this work were taken from Hu et al.,39 which was derived from the experimental investigation of ubiquitin and averaged over various residues. Therefore, it is not residue-dependent, and its accuracy is moderate. The merit function used to measure the agreement between the experimental J couplings and the calculated ones was defined as χ2 =

1 N

N

∑ i=1

( Ji

calc

− Ji )̂ 2

σi2

(2)

where ⟨Ji⟩calc is the averaged ith J coupling from the simulation, Ji ̂ is the experimental measurement, and σi, determined from the Karplus equation parameters themselves, is the estimated systematic error of each coupling.40 The main chain torsion space was classified into “α+” (−160° < ϕ < −20° and −120° < ψ < 50°); “αh”, with a more stringent definition (−100° < ϕ < −30° and −67° < ψ < −7°); “β” (−180° < ϕ < −90° and 50° < ψ < 240° or 160° < ϕ < 180° and 110° < ψ < 180°); “ppII” (−90° < ϕ < −20° and 50° < ψ < 240°); and other regions, in the same way as that used by Best et. al.13

3. RESULTS 3.1. Oligopeptides. Because the parameters were fitted from the potential energy surface of alanine dipeptide, a key question is whether the performance of these 2D force fields is consistent among different amino acids. A recent NMR and vibrational spectroscopy study of the α, β, and ppII populations of 19 capped dipeptides41 revealed nonuniform secondary structure distribution for amino acids, although they were all dominated by ppII. Pande et al.38 evaluated the quality of different force fields with different solvent models for 19 amino acids and came to the conclusion that recent force fields (AMBER99sb-ildn-phi and AMBER99sb-ildn-NMR) combined with explicit solvent show close agreement with the conformational populations estimated from a PDB-derived coil library. Adopting the same strategy, the quality of the 2D torsional force fields for 19 amino acids is evaluated by molecular simulations in this work. The conformational population, utilizing AMBER03, AMBER032D, AMBER99SB, and AMBER99SB2D force fields with the TIP3P water model, is shown in Figure 1. As indicated, the 2D force fields give a better agreement with the measured population from the vibrational spectroscopy experiment,41 which is slightly different from the work of Pande et al.38 It indicates that the 2D torsional force fields give a more accurate description of the (ϕ, ψ) distribution for dipeptides than AMBER03 and AMBER99SB force fields do. 3 J(HN, Hα), an indicator of secondary structure distribution, is calculated utilizing the Karplus equation for some other systems. The results are shown in Figure 2. AMBER99SB2D force field gives the best agreement with the experiments, whereas the AMBER032D force field gives a RMSD a little bit larger than its predecessor. This is a consequence of the coupling between the main chain torsions and various potential energy terms, such as the bonded term and van der Waals interaction, which complicates the parametrization.42

2. METHODS Some well-studied systems were chosen for the calibration including capped dipeptides (Ace-X-NME, X ≠ P), tripeptides (XXX, X ∈ {A, G, V }; GYG, Y ∈ {A, V, F, L, S, E, K, M }), alanine tetrapeptide, Ac−(AAQAA)3−NH2, and ubiquitin. All these systems have NMR data available in the form of chemical shifts, J couplings, or both. Other experimental data, such as VCD, IR, and Raman spectroscopy,19,36,37 were not taken into consideration because the resolution of these methods for structure determination is low, and direct calculation of these spectra from molecular dynamics simulations is not straightforward. All the simulations were performed in explicit water, and the production run extended to 20 ns for dipeptides and 25 ns for tripeptides and tetrapeptide, which followed Pande et al.38 For ubiquitin and Ac−(AAQAA)3−NH2, the simulations were extended to 50 and 45 ns, respectively. Simulations of ubiquitin were started from its crystal structure (Protein Data Bank entry: 4189

DOI: 10.1021/jp510215c J. Phys. Chem. B 2015, 119, 4188−4193

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Figure 1. Simulated average conformational population for dipeptides. Each axis denotes the population of α, β, ppII from bottom clockwise. The corners of the triangle represent distributions with all α, β, ppII, respectively. Also shown is experimental estimate.

which was consistent with the previous work of Case46 and Merz.47 All the calculations were carried out using the Gaussian 0948 program. Because of the large computational expense of the QM calculations, it is essential to keep the environment as small as possible but as realistic as possible. Therefore, only the water molecules hydrogen-bonded with the dipeptides were included in the QM calculations, and the outer shell was taken as a polarizable continuum medium.49 One hundred snapshots were extracted from each trajectory. The results are shown in Supporting Information Figure S2, which indicate that there is a good correlation between the Karplus equation and the QM calculations for J coupling of all three residues. The averaged J coupling values using the Karplus equation and QM method are listed in Table S1. It can be read from this Table that the structure ensemble from AMBER032D simulation is more consistent with experiment for Ala and Gly dipeptides, no matter which J coupling prediction method is used. Although for the Ser dipeptide, AMBER03 performs better than AMBER032D. Although there are some deviations in the computed values between the Karplus equation and the QM method, the tendency is concordant for these two methods. 3.2. A Longer Peptide: Ac−(AAQAA)3−NH2. Dipeptides and tripeptides, which were used to capture the intrinsic propensity for different minimums in the Ramachandran plot, are too short to form a helical structure. Hence, it is valuable to investigate a long system, such as Ac−(AAQAA)3−NH2, which is a peptide with a substantial helical population. Shalongo et al.50 measured the helical population of each residue in this peptide through NMR experiments. Best et al. studied the helical fraction of this peptide and compared with experiment among AMBER03, AMEBER03*, AMBER99SB, and AMBER99SB* force fields.23 They showed that the helical fraction was too high and too low relative to experiment under AMBER03 and AMBER99SB force fields, respectively. The simulated helical fraction in the current work, employing AMBER032D and AMBER99SB2D force fields with the polarization effect at 303 K, is shown in Figure 3a. Clearly, both AMBER032D and AMBER99SB2D force fields significantly improve the quality of original force fields and agree with the experimental estimate of fraction of helix more than its predecessors. The helical fraction estimated from the experiment is inferred by fitting a simple thermodynamic model, whereas the carbonyl carbon chemical shift can be directly measured in experiment and can serve as a better metric. NMR properties are calculated using the GIAO method51,52 within the Gaussian 09 package at the B3LYP/(6-311++G**/4-31G*) level, following Zhang et al.53 Water molecules hydrogenbonded with the dipeptides were included in the QM calculations, and the outer shell was taken as the polarizable continuum medium. A larger basis set, 6-311++G**, was used for water molecules, carbonyl carbon, and oxygen atoms, and 431G* for the rest. One hundred snapshots are extracted from each trajectory. The 13C isotropic shielding constant of tetramethylsilane (184.4618 ppm) computed at the same level is taken as the reference. The result is shown in Supporting Information Figure S3. It is indicated that the calculated chemical shifts are all overestimated. This result is consistent with the previous studies of Zhang et al.53 and Case et al.,54 in which they have found that the DFT-calculated chemical shift values differ systematically from the experimental results. However, neglecting the systematic error, the calculations for structures from AMBER99SB2D simulation are more consistent with the

19 the the the

Figure 2. Simulated 3J(HN, Hα) under AMBER03, AMBER032D, AMBER99SB, and AMBER99SB2D force fields as well as the experimental measurement. The RMSDs from the experimental values are also listed.

The χ2 contribution was also computed and compared with those from Pande et al., who had showed that the top performer was AMBER99sb-ildn-NMR plus TIP4P-EW for 3 J(HN, Hα) with a χ2 value of 2.15 Hz. The calculated χ2 values for AMBER032D and AMBER99SB2D force fields in this work are 3.45 and 2.49 Hz, respectively, which are close to that of Pande et al. Because the new 2D torsion parameters are fitted on the basis of the alanine dipeptide, the limited transferability among various amino acids may give rise to this deviation. Possible solutions to this difficulty are to average the main chain torsion energy over various residues or to calibrate specific parameters for each residue. Quantum mechanical calculation is a parameter-free and probably the most accurate way to calculate NMR properties, via which the conformational distribution can be examined. However, the computational expense of these calculations is very demanding. Therefore, three representative dipeptides (Ala, Gly, and Ser) were chosen for the calculations of the J coupling constants at the PW91PW9143,44/IGLO-III level,45 4190

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Figure 4. Comparison between the experimental and the calculated J couplings of ubiquitin under AMBER03 (black) and AMBER032D (red) force fields.

Figure 3. (a) The average fraction of helix per residue in Ac− (AAQAA)3−NH2 at 303 K calculated from the REMD simulations with AMBER032D (blue) and AMBER99SB2D (red) force fields compared with that estimated from the experiment (black lines). (b) Average carbonyl carbon chemical shifts calculated at B3LYP/(6-311+ +G**/4-31G∗) level compared with experimental shifts. The systematic deviations have been removed from the QM results. (c) Average carbonyl carbon chemical shifts calculated from simulations using SPARTA+ compared with the experimental shifts.

experiment. The mean unsigned errors (MUE) for AMBER032D and AMBER99SB2D are computed and are utilized to correct the calculated chemical shifts. The result shown in Figure 3b is after correction and indicates a good correlation with the experiment for both AMBER032D and AMBER99SB2D force fields. The carbonyl carbon chemical shifts were also calculated using SPARTA+, and the estimated error was ∼1 ppm. In Figure 3c, the predicted carbonyl chemical shifts from the simulations and those measured in the original experiments are compared, confirming the improvement brought by the 2D torsional force field. The standard error from predicted shifts is ∼1 ppm, which is within the systematical error. 3.3. Protein: Ubiquitin. Although the 2D torsional force fields are intended to improve the intrinsic conformational preferences, it is important to know that it does not adversely affect native protein stability or dynamics. To verify this, 50 ns simulations of ubiquitin, a well-characterized protein widely used in force field validations, were carried out in explicit water. No significant difference can be seen between the 2D force fields and their parents in examining RMSDs from the crystal structure, which is shown in Supporting Information Figure S2. J couplings, 3J(HN, Hα), 3J(Hα, C), 3J(HN, Cβ), and 3J(HN, C′), were computed and compared with experimental data. The correlation improves a little bit under AMBER032D and AMBER99SB2D force fields, indicating that the new torsional parametrization potential gives a better secondary structure distribution, as shown in Figures 4 and 5.

Figure 5. Comparison between the experimental and the calculated J couplings of ubiquitin under AMBER99SB (black) and AMBER99SB2D (red) force fields.

quantum chemical calculations in our previous work brings distinct improvements.25 In the present study, these 2D torsional force fields are further refined by implementing a better solvent model in the quantum chemical calculation of the potential energy surface. The improved accuracy of these force fields has been verified by the examination of the secondary structure distribution and NMR properties for several oligopeptides and ubiquitin utilizing the explicit solvent model. The results utilizing the implicit solvent model are shown in Figure S5 and Tables S2−S12 in the Supporting Information, which are in line with that utilizing the explicit solvent model. The balance in secondary structure population is essential for simulations of unfolded or disordered peptides and protein loops. Despite the overall improvement, the transferability of these force fields among various amino acids is still limited as a result of the coupling of various potential energy terms, which has also been pointed out by Pande et al.38 The electrostatic polarization effect during the secondary structure formation, which cannot be captured in the QM calculations of model dipeptides and therefore is missing in the torsion parameters, is important for the structural stabilization of long peptides and proteins.

4. CONCLUSION The quality of force fields is crucial for the success of molecular dynamics simulations. However, there indeed exist some distinct deficiencies in current traditional force fields, despite its widely successful applications. Refitting the torsional term with 2-dimensional Fourier expansions from high-level 4191

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(15) Rucker, A. L.; Pager, C. T.; Campbell, M. N.; Qualls, J. E.; Creamer, T. P. Host-Guest Scale of Left-Handed Polyproline II Helix Formation. Proteins: Struct. Funct. Genet. 2003, 53, 68−75. (16) Shi, Z. S.; Chen, K.; Liu, Z. G.; Ng, A.; Bracken, W. C.; Kallenbach, N. R. Polyproline II Propensities From GGXGG Peptides Reveal an Anticorrelation with Beta-Sheet Scales. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 17964−17968. (17) Chen, K.; Liu, Z. G.; Kallenbach, N. R. The Polyproline II Conformation in Short Alanine Peptides Is Noncooperative. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 15352−15357. (18) He, L.; Navarro, A. E.; Shi, Z.; Kallenbach, N. R. End Effects Influence Short Model Peptide Conformation. J. Am. Chem. Soc. 2012, 134, 1571−1576. (19) Toal, S.; Meral, D.; Verbaro, D.; Urbanc, B.; Schweiter-Stenner, R. PH-Independence of Trialanine and the Effects of Termini Blocking in Short Peptides: A Combined Vibrational, NMR, UVCD, and Molecular Dynamics Study. J. Phys. Chem. B 2013, 117, 3689−3706. (20) Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved Side-Chain Torsion Potentials for the Amber FF99SB Protein Force Field. Proteins 2010, 78, 1950− 1958. (21) Li, D.; Brüschweiler, R. NMR-Based Protein Potentials. Angew. Chem. Int. Ed. 2010, 49, 6778−6780. (22) Wang, Z.-X.; Zhang, W.; Zhang, W.; Wu, C.; Lei, H.; Cieplak, P.; Duan, P. Strike a Balance: Optimization of Backbone Torsion Parameters of AMBER Polarizable Force Field for Simulations of Proteins and Peptides. J. Comput. Chem. 2006, 27, 781−790. (23) Best, R. B.; Hummer, G. Optimized Molecular Dynamics Force Fields Applied to the Helix-Coil Transition of Polypeptides. J. Phys. Chem. B 2009, 113, 9004−9015. (24) Nerenberg, P. S.; Head-Gordon, T. Optimizing Protein−Solvent Force Fields To Reproduce Intrinsic Conformational Preferences of Model Peptides. J. Chem. Theory Comput. 2011, 7, 1220−1230. (25) Li, Y. X.; Gao, Y.; Zhang, X. Q.; Wang, X. Y.; Mou, L. R.; Duan, L. L.; He, X.; Mei, Y.; Zhang, J. Z. H. A Coupled Two-Dimensional Main Chain Torsional Potential for Protein Dynamics: Generation and Implementation. J. Mol. Model. 2013, 29, 3647−3657. (26) Garcia, A. E.; Sanbonmatsu, K. Y. α-Helical Stabilization by Side Chain Shielding of Backbone Hydrogen Bonds. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 2782−2787. (27) Kamiya, N.; Higo, J.; Nakamura, H. Conformational Transition States of a β-Hairpin Peptide between the Ordered and Disordered Conformations in Explicit Water. Protein Sci. 2002, 11, 2297−2307. (28) Higo, J.; Ito, N.; Kuroda, M.; Ono, S.; Nakajima, N.; Nakamura, H. Energy Landscape of a Peptide Consisting of α-Helix, 310-Helix, βTurn, β-Hairpin, and Other Disordered Conformations. Protein Sci. 2001, 10, 1160−1171. (29) Ono, S.; Nakajima, N.; Higo, J.; Nakamura, H. Peptide FreeEnergy Profile is Strongly Dependent on the Force Field: Comparison of C96 and AMBER95. J. Comput. Chem. 2000, 21, 748−762. (30) Wang, L.; Duan, Y.; Shortle, R.; Imperiali, B.; Kollman, P. A. Study of the Stability and Unfolding Mechanism of BBA1 by Molecular Dynamics Simulations at Different Temperatures. Protein Sci. 1999, 8, 1292−1304. (31) Duan, C.; Wu, Y.; Chowdhury, S.; Lee, M.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T. A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-Phase Quantum Mechanical Calculations. J. Comput. Chem. 2003, 24, 1999−2012. (32) Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.; Simmerling, C. Comparison of Multiple Amber Force Fields and Development of Improved Protein Backbone Parameters. Proteins 2006, 65, 712−725. (33) Lwin, T. Z.; Luo, R. Force Field Influences in β-Hairpin Folding Simulations. Protein Sci. 2006, 15, 2642−2655. (34) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric

ASSOCIATED CONTENT

S Supporting Information *

Simulation methods, the coupling value of each residue, and the secondary structure population.This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions #

Y.G. and Y.L. contributed equally to this work

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grants Nos. 10974054, 20933002, and 21173082) and the Shanghai PuJiang Program (09PJ1404000).

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REFERENCES

(1) Karplus, M.; McCammon, J. A. Molecular Dynamics Simulations of Biomolecules. Nat. Struct. Biol. 2002, 9, 646−652. (2) van Gunsteren, W. F.; Dolenc, J. Biomolecular Simulation: Historical Picture and Future Perspectives. Biochem. Soc. Trans. 2008, 36, 11−15. (3) Mackerell, A. D. Empirical Force Fields for Biological Macromolecules: Overview and Issues. J. Comput. Chem. 2004, 25, 1584−1604. (4) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 1995, 117, 5179−5197. (5) Jorgensen, W. L.; Maxwell, D. S.; TiradoRives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1995, 118, 11225−11236. (6) Buck, M.; Bouguet-Bonnet, S.; Pastor, R. W.; MacKerell, A. D. Importance of the CMAP Correction to the CHARMM22 Protein Force Field: Dynamics of Hen Lysozyme. Biophys. J. 2006, 90, L36− L38. (7) Shirts, M. R.; Pande, V. S. Solvation Free Energies of Amino Acid Side Chain Analogs for Common Molecular Mechanics Water Models. J. Chem. Phys. 2005, 122, 134508. (8) Deng, Y.; Roux, B. Computations of Standard Binding Free Energies with Molecular Dynamics Simulations. J. Phys. Chem. B 2009, 113, 2234−2246. (9) Chen, J. Z.; Liang, Z. Q.; Wang, W.; Yi, C. H.; Zhang, S. L.; Zhang, Q. G. Revealing Origin of Decrease in Potency of Darunavir and Amprenavir Against HIV-2 Relative to HIV-1 Protease by Molecular Dynamics Simulations. Sci. Rep. 2014, 4, 6872. (10) Fink, A. L. Natively Unfolded Proteins. Curr. Opin. Struct. Biol. 2005, 15, 35−41. (11) Bracken, C.; Iakoucheva, L. M.; Rorner, P. R.; Dunker, A. K. Combining Prediction, Computation and Experiment for the Characterization of Protein Disorder. Curr. Opin. Struct. Biol. 2004, 14, 570−576. (12) Yeh, I. C.; Hummer, G. Peptide Loop-Closure Kinetics from Microsecond Molecular Dynamics Simulations in Explicit Solvent. J. Am. Chem. Soc. 2002, 124, 6563−6568. (13) Best, R. B.; Buchete, N. V.; Hummer, G. Are Current Molecular Dynamics Force Fields too Helical? Biophys. J. 2008, 95, L07−L09. (14) Liu, Z. G.; Chen, K.; Ng, A.; Shi, Z. S.; Woody, R. W.; Kallenbach, N. R. Solvent Dependence of PII Conformation in Model Alanine Peptides. J. Am. Chem. Soc. 2004, 126, 15141−15150. 4192

DOI: 10.1021/jp510215c J. Phys. Chem. B 2015, 119, 4188−4193

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The Journal of Physical Chemistry B Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378−6396. (35) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Performance of SM6, SM8, and SMD on the SAMPL1 Test Set for the Prediction of Small-Molecule Solvation Free Energies. J. Phys. Chem. B 2009, 113, 4538−4543. (36) Hagarman, A.; Measey, T. J.; Mathieu, D.; Schwalbe, H.; Schweitzer-Stenner, R. Intrinsic Propensities of Amino Acid Residues in GxG Peptides Inferred from Amide I′ Band Profiles and NMR Scalar Coupling Constants. J. Am. Chem. Soc. 2010, 132, 540−551. (37) Graf, J.; Nguyen, P. H.; Stock, G.; Schwalbe, H. Structure and Dynamics of the Homologous Series of Alanine Peptides: A Joint Molecular Dynamics/NMR Study. J. Am. Chem. Soc. 2007, 129, 1179− 1189. (38) Beauchamp, K. A.; Lin, Y. S.; Das, R.; Pande, V. S. Are Protein Force Fields Getting Better? A Systematic Benchmark on 524 Diverse NMR Measurements. J. Chem. Theory Comput. 2012, 8, 1409−1414. (39) Hu, J. S.; Bax, A. Determination of ϕ and χ1 Angles in Proteins from 13C−13C Three-Bond J Couplings Measured by Three-Dimensional Heteronuclear NMR. How Planar Is the Peptide Bond? J. Am. Chem. Soc. 1997, 119, 6360−6368. (40) Wickstrom, L.; Okur, A.; Simmerling, C. Evaluating the Performance of the FF99SB Force Field Based on NMR Scalar Coupling Data. Biophys. J. 2009, 97, 853−856. (41) Grdadolnik, J.; Mohacek-Grosev, V.; Baldwin, R.; Avbelj, F. Populations of the Three Major Backbone Conformations in 19 Amino Acid Dipeptides. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 1794− 1798. (42) Cerutti, D. S.; Swope, W. C.; Rice, J. E.; Case, D. A. FF14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins. J. Chem. Theory Comput. 2014, 10, 4515−4534. (43) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822−8824. (44) Perdew, J. P.; Yue, W. Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation. Phys. Rev. B 1986, 33, 8800−8802. (45) Kutzelnigg, W.; Fleischer, U.; Schindler, M. Deuterium and Shift Calculation; NMR Basic Principles and Progress. Springer: Berlin, Heidelberg, 1991; Vol. 23; pp 165−262. (46) Case, D. A.; Scheurer, C.; Brüschweiler, R. Static and Dynamic Effects on Vicinal Scalar J Coupling in Proteins and Pepetides: A MD/ DFT Analysis. J. Am. Chem. Soc. 2000, 122, 10390−10397. (47) Wang, B.; He, X.; Merz, K. M. Quantum Mechanical Study of Vicinal J Spin−Spin Coupling Constants for the Protein Backbone. J. Chem. Theory Comput. 2013, 9, 4653−4659. (48) Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G. A. et al. Gaussian 09, Revision B.01; Gaussian,Inc.: Wallingford, CT, 2009. (49) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3094. (50) Shalongo, W.; Dugad, L.; Stellwagen, E. Distribution of Helicity within the Model Peptide Acetyl (AAQAA)3amide. J. Am. Chem. Soc. 1994, 116, 8288−8293. (51) Wolinski, K.; Hinton, J. F.; Pulay, P. Efficient Implementation of the Gauge-Independent Atomic Orbital Method for NMR Chemical Shift Calculations. J. Am. Chem. Soc. 1990, 112, 8251−8260. (52) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. A Comparison of Models for Calculating Nuclear Magnetic Resonance Shielding Tensors. J. Chem. Phys. 1996, 104, 5497−5510. (53) Zhu, T.; He, X.; Zhang, J. Z. H. Fragment Density Functional Theory Calculation of NMR Chemical Shifts for Proteins with Implicit Solvation. Phys. Chem. Chem. Phys. 2012, 14, 7837−7845. (54) Moon, S.; Case, D. A. A Comparison of Quantum Chemical Models for Calculating NMR Shielding Parameters in Peptides: Mixed Basis Set and ONIOM Methods Combined with a Complete Basis Set Extrapolation. J. Comput. Chem. 2005, 27, 825−836.

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DOI: 10.1021/jp510215c J. Phys. Chem. B 2015, 119, 4188−4193