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Significantly Improved Protein Folding Thermodynamics Using a Dispersion-Corrected Water Model and a New Residue-Specific Force Field Hao-Nan Wu, Fan Jiang, and Yun-Dong Wu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01213 • Publication Date (Web): 26 Jun 2017 Downloaded from http://pubs.acs.org on June 28, 2017

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The Journal of Physical Chemistry Letters

Significantly Improved Protein Folding Thermodynamics Using a Dispersion-Corrected Water Model and a New Residue-Specific Force Field

Hao-Nan Wu,† Fan Jiang,*,† and Yun-Dong Wu†,‡

†Laboratory of Computational Chemistry and Drug Design, Laboratory of Chemical Genomics, Peking University Shenzhen Graduate School, Shenzhen, 518055, China ‡College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, China *

To whom correspondence should be addressed.

1

ACS Paragon Plus Environment


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ABSTRACT: An accurate potential energy model is crucial for biomolecular simulations. Despite many recent improvements of classical protein force fields, there are remaining key issues: much weaker temperature-dependence of folding/unfolding equilibrium, and overly collapsed unfolded or disordered states. For the later problem, a new water model (TIP4P-D) has been proposed to correct the signiﬁcantly underestimated water dispersion interactions. Here, using TIP4P-D, we reveal problems in current force fields through failures in folding model systems (a polyalanine peptide, Trp-cage and the GB1 hairpin). By using residue-specific parameters to achieve better match between amino acid sequences and native structures, and adding a small H-bond correction for partially compensating the missing many-body effects in α-helix formation, the new RSFF2+ force field with the TIP4P-D water model can excellently reproduce experimental melting curves of both α-helical and β-hairpin systems. The RSFF2+/TIP4P-D method also gives less collapsed unfolded structures and well describes folded proteins simultaneously.

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With the rapid growth of computing power, molecular dynamics (MD) simulation has become increasingly popular for studying biomolecular systems,1–3 and its successful applications rely more on the quality of underlying physical models.4,5 Recently there have been many developments of classical (pairwise additive with fixed charges) protein force fields, especially the optimizations of backbone and/or side-chain torsional terms, to achieve more accurate conformational preferences.6–13 On the other hand, developments of additive water models are somewhat limited,14,15 although water molecules play essential role in dictating biologically relevant conformational behaviors of peptides and proteins.16,17 Indeed, MD simulations using state-of-the-art force fields coupled with the thirty-year-old TIP3P18 water model have proved to be quite accurate in modelling well-folded proteins or folding small proteins spontaneously.19–22 However, currently physical models cannot simultaneously give accurate reproductions of folding midpoint temperatures (Tm) and folding enthalpies (∆Hf), with absolute value of the later often significantly underestimated (i.e. much weaker temperature-dependence of the folded population).6,8,23,24 In fact, correctly describing the thermodynamic equilibrium between the folded and the unfolded states is quite difficult and become a stringent test of a force field.20 Besides, the simulations of unfolded or intrinsically disordered peptides/proteins (IDPs) have captured increasingly attentions.25–28 However, most popular force fields have been recently found to give overly collapsed disordered structures, indicating overestimated solute-solute and intra-protein interactions.5,29–31 In the recent few years, several solutions were proposed to address this problem.32–36 Piana et al.34 found that this 3



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problem may come from the severe underestimation of short-range dispersion interactions in popular water models, which is supported by high-level quantum mechanics (QM) calculations. By increasing the dispersion coefficient (C6) by ~50%, the new TIP4P-D water model produces larger radius of gyration (Rg) for disordered systems, in much better agreement with experiments.33,34,37 TIP4P-D can also stabilize the experimental structures of well-folded proteins for microseconds in MD simulations.34 However, in reversible folding simulations of small proteins, the TIP4P-D water model cannot provide enough stabilization of the native state against the unfolded state.34 Here we first investigated the ability of different force fields with the TIP4P-D water to fold a polyalanine-based α-helical peptide (A14), and two most popular folding models: the α-helical miniprotein Trp-cage38 and the GB1 β-hairpin.39 We found that, when using the TIP4P-D water, two popular force fields (OPLS-AA/L,40 AMBER-ff99SB-ildn7) and the newest CHARMM36m11 force field cannot fold these three systems, except for the GB1 hairpin with OPLS-AA/L. To rule out the possibility of inadequate conformational sampling, we carried out replica-exchange molecular dynamics (REMD)41 simulations initiated from the fully folded structures. As shown in Figure 1, when using either the AMBER or CHARMM force fields, the helicity of A14, and the folded populations of Trp-cage and the GB1 hairpin at 300K decreased rapidly to near zero (< 1.3%) during the simulations, whereas the corresponding experimental values should be >20%. Similarly, the OPLS-AA/L force field significantly underestimates the α-helicity of A14, and unfolds Trp-cage rapidly. Also, in the representative structures from all the simulations

4


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except the OPLS-AA/L simulation of the GB1 hairpin, we did not observe any α-helix/β-sheet structure or any hydrophobic core formation.

Figure 1. Time evolutions of folded populations of (A) Ace-Ala14-NHMe (A14), (B) Trp-cage and (C) the GB1 hairpin from REMD simulations (300 K replica) using different force fields with the TIP4P-D water model. The horizontal gray lines indicate corresponding experimental data. Three different folded fractions of the GB1 hairpin were reported by different experimental groups.39,42,43 The fully folded structure of each system was given in the left. In each plot, the time window for clustering analysis is given in grey shadow, and the obtained representative structure of the largest cluster was also given.

Noticeably, popular force fields actually can perform quite well with the TIP3P water model. For example, AMBER-ff99SB12 can excellently reproduce the folded populations (at

300K)

of

both

the

GB1

β-hairpin

and

the

Trp-cage

5


miniprotein.44,45


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CHARMM36m/mTIP3P can reproduce experimental α-helicity of the polyalanine-based peptide Ac-(AAQAA)3-NH2 and the folded population of the GB1 hairpin very well.11 We argue that this is possibly due to the error cancelation between protein force fields and water models. Water models like TIP3P give overly compact unfolded state, which may underestimate its conformational entropy and relatively over-stabilize the folded state. Thus, protein force field itself might not give enough stabilization of the native structures, and this problem was exposed by using the new TIP4P-D water model. Our previous works have indicated that the intrinsic conformational distributions of 20 amino acid residues obtained from statistical analysis of coil regions in protein crystal structures (PDB database) cannot be well reproduced by some popular force fields in simulations of dipeptides (terminally blocked amino acids).46,47 Thus, the match between sequence and structure may be sub-optimal using these force fields. We then improved the

backbone

and

side-chain

torsional

parameters

of

the

OPLS-AA/L

and

AMBER-ff99SB force fields using the PDB statistical distributions, resulting two residue-specific force fields: RSFF148 and RSFF2,49 respectively. In RSFFs, different torsional parameters were used for different amino acids, to better describe their different conformational preferences. RSFFs can give J-coupling of short peptides in much better agreement with NMR experiments,50 consistently fold a diverse set of small proteins to near experimental structures,51,52 and accurately reproduce the crystal structures of cyclic peptides.53 Motivated by our previous observations that RSFFs overestimate the stability of the folded state with the TIP3P or the TIP4P-Ew water model,51 we studied the possibility of 6


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successful folding using RSFFs with the TIP4P-D water model. First, there is no need to re-parameterize the RSFF force fields for the new water model (see SI for details). From REMD simulations of dipeptides, the similarity coefficients (S) between the ϕ, ψ plots from the original and the new water models are > 0.99 for nearly all cases (Figure S1 and S2, Table S2). Then, in REMD simulations initiated from fully unfolded structures, both Trp-cage and the GB1 hairpin, as well as another popular β-hairpin model Trpzip-2,54 can be well folded using the RSFFs/TIP4P-D combinations (Figure 2 A-C). Interestingly, using the same force field, different water models yield very similar (backbone RMSD < 1 Å) representative structures of the most populated cluster. Also, with TIP4P-D, the RSFF1 and RSFF2 force fields give quite similar structures (RMSD of 1.8 Å, 0.3 Å, 1.2 Å for Trp-cage, Trpzip-2 and the GB1 hairpin). These results imply high accuracy of the predicted native structures using these new methods.

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Figure 2. The representative structures of (A) Trp-cage, (B) Trpzip-2, and (C) the GB1 hairpin, from REMD folding simulations (300 K replica) using the RSFF1 (R1) and the RSFF2 (R2) force fields with different water models (T3P for TIP3P, T4P for TIP4P), superimposed on corresponding experimental structures. Backbone root-mean-square deviations (RMSDs) among all structures of each system are also given. (D) The calculated melting curves of Ac-Ala14-NHMe and the above three systems, compared with corresponding experimental data. The coloring for each method is consistent in all plots.

Encouraged by these results, we continued each REMD simulation to achieve folding-unfolding equilibrium, and obtained the folded populations as a function of temperature (i.e. the melting curve). As expected, for all systems at all temperatures, TIP4P-D gives lower population of the folded states compared with TIP3P and TIP4P-Ew (Figure 2D). Despite the very similar folded structures, the difference of folding free energies (∆Gf) between the TIP3P and TIP4P-D simulations can be >10 kJ/mol for Trp-cage (Table S3 and Figure S3). For both RSFF1 and RSFF2, better results for the two β-hairpins were obtained when TIP4P-D was used instead of TIP3P and TIP4P-Ew. Especially, RSFF2/TIP4P-D gave melting curves of Trpzip-2 and the GB1 hairpin in good agreement with experiments. In addition, the significant over-stabilization of the folded state of A14 and Trp-cage by RSFF1/TIP4P-Ew is no longer observed. Interestingly, the combination of RSFF2/TIP4P-D turned out to significantly underestimate the stabilities of the two α-helical systems. 8


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However, there is no evidence to support that RSFF2 disfavors α-helical (αR) conformation at single-residue level. Indeed, RSFF2 gives αR population of 19% for alanine dipeptide (insensitive to the water model),49 which is not less than 9% - 18% from experiments.55,56 Also, RSFF2/TIP4P-D can excellently reproduce experimental NMR J-couplings in the 19 dipeptides (Figure S4). Therefore, we speculate that the underestimation of α-helicity by RSFF2/TIP4P-D may relate to a fundamental approximation of all classic force fields: the lack of electronic degrees of freedom. Previous QM calculations of ours and others strongly support that the cooperativity (many-body effects) from long-range electrostatics and polarization uniquely stabilizes α-helical structures, which cannot be fully captured by classic force fields.57–59 Also, electrostatic polarization has been shown to aid the folding of an α-helical peptide.60,61 To test this hypothesis, we employed a simple correction to further stabilize α-helical H-bonds. As shown in Figure 3A, an additional Lennard-Jones (L-J) potential was added between backbone Oi and Hi+4 atoms indiscriminatingly for each residue i (if possible), regardless of its native structure. We deliberately set the distance parameter σ of the L-J potential (1.5 Å) to be smaller than usual H-bond length (~2.0 Å), such that it can give slightly shorter Oi…Hi+4 H-bonds in α-helix, as observed in previous QM calculations.62 With σ set to 1.5 Å beforehand, we only used the α-helical polyalanine peptide A14 to optimize the energy-well-depth parameter ε, and eventually found ε = 1.3 kJ/mol to be a near-optimal value (Figure 3B, Figure S5). Surprisingly, with this small energy correction of ~0.8 kJ/mol at ~2.0 Å for each α-helical H-bond, the melting curve of A14 can be excellently reproduced by this helix-corrected RSFF2 (RSFF2+ in short) force field when 9



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simulated with the TIP4P-D water. Subsequently, this new force field was assessed using a test set of another α-helical peptide Ac-(AAQAA)3-NH2 (AQ15),63 along with Trp-cage, Trpzip-2 and the GB1 hairpin (Figure 3C). The RSFF2+ force field reproduces the experimental melting curve of AQ15 very well. Compared with the original RSFF2 force field, the RSFF2+/TIP4P-D simulations also yield very similar folded structures for all three proteins, while the folded populations of α-helical Trp-cage were significantly increased and those of the two β-hairpins (Trpzip-2 and the GB1 hairpin) were only slightly decreased. Now, experimental melting curves of AQ15, Trp-cage, Trpzip-2, and the GB1 hairpin can be very well reproduced simultaneously.

Figure 3. The parameterization and evaluation of the RSFF2+ force field. (A) Adding extra Lennard-Jones potentials to all backbone Oi…Hi+4 atom pairs. (B) The melting curves of Ac-Ala14-NHMe (A14) using RSFF2/TIP4P-D with different ε parameters of the addition L-J potential. ε = 1.3 kJ/mol is finally chosen for the new RSFF2+ force field. (C) Simulated structures and melting curves of α- and β- peptides (as a test set) using RSFF2/TIP4P-D and RSFF2+/TIP4P-D, compared with the corresponding experimental 10


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data. For Trp-cage, up triangles and down triangles are from REMD simulations initiated from unfolded and folded structures, respectively.

As far as we know, it is the first time for an all-atom simulation to reproduce experimental melting curve of an α-helical system at full temperature range. Previously, a force field can be optimized to reproduce experimental α-helicity near 300K, but the obtained temperature dependence was always much weaker.64 The much flatter melting curves from previous simulations indicate insufficient folding enthalpies (∆Hf). As shown in Table 1, all previous AMBER, CHARMM, OPLS force fields give |∆Hf| of AQ15 and Trp-cage much smaller than experimental values. Some force fields also underestimate the |∆Hf| values of the two β-hairpins. On the other hand, our RSFF2+/TIP4P-D simulations can reproduce the experimental Tm and ∆Hf of AQ15, Trp-cage, and Trpzip-2 simultaneously. As the melting curves of the GB1 hairpin from different labs show significant differences, the experimental Tm and ∆HF of the GB1 hairpin are fitted from each of them. Using RSFF2+/TIP4P-D, both Tm and ∆Hf of the GB1 hairpin are in good agreement with certain experimental measurements,43 and slightly underestimated compared with the earliest experiments.39 We want to emphasize that the melting curve can be very sensitive to small energy change at residue level (Figure 3B), and any force field is certainly an approximation of the true potential energy surface. Thus, we cannot expect all experimental melting curves to be perfectly reproduced.

Table 1. Folding Thermodynamics Dataa of the Four Model Systems from Experiments 11



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and Simulations Using Different Force Fields and Water Models ff99SB-ild n6,24,49

Expt.

ff03*6,23

ff03ws32

C22*8,48

C3665

OPLS48

R2

R2

R2+

T3P

T4P-05

T3P

T3P

T4P-Ew

T3P

T4P-D

T4P-D

T3P Tm

273

--

229

233

233b

270

--

228

--

277

∆Hf

-36

--

-11

-14

-12b

-17

--

-9

--

-36

Tm

314

321c

366

317

--

n/a

--

355

--

313

∆Hf

-54

-28c

-32

-19

--

n/a

--

-64

--

-53

Tm

344

312

n/a

n/a

381

n/a

365

384

357

344

∆Hf

-59

-40

n/a

n/a

-65

n/a

-44

-69

-64

-55

AQ15

Trp-cage

Trpzip-2

Tm

29739,29042,26943

275

316

--

302

286

294

380

287

276

∆Hf

-4839, -4842, -2943

-22

-24

--

-30

-20

-32

-53

-23

-31

GB1 hairpin

a

Folding mid-point temperatures (Tm, K) and folding enthalpies (∆Hf, kJ/mol), fitted from

melting curves obtained in this work (for RSFF2 and RSFF2+) and previously reported (for other cases). C22*, C36, OPLS, R2 are short for CHARMM22*, CHARMM36, OPLS-AA/L, RSFF2, respectively. ‘--’ indicates that the folded populations are too small to provide meaningful Tm, and ‘n/a’ indicates no data available from literature. The values in good agreement with experiments are underlined. bThe charmm-modified TIP3P water model was used. cFrom Garcia and coworkers, the ff99SB force field was used instead.

Previous large-scale folding simulations using the CHARMM22*/mTIP3P66 and RSFF1/TIP4P-Ew51 methods produced overly collapsed unfolded structures with average Rg close to the folded state, which has been argued to be an artifact of inaccurate physical models. Similar phenomenon was observed here in the simulations using RSFF2/TIP3P and RSFF2/TIP4P-Ew (Figure 4). On the contrary, both the RSFF2/TIP4P-D and 12


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RSFF2+/TIP4P-D methods can sample more extended unfolded structures (larger Rg), although quite different fractions of the unfolded state (RMSD > 3Å) were obtained. Besides, using TIP4P-D, the RSFF2 and RSFF2+ force fields give very similar Rg values on two tested IDPs (GS10 and HIV-1 Rev), which are also significantly larger than those from the RSFF2/TIP3P simulations (Figure S6). We further simulated two other model IDPs: histatin 5 and the RS peptide, which were well studied by SAXS experiment. Using RSFF2+/TIP4P-D, their Rg values and SAXS curves were both well reproduced (Table S4, Figure S7). For HIV-1 Rev, TIP4P-D gives 3JHNHα values better than TIP3P, further supporting the advantage of using the new water model for IDPs (Figure S8). It is not surprising that the TIP4P-D water model has been found to produce conformational ensemble of intrinsically disordered peptides and proteins better than commonly used water models.33,34,37 More importantly, however, the RSFF force fields can give both enough stability of folded structures and reasonable Rg for unfolded structures simultaneously, which is conducive to achieve better balance between different states of protein structures. Understandably, when studying only the IDPs, this small (< 1 kJ/mol per H-bond) α-helix correction on RSFF2 may not have large effect. Besides, RSFF2+/TIP4P-D can also well maintain the native structures of well-folded proteins and well reproduce their dynamics (N-H order parameters) from NMR experiments, similar to the RSFF2/TIP3P and RSFF2/TIP4P-D methods (Figure S9).

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Figure 4. Free energy surfaces (∆G in RT unit) as a function of the backbone RMSD to corresponding folded structures and the radius of gyration (Rg), from REMD simulations (300 K replica) of (A) Trp-cage, (B)Trpzip-2 and (C) the GB1 hairpin using various combinations of force fields and water models.

Many protein systems contain both structured and intrinsically disordered regions, which can be both functionally important.67 Although all-atom force fields that can well describe the well-folded state and the unfolded/disordered state of peptides and proteins have been developed separately, a model that can work well for both is still an unsolved challenge and in urgent need.11 The study presented here implies that some previous successes of all-atom simulations might rely on the cancellation of errors in the solute force field and the water model. Thus, developing new water models might also be important, together with the optimizations of solute force fields. Also, our study suggests that some crucial effects of electronic polarization can be incorporated into a classical force field by using special non-bonded interactions beyond the simple combinational 14


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rule. This new RSFF2+/TIP4P-D method, as a proof-of-concept, may suggest further improvements of current additive biomolecular force fields.

ASSOCIATED CONTENT

Supporting information This material is available free of charge on the ACS Publications website at DOI:10.1021/acs.jpclett.xxxxxxx. A brief description of the residue-specific force fields and the detailed methods for the simulations (Table S1) and trajectory analyses; the local conformational preference of dipeptides REMD simulations (Table S2, Figure S1-S2); the folding free energy from experiments and simulations (Table S3, Figure S3); the 3JHNHα couplings of dipeptides from REMD simulations (Figure S4); the preliminary parameter optimization of RSFF2+ force field (Figure S5); and the performance of RSFF2+ for IDPs and well-folded proteins (Table S4, Figure S6-S9). (PDF) Files for implementing the RSFF2+ force field in Gromacs. (ZIP)

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] (F.J.)

Notes The authors declare no competing financial interest.

ACKNOWLEGEMENT 15



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We thank the financial supports from the National Natural Science Foundation of China (Grant No. 21573009). We also thank the Shenzhen Science and Technology Innovation Committee (JCYJ20170249) and Guangdong province (the Leading Talents Introduction Special Funds).

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