Refined Parameterization of Nonbonded Interactions Improves

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Letter

Refined Parameterization of Non-Bonded Interactions Improves Conformational Sampling and Kinetics of Protein Folding Simulations Jejoong Yoo, and Aleksei Aksimentiev J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01747 • Publication Date (Web): 12 Sep 2016 Downloaded from http://pubs.acs.org on September 14, 2016

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The Journal of Physical Chemistry Letters

Refined Parameterization of Non-Bonded Interactions Improves Conformational Sampling and Kinetics of Protein Folding Simulations Jejoong Yoo and Aleksei Aksimentiev∗ Center for the Physics of Living Cells, Department of Physics, University of Illinois at Urbana–Champaign, 1110 West Green Street, Urbana, Illinois 61801 E-mail: [email protected]

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Keywords Molecular dynamics; protein folding; intrinsically disordered proteins; WW domain; villin head piece; force field

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Prediction of the native, folded structure of a protein starting from the protein’s amino acid sequence has been the central problem of computational biophysics. 1–3 The typical timescale of a protein folding process (milliseconds to seconds) and the intrinsic sensitivity of the folding process to atomic level details present formidable challenges to the structure prediction efforts. Nevertheless, a number of computational approaches have been successful in predicting the structure of small water-soluble proteins, including statistical mechanics models, 4,5 implicit 6 and explicit 2 solvent molecular dynamics (MD) simulations, and distributed computing, 7 culminating in successful brute-force folding of several model proteins using special purpose supercomputer hardware. 8,9 The advent of explicit solvent brute-force protein folding simulations has put the physicsbased models of proteins—the molecular force fields—to a rigorous test. 10–13 One of the common deficiencies of the force field models that emerged from protein folding simulations is the abundance of compact protein conformations in the denatured state ensemble. 13 The results of hydrogen-exchange experiments 14 strongly suggest that such collapsed denatured conformations are caused by the imperfections of the molecular fields. Such artifacts are not limited to a particular force field variant and are common to most protein force fields. 9,10,13 Although the artificial aggregation problem clearly originates from the solute–solute interactions being artificially stronger than the solute–water interactions, a general solution to the problem is yet to be found.

Potential solutions include optimization of the water

model to increase solute–water affinity, 15–17 reparameterization of partial charges of the protein side chains, 10 or development of polarizable force fields. 18,19 However, modification of a water model or adjustment of side chain charges affect a large number of non-bonded interactions and can have detrimental side effects. For example, increasing solute–water affinity can destabilize the native structure of a protein. 15,16 Although a polarizable force field could be an ultimate solution to the problem, the suitability of presently available polarizable force fiels for protein folding simulations have not been fully validated yet. 20 Here, we show that the realism of protein folding simulations can be improved by in-

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bonded interactions is accurate enough to describe non-bonded interactions between polar backbone atoms. 27 Prompted by the previous studies that reported significant overestimation of hydrophobic interactions within ff99 and ff03 force field variants, 15,30 we refined pairspecific LJ parameters describing such interactions. To optimize pair-specific LJ parameters defining the strength of hydrophobic interactions, we simulated 1 M solution of N-acetyl-leucine-methyl-amide (NALMA); Figure 1 A shows the chemical structure of NALMA. Supporting Information Methods SM1–SM3 provide a complete description of the simulation setup. Similar to previous studies, 15,30 NALMA molecules were found to aggregate when simulated using the standard ff99 and CHARMM22* models, Figure 1 B,C, which is inconsistent with the X-ray scattering data suggesting that NALMA molecules remain soluble at such concentration, see Figure S1. 31 Specifically, the radial distribution function (RDF) of the inter-solute carbon–carbon pairs shows a prominent peak at the carbon–carbon distance of ∼5 ˚ A, purple curve in Figure 1 B. Because inter-solute interactions in the NALMA solution are dominated by aliphatic carbon atoms described by the CT type in the ff99 models, Figure 1 A, we could alter the overall strength of NALMA–NALMA interactions by changing the LJ σ parameter describing the interaction of the CT–CT pair. Whereas increasing σ did not lead to any improvements, decreasing σ alleviated artificial aggregation, Figure 1 B,D. Setting ∆σ to −0.4 ˚ A produced RDF curves that reasonably matched the results obtained using the AMOEBA polarizable force field 30 or the ff99sb force field used in combination with the optimized solute–water LJ parameters. 15 Hereinafter, we refer to the combination of the ff99sb-ildn-phi model with our pair-specific LJ parameters for amine nitrogen–carboxylate oxygen 26–29 and aliphatic carbon–carbon pairs as ff99sb-ildn-phi-CUFIX, or ff99cufix for brevity. Gromacs formatted ff99cufix parameters are available at http://bionano.physics.illinois.edu/CUFIX. To elucidate the effect of non-bonded corrections on protein folding simulations, we performed explicit solvent replica-exchange MD (REMD) simulations 34,35 of the WW domain and the villin head piece (HP35) using the ff99cufix, ff99, and ff03ws 16 models and the Gro-

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were 0.02 and 12 ˚ A, respectively. Figures 2 C,E and G illustrate the progress of REMD simulations performed using different force field models by quantifying the abundance of microscopic states in the 297 K replica characterized by the given range of Q values as a function of simulation time. For the ff99cufix model, the ensemble of conformations gradually changes from being dominated by the unfolded states (Q < 0.1) to being predominately populated by the folded conformations (Q > 0.9), with the first fully folded conformation (Q = 0.95) appearing 0.5 µs after the beginning of the REMD simulation, Figure 2 C. For the ff99 model, the folding proceeds considerably slower, with the first completely folded conformations appearing after 1.6 µs, Figure 2 E. Similar conclusions can be reached by analyzing the progress of REMD folding simulations using RMSD as the reaction coordinate, Figures S2 A,C, or examining the change of the β-sheet content over time, Figures S3 A,B. 50 For the ff03ws model, which has increased solute–water affinity for all solute atoms in comparison to the ff99 model, 16 we failed to observe any progress in the folding simulation within 1.3 µs, Figure 2 G, suggesting that destabilization of backbone hydrogen bonds due to water reparameterization was detrimental to the formation of long-ranged β-sheet structures, Figure S3 C. Statistical analysis of the microscopic conformations observed within the last 0.5 µs of the respective REMD trajectories yielded the free energy landscape of the WW domain as a function of Q, Figure 2 D,F,H, or RMSD, Supporting Information Figures S2 B,D,F. For ff99cufix, the folded conformations (Q = 0.95 and RMSD = 1.0 ˚ A), Figure 2 B, correspond to the global minimum with ∆G = −4 kcal/mol at 297 K, Figure 2 D. The free energy gradually decreases as Q increases from 0 to 1, passing through several local barriers (< 1 kcal/mol), which is consistent with the downhill folding mechanism of the WW domain suggested by experiment. 32,42 The free energy landscape also exhibits the expected dependence on temperature: the stability of the folded state decreases as the temperature increases, Figure 2 D and Figure S2 B. For the ff99 model, the folded conformation (Q = 0.95 and RMSD = 1.8 ˚ A) is hardly at the global free energy minimum at room temperature, Figure 2 F and Figure S2 D.

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ensemble explored by the system in the ff99cufix simulation at 297 K is scattered over the range of Q values, except for the accumulation at the native conformation, Figure 3 C. Conversely, the ensemble of conformations in the ff99 simulation is clustered near Q = 0.7, possibly due to artificial collapse of the protein conformations, 14 Figure 3 E. The free energy landscapes obtained from the analysis of the last 0.5 µs of the respective REMD trajectories quantify the improvements brought about by the ff99cufix model with respect to the ff99 one, Figure 3 D,F and Figure S4 B,D. For ff99cufix, the free energy landscape is smooth over the range of the reaction coordinate, with barriers as low as 0.5 kcal/mol at Q = 0.75, Figure 3 D, consistent with the experimentally estimated barrier of less than 1 kcal/mol. 38 For ff99, the energy landscape has a significant energy minimum near Q = 0.7 and RMSD = 3.5 ˚ A with the energy barrier of 1.5 kcal/mol, Figure 3 F and Figure S4 D. Secondary structure analysis performed using the database of secondary structure assignments (DSSP) indicates a slightly higher α-helical contents in the ff99 simulation compared to that of the ff99cufix one, Figure S5, likely because of the high population of Q = 0.7 conformations in the former model. To quantify the effects of the CUFIX corrections on the radius of gyration, Rg , of the simulated proteins, we analyzed our REMD simulations by computing the two-dimensional (2D) free energy landscapes using Q and Rg as independent reaction coordinates, Figure 4. For both WW domain and HP35, the 2D landscapes show significant populations of conformations characterized by Rg > 10 ˚ A at Q < 0.5 in the ff99cufix simulations, Figure 4 A,C, whereas Rg < 10 ˚ A over the entire range of Q for the ff99 simulations, Figure 4 B,D. For WW domain, the CUFIX corrections increased the denatured populations (Q < 0.5) at Rg > 10 ˚ A from 5 to 25% at 300 K and from 8 to 30% at 360 K; for HP35, the increase was from 5 to 35% at 300 K and from 14 to 49% at 360 K. These results suggest that our surgical corrections to non-bonded interactions effectively alleviate the over-representation of collapsed unfolded conformations seen for the standard force field models 14 without affecting stability of the native conformation. Previously, the occurrence of collapsed unfolded

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which the hairpin structures form. Thus, 4 out 5 folding events observed in the ff99cufix simulations proceeded via the second-hairpin-first folding pathway. In the ff99 simulation, the two folding pathways were equally probable (2 out of 4 for each). For HP35, folding of the second and third helices occurred before the folding of the first helix in most simulations (11 out of 12 for ff99cufix and 12 out of 15 for ff99), consistent with the previous MD study. 10

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Figure 5: Brownian dynamics (BD) analysis of WW and HP35 folding. (A) Position-dependent diffusion coefficient D(Q) of the WW domain computed using fragments of the REMD trajectories. (B) The distribution of the WW domain folding times computed using the BD approach. 51 (C,D) Same as in panels A and B, respectively, but for the HP35 folding. Calculations of D(Q) from REMD trajectories and BD procedures are described in Supporting Information Methods SM7 and SM8, respectively.

To quantify the effects of the CUFIX corrections on folding kinetics, we computed position-dependent diffusion coefficients along Q, D(Q), and folding times using the Brownian dynamics (BD) method, 51 Figure 5A,C. For both WW domain and HP35, the positiondependent diffusion coefficients, D(Q), at Q < 0.6 are about 2-fold higher for ff99cufix in comparison to ff99, Figure 5 A,C, suggesting that excessive non-bonded contacts in the ff99 simulations retard the overall folding-unfolding kinetics. Using D(Q) and the free energy landscapes, Figure 2 D,F and Figure 3 D,F, we performed BD simulations of the protein folding. 51,52 The histograms of the folding times show about a 2-fold increase of the folding rates for ff99cufix in comparison to ff99 for both WW domain and HP35, Figure 5 B,D. Due to over-simplification of the BD approach, direct quantitative comparison with the experimen-

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tal folding times (4.3 and 0.7 µs for WW domain and HP35, respectively) is not possible. Nevertheless, the shorter folding times brought about by the CUFIX corrections likely indicate an improvement of the protein folding simulations, as previous MD simulations of protein folding were shown to overestimate the folding times. 13 Through comparisons with the NMR data (J-couplings and S2 order parameters), we confirmed that our CUFIX corrections specifically improve long-range interactions without affecting local conformations of Ala5 and Val3 peptides, Figure S7, or the native structure of ubiquitin, Figure S8. For both Ala5 and Val3 , the J-coupling values obtained with and without the CUFIX corrections are both in excellent agreements with experiment, 53 Figure S7 A,D. Similarly, the Ramachandran plots for Ala5 and Val3 , Figure S7 B,C,E,F, are not affected by the CUFIX corrections. Furthermore, 500 ns simulations of ubiquitin performed with and without the CUFIX corrections showed negligible effect of the CUFIX corrections on the stability of the native structure, Figure S8 B, S2 order parameters, Figure S8 C, and J-couplings, Figure S8 D–G. See SM 9 and SM 10 for simulation details. To quantify the effect of the CUFIX corrections on the conformation of denatured proteins, we computed the fraction of denatured (Q < 0.5) conformations at 360 K characterized by Rg > 10 ˚ A, Figure S9. Using CUFIX in the simulations of the WW domain and HP35 increases the denatured population by 22 and 35%, respectively. Interestingly, using CHARMM22* for simulations of the WW domain or HP35 9 was also found to increase the population of denatured conformations by 56 and 28% in comparison to analogous simulations performed using ff99, Figure S9. Among factors that might have contributed to extending the conformations of denatured proteins in the CHARMM22* simulations are replacement of the first two negatively charged residues (Glu1 and Glu2 ) of the WW domain structure with neutral side chains (Gly1 and Ser2 ) and scaling of the partial charges of the Arg side chain. In summary, we have shown that pair-specific modification of LJ parameters can substantially improve the realist of protein folding simulations without introducing additional

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artifact. 26,27,54 Indeed, using our CUFIX corrections in REMD simulations of protein folding alleviates artificial compaction of the denatured protein but does not compromise stability of the protein’s native, folded conformation. Improvements brought about by the CUFIX corrections reduce the ruggedness of the folding free-energy landscape but do not affect the accuracy of the folded conformation prediction. As our CUFIX corrections have been found to reduce the protein folding time, their use may present an attractive practical means for considerable acceleration of protein folding simulations.

Acknowledgement This work was supported by the National Science Foundation grant PHY-1430124. The authors acknowledge supercomputer time at the Blue Waters Sustained Petascale Facility (University of Illinois) and at the Texas Advanced Computing Center (Stampede, allocation award MCA05S028). The authors thank Martin Gruebele for his insightful comments on the manuscript. We thank D. E. Shaw Research for providing access to their simulation trajectories.

Supporting Information Available Detailed description of MD simulation protocols and analysis procedures; plots of the X-ray scattering intensities; characterization of the REMD simulations using the RMSD coordinate; secondary structure analysis of WW domain and HP35 trajectories; plots characterizing the effect of CUFIX corrections on the 2D free energy landscapes and the unfolded proteins’ conformations; validation simulations using Ala5 and Val3 peptides and ubiquitin. material is available free of charge via the Internet at http://pubs.acs.org/.

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Refined Parameterization of Nonbonded Interactions Improves

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