Test and Evaluation of ff99IDPs Force Field for Intrinsically Disordered Proteins

Abstract

Over 40% eukaryotic proteomic sequences have been predicted as intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) and confirmed to be associated with many diseases. However, widely used force fields could not well reproduce the conformers of IDPs. A previously ff99IDPs force field was released with CMAP energy corrections for the 8 disorder promoting residues to simulate IDPs. In order to further confirm the performance of ff99IDPs, three representative IDPs systems (arginine-rich HIV-1 Rev, aspartic proteinase inhibitor IA₃, and α-Synuclein) were used to test and evaluate the simulation results. For free disordered proteins, the results show that the chemical shifts from the ff99IDPs simulations are in quantitative agreement with those from reported NMR measurements and better than those from ff99SBildn. Then, ff99IDPs can sample more clusters of disordered conformer than ff99SBildn. For structural proteins, both ff99IDPs and ff99SBildn can reproduce the conformations. In general, ff99IDPs can success in simulating the conformation of IDPs or IDRs both in bound and free states. However, relative errors could still be found at the boundaries of the scattering order-disorder promoting residues. Therefore, polarizable force fields might be one of possibility ways to further improve the performance on IDPs.

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Introduction

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) in structured proteins have been confirmed to play key roles in protein function. Although they cannot automatically fold into stable and ordered structures, the structural flexibilities have important functions in many cellular processes, such as molecular recognition, assembly, and post-translational modifications^1–5. Over 40 % eukaryotic proteomic sequences have been predicted as disorder with more than 40 consecutive amino acids, indicating IDPs’ wide spreading^{6, 7}. Recently, IDPs are intensively studied on their association with many diseases: such as cancer⁸, cardiovascular diseases⁹, and neurodegenerations^10–14. Thus, IDPs obviously provide exciting opportunities and bring huge challenges to the understanding of the protein structure-function paradigm.

Interestingly, IDPs can rapidly fold into structural proteins upon binding with their partners. Typical observations could be found in tumor suppressor p53, which acts as a central hub in multiple signaling pathways^{8, 15–17}, through interacting with hundreds of partners. Since the significant conformational adjustments from disordered structures to ordered, essential challenges are also brought to molecular dynamics (MD) simulations on IDPs.

Indeed, MD simulation becomes a powerful tool to investigate the dynamic motions in macromolecules at the long time scale (~ns-μs)^18–22. However, accuracy of force field remains to be an issue in applications of MD simulations^{23, 24}. In the case of IDPs, the issue is that most protein force fields are often too stable to model the unstructured proteins based on our tests. To overcome this issue, we developed an AMBER²⁵ force field, ff99IDPs²⁶, with the addition of grid-based energy correction maps (CMAP)^{27, 28} on the standard ff99SBildn force field^{29, 30} to reproduce the main chain torsional distributions of 8 disorder promoting residues (A, G, P, R, Q, S, E, and K) which were reported in the literature³¹. Tests on the apo- and bound-state of measles virus nucleoprotein (MeV N_TAIL) and p53 show that ff99IDPs could reproduce IDPs better than the widely-used ff99SBildn. In addition, the rigid secondary structures in bound state could be well maintained under ff99IDPs.

In this study, three IDPs were used to test and evaluate the performance of ff99IDPs in both disordered apo-state and ordered bound-state. The arginine-rich HIV-1 Rev is a RNA-binding protein and regulates the HIV-1 replication cycle^32–34. Another test was conducted on IA₃, the aspartic proteinase inhibitor. Aspartic proteinase has been confirmed to express in many human infectious agents life cycle^35–37. Among its few natural inhibitors, IA₃ is a typical IDP which could fold into highly rigid helix upon binding with aspartic proteinase^{38, 39}. The third test was α-Synuclein. It is an IDP on the cell membrane in substantia nigra pars compacta (SNc), which is crucial in the pathogenesis of Parkinson’s disease. It may misfold into highly ordered cross-β fibrils and form Lewis bodies^{18, 40–42}. Our tests show that ff99IDPs can reproduce highly disordered conformations of three tested IDPs, consistent with the experimental observations. Furthermore, the performance of ff99IDPs is better than that of ff99SBildn to sample the conformers of IDPs. For bound-state, both force fields have reproduced the conformers with stable secondary structures.

As a reference, we also tested the applicability of ff99IDPs on structured proteins, lysozyme and ubiquitin³⁰. Our data show that the newly developed force field behaves similar to that of ff99SBildn in the tested structured proteins. However, our test data show that disagreement with experiments still exist for the ordered residues when they are scattered in long disorder-promoting sequences. The possible causes are discussed and remedies with the deployment of polarizable force fields are also proposed.

Materials and Methods

Selection of test systems

In order to quantitatively validate the performance of the newly developed AMBER force field ff99IDPs, intrinsically disordered proteins were searched in PubMed (http://www.ncbi.nlm.nih.gov/pubmed) and Biological Magnetic Resonance Data Bank (BMRB)⁴³ with the following criteria: 1) The proteins which are exactly described as IDPs; 2) Thermodynamic data, such as chemical shift and order parameter (S²), are available. Under these criteria, three representative systems: arginine-rich motif of HIV-1 Rev (termed HIVRev, PDB code: 1ETF)⁴⁴, the aspartic proteinase inhibitor IA₃ (termed IA₃, PDB code: 1DP5)³⁹, and the disordered region of micelle bound α-synuclein (termed αSyn, PDB code: 2KKW)⁴⁵, were selected to evaluate the performance of ff99IDPs. HIVRev has a very high proportion of disorder-promoting residues, with only 4 order-promoting ones out of 21 residues. As a distinct contrast, IA₃ has a high proportion of order-promoting residues, with 14 order-promoting residues out of 31-mer polypeptide. Both HIVRev and IA₃ could fold into rigid α-helices in bound-state. αSyn is another typical IDP that consists of a long structured region and a long disordered loop. For HIVRev and IA₃, both disordered state and ordered state were tested. Furthermore, we also tested two widely-used proteins for the validation of previous force fields³⁰, hen egg white lysozyme (HEWL, PDB code: 6LYT)⁴⁶ and ubiquitin (PDB code: 1UBQ)⁴⁷, to check if the IDP-specific force field could be used for structural proteins. All the simulations were done under ff99IDPs and ff99SBildn.

Overview of ff99IDPs Implementation

The total energy of IDP specific force field ff99IDPs is the summation of ff99SBildn total energy and the dihedral energy correction term with parameters for the 8 disorder-promoting residues, as shown in Eq. 1²⁶. All tested structures with PDB file format were first converted into AMBER topology files, using ff99SBildn force field. CMAP parameters were then added using the in-house PERL script²⁶.

$$E_{ff99\mathit{\text{IDPs}}}=E_{ff99\mathit{\text{SBildn}}}+E_{\text{CMAP}}$$ (1)

All other energy terms of ff99IDPs except the dihedral energy term remain the same as a chosen base additive force field of ff99SBildn. Furthermore, only the backbone dihedral parameters for the 8 disorder-promoting residues were optimized while the parameters for the other 12 residues remain the same to minimize the perturbation to folded structure distributions.

CMAP is a matrix of corrections on dihedral-grids with the corrections between grid points calculated with a two-dimensional bicubic interpolation method.²⁸ The correction matrix for each residue was set up with a dihedral angle grid in the resolution of 15 degrees. Specifically we used relative conformational free energies (ΔG_i,j) converted from φ/ψ distributions from the disordered protein structures to compute the correction matrix with Eq. 2.

$$\mathrm{\Delta }{G}_{i,j}=-RT\text{ln}\left(N_{i,j}/N_0\right)$$ (2)

where N_i,j is the population of φ/ψ dihedral bin (i, j), and N₀ is the population of the most-populated bin. In this equation, sparsely populated bins could have huge relative free energies, leading to over-correction. To overcome this limitation, we used an iterative optimization process to determine the CMAP correction matrix self-consistently. Here CMAP energy terms were calculated at each iteration step with Eq. 3.

$$E_{i,j}^{\text{CMAP}}=\mathrm{\Delta }{G}_{i,j}^{\text{DB}}-\mathrm{\Delta }{G}_{i,j}^{\text{MD}}$$ (3)

where $\mathrm{\Delta }{G}_{i,j}^{\text{DB}}$ and $\mathrm{\Delta }{G}_{i,j}^{\text{MD}}$ are database and MD simulation converted free energies for φ/ψ dihedral bin (i, j), respectively. The iteration starts with a CMAP correction matrix initialized as zero, so the initial $\mathrm{\Delta }{G}_{i,j}^{\text{MD}}$ are derived from the simulations in the base additive force field, ff99SBildn. At each iteration step, the CMAP correction matrix derived from the previous step’s simulation was added to the base force field ff99SBildn. Root mean square deviations of population (termed RMSp) among all bins were calculated to quantitatively measure the difference between MD and database populations until RMSp was less than 0.15%.

Molecular dynamics simulations

All chosen structures were first minimized in SYBYL^®-X 2.1.1⁴⁸ to eliminate any possible overlaps or clashes. All simulations and most analyzing procedures were performed using the AMBER12 software package²⁵. Hydrogen atoms were added using the LEaP module of AMBER12. Counter-ions were used to maintain system neutrality. All systems were solvated in a truncated octahedron box of TIP3P waters with a buffer of 10 Å. Particle Mesh Ewald (PME)⁴⁹ was employed to treat long-range electrostatic interactions with the default setting in AMBER12. The newly developed ff99IDPs was added as described in the previous literature²⁶ based on ff99SBildn, which was also taken as the benchmark to compare with the experimental data. All the MD simulations were accelerated with the CUDA version of PMEMD^{50, 51} in GPU cores of NVIDIA® Tesla K20. The SHAKE algorithm⁵² was used to constrain bonds involving hydrogen atoms. Up to 20,000-step steepest descent minimization was performed to relieve any structural clash in the solvated systems. This was followed by a 400-ps’ heating up and a 200-ps’ equilibration in the NVT ensemble at 298K with PMEMD of AMBER12. Langevin dynamics with a time step of 2 fs was used in the heating and equilibration runs with a friction constant of 1 ps⁻¹. To evaluate the performance of ff99IDPs and compare with ff99SBildn, five independent trajectories of 100 ns each were simulated for apo- and bound-HIVRev, apo- and bound-IA₃, and apo-αSyn, under ff99IDPs and ff99SBildn, respectively. To show the compatibility of ff99IDPs on normal proteins, five 100ns’ trajectories were also conducted on HEWL and ubiquitin under both force fields. A total of 6.6 μs simulations was collected at 298K, taking about 3,500 GPU hours. Detailed simulation conditions are listed in Table 1.

Table 1.

Simulation conditions for all models.

System	Force Field	Traj. Num.	Simulation Time (ns)	Ions	Waters	BMRB Accession No.
Apo-HIVRev	ff99IDPs ff99SBildn	5 5	100 100	9 Cl−	4409	18851
Bound-HIVRev	ff99IDPs ff99SBildn	5 5	100 100	23 Na+	12480	18852
Apo-IA3	ff99IDPs ff99SBildn	5 5	100 100	1 Na+	6434	6078
Bound-IA3	ff99IDPs ff99SBildn	3 3	100 100	24 Na+	11781	–
αSyn	ff99IDPs ff99SBildn	5 5	100 100	9 Na+	47408	16302
HEWL	ff99IDPs ff99SBildn	5 5	100 100	8 Cl−	5799	4562, 18304(S2)
Ubiquitin	ff99IDPs ff99SBildn	5 5	100 100	–	4669	5387, 6470(S2)

Data Analyses

Root mean square deviations (RMSD) and fluctuations (RMSF) in MD trajectories were calculated with the PTRAJ module in AMBER12 and AmberTools13²⁵. Structural cluster was conducted with the kclust program in MMTSB toolset⁵³. Secondary structures of all the snapshots were identified with DSSP^{54, 55}. Disorder population was calculated as the disordered (predicted by DSSP as “disordered loop” and “bend”) population during the production runs. Disorder population within every 10 ns’ period along all the IDP trajectories under ff99IDPs and ff99SBildn were plotted to test if both force fields can converge to sample the disorder conformers. STRIDE^{56, 57} was also used for HIVRev to compare with DSSP. Experimental Cα chemical shift data for all models and N-H order parameters (S²) for HEWL and ubiquitin were retrieved from the Biological Magnetic Resonance Data Bank⁴³. Accession numbers could also be found in Table 1. PMF free energy landscapes were mapped by calculating normalized probability from a histogram analysis, and plotted with Origin 8.5. For each simulation, sampling was conducted every 50 ps (10000 snapshots for 5×100 ns’ simulations). Radius of gyration (RG) and RMSD were both separated into 8 bins. The energy landscape was plotted among these 64 (8×8) bins. The secondary chemical shift data for the simulated structures were calculated with SPARTA version 1.01⁵⁸. N-H J-coupling data of free and bound-HIVRev were calculated with Karplus Equations^59–61. All the structural visualizations were represented with PyMOL 1.7⁶².

Results and Discussion

We performed MD simulations on the models mentioned above. Then, the evaluations were performed through conformation sampling, structural clustering, helicity evolution, secondary Cα chemical shift, and other structural or thermodynamic indices. For every model, RMSD and Cα fluctuation (RMSF) were first calculated to ensure that ff99IDPs could sample rational conformations. Comparing to the initial structures, RMSD of each trajectory under both ff99IDPs and ff99SBildn (supplementary Figure S1) indicates that 100 ns simulations are sufficient to become dynamics equilibration at room temperature. Furthermore, RMSDs of free IDPs under ff99IDPs were mostly higher than those under ff99SBildn. This indicates that ff99IDPs might sample more flexible conformations than ff99SBildn.

In order to test the convergence of conformation sampling, the disorder populations within every 10 ns’ simulation time were shown in Figure 1. For all the IDP systems, the disorder population became stable before 100 ns, indicating 100 ns simulation is sufficient for the convergence of conformation sampling. Taking HIVRev as an example, we also compared the representative structures and their occupation in the total conformation within first 70 ns, 80 ns, 90 ns, and 100ns, as shown in supplementary Figure S2. Most representative structures found in 100 ns could also be found in the other 3 time durations, with similar occupation ratios. This indicates that 100 ns simulations are sufficient for the conformation sampling.

Figure 1.

Disorder population within 10 ns’ time period along all the trajectories for three test IDPs, under ff99IDPs (red) and ff99SBildn (blue).

HIV Rev ARM (HIVRev)

Secondary Cα chemical shift, clustering, and helicity of apo-HIVRev under ff99IDPs and ff99SBildn were shown in Figure 2. Apparent differences could be found in the structural clustering (Figures 2A and 2B). Top 10 clusters under ff99IDPs occupy 30.45 % of the total conformations (top 58 for 70 %), many of which have high ratio of population for disordered structures. However, under ff99SBildn, top 10 clusters occupy up to 55.47 % of the total conformations (top 20 for 70 %), only 2 of whose conformers are highly disordered. The PMF free energy landscapes with the reaction coordinates of RMSD and the radius of gyration (RG) (Figures 2C and 2D) show that the distribution of conformers from ff99IDPs is between RMSD at 1~11 Å and RG at 9 Å ~19 Å, and between RMSD at 1~10 Å and RG at 9 Å ~16 Å for ff99SBildn. This indicates that ff99IDPs could sample more flexible conformers than ff99SBildn, which is in agreement with the structural clustering. Using the clustered representative structures which occupy no less than 70% conformations and their occupancy, secondary Cα chemical shifts were calculated and compared with the experimental data (Figure 2E). The full length RMSd was 0.748 ppm for ff99IDPs and 1.111 ppm for ff99SBildn between predicted chemical shifts and experimental data, respectively. This suggests that the predicted chemical shifts under ff99IDPs are more approaching to experimental values than those under ff99SBildn. Calculated J-coupling values are shown in supplementary Figure S3. Because of the lack for the exact experimental data, the full length RMSd was not calculated. However, similar to that of chemical shift, the predicted J-coupling values of ff99IDPs are better than those of ff99SBildn. The helicity of HIVRev is shown in Figures 2F and 2G. These figures indicate that ff99IDPs reproduces significantly lower helical conformations than ff99SBildn, both in different statistics strategies. We also used STRIDE to yield the helical population for HIVRev, as shown in supplementary Figure S4. The results are similar to those of DSSP which indicates the reliability and reproducibility of DSSP algorithm. Detailed representations of secondary structures along simulation time could be found in Figures S5–S12 in supporting information.

Figure 2.

Simulation and thermodynamic data derived from ff99IDPs and ff99SBildn for apo-HIVRev. (A)(B) Representative structures of top 10 clusters and their occupations. (C)(D) PMF free energy landscape on 2D space of radius gyration (RG) and RMSD, showing ff99IDPs could sample wider and more flexible conformation space. (E) Comparison of the secondary chemical shift data. (F)(G) Comparison of the average helicity under both force fields, with residual averaging (F) and time averaging (G), respectively.

Our tests so far show that ff99IDPs performs better than ff99SBildn for IDPs simulation. The clustering analysis shows a higher structural flexibility derived by ff99IDPs. Structure trinity of IDPs, i.e. ordered, molten globular, and disordered structures³, could also be observed in the ff99IDPs derived structure representatives, especially in the middle region and C-terminus. In the N-terminus, the performance of ff99IDPs is similar to ff99SBildn for chemical shift or J-coupling prediction. We detected the internal interactions in apo-HIVRev under both force fields. Long-range interactions, other than short-range hydrogen bonds and hydrophobic interactions, play key roles in the internal contacts. Under ff99IDPs, hydrogen bonds and electrostatic interactions were only found in the N-terminus (A-T-R-Q), as the threonine, arginine and glutamine have long side chains which can tangle with the charge-charge interactions; while under ff99SBildn, these interactions were also found in the middle region. The over-stability in the N-terminus under ff99IDPs may be caused by the only consideration of correction on the backbone dihedrals, while the charges and electrostatic interactions should be considered as another important aspect in the IDPs modeling. This could be implemented to improve the force field in the future.

For DNA-bound HIVRev, both ff99IDPs and ff99SBildn have good performance to reproduce the conformation of structured HIVRev. Calculated secondary Cα chemical shift of bound-HIVRev under both force fields is shown in Figure 3 and compared with experimental data. The RMSD is 0.698 ppm under ff99IDPs and 0.604 ppm under ff99SBildn, respectively. In Figure S13, helical structures of HIVRev were very stable upon DNA binding, indicating that ff99IDPs could also be used to ordered proteins. Time evolutions of secondary structure for bound-HIVRev under both force fields are shown in Figure S6.

Figure 3.

Comparison of the secondary chemical shift data of bound-HIVRev under ff99IDPs and ff99SBildn. RMSd values are calculated with the outlier terminal threonine omitted.

Aspartic Proteinase Inhibitor (IA₃)

IA₃ is another intrinsically disordered protein, which folds rigidly upon binding with aspartic proteinase. Similar to HIVRev, the structural cluster also indicates that ff99IDPs reproduces more disordered and flexible conformations than ff99SBildn (Figures 4A and 4B). Top 10 clusters under ff99IDPs occupy only 14.09 % of the total conformations (top 172 for 70 %); meanwhile under ff99SBildn, top 10 clusters occupy 23.63 % of the total conformations (top 85 for 70 %). Therefore, the disordered level of conformer from ff99IDPs was also higher than that from ff99SBildn. The full length RMSd between predicted secondary Cα chemical shifts and experimental data is 0.835 ppm for ff99IDPs and 1.186 ppm for ff99SBildn, respectively. Time evolutions of secondary structure for apo-IA₃ under both force fields are shown in Figure S7. This also shows that the performance of ff99IDPs is better than that of ff99SBildn to simulate IDPs. However, both force fields could not well reproduce the disorder conformers for the middle region of apo-IA₃ because of over stabilized α-helical structures. CMAP corrections are only added onto disorder-promoting residues, which might cause an energy gap between order- and disorder-promoting residues. As a result, most significant disparities in IA₃ were found at the boundaries between order- and disorder-promoting residues. This might be eliminated by the polarizable charge model.

Figure 4.

Simulation and thermodynamic data derived from ff99IDPs and ff99SBildn for apo-IA₃. (A) Representative structures of top 10 clusters and their occupations from ff99IDPs. (B) Representative structures of top 10 clusters and their occupations from ff99SBildn. (C)(D) PMF free energy landscape on 2D space of radius gyration (RG) and RMSD. (E) Comparison of the secondary chemical shift data.

The structures of aspartic proteinase bound-IA₃ modeled in both force fields are similar. Because of the lack of experimental data, we cannot quantitatively evaluate the performance. Chemical shift for bound-IA₃ could be found in supplementary Figure S14.

α-Synuclein

The NMR structures of αSyn have two long α-helices linked with a short turn (Res. 1–94, Figure 5A). In the crystal experiment, this region binds with vesicle and micelle⁴⁵. In this test, we focused on the disordered region (Res. 95–140) and compared the thermodynamics data with the experiments. Therefore, all analysis results are focused on this IDPs region. Structural clustering is shown in Figures 5B and 5C and secondary structure evolutions are listed in supplementary Figure S9. The conformers of top 10 clusters occupies of 20.05 % (ff99IDPs) and 23.77 % (ff99SBildn), respectively. As shown in Figure 5, the whole conformers are highly disordered under ff99IDPs; however, the conformers evolve some helical structure under ff99SBildn. This shows that the disordered magnitude is higher under ff99IDPs than under ff99SBildn. The full length RMSd between predicted secondary Cα chemical shifts and experimental data is 0.461 ppm for ff99IDPs and 0.588 ppm for ff99SBildn, respectively. This also shows that the performance of ff99IDPs is better than that of ff99SBildn to simulate IDPs.

Figure 5.

Simulation and thermodynamic data derived from ff99IDPs and ff99SBildn for apo-αSyn. (A) Cartoon representative of α-Synuclein, with the ordered and disordered parts labelled. (B) Representative structures of top 10 clusters and their occupations from ff99IDps. (C) Representative structures of top 10 clusters and their occupations from ff99SBildn. (D)(E) PMF free energy landscape on 2D space of radius gyration (RG) and RMSD. (F) Comparison of the secondary chemical shift data.

Lysozyme and Ubiquitin

Lysozyme and ubiquitin have been tested for the evaluation of previous force field many times^{30, 63}. Here these two intensively studied proteins were also employed to evaluate the quality of ff99IDPs. Figures 6 and 7 show the secondary Cα chemical shift and the order parameter (S²) derived by ff99IDPs and ff99SBildn and their comparison with the experimental data. Both force fields have good performance, showing the newly development ff99IDPs is also suitable for the normal protein. Calculated chemical shift results from both force fields are similar. It is interesting to note that ff99IDPs leads to more disordered properties in the loop and turn regions, as shown in S² values, which is consistent with the destabilization of CMAP energy term. Their secondary structure evolutions are shown in Figures S10 and S11.

Figure 6.

Secondary chemical shift data comparison for lysozyme (A) and ubiquitin (B).

Figure 7.

Order parameter data (S²) comparison for lysozyme (A) and ubiquitin (B).

Conclusion and Perspectives

In this study, we validated the quality of newly developed ff99IDPs force field with three intrinsically disordered proteins (HIVRev, IA₃, and αSyn) and two ordered proteins (lysozyme and ubiquitin) with extensive all-atom molecular dynamics simulations. Thermodynamic data were calculated and compared with experimental data. Overall, ff99IDPs leads to more consistent chemical shift than ff99SBildn, and reproduces more flexible disorder conformations for IDPs. Thus, the validation data indeed show that ff99IDPs has better performance on IDPs than ff99SBildn. At the same time, ff99IDPs can also be used to simulate structural proteins.

Nevertheless, some limitations do exist. ff99IDPs cannot perfectly reproduce the full length of the intrinsically disordered proteins, e.g. the N-terminus of HIVRev and the middle region of IA_3. The stable secondary structures (α-helix in most time) in these regions were observed in simulations, which may be the cause of the high Cα chemical shift. The electrostatic and hydrogen bonding interactions in these regions might play key roles in the structural stabilization, rather than the dihedral energy correction in CMAP energy term. Thus, the next step for improving the performance and accuracy of the IDP specific force field might be focused on the polar interactions. Indeed, the charge distribution of a residue should be perturbed by its neighboring residues, which is the principle of polarizable force fields. Therefore, our effort next step will be to explore how to improve the accuracy of the inter-residues’ interactions in the disordered regions with strategies in polarizable force fields and incorporate these to improve the IDPs force fields.