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Computed binding of peptides to proteins with MELD-accelerated molecular dynamics Joseph A Morrone, Alberto Perez, Justin L MacCallum, and Ken A Dill J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b00977 • Publication Date (Web): 02 Jan 2017 Downloaded from http://pubs.acs.org on January 3, 2017
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Computed binding of peptides to proteins with MELD-accelerated molecular dynamics Joseph A. Morrone,†,k Alberto Perez,† Justin MacCallum,‡ and Ken A. Dill∗,†,¶,§ †Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794 USA ‡Department of Chemistry, University of Calgary, Calgary, Alberta T2N 1N4, Canada ¶Department of Chemistry, Stony Brook University, Stony Brook, NY 11794 USA §Department of Physics & Astronomy, Stony Brook University, Stony Brook, NY 11794 USA kPresent Address: IBM T.J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, NY 10598, USA E-mail:
[email protected] Abstract
proteins. Free-energy perturbation and other techniques have been developed 1–3 and are becoming increasingly accurate for computing relative binding affinities. 4 These methods typically presuppose a binding mode, although in some cases (T4 lysozyme) it has been possible to sample the binding poses using Hamiltonian replica exchange molecular dynamics. 5 Free-energy methods have also mainly been limited to small-molecule ligands, for which there are relatively few conformations that must be sampled. It would be of great value to have free-energy methods that could address more complex, flexible ligands, such as peptides. Peptides are increasingly interesting as pharmaceuticals, in part because they can be used to target ‘undruggable’ sites where small molecule ligands have not been successful. 6 So far, the few computations of peptide-protein binding affinities appear to be mainly end-point methods such as MM-GBSA. 7–9 A recent work has presented a peptide-protein binding mode search using replica exchange MD in which a new mode was found starting from a helical peptide conformation in contact with the protein surface. 10 Here we present a computational method for computing peptide-protein binding poses and
It has been a challenge to compute the binding poses and affinities of peptides to proteins by molecular dynamics (MD) simulation. Such computations would be valuable for capturing the physics and the conformational freedom of the molecules, but are currently too computationally expensive. Here we describe using MELD-accelerated MD for finding the binding poses and approximate relative binding free energies for flexible-peptide / protein interactions. MELD uses only weak information about the binding motif and not the detailed binding mode that is typically required by other free-energy-based methods. We apply this technique to study binding of P53-derived peptides to MDM2 and MDMX. We find that MELD finds correct poses, that the binding induces the peptide into the correct helical conformation, and that it is capable of roughly estimating relative binding affinities. This method may be useful in peptide drug discovery.
1
Introduction
There is a need for free-energy based methods for computing the binding of ligands to
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binding free energy between peptides A and B, ∆∆GBA : PA → P + A P + B → PB A → A∗ B∗ → B
− ∆GA ∆GB ∆GA*A − ∆GB*B
PA + B∗ → PB + A∗
∆GMELD
K as replicas ascend the ladder. Full details of the replica exchange and constraint protocols are given in the Supporting Information. Peptides in lower temperature replicas occupy the bound or reference states whereas at higher temperatures and low or zero restraint energy they may unbind and explore space more freely. The consistency of bound states at lower replicas and the good mixing of replicas amongst lower and higher replica states are discussed in the Supporting Information. The hydrophobic residues of the target protein to include as possible peptide biding partners in the MELD binding restraint were chosen to be within 0.8 nm from four MDM2 residues (G58, D68, V75 and C77 from chain A of PDB 1YCR) determined by experiment to be critical for binding. 33 The constraint residues for MDMX are determined by a sequence alignment to MDM2. The reference state is chosen so that the center of mass of the unbound peptide is confined to a spherical shell ≈ 5 − 7 nm from the protein center away from the protein center of mass. Additional restraints are employed for all replicas. There is an energy penalty if the peptide - protein distance exceeds 7 nm. Peptide aggregation is suppressed by a term that penalizes conformations where the peptide-peptide center distance is less than 3 nm. So that the protein does not unfold at high temperatures, the protein backbone is constrained during the course of the simulation. This constraint nonetheless allows a large degree of local fluctuation and rearrangement in the protein. The reference structure for MDM2 and MDMX was taken from PDB entries 1YCR and 3JZP, respectively. No constraints are placed on peptide internal degrees of freedom, and all MELD runs are initially seeded with the peptide fully extended and placed far way from the protein target. A sample starting configuration and setup files are provided in the Supporting Information. Accurate assessments of the free energy rely on well converged MELD simulations. We generate at least one microsecond trajectories for all systems. The Amber FF12sb force field 34 with AMAP corrections 35 is employed along-
(1) (2) (3) (4) (5)
∆GMELD = ∆∆GBA + (∆GA*A − ∆GB*B ) (6) As noted above, the reference state (A∗ or B ∗ ) is chosen such that the peptide is confined to a spherical shell sufficiently far from the rest of the system such that the two groupings can be considered non-interacting. In this way, the reference state differs from the standard unbound state (A or B) only in its confinement to the shell. Thus, the free energy difference, ∆GA*A or ∆GB*B is independent of peptide identity and the term in parentheses in Eq. 6 is zero. In the limit of good sampling and convergence, ∆GMELD = ∆∆GBA . Naturally, the accuracy of the technique also depends upon the description of interactions and the solvation model with which the technique is paired. Access to the relative free energy facilitates the direct comparison with experimentally determined inhibition constants: ∆∆GBA = −kb T ln
KiA KiB
(7)
where KiA and KiB are the inhibition constants of peptides A and B, respectively.
3
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Simulation details
MELD has been developed as a plugin to the OpenMM library. 32 It is optimized to run on GPU hardware using a temperature and Hamiltonian replica exchange scheme where a single GPU is assigned a replica system. Thirty (30) replicas are used in all simulations. The binding and reference state restraints are turned off and the temperature is raised from 300 K to 500
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side the GBNeck2 solvation model. 36 A reaction field model is used to describe electrostatics beyond a cutoff of 1.8 nm. This description of the interactions and solvation has been shown to successfully predict protein structures and peptide conformations in prior studies. 11,12,35 We studied the binding of a set of eleven 12residue peptides selected from Phan, et al. 20 to both MDM2 and MDMX. The peptide P6W was used as the reference peptide in these simulations. P53 binding to MDM2 against P63 was run in order to assess the structural differences between P53 and P63, the latter of which binds poorly to MDM2 (see e.g. Shin, et al. 31 ). P73 peptide binding to MDM2 was also run, so as to compare to PDB entry 2MPS. 31 The free peptides P53, P63, and PDIQ were also simulated with standard replica exchange molecular dynamics so as to assess their helicity. The peptide name and sequences presently considered are given in Table 1. Binding poses and their populations are extracted from the lowest temperature replica of the MELD simulation using a recently developed density based clustering algorithm. 37 The alpha and beta carbon of residues at positions ranging from the anchor phenylalanine to the anchor leucine are considered in the RMSD and the conformations are aligned to the alpha carbon positions of the target protein. In principle it is possible to improve statistics by making use of higher temperature replicas in extracting the clusters, particularly if a reweighing scheme is employed to account for the differing temperatures and Hamiltonians of replicas. 38
4 4.1
in the mdtraj library 40 was used to evaluate the secondary structure. 1
Helicity
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P53
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PDIQ
C
0.6 0.4 0.2 0
5
10
15
Residue Index
Figure 3: Upon binding, the peptide is induced to become helical. The helicity of the peptide as a function of reside helix for 15-residue P53, P63, and 12-residue PDIQ in panels A, B and C, respectively. The helicity of the bound state (black) and unbound state (red) is shown.
Results Binding induces peptide helicity
In Figure 3A it is shown that in our simulations, the P53 peptide has less pronounced helicity when it is free, but attains a helical structure upon binding. The engineered peptide PDIQ, which has a higher potency than P53 20 is also helical upon binding but shows a greater helical propensity in the free state than P53 (Fig 3C). Note that our initial seeding and informational constraints make no assumptions of peptide helicity, and this finding results
In the experimental binding mode, P53 and related peptides form an alpha-helical structure, and agreement with this observation is a key test of our method. To this end, we compute the helicity of the peptide as a function of residue index for free and bound conformations. The DSSP algorithm 39 as implemented
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Table 1: Name and sequence for peptides used in this study. p53 p63 D p73 pMI pDI p6W p6S p1E6N p6N p6W9S p4T6W p1E6W pDIQ
S S G
Q P G
E T F S E V F Q T T F E T S F A L T F E L T F E L T F E E T F E L T F E L T F E L T F T E T F E E T F E
D H H E H H H H H H H H H
from sampling the free energy surface driven by MELD. The helical binding motif is less pronounced in the P63 peptide ( Fig. 3B), in agreement with the literature. 31 P63 is also known to be a weaker binder to MDM2 than P53. 7,31 This is consistent with our simulation where the population of P53 in the bound state relative to P63 is 9 : 1.
4.2
L I L Y Y W S N N W W W W
W K W D W S W N W A W A W A W A W A W A W A W A W S
L L F L S L L L Q L Q L Q L Q L Q L S L Q L Q L Q L
P E E S T T T T T T T T L
E Q P P S S S S S S S S S
N P D
1.00
0.75
population
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Binding modes are in good agreement with experiments
Binding MDM2 to MDM2 Binding MDMX to MDMX
0.50
0.25
A key test for MELD is how well it is able to predict the correct binding mode of P53 and analogous peptides to both MDM2 and MDMX. We have chosen nine PDB structures of peptide binding to MDM2 or MDMX that have been experimentally determined. 18,20,24,28,31 All exhibit essentially the binding mode depicted in Figure 1 where the peptide adopts a helical structure and binding is mainly characterized by three hydrophobic anchor residues (PHE, TRP, LEU). In all nine systems, we recover the experimentally determined binding mode, as determined by the presence of conformations with binding modes less than 2.0 ˚ A RMSD from this pose. However, it is not sufficient to simply compare the MELD ensemble of conformations with experiment in this fashion, particularly if one is interested in blind prediction of binding modes. MELD is a physics-based simulation tool and
0.00
3 3 I I I Q Q P5 P7 PDI P6W PM PDI P6W PM PD
Figure 4: Usually the computed mostpopulated state corresponds the experimental binding pose. Populations extracted from a clustering analysis of the MELD trajectory where the cluster center corresponds to the experimentally determined binding mode. Bars are labeled according to the peptide in the bound state and colored red (blue) with respect to target protein MDM2 (MDMX).
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are compared with the experimental results 20 in Figure 6. The reference peptide is taken to be P6W in all reported data points and the other peptide are listed in Table 1, with the exception of P63 and P73 which are not considered. For P53, a 12-residue variant is considered as in the experimental reference. Overall, our agreement with experiment is promising. Most deviations lie within 1 kcal/mol, and the strongest binding peptide to MDM2 as predicted by MELD (PDIQ) is the same as that experimentally determined. 20 However in the case of MDMX, PMI is experimentally the most favored peptide, but as discussed above, we have difficulty predicting its correct binding mode and so the second ranked peptide (PDIQ) is predicted to be the strongest binder to MDMX. Yet it must be noted that our results are significantly worse when considering weak binding partners. Our results fail to predict the inactivity of an experimentally determined inert set of peptides (arbitrarily set to ∆∆Gexp = 3.0 kcal/mol in Figure 6). Although the sign of the relative affinity is correct, the predictions are strongly over-bound. The largest deviation is seen for P53 binding to MDM2 in with respect to P6W. An examination of the clustering analysis indicates that P6W never quite finds the proper binding pose in this run. The experimental binding mode population is 0.17, far below the value averaged over all runs of ≈ 0.6 reported in Figure 4. Results such as this indicate the challenge of convergence in our simulations, particularly as metastable binding modes can persist in the replica ladder.
populations reflect the underlying free energy surface. Therefore the population of a binding mode extracted from clustering analysis provide us with a way to assess our results. In Figure 4 we show the populations for each peptide associated with clusters whose centers are within 2.0 ˚ A RMSD of the experimental pose. It can be seen that in 7 of 9 of the peptides considered, the experimental binding modes represent at or near a majority of the bound states that are observed in our simulation. The experimental binding mode appears less favored in the case of peptide PMI, particularly with regards to its binding to MDM2. Overall, the population of the experimental binding mode appears to be higher for binding to MDMX, and this observation may reflect the fact that MDMX is known to be a less permissive binder. In Figure 5, the highest population binding mode for all nine peptides is shown. In 7 of 9 systems, the mode is in agreement with experiment. As can be seen the peptide ends often adopt a diverse set of conformation, but this flexibility is reasonable and our RMSD score only considers nine central residues in the binding motif (see Sec. 3). In the case of the peptide PMI, alternative modes are favored. In the case of binding to MDM2, the results favor sampling a configuration where PHE and TRP are buried but the anchor LEU is not. Even tryptophan is not buried in the case of PMI binding to MDMX, but here the experimental binding mode more significantly contributes to the sampled trajectory.
4.3
Binding affinities estimations are encouraging
5
An important part of our algorithm is its ability to search for binding modes and adequately sample peptide degrees of freedom. As shown above, we are overall successful with respect to these tasks. Next we consider the possibility of using MELD to compute relative binding affinities as outlined in Sec. 2. This requires more stringent convergence in order to extract reliable population ratios of peptide B bound with respect to peptide A bound. The computed relative binding free energies
Conclusions
We describe here how MELD-Accelerated MD can be applied to search for binding modes and evaluate binding free energies of peptideprotein complexes. We have shown that it can predict binding modes of P53 and analogous peptides binding to MDM2 and MDMX proteins. Importantly, nothing was assumed of the peptides’ internal structures and simulations were seeded with fully extended conformations.
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Supporting Information provides further details of the computation and methodology, as well as an assessment of the convergence and sampling of the replica exchange simulations (PDF file). Additionally, a sample initial configuration of two peptides (P6W and PDIQ) with target protein MDM2 is provided in PDB format. This material is available free of charge via the Internet at http://pubs.acs.org/.
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