Extended Concerted Rotation Technique Enhances the Sampling

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Extended Concerted Rotation Technique Enhances the Sampling Efficiency of Computational Peptide-Design Algorithm Xingqing Xiao, Yiming Wang, Joshua N. Leonard, and Carol K Hall J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b00714 • Publication Date (Web): 12 Oct 2017 Downloaded from http://pubs.acs.org on October 16, 2017

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Journal of Chemical Theory and Computation

Extended Concerted Rotation Technique Enhances the Sampling Efficiency of Computational Peptide-Design Algorithm Xingqing Xiao†, Yiming Wang†, Joshua N. Leonard‡, Carol K. Hall*,† †

Chemical and Biomolecular Engineering Department, North Carolina State University, Raleigh, North Carolina 27695-7905, United States

‡

Chemical and Biological Engineering Department, and Chemistry of Life Processes Institute, Northwestern University, Evanston 60208, Illinois, United States

ABSTRACT: To enhance the sampling efficiency of our computational peptide-design algorithm in conformational space, the concerted rotation (CONROT) technique is extended to enable larger conformational perturbations of peptide chains. This allows us to make relatively-large peptide conformation changes during the process of designing peptide sequences to bind with high affinity to a specific target. Searches conducted using the new algorithm identified six potential λ N(2-22) peptide variants, called B1 to B6, which bind to boxB RNA with high affinity. The results of explicit-solvent atomistic molecular dynamics simulations revealed that four of the evolved peptides, viz. B1, B2, B3 and B5, are excellent candidate binders to the target boxB RNA as they have lower binding free energies than the original λ N(2-22) peptide. Three of the four peptides, B2, B3 and B5, result from searches that contain both sequence and conformation changes, indicating that adding backbone motif changes to the peptide-design algorithm improves its performance considerably.

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KEYWORDS: Computational peptide-design algorithm, Concerted rotation technique, Peptide backbone flexibility, λ N peptide and boxB RNA

1. INTRODUCTION Short peptides that bind to specific biomolecules, such as DNA, RNA and proteins, are useful tools for basic research and have great potential as therapeutics1,2 and biosensors3,4 due to their strong selectivity, high thermo-stability and low cost. To date, most of the binding peptides used in clinical research and biotechnology are derived from natural selection processes in bacteria and viruses,5 or are obtained from phage display technology.6 We have been working to develop a rapid computational peptide-design algorithm to identify peptide sequences with high affinity to bind to specific RNA-, or protein-based biomolecule targets.7-10 A key ingredient in this algorithm is the concerted rotation (CONROT) technique, a method originally proposed by Scheraga et al. for conformational deformations of chain molecules11 and first applied by Theodorou et al. for simulation of polymers12 and by Knapp et al. for proteins13,14. In this method, three consecutive residues along the peptide are displaced simultaneously, keeping the conformations on the two ends fixed. In this paper, we extend the CONROT technique to enable displacement of a peptide fragment of any length, keeping its ends fixed. This allows us to make larger changes in the peptide conformation, enhancing the efficiency with which the algorithm samples peptide conformational space. Our computational design algorithm is an iterative procedure that searches for peptide sequences that bind more sensitively and selectively to a target protein than does an initial “guess” peptide, which may be identified via an experimental method such as phage display. The target’s conformation is fixed throughout the search. The algorithm has two types of trial moves; peptide sequence change moves (mutation) during which the peptide conformation is fixed, and peptide conformation change moves (2) ACS Paragon Plus Environment

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during which the peptide sequence is held fixed. Trial moves are accepted or rejected using a Monte Carlo algorithm based on a score that depends in part on the energy of the peptide-target complex. After 10,000 evolution steps, the best peptides are identified and further examined using explicit solvent atomistic molecular dynamics simulations to evaluate their binding capabilities during a kinetic process. The computational peptide-design algorithm has incorporated several advanced techniques over its period of development, including self-consistent mean field (SCMF), CONROT, Monte Carlo (MC) and Molecular Mechanics/Generalized Born Surface Area (MM/GBSA). The SCMF technique was introduced to determine the best combination of rotamers from Lovell’s rotamer library15 for side-chain repacking during the search for sequence candidates.7 Subsequently, the algorithm was further advanced by replacing the SCMF technique by an energy minimization strategy that optimized the configurations of amino acid sidechains to better contact the target.10 The CONROT technique was used to displace three consecutive residues in the middle of the peptide chain, allowing us to generate new backbone conformation candidates.8 The score function used in the algorithm to evaluate the merits of peptides initially involved only the binding energy of the peptide-target complex. This was later improved by taking into account both the binding energy of the peptide-target complex and the free energy of the peptide when stabilized in the bound conformation.9 The peptide’s binding free energy and free energy in the bound state were calculated by using the implicit-solvent MM/GBSA approach with the variable internal dielectric constant model.16-18 An early version of the algorithm was used to computationally design a 15-mer peptide to have good ability to recognize human lysine tRNA species (tRNALys3), a primer for HIV reverse transcription. Synthesis of the computationally-designed peptide and experimental characterization by the Agris group revealed that the designed peptide has an affinity (Kd=0.05 µM) that is 10-fold better than that of a peptide identified experimentally via phage display.19 (3) ACS Paragon Plus Environment


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The computational algorithm still faces the challenge that each conformation change move enables only a slight perturbation in the peptide backbone scaffold, greatly limiting the sampling efficiency of the computational peptide-design algorithm. Short peptide chains have a large number of degrees of freedom associated with translation and rotation, making the peptides extremely flexible when accessed to the target.20 The old CONROT technique in our algorithm works well for the case when three consecutive residues form a β-strand in the middle of a chain, but not when the three consecutive residues form, or are in, a helical structure. In fact, in the latter case, it is impossible to obtain new backbone conformations through the old CONROT technique because of atomic overlaps. Accommodating backbone flexibility is a challenging issue in the field of computational protein/peptide design. So far, there are three primary computational strategies proposed by researchers to address this issue. The first strategy by Król21 and Chaudhury22 is to employ molecular dynamics (MD) simulations to generate an ensemble of protein backbone conformers prior to protein design. The MD-generated protein backbone conformers are fixed during the protein design. The trial sequence candidates are draped on these conformers, and the scores of the protein sequences on all backbone conformers are evaluated. The protein sequence with the best score as well as the corresponding conformer is identified as the best binder to the target. The second strategy by Georgiev23 and Smith24 uses the “backrub” motion technique to move the protein backbone. In this technique, a protein fragment is allowed to have a slight rotation (≤ 11°) along its primary backbone axis, leading to a rigidbody move for the residues within the fragment. Next, through adjusting the bond angles, the protein fragment is successfully attached at a fixed endpoint to generate new protein backbone conformers. Finally, sequence changes take place on these new conformers to design proteins. The third strategy by Grünberg25 and Wang26 uses a combination of coarse-grained and all-atom models to obtain new protein backbone conformations. A MC protocol is employed to move the centroid spheres on a coarsegrained centroid-sphere chain model to new low-resolution backbone motifs, which are then converted (4) ACS Paragon Plus Environment

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to high-resolution all-atom structures, yielding new backbone conformers for use in the protein designs. Although the aforementioned computational strategies are effective at perturbing the protein backbone scaffold, generation of new backbone conformations is time-consuming. The CONROT technique, which was utilized by Ulmschneider et al.27,28 to investigate the folding process of polypeptides, can greatly reduce the computational time to identify new backbone conformations. In their work, five residues, viz. 4 for pre-rotation and 1 for the chain closure, were chosen randomly along the peptide chain to experience a CONROT move through adjusting a series of consecutive bond and dihedral angles, thereby leading to a large backbone perturbation. In this article, we describe the expansion of the CONROT technique previously used in our peptide-design algorithm to enable global conformational perturbations of peptide chains. Theoretically, the extended CONROT technique allows peptide fragments of any length to change their backbone conformation so long as the backbone motif has no overlaps with other molecules. Incorporating the extended CONROT technique into our computational algorithm can assist the evolved peptides to find better contacts to biomolecular targets. It, therefore, increases the possibility that the peptides discovered during the search are in low free energy conformations. Note that the conformation change move is not an equilibrium sampling technique (not Metropolis MC) because the moves are not random or reversible. It is an optimization local minimization scheme in that the moves are biased by minimization. The paper is organized as follows. Firstly, the extended CONROT technique is tested on the λ N(222) peptide to perturb the backbone motifs of peptide fragments with various lengths. Next, the efficiency of the new algorithm with the extended CONROT technique in sampling the λ N(2-22) peptide’s structures in conformation space is examined. Thirdly, the new algorithm is employed to evolve other high-affinity peptides that bind to the target boxB RNA, resulting in six best-scoring peptide sequences. Finally, the binding strength of the six peptide sequences to boxB RNA is examined (5) ACS Paragon Plus Environment


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in explicit-solvent atomistic MD simulations. Simulation results reveal that four out of the six evolved peptides are better at binding to boxB RNA than the naturally-evolved λ N(2-22) peptide and our previously-discovered peptides resulted from the case of no conformational change moves.10 Among the four promising peptides, three peptides called B2, B3 and B5 are generated by making changes in the peptide backbone motifs. This suggests that the new algorithm with the extended CONROT technique improves its performance in the search for good RNA-binding peptides.

2. COMPUTATIONAL METHODS 2.1 Structure of the complex between the λ N(2-22) peptide and boxB RNA Our computational algorithm requires a binding conformation between peptide and target to initiate the search for other peptide binders. Figure 1 shows an initial binding conformation of the λ N(2-22) peptide and boxB RNA obtained from a 120-ns atomistic MD simulation in our previous work.10 The complex is stabilized in solution through inter-chain interactions between the amino acids at sites 3 to 10 (namely, the peptide α-helix at the N-end) and the nucleotides at sites 1 to 7 (namely, the 5´ strand along the RNA). The C-end of the λ N(2-22) peptide adopts a flexible β-strand conformation to contact the boxB RNA. This binding structure of the λ N(2-22) peptide and boxB RNA is consistent with experimental observations by Xia et al.29 and Zhang et al.30

[Figure 1 should be placed here]

2.2 Extended concerted rotation technique (6) ACS Paragon Plus Environment

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To sample peptide structures in a broad conformation space, we extend the CONROT technique to displace more consecutive residues simultaneously. In the extended CONROT method, three sites anywhere along the peptide chain are chosen randomly. Take sites 1, 2 and 3 of Figure 2a as an example. We label the heavy backbone atoms of the residues on the three sites as (N1, Cα1, C1), (N2, Cα2, C2) and (N3, Cα3, C3), respectively (Figure 2a). The skeletal dihedral angles which describe the individual rotations of the bonds (N-Cα), (Cα-C) and (C-N) are denoted by (ϕ, ψ, ῶ), respectively, and the skeletal bond angles with apexes at (N, Cα and C) are specified by (θῶ, θϕ, θψ), respectively (Figure 2b). When the six skeletal dihedral angles {ϕ1, ψ1, ϕ2, ψ2, ϕ3, ψ3} of the three residues on the randomlychosen sites experience a CONROT move, the other residues sandwiched in between the three sites undergo backbone conformation change as a rigid body (Figure 2b). It is worth noting that if site 2 is in the vicinity of site(s) 1 or 3 along the peptide chain, the skeletal dihedral angle ῶ of the bond (C-N) between the two sites would become a conventional dihedral angle ω, which always has ω=π. However, when site 2 is not in the vicinity of site(s) 1 or 3, the skeletal dihedral angle ῶ is fixed at a constant (Figure 2). When a peptide fragment is chosen to encounter conformation change, all the bond lengths and bond angles of this peptide fragment are kept fixed, and only the six skeletal dihedral angles of the three residues are varied. Theoretically, the extended CONROT method allows a peptide fragment of any length to change its backbone conformation as long as the backbone motif has no overlaps with other molecules. In the extended CONROT method, we change the peptide backbone conformation spanning from site 1 to site 3 by rotating the torsion angles {ϕ1, ψ1, ῶ1, ϕ2, ψ2, ῶ2} and leaving the positions of the residues before site 1 and after site 3 on the peptide backbone unchanged, as shown in Figure 2. As described above, the skeletal dihedral angles ῶ1 and ῶ2 are kept fixed and can be pre-determined. Thus, four variables ϕ1, ψ1, ϕ2 and ψ2 remain to be calculated, only one of which is independent. Assuming that the torsion angle ϕ1 is a “driver angle”, the other three torsion angles {ψ1, ϕ2, ψ2} can be expressed (7) ACS Paragon Plus Environment


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as functions of ϕ1 using the new extended CONROT technique. The “driver angle” ϕ1 is rotated to scan the entire domain ranging from (-π, π]. For any given ϕ1, solution sets for {ψ1, ϕ2, ψ2} may or may not exist. If the solution sets for {ϕ1, ψ1, ϕ2, ψ2} exist and each pair of (ϕ, ψ) does not violate the Ramachandran plot for the general case, we rotate these skeletal bonds according to the solution sets, thereby generating a new peptide backbone conformation. The values of ϕ3 and ψ3 that are associated with this new conformation can be determined. The total number of solution sets {ϕ1, ψ1, ϕ2, ψ2, ϕ3, ψ3} found as a result of the scan of the driver angle over the domain (-π, π] is the number of new peptide backbone conformations. More details on how to obtain the solution set {ϕ1, ψ1, ϕ2, ψ2, ϕ3, ψ3} are given in the Supporting Information. Figure S2 exhibits a flow diagram to explain how we conduct the extended CONROT method to produce new peptide backbone conformations.


2.3 Procedure for computational peptide-design algorithm The new algorithm with the extended CONROT move implements peptide backbone motif changes to generate a library of potential peptides with the same or even higher affinity than the naturallyevolved λ N(2-22) peptide when bound to boxB RNA. Figure 3 shows a flow sheet for the iterative procedure that underlies the new peptide-design algorithm. The algorithm is initialized by choosing a starting peptide binder to the target (hereafter, the target will be boxB RNA), and determining the initial structure of the peptide-target complex from the PDB or crystallography or atomistic MD simulations. The starting peptide in the algorithm is either a known sequence or a randomly-generated sequence. The target’s conformation is held fixed throughout the entire sequence search, while the peptide’s conformation varies as the sequence evolution proceeds. (Justification regarding this point is that for a (8) ACS Paragon Plus Environment

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21-mer peptide in this work, there are a total of 2021 sequence alignments. For each possible sequence alignment, the conformational space of the amino acid side-chains and the peptide backbone motif is infinite. If we had allowed the target to change its conformations in the algorithm, the process of designing peptides would have become extremely computer-intensive because the conformational space of the target is infinite too.) The score Γscore for the initial peptide-target complex is calculated using a function that estimates the ability of the peptide to bind to the target and the peptide’s stability when it is in the bound conformation.9,10 We classified the 20 standard amino acids into six residue types according to their hydrophobicity, polarity, size and charge7. The 21-mer λ N(2-22) peptide that is of interest to us contains one hydrophobic residue (Nhydrophobic=1), three negatively-charged residues (Nnegative positively-charged residues (Npositive

charge=7),

charge=3),

seven

five hydrophilic residues (Nhydrophilic=5), five other

residues (Nother=5), and no glycine (Nglycine=0). In this work, these numbers (Nhydrophobic, Nnegative charge, Npositive charge, Nhydrophilic, Nother, and Nglycine) are kept the same during the process of sequence evolution. By doing so, we can maintain the hydration properties of all the evolved peptides to be the same as that in the λ N(2-22) peptide. In this way, we can avoid introducing excess hydrophilicity or positive charges in the evolved peptides due to strong negatively charges on boxB RNA.


At the start of the iteration procedure, a random number is generated to determine whether the peptide undergoes a sequence change move or a conformation change move. When a sequence change move is selected, there are two possible types of moves. In the first type of sequence change move, a randomly-chosen amino acid is mutated to become a new randomly-chosen amino acid of the same (9) ACS Paragon Plus Environment


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residue type. In the second type of sequence change move, two randomly-chosen amino acids along the peptide are exchanged, regardless of their residue types.7 Both types of moves are subjected to the constraint that the number of positively-charged, negatively-charged, hydrophobic, polar, glycine and other amino acid types remain the same as in the starting peptide sequence.7 The initial rotamers for the mutated or exchanged amino acid(s) are taken from Lovell’s rotamer library.15 Broyden-FletcherGoldfarb-Shanno (BFGS) energy minimization10 is then conducted to determine optimal sidechain configurations for repacking each trial amino acid on the chain. Thus, a new peptide sequence, Si, is i generated. The score Γscore of the new peptide is evaluated, and the MC algorithm, which is grounded

in the Metropolis sampling technique, is used to accept or reject the new peptide. The criterion for accepting

{

the

[(

peptide

)

sequence

change

is

based

on

the

probability

]}

old new P = min 1, exp Γscore − Γscore kTsequence , where kTsequence is set to 1.0 kcal/mol.

When a conformation change move is selected, there are three possible types of peptide backbone conformation changes. The first uses the extended CONROT method to displace a series of consecutive residues in the middle of the peptide chain, leaving the other residues fixed. The second rotates a peptide fragment on one of the two ends (N- and C- terminus) and the third translates the entire peptide backbone conformation. Peptide’s sidechains are removed during the conformation change moves, and get repacked later in the BFGS energy minimization step. All attempts to generate new peptide backbone conformers are considered as long as (1) the torsion angles (ϕ and ψ) satisfy the Ramachandran plot31,32 and (2) there are no atomic overlaps occurring between the peptide’s backbone and the target. Two parameters, δmax and kTconformation, are used to control the magnitude of the conformation change moves. The root mean-square deviation (RMSD), δrmsd, of the new trial conformer from its original peptide conformation is evaluated to make sure that it is not too big (δmin). In this work, δmin=0.3 Å and δmax is a controllable parameter (Unit: Å). The BFGS energy minimization is then conducted to optimize the sidechain configurations, repacking them (10) ACS Paragon Plus Environment

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on the trial conformers. When repacking of sidechains for a trial conformer fails due to atomic overlaps, that trial conformer is discarded. Thus, new candidate conformers Si are generated, and the scores i min is chosen among for each one are evaluated. The conformer associated with the minimum Γscore Γscore

the new candidate conformers. Finally, that “best” conformer is either accepted or rejected by employing

{

the

[(

MC

algorithm

)

old new P = min 1, exp Γscore − Γscore kTconformati on

]} ,

to

calculate

the

acceptance

probability

where kTconformation is an adjustable parameter for

conformation change move (Unit: kcal/mol). The parameter kTconformation controls the likelihood that a new peptide conformer will be accepted, with higher values making acceptance easier. During the process of sequence evolution, conformation change moves of peptides usually cause relatively-large fluctuations in the score as compared to those during sequence change moves. The setting for the parameter kTconformation depends on the system of the interest. Setting a proper parameter for kTconformation enables the peptide-design algorithm to search for the potential peptides in a more efficient manner. The entire iterative procedure of sequence change moves and conformation change moves is repeated 10,000 times. Thus, the search for the best peptide samples a broad sequence and conformation space. In this work, each sequence change move consists of a total of 21 mutation and exchange attempts, while each conformation change move generates at most 6 candidate conformers.

2.4 Procedure for atomistic molecular dynamics simulation Explicit-solvent atomistic MD simulations were performed using the AMBER 15 package to examine the dynamics of the binding process of the original λ N(2-22) peptide and the six best-scoring evolved peptides (viz. peptides B1 to B6 that were obtained via the algorithm) to boxB RNA. The AMBER14SB force field33 was used in all the simulations to describe the nucleotides and amino acids. (11) ACS Paragon Plus Environment


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The starting conformations of boxB RNA complexed with the six best-scoring evolved peptides for the simulations were obtained from the search algorithm. Three independent simulations were carried out for each peptide-boxB RNA complex in 120 ns to assure that our systems reached an equilibrated state. To accurately evaluate the charge-charge interactions between charged (or polar) molecules, we employed a variable internal dielectric constant model to capture electrostatic shielding effects16-18. Using the implicit-solvent MM/GBSA approach with the variable internal dielectric constant model, we post-analyzed the last 5-ns simulation trajectories of the peptide-boxB RNA complexes to calculate their binding free energies. Details of the procedures and post-analysis of the atomistic MD simulations can be found in our previous work.34

3. RESULTS 3.1 Testing the ability of the extended CONROT technique to generate new backbone conformations for peptide fragments of various lengths The extended CONROT technique allows many more residues to move their backbone conformation at one time than did the old CONROT technique, which could only move three consecutive residues at one time. We tested the ability of the extended CONROT technique to perturb peptide backbone motifs on the λ N(2-22) peptide chain of length 21. It is important to note that during the CONROT move, the bond lengths and bond angles of the peptide fragment are kept fixed; it is only the six dihedral angles of the three randomly-chosen sites that are varied. The number of new peptide backbone conformations found in the CONROT move depends on the number of solution sets {ϕ1, ψ1, ϕ2, ψ2, ϕ3, ψ3}. If no solution is found, then no new backbone conformation will be obtained for the peptide fragment subjected to the conformation change.


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To test the efficiency of our algorithm, we considered ten different peptide fragments of various lengths. These fragments were selected by randomly choosing three sites anywhere along the chain, and are summarized in Table 1. The extended CONROT technique was performed on the ten peptide fragments and the number of newly-generated backbone conformations was calculated for each peptide fragment (Table 1). A CONROT move for the peptide fragment is judged to be successful if one or more new backbone conformations are found. Otherwise, the CONROT move is judged to be a failure. As seen in Table 1, the CONROT technique failed to perturb the backbone conformations of two 3-mer peptide fragments with consecutive residues, viz. (site 11-site 12-site 13) and (site 14-site 15-site 16), but succeeded in generating new backbone conformations for longer peptide fragments. Perturbing the 3-mer peptide fragments in this work easily triggers atomic overlaps because of the relatively-helical conformation of λ N(2-22) peptide chain (Figure 1). When applying the CONROT moves to the ten peptide fragments, we found that a peptide fragment of length 5, viz. (site 17-site 19-site 21), had a maximum of four new backbone conformations. For the peptide fragment (site 12-site 18-site 21), the longest 10-residue fragment in our tests, two new backbone conformations were identified. Overall, in this work, the extended CONROT technique was able to successfully perturb peptide fragments with a length of up to 10 residues, thereby broadening the conformational space accessed during the search.

[Table 1 should be placed here]

3.2 Efficiency of our algorithm in perturbing the peptide backbone motif Ten independent attempts at perturbing the conformation were made for each of the four types of peptide backbone conformation change moves: fragment in the middle, N-terminus, C-terminus and whole chain. An attempt is judged to be successful when at least one new peptide backbone (13) ACS Paragon Plus Environment


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conformation is identified after the conformation change move. Otherwise, the attempt is a failure. Our goal here is to examine the efficiency of the new algorithm in perturbing the λ N(2-22) peptide backbone motif. A high efficiency means attempts to generate new peptide backbone conformations are highly likely to be successful. In calculating this efficiency, we only make conformation change moves; the peptide’s sequence is not changed and the score is not evaluated. Figure 4 shows examples of new backbone conformations when the λ N(2-22) peptide experiences conformational changes for a fragment in the middle, the N-terminus, the C-terminus and the whole chain. The peptide α-helix, viz. the fragment spanning from sites 3 to 10, is always preserved as a rigid body, meaning the α-helix always moves as a whole. To measure the extent to which the new algorithm perturbs the peptide’s conformation, we calculated the RMSD, δrmsd, of the new peptide conformation relative to the original λ N(2-22) peptide conformation, i.e. there are no sequence change moves. Small values of δrmsd (e.g. N-terminus moves of Figure 4a) indicate slight backbone conformation changes, while large values (e.g. C-terminus moves of Figure 4b) indicate large changes in the backbone conformation. Comparing the four types of conformation moves of the λ N(2-22) peptide in Figure 4, we can see that our algorithm perturbs the peptide’s N-terminus slightly (δrmsd=0.90 Å and 0.93 Å), but allows broad conformational changes in the peptide’s C-terminus (δrmsd=0.49 Å and 6.12 Å). Mediumsized conformational changes were also observed for the moves of the peptide fragment in the middle and the whole chain. The slight perturbation of the peptide’s N-terminus is due to the tight entanglement of the peptide’s α-helix with the boxB RNA hairpin. We calculated the success rates in generating new peptide backbone motifs during the ten independent attempts to make each type of conformation change move. The success rate is the fraction of the ten independent attempts that succeed in generating new conformation(s). The peptide Cterminus move has the highest success rate (100%), followed by the peptide fragment in the middle move (80%), the peptide N-terminus move (60%) and the peptide whole-chain move (60%). For the (14) ACS Paragon Plus Environment

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previous algorithm with the old CONROT technique8, the peptide C-terminus move had a success rate of 100% in perturbing three consecutive residues, but the peptide N-terminus move, the fragment in the middle move and the peptide whole chain move were all failures (0%). Thus, for the λ N(2-22) peptideboxB RNA complex, the new algorithm is effective in generating potential peptide conformations.


3.3 Implementation of new algorithm with and without conformation changes to search for highaffinity peptide binders to boxB RNA We employed the new algorithm with the extended CONROT technique to search for potential λ N(2-22) peptide binders with exceptional ability to bind the target boxB RNA. A randomly-generated starting peptide sequence is draped on the scaffold of the original λ N(2-22) peptide, and then the sequence evolution proceeds. Figure 5 shows the profiles of score vs. number of evolution steps for the sequence-change-only searches and for the searches which include both sequence and conformation changes. For the case of sequence change only (Figure 5a), the score profile is observed to have a sharp drop at an initial stage and then fluctuate moderately due to variations in the identities of the amino acids at the various sites along the peptide chain on the fixed backbone scaffold.7 The peptide sequence and conformation change moves are controlled by the two adjustable parameters δmax and kTconformation. Taking as an example (δmax, kTconformation)=(4.0, 2.0) (Figure 5b), it was found that the conformation change moves caused a persistent variation in the RMSD profile and induced considerable fluctuation in the score profile. In this search, there are 143 trial conformation change move attempts and 9857 trial sequence change move attempts out of 10,000 evolution steps. Of the 143 conformation change move attempts approximately 600 trial peptide backbone conformers were generated and examined (15) ACS Paragon Plus Environment


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with an acceptance rate of around 73.4%. (Note: as shown in Figure3, at most 6 trial peptide conformation conformers are examined in each conformation change move attempt to repack their amino acid sidechains.) By setting δmax=4.0, the new peptide conformations were limited to a maximum variation, viz. δrmsd≤4.0 Å (see the RMSD profile of Figure 5b). The scores associated with the new peptide conformations initially encounter a very large drop but eventually get down to an even lower value than in absence of conformation changes. This is evidence for a relatively good acceptance probability for the conformation change moves at kTconformation=2.0 and implies that the search is accessing a fairly broad range of conformational space. To avoid local searches, we perform a series of sequence evolutions at different sets of values of parameters (δmax, kTconformation), including (5.0, 2.0), (4.0, 3.0), (5.0, 3.0), (4.0, 4.0) and (5.0, 4.0). By ranking the scores of the evolved peptide sequences resulting from the searches without and with conformation changes, we identified a total of six best peptide sequences. (Note that as the scores become lower, the corresponding peptide sequences are expected to be better binders to the target.) For convenience, we call the six best-scoring evolved peptide sequences “B1” to “B6”. The specific sequences of the original λ N(2-22) peptide and the six evolved peptides B1-B6 are listed in Table 2 along with their associated scores. Peptide B1 resulted from the search with sequence change only using a random peptide as starting point. Peptides B2, B3, B4, B5 and B6 resulted from the searches with both sequence and conformation changes, but at different settings of (δmax, kTconformation) = (4.0, 2.0), (5.0, 2.0), (4.0, 3.0) (5.0, 3.0) and (4.0, 4.0), respectively. It is clear to see from Table 2 that our evolved peptides B1-B6 have much lower scores than the λ N(2-22) peptide when accessing boxB RNA, implying that the six evolved peptides probably have better capability to bind to boxB RNA. Also in Table 2, we find that, with the exception of peptide B5 (score: -110.08 kcal/mol), the scores of peptides B2, B3, B4 and B6 are lower than that of peptide B1 (score: -111.03 kcal/mol). This indicates


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that introducing peptide backbone motif changes into the algorithm facilitates the search for potential RNA binding peptides with low scores. We extracted the binding structures of peptides B1-B6 and boxB RNA from the searches with and without conformation changes. Figure 6 shows the structures of peptides B1, B2, B3 and B5 complexed with boxB RNA. The peptides maintain a stable α-helical conformation at the N-terminus, stacking with the boxB RNA hairpin, but adopt multiple discrete β-strand conformations at the C-end that contact with boxB RNA.




3.4 Verification of the binding ability of the λ N(2-22) peptide and six evolved peptides to the target boxB RNA by explicit-solvent atomistic molecular dynamics simulations The binding kinetics of the original λ N(2-22) peptide and the six best-scoring evolved peptides B1B6 with boxB RNA are examined in explicit-solvent atomistic MD simulations. Motivation for these simulations is that low scores in the algorithm do not guarantee that the evolved peptides have a better binding ability to boxB RNA than the λ N(2-22) peptide. The binding structure of boxB RNA and the λ N(2-22) peptide was studied in a 120-ns MD simulation in our previous work10. To make a consistent (17) ACS Paragon Plus Environment


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comparison, the binding simulations of boxB RNA with the six evolved peptides B1-B6 are carried out for 120 ns as well. The starting conformations of boxB RNA complexed with the six best-scoring evolved peptides for the atomistic MD simulations come from the searches using the new algorithm. The RMSDs of the heavy atoms on the phosphodiester and sugar ring of boxB RNA and on the backbone of the peptides are calculated over the course of the simulations. The peptide-boxB RNA complex was assumed to reach conformational equilibrium when the standard deviation for the fluctuation of the RMSD profile in the last 30-ns simulation is within ± 1 Å. The time course of the RMSDs for the complexes B1-boxB RNA, B2-boxB RNA, B3-boxB RNA and B5-boxB RNA is shown in Figure 7. All of these eventually reach a smooth plateau that lasts until the end of the simulations, indicating that the simulated structures of these complexes arrive at an equilibrated state after the 120ns. (The results for the other two complexes B4-boxB RNA and B6-boxB RNA are similar to those for peptides B1, B2, B3 and B5, and are not shown for brevity.) A clustering analysis was then conducted using the K-means method35 for the last 5-ns of the trajectories to determine a good representative structure for each individual peptide-boxB RNA complex. Figure 7 shows the simulated representative structures of boxB RNA with peptides B1, B2, B3 and B5. Furthermore, a comparison of structures for the four complexes before (Figure 6) and after (Figure 7) the atomistic MD simulations revealed that when these peptides tether boxB RNA, they retain an α helix-β strand conformation similar to that predicted in the algorithm.


The implicit-solvent MM/GBSA approach with the variable internal dielectric constant model was used to calculate the binding free energy and the associated enthalpic and entropic contributions for the (18) ACS Paragon Plus Environment

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six evolved peptide-boxB RNA complexes, using the last 5 ns of the relevant trajectories, as listed in Table 3. Analysis of the binding energy conducted using this approach revealed that our computed binding free energy of the λ N(2-22) peptide-boxB RNA complex is -9.60 kcal/mol, which is reasonably close to the experimentally-measured value -12.60 kcal/mol in the Leonard lab. This helps to confirm the validity of the MM/GBSA approach with the variable internal dielectric constant model avg ) of the six in the evaluation of binding free energy. As seen in Table 3, the entropies (ܶ∆ܵ௕௜௡ௗ௜௡௚

complexes did not vary widely, from -51.45 kcal/mol for the B5 peptide-boxB RNA complex to -42.22 avg ) experienced a more kcal/mol for the B3 peptide-boxB RNA complex. The enthalpies ( ∆‫ܪ‬௕௜௡ௗ௜௡௚

significant variation, ranging from -76.33 kcal/mol for the B5 peptide-boxB RNA complex to -53.14 kcal/mol for the B6 peptide-boxB RNA complex. The enthalpy dominates the binding free energy of the peptides with boxB RNA, implying that the binding dynamics is an enthalpy-controlled process. The results of the MD simulations revealed that peptide B2 has the best binding capability with boxB avg RNA; it has the lowest binding free energy, viz. ∆‫ܩ‬௕௜௡ௗ௜௡௚ = -32.69 kcal/mol. Peptides B5, B3 and B1

also had lower binding free energies (viz. -24.88 kcal/mol, -23.75 kcal/mol and -21.74 kcal/mol) than did the original λ N(2-22) peptide (-9.60 kcal/mol). Peptide B4 is not a very excellent candidate binder to the target boxB RNA, because its binding free energy (-13.81 kcal/mol) is not much lower than that of the initial λ N(2-22) peptide. The binding free energy (-8.71 kcal/mol) for peptide B6 is even worse, indicating a failure of the peptide design. By comparing the scores (Table 2) and binding free energies (Table 3) of the original and evolved peptides, we also realize that some of the low-score evolved peptides exhibit poor affinity to the target in a kinetic binding process. For example, the peptide B6 bound to boxB RNA with a score of -111.60 kcal/mol in the search algorithm but had a binding free energy of -8.71 kcal/mol in the atomistic MD simulation. This is not surprising. Peptide evolution in the algorithm is a static process as the target is not allowed to move in response to changes in the peptide sequence. The best evolved peptides need to be further evaluated by atomistic MD simulations (19) ACS Paragon Plus Environment


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to examine the dynamic properties of these binding structures. Overall, our computational strategy, combined with the search algorithm and atomistic MD simulations, yielded four highly promising peptide binders, viz. B1, B2, B3 and B5. It is interesting to note that three of the four promising peptides, B2, B3 and B5, resulted from searches that contained both sequence and conformation changes, and only one peptide B1 comes from the search with sequence change only. Furthermore, based on the computed binding free energies, peptides B2, B3 and B5 have a stronger ability to bind to boxB RNA than does peptide B1. We interpret this to mean that our improved search algorithm samples a broader conformational space than before and hence is able to find more potential peptide binders to the target.


4. CONCLUSION The goal of this work was to optimize a peptide’s conformation during the process of searching for sequences that bind well to a target of interest. To enhance our ability to sample a wide variety of peptide conformations, the concerted rotation (CONROT) technique was extended to displace more than three consecutive residues at one time, thereby leading to medium-sized or even global changes in the peptide backbone scaffold. Theoretically, the extended CONROT technique allows peptide fragments of any length to change their backbone conformations so long as their backbone motif has no overlaps with other molecules. Incorporating the extended CONROT technique into our computational algorithm helps the evolved peptides to find better contacts to biomolecular targets. It, therefore,


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increases the possibility that the peptides discovered during the search are in low free energy conformations. The system of interest in this work is the coat protein of the λ bacteriophage (λ N protein), which binds its cognate RNA stem loop (termed boxB RNA) with a Kd of 1.3×10-9 M. An attractive feature of the λ N-boxB system is that only 21 amino acids of the λ N protein are required to mediate boxB RNA binding. However, λ N peptide binds boxB RNA with an affinity that is too low for some applications. Thus, developing λ N peptide variants that bind boxB RNA with a higher affinity, and potentially with a range of affinities, would comprise unique and powerful tools for biotechnology and basic research. Firstly, the ability of the extended CONROT technique to generate new λ N(2-22) peptide backbone conformations was tested on ten peptide fragments of various lengths. Our results revealed that the extended CONROT technique succeeds in generating new backbone conformations for peptide fragments longer than 3 contiguous residues. The efficiency of the new algorithm in perturbing the peptide backbone motif was examined for four types of peptide backbone change moves: fragments in the middle, N-terminus, C-terminus and whole chain. The peptide C-terminus move had the highest success rate (100%), followed by the peptide fragment in the middle move (80%), the peptide fragment at the N-terminus move (60%) and the peptide whole-chain move (60%). The old CONROT technique allows us to displace only three consecutive residues along the chain, resulting in local conformation changes in the peptide C-terminus, but no conformation changes in the peptide N-terminus, the fragment in the middle, or the whole chain. This implies that our new algorithm is effective in sampling peptide structures in a broad conformation space. Secondly, the new algorithm was implemented with and without conformation changes to search for potential high-affinity λ N(2-22) peptide variants to boxB RNA, resulting in six best-scoring peptide binders called “B1” to “B6”. Peptide B1 resulted from the search with sequence change only, and (21) ACS Paragon Plus Environment


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peptides B2, B3, B4, B5 and B6 resulted from the searches with both sequence and conformation changes but at different settings of parameters (δmax, kTconformation). The parameter δmax is defined to be the maximum allowable conformational deviation of trial conformers from the original conformation. The parameter kTconformation controls the likelihood that trial peptide conformers will be accepted, with higher values making acceptance easier. The affinities of these best-scoring evolved peptides to boxB RNA were examined in explicit-solvent atomistic MD simulations. Peptides B1, B2, B3 and B5 were found to have lower binding free energies to boxB RNA than the λ N(2-22) peptide. Three of the four promising evolved peptides, viz. B2, B3 and B5, were generated by implementing both sequence and conformation change moves in the algorithm; only one of the promising evolved peptides, viz. B1, was generated by implementing sequence change moves only. This signifies that adding peptide backbone motif changes to the algorithm improves the performance of the search for good RNA-binding peptides. The motivation for developing a search algorithm that enables evolved peptides to have relativelylarge peptide conformational changes during sequence evolution is based on the experimental observations of the λ N(2-22) peptide and boxB RNA system by Xia et al.29 and Zhang et al.30 They found that the complex exists in a dynamic equilibrium with the N-terminal domain of the λ N(2-22) peptide, forming a helix that stacks with the RNA, but that the C-terminal domain adopts multiple discrete conformations within the complex. A strength of this testbed is that the validity of the new algorithm may be examined by experimentally synthesizing and testing the peptide sequences designed in this manner against the target boxB RNA. In effect, we have already validated the new algorithm in an unpublished targeting-peptide design project aimed at developing high performance biosensors for detection of cardiac troponin I (cTnI), a critical biomarker for the diagnosis of cardiovascular disease. Application of our computational peptide-design algorithm led to the identification of a 12-mer peptide with a binding affinity of (Kd=0.27 nM) to cTnI according to surface plasmon resonance measurements conducted by our experimental collaborators at the Air Force Research Laboratory. This compares very (22) ACS Paragon Plus Environment

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favorably with the cTnI-binding affinity of the best phage-display identified peptide (Kd=4.3 nM) and is nearly as good as the natural cTnI antibody (Kd=0.12 nM).36

ASSOCIATED CONTENT Supporting Information Detailed descriptions of the calculations of the torsion angles (ϕ1, ψ1, ϕ2, ψ2, ϕ3, ψ3) in extended CONROT move. This material is available free of charge via the internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ORCID Joshu N. Leonard: 0000-0003-4359-6126 Carol K. Hall: 0000-0002-7425-587X Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS (23) ACS Paragon Plus Environment


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Financial support for this work was awarded to C.K.H. by the National Institutes of Health USA (EB006006) and by the Air Force Office of Scientific Research (Award # FA9550-16-10078). This work was also supported in part by the NSF’s Research Triangle MRSEC, DMR-1121107. J.N.L would like to acknowledge support from a 3M Non-tenured Faculty Award and the Northwestern University Prostate Cancer Specialized Program of Research Excellence (SPORE) through NIH award P50 CA090386. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053573. We thank Texas Advanced Computing Center (TACC), San Diego Supercomputer Center (SDSC) and Pittsburgh Supercomputing Center (PSC) for providing us computing time.

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(16) Zhu, K.; Shirts, M. R.; Friesner, R. A. Improved Methods for Side Chain and Loop Predictions via the Protein Local Optimization Program: Variable Dielectric Model for Implicitly Improving the Treatment of Polarization Effects. J. Chem. Theory Comput. 2007, 3, 2108–2119. (17) Ravindranathan, K.; Tirado-Rives, J.; Jorgensen, W. L.; Cuimarães, C. R. W. Improving MMGB/SA Scoring through the Application of the Variable Dielectric Model. J. Chem. Theory Comput. 2011, 7, 3859–3865. (18) Xiao, X.; Zhao, B.; Yang, L.; Liang, X.; Ren, Y. Probe the Binding Mode of Aristololactam-β-Dglucoside to Phenylalanine Transfer RNA in Silico. ChemistrySelect 2016, 1, 5430-5439. (19) Spears, J. L.; Xiao, X.; Hall, C. K.; Agris, P. F. Amino acid signature enables proteins to recognize modified tRNA. Biochemistry 2014, 53, 1125–1133. (20) Mandell, D. J.; Kortemme, T. Backbone flexibility in computational protein design. Curr. Opin. Biotechnol. 2009, 20, 420–428. (21) Król, M.; Chaleil, R. A. G.; Tournier, A. L.; Bates, P. A. Implicit flexibility in protein docking: Cross-docking and Local refinement. Proteins: Struct., Funct., Bioinf. 2007, 69, 750–757. (22) Chaudhury, S.; Gray, J. J. Conformer Selection and Induced Fit in Flexible Backbone ProteinProtein Docking Using Computational and NMR Ensembles. J. Mol. Biol. 2008, 381, 1068–1087. (23) Georgiev, I.; Keedy, D.; Richardson, J. S.; Richardson, D. C.; Donald, B. R. Algorithm for backrub motions in protein design. Bioinformatics 2008, 24, i196– i204. (24) Smith, C. A.; Kortemme, T. Kortemme. Backrub-Like Backbone Simulation Recapitulates Natural Protein Conformational Variability and Improves Mutant Side-Chain Prediction. J. Mol. Biol. 2008, 380, 742–756. (25) Grünberg, R.; Leckner, J.; Nilges, M. Complementary of Structure Ensembles in Protein-Protein Binding. Structure 2004, 12, 2125–2136. (26) Wang, C.; Bradley, P.; Baker, D. Protein-Protein Docking with Backbone Flexibility. J. Mol. Biol. 2007, 373, 503–519.


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Tables: Table 1. The number of newly-generated backbone conformations for ten randomly-chosen peptide fragments of various lengths after the CONROT moves.

Table 2. Sequences and scores of the original λ N(2-22) peptide and six best-scoring evolved peptides from the search algorithm.

Table 3. The mean values of the binding free energy, enthalpy and entropy for the λ N(2-22) peptide and the six evolved peptides bound to boxB RNA in the last 5 ns of atomistic explicit-solvent MD simulation trajectories. Unit: kcal/mol.


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Table 1. The number of newly-generated backbone conformations for ten randomly-chosen peptide fragments of various lengths after the CONROT moves. Length of the peptide fragment subjected to CONROT move

The labels of three randomly-chosen sites

The amount of newly-generated

First

Second

Third

backbone conformations

11

12

13

0

14

15

16

0

4 residues (4-mer)

16

18

19

2

5 residues (5-mer)

17

19

21

4

6 residues (6-mer)

16

17

21

2

11

14

17

1

13

14

19

3

8 residues (8-mer)

13

16

20

1

9 residues (9-mer)

12

15

20

1

10 residues (10-mer)

12

18

21

2

3 residues (3-mer)

7 residues (7-mer)

Total success rate of the ten CONROT moves: 80%



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Table 2. Sequences and scores of the original λ N(2-22) peptide and six best-scoring evolved peptides from the search algorithm. site

Score 2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19

20 21 22

(kcal/mol)

λ N(2-22)

D A Q T R R R E R R A E K Q A Q W K A A N

-71.03

B1a

P A R C Q R R A R K C Q N N E E R R N E W

-111.03

b

P W Q K R R Q C R Q C C R Q R E E R Q A D

-119.77

B3c

C W Q R R R Q A R R A E N R C D Q Q E A R

-119.32

d

R Y R C R R R A K N A Q R Q C D C Q E Q E

-116.43

e

P A Q R R R R A R R E A N N C E Q Q W E R

-110.08

f

R W R C R R R A R K C E N Q C C N Q H E D

-111.60

B2

B4

B5

B6

(a) peptide B1: best peptide evolved from sequence change only; (b, c, d, e and f) peptides B2, B3, B4, B5 and B6: best peptides evolved from both sequence and conformation changes at (δmax, kTconformation)=(4.0, 2.0), (5.0, 2.0), (4.0, 3.0), (5.0, 3.0) and (4.0, 4.0), respectively. Starting peptide sequence for the searches is CSRRNRYAKSKDQPDPAKENK, score: -27.72 kcal/mol.


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Table 3. The mean values of the binding free energy, enthalpy and entropy for the λ N(2-22) peptide and the six evolved peptides bound to boxB RNA in the last 5 ns of atomistic explicit-solvent MD simulation trajectories. Unit: kcal/mol. avg ∆Gbinding

avg ∆Hbinding

avg T∆ S binding

λ N(2-22) peptidea

-9.60±0.17

-61.69±0.14

-52.09±0.10

B1 peptide

-21.74±0.17

-67.31±0.14

-45.57±0.10

B2 peptide

-32.69±0.18

-75.80±0.14

-43.11±0.09

B3 peptide

-23.75±0.18

-65.97±0.16

-42.22±0.10

B4 peptide

-13.81±0.17

-59.72±0.15

-45.91±0.09

B5 peptide

-24.88±0.17

-76.33±0.14

-51.45±0.10

B6 peptide

-8.71±0.18

-53.14±0.15

-44.43±0.10

(a) The values of the binding free energy, enthalpy and entropy related to the λ N(2-22) peptide and boxB RNA come from our previous work.10



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Figure Captions: Figure 1. Initial binding conformation of the λ N(2-22) peptide-boxB RNA complex for the computational peptide-design algorithm. The boxB RNA and λ N(2-22) peptide are represented by the green and orange ribbons, respectively. The positively charged amino acids are colored in blue, and the negatively charged amino acids in red. The other nucleotides and amino acids are not shown for clarity. The secondary structure of the 15-mer nutR boxB RNA is shown in the box on the left. The primary sequence of λ N peptide from aspartate (D) at site 2 to asparagine (N) at site 22 is shown in the box at the top. The complex is the same as the structure of Figure 8a in our previous paper10, and was obtained from a 120-ns atomistic MD simulation.

Figure 2. Three sites (multicolored beads) are randomly chosen in the middle of peptide chain. The residues on the randomly-chosen sites are subjected to bond rotations in their backbone scaffolds by using the extended CONROT technique, and two other residues (green beads) at the ends of peptide chain are kept fixed. As the skeletal dihedral angles of the three residues experience a CONROT move, the residues (translucent beads) sandwiched in between the three sites undergo backbone conformation change as a rigid body. (a) The first bond (N1-Cα1) of the residue on site 1 is designated as Bond 1, the bond preceding Bond 1 is designated as Bond 0. (b) The dihedral angles (ϕ, ψ, ῶ) and bond angles (θϕ, θψ, θῶ) are marked.

Figure 3. The flow sheet for the iterative procedure that underlies the computational peptide-design algorithm.

Figure 4. Four types of peptide backbone conformation moves: (a) N-terminus, (b) C-terminus, (c) fragment in the middle, and (d) whole chain. The green and orange ribbons indicate the original backbone conformations of boxB RNA and the λ N(2-22) peptide, respectively. The other multicolored ribbons show the new backbone motifs of the λ N(2-22) peptide when subjected to conformation changes. The values of the RMSD of the new peptide conformations relative to the original peptide conformation are shown to illustrate how far our algorithm perturbs the peptide’s backbone conformation.

Figure 5. The profiles of score vs. number of evolution steps. (a) Sequence evolution with sequence change only, resulting in peptide B1. (b) Sequence evolution with both sequence and conformation changes at (δmax, kTconformation)=(4.0, 2.0), resulting in peptide B2.


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Figure 6. Snapshots of the complexes formed by boxB RNA and the four best-scoring evolved peptides B1, B2, B3 and B5. The structures with the lowest scores are extracted from the searches without and with conformation changes in the algorithm. The boxB RNA is represented by the green ribbons and the evolved peptides B1, B2, B3 and B5 are represented by the orange ribbon. Positively charged amino acids are colored in blue, and negatively charged amino acids in red. The other nucleotides and amino acids are not shown for clarity.

Figure 7. Atomistic MD simulation studies of the binding of boxB RNA with peptides (a) B1, (b) B2, (c) B3, and (d) B5. The profile of RMSD versus time is shown on the left side of each subpicture, and the structure of the peptide-boxB RNA complex is shown on the right side of each subpicture.



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For Table of Contents Only


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Figure 1. Initial binding conformation of the λ N(2-22) peptide-boxB RNA complex for the computational peptide-design algorithm. The boxB RNA and λ N(2-22) peptide are represented by the green and orange ribbons, respectively. The positively charged amino acids are colored in blue, and the negatively charged amino acids in red. The other nucleotides and amino acids are not shown for clarity. The secondary structure of the 15-mer nutR boxB RNA is shown in the box on the left. The primary sequence of λ N peptide from aspartate (D) at site 2 to asparagine (N) at site 22 is shown in the box at the top. The complex is the same as the structure of Figure 8a in our previous paper10, and was obtained from a 120-ns atomistic MD simulation. 192x178mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Figure 2. Three sites (multicolored beads) are randomly chosen in the middle of peptide chain. The residues on the randomly-chosen sites are subjected to bond rotations in their backbone scaffolds by using the extended CONROT technique, and two other residues (green beads) at the ends of peptide chain are kept fixed. As the skeletal dihedral angles of the three residues experience a CONROT move, the residues (translucent beads) sandwiched in between the three sites undergo backbone conformation change as a rigid body. (a) The first bond (N1-Cα1) of the residue on site 1 is designated as Bond 1, the bond preceding Bond 1 is designated as Bond 0. (b) The dihedral angles (ϕ, ψ, ῶ) and bond angles (θϕ, θψ, θῶ) are marked. 344x107mm (300 x 300 DPI)


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Figure 3. The flow sheet for the iterative procedure that underlies the computational peptide-design algorithm. 278x348mm (300 x 300 DPI)



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Figure 4. Four types of peptide backbone conformation moves: (a) N-terminus, (b) C-terminus, (c) fragment in the middle, and (d) whole chain. The green and orange ribbons indicate the original backbone conformations of boxB RNA and the λ N(2-22) peptide, respectively. The other multi-colored ribbons show the new backbone motifs of the λ N(2-22) peptide when subjected to conformation changes. The values of the RMSD of the new peptide conformations relative to the original peptide conformation are shown to illustrate how far our algorithm perturbs the peptide’s backbone conformation. 293x99mm (300 x 300 DPI)


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Figure 5. The profiles of score vs. number of evolution steps. (a) Sequence evolution with sequence change only, resulting in peptide B1. (b) Sequence evolution with both sequence and conformation changes at (δmax, kTconformation)=(4.0, 2.0), resulting in peptide B2. 517x184mm (300 x 300 DPI)



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Figure 6. Snapshots of the complexes formed by boxB RNA and the four best-scoring evolved peptides B1, B2, B3 and B5. The structures with the lowest scores are extracted from the searches without and with conformation changes in the algorithm. The boxB RNA is represented by the green ribbons and the evolved peptides B1, B2, B3 and B5 are represented by the orange ribbon. Positively charged amino acids are colored in blue, and negatively charged amino acids in red. The other nucleotides and amino acids are not shown for clarity. 235x96mm (300 x 300 DPI)


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Figure 7. Atomistic MD simulation studies of the binding of boxB RNA with peptides (a) B1, (b) B2, (c) B3, and (d) B5. The profile of RMSD versus time is shown on the left side of each subpicture, and the structure of the peptide-boxB RNA complex is shown on the right side of each subpicture. 281x128mm (300 x 300 DPI)


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