Electrostaticaly driven Monte Carlo (EDMC). The first step consisted in generating feasible target peptide conformations using the EDMC method. The method combines stochastic Monte Carlo algorithms and the optimization of the electrostatic interactions, whereby the molecule evolves toward conformations in which the charge distribution becomes energetically more favourable.

An all-atom chain representation was used with the ECEPP3 force field 1819202122. Two alternative forms of the potential energy function were used to evaluate the total energy during the conformational search. One, in vacuum corresponding to the ECEPP/3 force field and the other adding a simple solvent interaction model of surface accessibility 232425.

The amino and carboxyl termini of the target fragment of the P protein molecule were blocked by amino-COCH3 and carboxyl-NH2 groups, respectively. An ensemble of conformations was generated for each peptide starting from (I) canonical α-helix, assigning the values (-60°,-40°) to dihedral angles (Φ,Ψ) of each amino acid residue, while keeping all values of ω to 180°. (II) polyproline conformation, assigning the values (-80°,150°) to dihedral angles (Φ,Ψ) of each amino acid residue, while keeping all values of ω to 180° (III) canonical β-strand, assigning the values (-139°,135°) to dihedral angles (Φ,Ψ) of each amino acid residue, while keeping all values of ω to 180° (IV) Random conformation, the simulations were started from two different initial random conformations, for each of these random conformations, all backbone and side-chain dihedral angles were chosen randomly between 180.0° and -180.0°, with the exception of the dihedral angles ω of the peptide group, which were always chosen in the trans (180.0°) conformation. All backbone and side-chain dihedral angles were allowed to vary freely during the simulations.

Many research groups 22262728293031 have devoted a large amount of effort to develop fast and reliable algorithms provide a solution to the problem of ionization equilibrium. However, the incorporation of these algorithms into conformational searches of short peptides is computationally too time consuming. Here, we used an alternative approach in which the energy of the whole ensemble of conformations, generated in a conformational search, is re-evaluated by considering the problem of ionization equilibrium at a given pH explicitly 32. This methodology permitted us to compute the average degree of charge to each of the ionizable groups in the sequence. Allowing us to find out the importance and influence of the ionizable groups in the peptides, the influence of solvent polarization effects and electrostatic interactions in the discrimination of the lowest-energy conformation.

The evaluation of the conformational energy follows the procedure previously published 22. The total free energy E(r_p, pH) associated with the conformation, r_p, of the molecule in aqueous solution at a given pH, is defined by considering a three-step thermodynamic process: cavity creation, polarization of the solvent, and alteration of the state of proton binding. This free energy involved in transferring the neutral peptide from the gas phase to the aqueous solution is given by:

Where E_int(r_p) is the internal conformational energy of the molecule in the absence of solvent, corresponding to the ECEPP/3 energy of the neutral molecule 1819202122; F_vib(r_p) is the conformational entropy contribution calculated by the harmonic vibrational contribution with zero charge 3334. F_cav(r_p) is the free energy associated with the process of cavity creation when transferring the molecule from the gas phase into the aqueous solution; this term is proportional to the solvent accessible surface of the molecuele. F_solv(r_p) is the free energy associated with the polarization of the aqueous solution calculated by using the Multigrid Boundary Element method developed by Vorobjev and Scheraga 31. F_inz(r_p, pH) is the free energy associated with the change in the state of ionization of the ionisable groups due to the transfer of the molecule from the gas phase to the solvent at a fixed pH value. This energy is calculated by using the general multi-site titration formalism 2628. This approximation computes the 2^N ionization states, where N is the total number of ionisable groups. The present method provides an accurate calculation of the potential of mean forces between ionized groups of the protein and the pK shifts of the ionisable groups as a function of the peptide environment.

First, the structure of the mAb17.2 Fv domain was modelled with MODELLER 35, using as template the PDB code 1NBV (82% sequence identity). PDB code 1S5I was used to model the heavy chain CDR3 (TYWGQGTLVTVS, 100% sequence identity). BLAST 36 and T-Coffee 37 were used to search for the templates and perform the alignment, respectively.

Second, the model of human rhodopsin was generated in a similar way using the bovine rhodopsin structure as template (PDB 1U19, 93% sequence identity). The quality of the models was assessed by the WHAT_CHECK standalone program 38.

The docking of peptides R13, P013 and SEL into mAb17.2 was done using BIGGER (Biomolecular complex Generation with Global Evaluation and Ranking) implemented on Chemera 2.0 39. BIGGER has a soft docking algorithm, an intermediate approach between flexible and rigid docking. The flexibility of the side chains was treated in a crude implicit way by allowing partial superposition of the side chains. Default options were used except for the angular step that was set at 12°. For R13, 5000 putative complexes were generated and then clustered using a 2.5 Å RMSD. P013 was treated in the same way. About 8000 complexes were generated with full length rhodopsin and then clustered using a 2.5 Å RMSD. An additional score based on the distance from the amino acids of the probe to the amino acids of the CDRs was generated. In order to discard unreal solutions, the best results were analysed visually. Three results were chosen for rhodopsin. For the R13 and P013 peptides the final sets were around 15 possible solutions. The final complexes were minimized using the Polak-Ribiere conjugate gradient method using the AMBER99 force field 40. The value of the potential energy, visual analysis and the comparison among all the different docking runs allowed the selection of just one ligand-antibody complex. They were submitted, for further refinement, to a simulated annealing protocol using the molecular dynamic software NAMD 41.

The complexes obtained from molecular docking were submitted to a regular molecular dynamics simulation with NAMD 41 of 7.5 ns, at 300 K, allowing the whole system to move. This simulation did not show significant changes with respect to unrefined docking results.

The next step was to refine the complexes obtained from the molecular docking, using simulated annealing through molecular dynamics simulation with the software NAMD 41. The parameters of the simulation were optimized, through shorts runs, allowing all system parameters to move.

The optimized protocol was as follows: the system was solvated using a sphere of TIP3 42 water model. Spherical boundary conditions were applied to avoid the evaporation of water molecules. The motion of the antibody was restricted, allowing only the CDRs residues to move. A langevin piston 4344 was implemented to keep the pressure at 1 atm. The regulation of the temperature was enforced by a langevin thermostat 45. An integration time step of 2 fs was used. The simulation started at 300 K and the whole system was heated up to 600 K by 50 K jumps every 10 ps. Then, the temperature was held at 600 K during 120 ps. Afterwards, the temperature was decreased by 50 K jumps. The first jump was done after 10 ps, the second one after 20 ps, then 40 ps, 60 ps and 100 ps. Then, the system was kept at 300 K during 160 ps. The whole process was iterated three times.

The structure of P013 (EDDDDDFGMGALF) was calculated as explained in the methods section. The whole conformational search carried out produced almost 12000 conformations. The lowest energy conformation, shown in Figure 1a, had a much lower energy values than the rest of the solutions. The average degree of charge state per residue was determined using the coupling between the conformations versus the pH model. The Boltzmann average over all the conformations was completely determined by the lowest energy conformation. It was found that at pH 7 only one out of six chargeable amino acids is neutral despite the proximity of these residues among themselves (see figure 1b).

The structure of P013 can be briefly described as a bend in which the five negatively charged residues (E1, D3, D4, D5, D6) are pointing towards the solvent. The uncharged D2 is interacting with M9 which is in a cluster of residues that form a kind of hydrophobic core (F7, G8, M9, G10, A11, L12 and F13).

The EDMC of the R13 (EEEDDDMGFGLFD) can be also described as a bend. The lowest energy conformation out of the 12000 conformation sample is shown in Figure 2a. In this case, the average degree of charge state per residue at pH 5 and pH 7 was determined, showing that E1 and D4 were uncharged. The minimum energy conformations were the same at both pHs. At pH 7 the energy was slightly lower and the mean charge state was slightly different (Figure 2b). As we saw with P013, the result of the Boltzmann average is entirely determined by the lowest energy conformation. The reason for calculating the structure at pH 5 was to compare our results directly with the ones obtained by the NMR studies of this peptide by Soares et al 17. They found that R13 behaves as a random coil in solution, and that the binding to antibody reduces the peptide flexibility, inducing a more defined conformation. We found that both, P013 and R13, are bends. It is possible to argue that the flexibility of R13 hinders the assignment of a defined structure. We could report a definite structure because in our method we only analyzed the minimum energy conformation without taking into account the flexibility of the peptides.

Superposition of P013 and R13 showed that they were quite similar in the curved region of the bend (residues 3 to 6) while the conformation for the rest of the residues was different. The next step was to compare them with SEL (the second extra-cellular loop of our homology model of human rhodopsin, based on the bovine crystal structure) and the experimental NMR structures of H13 (PDB code 1S4J) and A13 (PDB code 1S4H). The structural alignment RMSD values, against R13, can be seen in Figure 3a. The structural alignment of the five peptides showed a surprising conformational similarity to residues 3 to 6 (Figure 3b).

Experimental data demonstrated that the affinity of these peptides towards monoclonal antibody 17.2 follows the order R13 > H13 ≈ P013 > A13 1417. Remarkably, their conformational differences, which are reflected in the RMSD values of the structural alignment, followed an identical order suggesting that there may be a correlation between the conformation of the bend and its affinity. See figure 3.

Another important outcome was finding out that SEL13, a portion of the second extra cellular loop of rhodopsin, has a matching shape in spite of not having sequence identity with these peptides. This fact strongly reinforces the results of studies that have associated the dysfunction of the retina in chagasic patients with an autoimmune mechanism in which anti-P auto-antibodies would cross-react with the visual pigment rhodopsin 13. Our findings also support one of the conclusions of a previous study by Soares et al. 17 about the importance of the conformational state in the peptide-antibody interaction.

The electrostatic potential surface of the antibody revealed that the antigen-binding site, formed by the six CDR loops from the two variable chains, is a positively charged depression with a small and narrow cavity at the bottom. See Figure 4.

The docking of the R13 peptide into the antibody showed that the curve formed by E3, D4, D5 and D6 binds very deeply into the cavity while the residues forming the hydrophobic core (residues 7 to 13) were associated with the first hypervariable loop of the light chain.

The most dominating feature of the docking is the neutralization of the charged residues in the peptide through the formation of ion pairs between R50 (CDR2, heavy chain) and E3 plus R52 (CDR2, heavy chain) with D5 and D13. D6 is pointing towards the solvent. See figure 4. These interactions were observed before and after the refinement process, except in the case of D13 which after the refinement, and due to the elongation of the peptide, is now pointing towards the solvent, as can be seen figure 5.

Other observed electrostatic interactions were of the hydrogen bond type. E2 backbone carbonyl is hydrogen bonded to R165 (light chain) and G101 (heavy chain). E3 hydroxyl is hydrogen bonded to Y215 hydroxyl (light chain) D4 is forming and hydrogen bond with L152 and G210 (light chain).

The docking of the P013 peptide showed that the bend residues (3 to 6) bind similarly but less deeply than R13. D3 and 5 are again neutralized by R50 and 52 (heavy chain). The main difference observed when comparing electrostatic interactions between these two peptides is the ion pair formed between D4, which is unprotonated in P013, and R165 (light chain). The remaining residues (7 to 13) are exposed to the solvent instead of interacting with the CDR1 of the light chain as in the case of R13.

The results obtained directly from the docking of the P013 peptide (without refinement) showed that the bend residues 3 to 6 bind similarly but less deeply than R13. After the refinement, the curved region (residues 3 to 6) becomes less curved and there is a change in the relative position of the C terminal with respect to the antibody, this is shown in figure 5. The E1 backbone carbonyl is forming a hydrogen bond with the side chain amide nitrogen of K149 (light chain). D2, D4, D5 and D6 are neutralizing K172, R165 (both at the light chain), R50 and R52 (both at the heavy chain), respectively. The remaining residues (7 to 13) are exposed to the solvent. See figure 6.

Another difference observed between the interactions of the two peptides with the antibody is the variation of the solvent accessible surface between the free and the docked state. The change in the solvent accessible surface was 10% for P013 and 13% for R13 after refinement. This parameter is a measure of the entropy increase in the complex formation and is given by the water molecule exclusion in the interaction surface.

The third docking study was about rhodopsin (this complex was not refined due to the size of the system). It was found that the residues PEVN of the second extra cellular loop bind in a similar fashion as to residues 3 to 6 in the R13-P013 complexes. Rhodopsin E197 is occupying the same position as E3 in the R13 complex. It is stabilized by the formation of two ions pairs: the first with R50 (heavy chain), remaining in the same conformation as it had in the previous complexes, and the second with R52 (heavy chain), which has moved from the position it had in the R13 complex being now in a conformation that allows the interaction with E197.