Bulk behaviour To characterise the conformational behaviour of the peptide, first we looked at the statistics of alpha carbons and the torsion angles. Then they were correlated with positions of positively charged end groups R and K and negatively charge group D. K P A R 3 4 Proline Arginine L 5 6 Lysine Alanine Leucine Aspartic Acid D FIG.. Chemical structure of the RKLPDA peptide. Numbers on the left mark alpha carbons. The information was gathered from three independent MD runs and added up to build the probability distributions. The distance distribution between next neighbour alpha carbons was found to be the same (about 3.87+/-0.0A) for -, -3, 4-5, and 5-6 pairs, while 3-4 was slightly longer (about 3.9+/-0.0A) due to the presence of the proline ring. This ring also results in narrow distribution of distances -4 and especially 3-5 making this part of the backbone relatively stiff. Cα Cα 3 3 FIG.. The part of the backbone between two alpha carbons + 3 bonds and their torsion angles. Figure shows a typical CO-NH amide bond which forms a planar arrangement with alpha carbons. It also shows a typical orientation of bonds coming out of each alpha carbon, Cα in this example. There are three sp3 bonds: bond # to the hydrogen is within the plain of the peptide bond, bond # belongs to the amino acid and is above this plain, bond #3 leads to the next carbon in the backbone. The bond angles between these three bonds and the NH-C bond fluctuate between 05 and 6 degrees. The torsion angles between these three bonds and the peptide bond are more flexible and fluctuate within +/-30 degrees from their equilibrium positions (see Fig. b). Most flexible is the torsion angle between the peptide bond planes (psi), i.e. the orientation of the next plane in respect to the previous. The Ramachandran plot in Fig. 3 demonstrates the phase trajectories in (phi, psi) plane for each amino acid (I used the data from six configuration files for each MD run Adam sent me, and phi and psi are defined as torsion angles CO-NH-C-CO and NHC-CO-NH respectively). Here, L and P always stayed in beta sheet conformation, D and A were changing between beta and alpha conformations, R and K could exist in both conformations but
Beta sheet Alpha helix FIG. 3. Ramachandran plot colour-coded according to each amino acid. The shape of the symbol corresponds to the MD run (circle - first, square - second, triangle third). seem to stay in a particular conformation for much longer than D and A. There was no transition for K group which were in the beta conformation in first and second runs and alpha in the third run, whereas R (this time beta in second and third run and alpha in the first run) managed to go from alpha to beta conformation in the first MD run: R K L P D A run α, α, α, run α, α, run 3 α α, α, Tab.. Conformations of each peptide bond in each run. There is a stiff part (L, P) with a wiggly tail (D, A) on one side and two slow moving charged groups (R, K) on the other. There are two distinct conformations of the backbone characterised by two peaks in distribution of distances between alpha carbons and 6 (we did not look at the end-to-end distance but it is expected to have a similar double peak distribution). CONFORMATION CONFORMATION less probable (8%) (-6) =.7A +/- 0.6A short (D-R) of about 5A long (D-K) of about 3A more probable (7%) (-6) = 5.7A +/- 0.7A long (D-R) of about 4A to 8A short (D-K) of about 8A FIG. 3. Two typical conformations of the backbone defined by the peaks in -6 alpha carbon distance distribution.
This agrees well with the distribution of distances between alpha carbons and 4, which also has two clear peaks with the same area ratio. Figure 4a illustrates that there is also a correlation between distance -6 and the distances between unlike charged amino acids. run run run 3 FIG. 4. (a) Phase trajectory for three MD runs shows correlation between peptide conformation and and the distances between unlike charged end groups. Each colour represents a run (RGB -,, 3), solid lines are for D-R distances and dashed lines are for D-K distances. (b) cos(dihedral angle between alpha carbons). Figure 4b shows dihedral angles between alpha carbons --3-4 (red), -3-4-5 (green), 3-4-5-6 (blue). Clearly, angle --3-4 is different in run 3 from that in the first and second runs. beta, beta beta, alpha run run 3 alpha, beta run FIG. 5. Relation between the conformation of the backbone and two first dihedral angles psi (NH-C-CO-NH angles, where alpha carbon C belongs to R or K).
!!! The backbone conformation is defined entirely by the NH-C-CO-NH angle where alpha carbon C belongs to the Lysine (K). CONFORMATION. If this angle has a typical alpha helix value, then groups R and D are on the same side of the backbone. Group R is always in beta conformation (otherwise it would be facing away from negatively charged group D). So no (alpha, alpha) conformation. CONFORMATION. If this angle has a typical beta sheet value, then groups K and D are on the same side of the backbone while group R faces away. Group R can form either beta or alpha conformation with the backbone. In run, we saw one alpha to beta transition which implies that beta conformation might be more favourable. Three typical conformations from each MD run are shown in Fig. 5. Each configuration is orientated so the plane of the peptide bond connecting R and K groups is perpendicular to the plane of the page and N-H bond is pointing out of the page. The consequential peptide bond connecting groups K and L (highlighted in the picture) has different orientation in each case. Since the section of the backbone between alpha carbons and 5 never changes its conformation, the orientation of the highlighted bonds defines the orientation of this whole segment of the backbone. In runs and two it points up (slightly out and into the page) while in run3 it points down and aspartic acid can approach arginine very close. Note that 8% and 7% occurrence for conformations and is entirely because we averaged the distributions together from three runs: two for type and for type (it would have been 33% and 66% if we had the same number of configurations for each run. I guess they were different.) There were no transition between conformation and type in a single MD run. There seems to be no correlation between these two conformations and bimodal distribution of distance (-R). This bimodal behaviour comes from the discrete structure of arginine: the cis- or trans- conformation of the carbon chain to which the charged group is attached. Compare the conformation of the arginine group in Fig. 5 in runs and. Similarly the complex conformational behaviour of the lysine group (K) can be explained. Note that alpha conformation of the first NH-C-CO-NH torsion angle (R) means that both lysine and arginine amino acids are on the same side of the backbone. This causes both the entropical frustration and electrostatic repulsion between positively charged end groups. If we look at the first carbon-carbon bond giving the direction to R and K groups, the angle between these bonds correlates well with the above torsion angle. Therefore, whole run might have been just a relaxation to a more favourable beta conformation. run run run 3 FIG. 6. Orientation of groups R and K in respect to each other: two bonds C-C give orientation of the two amino acids (red), psi is the dihedral angle NH-C-CO-NH, where alpha carbon C belongs to R (green). To conclude, assuming that all chemical bond lengths and angles are constant, the peptide conformation is defined entirely by its dihedral angles (phi, psi, omega). Omega is close to 80 degrees meaning that all peptide bonds are planar, phi is always negative (no left-haded helix) and psi is the most flexible degree of freedom. Positive value for psi_r provides groups R and K are on different sides of the backbone, psi_k defines which positively charged group will end up close to the aspartic acid (D), psi_l and psi_p are fixed in beta conformation due to the proline ring and dihedral angles psi_d and psi_a do not affect the rest of the peptide conformation.
Peptide on TiO surface The conformational behaviour of the peptide was analysed using data from 5 MD runs: 4700 conformations to build the distribution functions, 9 typical conformations used for the analysis below. First, let us look at the Ramachandran plot built for each amino acid and compare it tho the one observed in the bulk. Here, though groups P and L are still more likely to be found in beta-sheet conformation, their alpha-helix conformations have also been observed. The wiggly tail, groups D and A are still changing between beta and alpha conformations. This time there were even some conformations having positive phi torsion angle for group A. Beta sheet Alpha helix FIG. 7. Ramachandran plot for the peptide adsorbed on TiO surface colour-coded according to each amino acid. -6 distance FIG. 8. (a) Correlation between distance between alpha carbons -6 and D-R (circles) and D-K (triangles). The colours correspond to a particular configuration file from to 9. (b) When peptide is adsorbed on the surface there are 3 typical conformations of the backbone. Figure 8 shows that for the adsorbed peptide the correlation between -6 and and D-R and D-K distances is less profound than it was in the bulk some conformations have high values of D-R
and D-K simultaneously. There is also three typical -6 distances marked by green lines in Fig. 8a. The shortest -6 distance of about.8a corresponds to short D-R distances of about 5A and long D-K distances of about 4A. Most of the conformations contributing to the second peak in -6 distribution have the opposite feature D-K is shorter then D-R. The same is true for the conformations contributing to the third peak in -6 distribution. Therefore, the appearance of the middle peak in Fig. 8b comes from type conformations, i.e. psi_k is in beta conformation. Table summarises the parameters specific to peptide's conformation and having complex probability distributions measured for 9 configurations Adam sent me (there were 0 conformations, but files 0 and appeared to be identical). 9 4 0 3 3 8 6 8 9 4 7 5 6 7 5 0-6 dist.5.7.3 3.9 3.9 3.9 3.9 4.0 4.4 4.5 4.9 5.6 5.9 6.0 6. 6. 6.3 6.8 6.9-4 dist 7.5 7.6 7.6 9.6 9.5 9.6 9.7 9.8 0.0 9. 9.0 9.3 9.9 9.3 9.6 9.6 9.7 0. 0.5 3-5 dist 6.7 6.5 6.3 5.3 7.3 7.3 6.8 6.4 6.4 7. 6.5 6.7 6.6 6.8 6.6 7.3 6.9 D-R dist 6.0 5. 4.8 4. 8.4 8.8 3.4 8.6 8.8 6.9 5.6 0.5..0 4.4 7.6 4.6 6. 6. D-K dist 4.5.7 4.0 6. 6.4 9.8..9 3.8 3.6.5 9.8 3.3 3.7 3.3.4 9.7 9.4 3.6.9. 09 psi R 93 86 75 6-80 -69-60 -83-94 84 54 56 9 0 89 7 5 4 psi K -63-63 -58 96 00 3 09 93 99 46-33 46 54 56 8 36 70 4 37 psi L -6-7 54 85 99 0 87 04 35 7 4 7 34-59 53 49 40 54 psi P 39 4 6-8 75 70 73-66 -74 78 69 46 49 7 43-74 50 0 4 Zc.m. 3.94 3.94 8.5 6.04 3.6 3.64 9.76 4.96 6.74 5.04 5.73 6.55 6.3 6.4 4. 4.4 4.38 3.3 3.46 Tab.. Various distances and torsion angles are measured for 9 different conformations. The data is ordered by -6 distance. Blue colour indicates typical low values, purple typical high values. If there is a typical middle value, it is shown in green. For the torsion angles yellow corresponds to the beta conformation and orange to the alpha. Last row contains distances from the geometrical centre of mass to the plane of the bridging oxygens. Similar to the bulk situation all conformations can be divided in three groups according to psi_r and psi_k torsion angles: (beta, alpha), (alpha, beta), and (beta, beta). Three configurations, 3 and 7, however, have some features which do not follow the general trend. Group : files 9, 4, 0 (beta, alpha). With files 4 and 9 being nearly identical, there are two configurations in this group one is further away from the surface than the other. This gives some insight into how (beta, alpha) conformation might be adsorbed. First, the peptide approaches the TiO surface with groups R and D facing the surface. Then, when it hits the surface, the torsion angle psi_l adopts alpha conformation the proline ring buckles up as a result. The peptide binds to the surface by four oxygens they take the place of oxygens in water layers formed at the TiO surface. Figure 9 shows both side and top views for configuration files 0 and 9. One of these oxygens belongs to aspartic acid, whereas the other three belong to NH-CO complexes on the backbone. Additionally arginine (R) forms a hydrogen bond with one of the bridging oxygens and there are two more hydrogens attracted to the bridging oxygens.
0 9 FIG. 9. Configurations 0 and 9: side views at the top, top views at the bottom. Black circles marked binding oxygens, yellow circles binding hydrogens. Group : files 3, 8, 6, 8, 9 (alpha, beta). From the bulk simulations we know that alpha conformation of the psi_r torsion angle results in R and K amino groups to be on the same side of the backbone. This, however, does not mean that this conformation will be definitely unfavourable when adsorbed on TiO surface, since the peptidesurface interaction might be significant. Configurations 3 and 8 are very similar, configuration 6 located far away from the TiO surface with charged amino groups facing away from the surface (plus that chloride ion, present in every file, is situated right between the peptide and the surface), so there are three configurations to analyse. Figure 0 shows configurations 9, 8, and 8 (in order the distance between the peptide and the surface decreases). Similarly to Fig. 9. in all three cases the segment of the peptide around alpha-helix torsion angle (this time psi_r) ends up nailed down to the surface by two oxygens from the backbone. Consequently, the hydrogen from the next peptide bond CO-NH binds to the bridging oxygen and the oxygen from the following CO-NH bond (the one right before the proline ring) is also bound to the surface in all three configurations in Fig. 0. Note that the arginine (R) is not bound in any of these conformations.
9 8 8 FIG.. Configurations 9, 8, and 8: side views at the top, top views at the bottom. Group 3: files 4, 5, 6,,, 5, 0 (beta, beta). Let us start again from the conformations which are further away from the TiO surface, as defined by the last row in table. Configurations 5 and 6 are very similar in both cases the lisyne is located very close to the aspartic acid and the peptide attaches to the surface by forming a hydrogen bond between the lisyne charged group and a bridging oxygen on the TiO surface. This conformation is typical for the bulk and the effect of the surface seems to be small. Configuration 7 appears to be an early stage of adsorption aspartic acid brakes hands with lisyne and turns to the TiO surface. There is however no direct binding yet. Configuration 4 (Fig. ) has already two oxygens bound to the surface one belongs to the aspartic acid (D) and the other one is from the very first peptide bond. Both positively charged groups R and K are facing away from the surface. 4 FIG.. Configurations 4,, and : side views at the top, top views at the bottom.
5 3 7 FIG. 3. Configurations 5,, 3 and 7: side views at the top, top views at the bottom. All other configurations in this group (,, 5, 0) have these two oxygens also bound to the TiO surface this is the signature of adsorption in (beta, beta) conformation. Indeed, all bulk conformations of this type already have these two oxygens on the same side of the peptide and the average distance between them is about 4A. This commensurates with twice the period of the TiO surface structure. There remains three more conformations which do not follow the trend. In configuration, the very last peptide bond is bound to the TiO surface similarly to configuration 9 and 5. The aspartic acid is located on the same side of the backbone as in configuration 5 but as not as close to the surface. Another similarity between and 9 is that torsion angle psi_l is in its alpha-helix conformation (you can see the proline ring buckling up from the TiO surface in both cases). Configuration 3 is the only one with psi_p in the alpha conformation, which also results in short
distances between alpha carbons 3 and 5. This was probably caused by the aspartic acid (D) being pulled towards the surface by the electrostatic interactions. Configuration 7 has an unusually high torsion angle psi_k. I believe that given enough time it would relax (or may be it did, Adam would know) to conformation. To conclude, there are two mechanism of adsorption:. Having an alpha-helix configuration of a psi angle results in two oxygens from the two peptide bonds around the common alpha carbon to be on the same side of the backbone. All three amino acids around this conformation are naturally facing away from the oxygens, making it easier for them to bind to the TiO surface.. Aspartic acid and the oxygen from the very first peptide bond are situated on the same side of the peptide when all psi angles are in their beta sheet conformations. In all observed cases the binding to the TiO surface occurred in the direction perpendicular to the grooves formed by the bridging oxygens. It is known from experiment (JACS, 5, 434 (003)), that the arginine group (K) is much more important for the adsorption than the lysine (R). Even more than that, when the lysine is substituted with neutral alanine, the adsorption improves. This rules out the scenario of adsorption for group, because in all adsorbed conformations the arginine group was not even bound to the TiO surface (Fig. ). In group one, however, it is the lysine which is not bound to the surface and replacing it with a shorter neutral alanine group would () make the bulk peptide conformation with groups K and D close to each other most favourable () decrease entropic (and may be energetic) penalty upon adsorption in a configuration like 9. The JACS paper also suggests that the proline changes its conformation from trans to cis. We did not see this in the simulation. Instead, the torsion angle psi (NH-C-CO-NH) just before the ring changed from beta to alpha, so aspartic acid could reach the TiO surface. Maybe replacing this bit of the peptide with cis-proline will do the same trick. It actually might be the other way around first the aspartic acid and arginine attach to the TiO surface and then the backbone between them has to twist so the two oxygens can also bind. I hope Adam could clear these things out. As to the adsorption in group three (beta, beta) it is not clear yet why it should not take place. Some of the bond angles and torsion angles in conformation 5 seem to have values quite high values. Also the substitution of the lysine with alanine and the effect of the proline ring are not quite clear. hydrogen binding oxygen binding FIG. 4. Peptide binds to TiO surface via highly structured water layer. In this report I concentrated on the oxygen binding but there is also strong coupling between the peptide's hydrogens and water molecules.
Appendix I used words dihedral or torsion angles to describe the same thing a four body ABCD angle between planes ABC and BCD. Note that ABCD = DCBA. FIG. 5. Definition of dihedral (torsion) angles. Angles phi, psi, omega are specific angles used to describe conformation of a peptide backbone. To a good approximation omega is 80 degrees (it had a trans-conformation throughout all simulations, see Fig..) The same way peptide and and amide mean the same CO-NH bond in the peptide backbone.