# Fast and Interactive Positioning of Proteins within Membranes
## 3 Results
### Comparison of IMPALA/BioSpring and Reference Data  
We were interested in validating our implementation with respect to the studies of [PERSON]'s team on the OmpA protein, so we used a rigid body representation. The rigid body dynamics were implemented in our BioSpring engine specifically for this study, as described in Section 2. For validation purposes, we used exhaustive sampling with discrete values offset by 1 A or 1\({}^{\circ}\) for all positions that the protein can occupy either fully or partially in the membrane. First, we applied our protocol to determine the energies for each insertion depth and angle separately, as in the results in Figure 2 of [17]. For direct comparison, we extracted the data points from the original plots using the WebPlotDigitizer tool [33] and integrated them into the plots as blue points. The energy term IMP is defined in kcal/mol and is a restraint term rather than an actual energy function, since it does not correspond to the actual physical interactions [18]. The residues chosen to represent the insertion vector and thus measure the angle with respect to the membrane are Lys34 and Val45, which correspond to the reference strand (second \(\beta\)-strand) given in the original publication. However, there is an ambiguity because, in contradiction to this indication in the text of the article, residues 31B-36B, i.e., residues 31 and 36 of chain B, are indicated in Table 2 of [17]. However, only K34 and V45 agree with the structural representation in Part A, Panel (F) of Figure 3 of [17], so we discarded the other pair. The particles chosen to represent this vector are the \(\alpha\)-carbons of these residues. Figure 7 shows 9523 steps, where each successive step corresponds to a position where the insertion angle varies from 0\({}^{\circ}\) to 90\({}^{\circ}\) in steps of 1\({}^{\circ}\). This range of positive insertion angles (between 0\({}^{\circ}\) and 90\({}^{\circ}\)) was chosen to allow consistent comparison with [PERSON]'s data and to measure the same range of insertion angles. As explained above, each step also corresponds to the minimum energy roll for a given insertion angle. The experiment was performed for OmpA with an insertion depth of about 53 A to \(-\)53 A, as we can see in Figure 7A. This range extends the insertion to the entire membrane and shows us in Figure 7C that the preferred insertion depth for positive insertion angles is about \(-\)5 A +/\(-\) 5 A, while the reference value given by [PERSON] is \(-\)7 A. These preliminary results for the insertion angles do not show clear preferred ranges for the angles, but some local stabilities around 20\({}^{\circ}\), 35\({}^{\circ}\), and 45\({}^{\circ}\). For OmpA, [PERSON]'s reference angle is 50\({}^{\circ}\) to 55\({}^{\circ}\) with respect to the membrane surface. However, they point out in their paper that the literature assumes that all strands (of which the insertion vector is a representative) are tilted by about \(\sim\)45\({}^{\circ}\) with respect to the membrane surface, which is consistent with our results. We also recall that it remains unclear how exactly the roll degree of freedom was handled in the reference work. Since we find non-negligible differences in the insertion angles between the approach proposed here and the reference Monte Carlo calculations, further analysis is required. For a more detailed discussion, see Section 4. Appendix A contains additional experiments and references to alternative solutions. It is interesting to note that this automatic sampling procedure seems to reproduce some trajectory-like patterns that we will find in the interactive simulations in the next section. Figure 7: Automatic scanning of the membrane insertion of the OmpA membrane protein. The blue dots correspond to the energies of the reference Monte Carlo calculations, as indicated in the text. The results of our own calculations are represented by the gray and black dots. The black dots are the minimum energy values at a given insertion angle or depth, rounded to the nearest multiple of 0.5.