# Fast and Interactive Positioning of Proteins within Membranes
## 3 Results
### Graphical Analysis of Interactive Insertion Experiments  
We designed a graphical representation to show the details of protein insertion. As shown in Figures 9 and 10, it is possible to determine the most favorable insertion angle and the associated roll for a given insertion depth. The diagrams show us in detail the region of most favorable insertion depth, with a region at \(-10^{\circ}\) corresponding to two categories of narrow insertion angles, \(35^{\circ}\) and \(45^{\circ}\), where we see an increase in atoms in the interfacial region of the membrane. The second region in the core of the membrane around \(0\) A is related to the lower insertion angles around \(15^{\circ}\) to \(20^{\circ}\), where we suspect that the protein is more horizontal within the hydrophobic core, as the percentage of particles at the interface decreases in this region, as indicated by the green curve. Note that intuitively, the insertion angle does not give us a clear idea of the overall position of the structure, and the chosen definition of the insertion angle for \(\beta\)-barrel proteins such as OmpA does not pass through the barrel axis. The energy barrier between \(-10\) A and \(-5\) A can be equated with a transition zone between the two regions mentioned above. This transition involves straightening of the protein reaching higher angles in the membrane, with partial exposure of the protein in the hydrophilic phase, as shown by the indentation in the orange curve. These results, together with the interactive simulations, give more credible information about the transitions between the favorable angular and depth zones than the absolute values, which must be related to uncertainties associated with the choice of atomic radii, rigid body dynamics, atomic transfer energies, IMPALA equations, etc. The core of this work lies in  
Figure 8: Interactive membrane insertion of OmpA. The blue dots correspond to the energy values of the Monte Carlo reference calculations. The windows for insertion depth (Å) and insertion angle (\({}^{\circ}\)) remain unchanged. The results of our own experiments 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. The gray dots correspond to all other energy values. Both plots have a common \(Y\)-axis on which the IMPALA energy term is shown in kcal/mol. the implementation of an interactive insertion protocol that allows the user to control and quickly simulate all input parameters. The interactive simulations of our protocol with the simulation-visualization coupling allow us to provide live visual feedback and to capture and analyze positions after the fact, as shown in Figure 11.  
Figure 10: Enlargement of Figure 9, with focus on the area spanned by the reference insertion calculations. Figure 9: Detailed illustration of a membrane insertion experiment performed for OmpA. The colored circles mark the steps with the most favorable insertion angle at a given insertion depth. Each step can be associated with its IMPALA constraint (left vertical axis) corresponding to its insertion depth (horizontal axis), and the color provides information about the insertion angle; see color scale for correspondence. A black line starts at each step and its slope in the diagram represents the insertion angle, ranging from \(0^{\circ}\) (vertical line) to \(90^{\circ}\) (horizontal line). This is shown schematically in the reference circle on the right side of the figure. The vertical bars in transparent green represent the interface regions of the IMPALA membrane model. The green curve with the filled transparent-green region and the orange curve represent the percentage presence of atoms in the interfacial regions and in the whole membrane region, respectively. These two curves can be read on the right vertical axis.