# Fast and Interactive Positioning of Proteins within Membranes
## 2 Materials and Methods
### Monitoring, Interaction Design and Visual Analysis
#### 2.4.1 Definition and Measurement of Important Descriptors  
Insertion angle. For the implementation, we apply the controlled simulation of the insertion angle parameter by defining an insertion vector based on two particles. These two particles are selected according to the alpha carbon atoms CA of the reference residue pairs described in [17] that define a reference secondary structure element--in our case, a beta strand. The insertion vector is different from the major axis of the protein (e.g., the central axis of a \(\beta\)-barrel), and so the insertion angle gives the tilt angle of the membrane protein strands for \(\beta\)-proteins with respect to the membrane surface, as explained in [17]. We create a reference axis that passes through the insertion vector. This reference axis allows us to freely simulate the degree of freedom of the roll rotation, which is not captured by the insertion angle alone. The roll value is not explicitly captured, but evolves according to the trajectory of the protein at a given insertion angle. The pseudo-code of the corresponding function \"computeAngle\" is given in Figure 6.  
Figure 5: Performance benchmark on a structure with 12,000 particles. The colored crosses correspond to the workstations described in the text, with sablons, han, hal, and dell shown in blue, green, gray, and red, respectively.  
In the implementation of the automatic scan, a rotation of 180\({}^{\circ}\) range is performed with a step of 1\({}^{\circ}\) along the axis perpendicular to the unit vector z and the insertion vector (vector product). This range corresponds to a variation of +90\({}^{\circ}\) to \(-\)90\({}^{\circ}\) as the latitude of the geographic coordinates.  
Insertion depth. More precisely, the insertion depth is the value of the z-component of the center of mass (COM) of the protein, with the z-axis being perpendicular to the membrane plane. For proteins with detailed information about all atoms (including hydrogen atoms), the COM is the average of the positions of the atoms weighted by their mass. We calculated the initial and final z values as a function of the distance d\({}_{\rm max}\), beyond the implicit membrane width spanning from +18 A to \(-\)18 A, that lies between the COM and the structurally most distant atom. Thus, the z value of the COM varies with a decrease of \(-\)1 A at each step in a range of \(\pm\)(18 + d\({}_{\rm max}\)), where 18 is the z value in A of the outer membrane boundary.  
Roll angle. The roll rotation along the axis passing through the insertion vector varies from 0 to 360 degrees. We included the measurement of the roll angle in this study. It is a degree of freedom that was not explicitly mentioned in the studies of [PERSON]'s team, although it was necessarily simulated as a hidden variable in their Monte Carlo experiments. In fact, this variable seems to be important because there are several possible positions for a given insertion angle. It is therefore necessary that the sampling approach explicitly contains this roll rotation for all insertion angles. On the other hand, we do not keep all steps for each roll angle, but only the step for a particular angle that has the lowest energy among all roll angles, which is a form of dimensionality reduction. It is, of course, possible to find multiple local energy minima at different roll angles for the same insertion angle. In this case, exploratory research with interactive simulations is useful to discover the transition states between multiple local minima.