## 3 Results and Discussion
This reflects a lower variability of the results obtained from different executions of IGLOO compared to the two other methods. Due to the stochastic nature of the three algorithms, some runs deviate from their average behavior, as illustrated by the outliers shown in Figure 1. This confirms the need for a sufficient number of runs to obtain sufficient statistics for a meaningful comparative analysis of these methods. In summary, at short exploration times, the IGLOO algorithm locates structures of lower energy than the BH and HYBRID algorithms and with lower variability, demonstrating its ability to rapidly explore the PES with the objective of finding the global minimum. The lowest-energy structures identified by each global optimization method during long runs are depicted in Figure 2 for Met-enkephalin, and in Figure 3 for df-c-Myb, together with their energy and the execution time at which they were found. Regarding Met-enkephalin, the structures found by the three algorithms are similar and have very similar energies. The structure obtained by IGLOO was the one with the lowest-energy, followed by BH (+0.41 kcal/mol) and HYBRID (+0.80 kcal/mol). These energy differences come from the side-chain of residue 5 which breaks the stabilizing stacking interaction between the phenol group of residue 1 and the phenyl group of residue 4. The time needed  
Figure 1: Evolution of the Met-enkephalin (top) and df-c-Myb (bottom) lowest energy (in kcal/mol) for BH (red), HYBRID (blue) and IGLOO (green) algorithms as a function of CPU time (in s). The solid lines represent the average value over ten runs of each algorithm. The variability of their performance is illustrated by the colored area between the first and third quartile (dashed lines). Outliers are represented by red circles (BH), blue diamonds (HYBRID), and green crosses (IGLOO). for IGLOO to discover the lowest-energy structure of Met-enkephalin is around 2 and 20 times shorter than the one needed for the HYBRID and BH algorithms, respectively, to locate their optimal structures (which are still slightly less energetically favorable than the one found by IGLOO). This confirms the better performance of IGLOO in terms of convergence to the global minimum. The lowest-energy structures of df-c-Myb corresponding to each of the structural motifs (HPN1, HPN2 and HLX) are presented in Figure 3 for each of the three algorithms, including the time step when the structures were observed. A secondary structure was  
Figure 3: df-c-Myb HPN1, HPN2 and HLX lowest-energy structures found by BH (red), HYBRID (blue) and IGLOO (green) and associated energy (in kcal/mol) and CPU time (in s). Residue numbers are depicted in white. Figure 2: Met-enkephalin lowest-energy structure found by BH (red), HYBRID (blue) and IGLOO (green) and associated energy (in kcal/mol) and CPU time (in s). Residue numbers are depicted in white. classified as a hairpin when it contains a \(\beta\)-turn H-bond (\({}^{7}\)NH-\({}^{4}\)O for HPN1 and \({}^{6}\)NH-\({}^{3}\)O for HPN2) associated to at least one inter-strand H-bond. The possible inter-strand H-bonds are \({}^{9}\)NH-\({}^{2}\)O, \({}^{3}\)NH-\({}^{8}\)O, \({}^{8}\)NH-\({}^{3}\)O and \({}^{4}\)NH-\({}^{7}\)O for HPN1 and \({}^{8}\)NH-\({}^{1}\)O, \({}^{2}\)NH-\({}^{7}\)O and \({}^{3}\)NH-\({}^{6}\)O for HPN2. A secondary structure was classified as a helix when it contains at least two hydrogen bonds among \({}^{6}\)NH-\({}^{2}\)O, \({}^{8}\)NH-\({}^{4}\)O, \({}^{5}\)NH-\({}^{1}\)O, \({}^{7}\)NH-\({}^{3}\)O and \({}^{9}\)NH-\({}^{5}\)O. A H-bond was considered to be present when the distance between a donor and an acceptor atom was shorter than a threshold value set to 3.3 A. The three global optimization methods all succeed in visiting the three structural motif regions: HPN1, HPN2, and HLX. However, the methods differ in their ability to locate the lowest-energy structure for each motif.