## 3 Results and Discussion  
To analyse the performance of the algorithms, two molecules with different size and conformational behavior were chosen, as they allow different properties to be evaluated. The first molecule, Met-enkephalin, is an endogenous opioid pentapeptide (Tyr-Gly-Gly-Phe-Met) exhibiting a stable conformational state and various metastable ones [42]. The second molecule, referred to as df-c-Myb in the following, is an heptapeptide (Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-NMe) derived from the recognition helix of the c-Myb DNA-binding protein [43]. It presents a more complex PES containing regions of the conformational space characterised by different structural motifs [44]. A good characterization of the PES of these two molecules therefore requires an algorithm able to accurately locate the global minimum while exhaustively exploring the diversity of local minima, both with a high convergence rate. In the following, the performance of the three algorithms presented in Section 2.1 will be compared on the basis of (\(i\)) their convergence towards the global energy minimum, (\(ii\)) the associated atomic structures and computing costs, and (\(iii\)) their ability to explore different regions of the conformational space of the df-c-Myb PES corresponding to three different structural motifs: an \(\alpha\)-helix (HLX) and two \(\beta\)-hairpins (HPN1 and HPN2). Note that we have used parallelized versions of the three algorithms. Therefore, the computing times mentioned below correspond to the sum of the CPU time for each thread. Given that we used 45 threads and that the speedup of the parallel version is almost linear with the number of threads, the wall-clock time is approximately the total CPU time divided by 45. Figure 1 shows the evolution of the observed minimum energy as a function of the CPU time for the molecules used in our analyses. Here we depict, as a function of time, the value of the minimum energy averaged over 10 runs, together with a quartile-based estimate of the spread of the minimum energies observed. In the plot at the top, corresponding to Met-enkephalin, the IGLOO curve remains below the BH and HYBRID ones throughout the exploration. The IGLOO lowest energy decreases very rapidly until around \(2\times 10^{4}\) s, after which the slope decreases markedly and the average energy improves very little beyond \(4\times 10^{4}\) s. The overall behaviour of the HYBRID algorithm is similar to that of IGLOO but with a smaller initial slope and a stagnation of the observed minimum energy after \(3\times 10^{4}\) s. The BH curve looks very different, with a much shallower slope and large plateaus. After \(6\times 10^{4}\) s of exploration, the IGLOO energy (\(-224.43\) kcal/mol) is much lower than the energies of the other two algorithms (\(-221.63\) kcal/mol for HYBRID and \(-221.77\) kcal/mol for BH, respectively). The curves representing the evolution of the lowest energy of df-c-Myb (Figure 1, bottom panel) show a better performance of IGLOO in terms of convergence towards the minimum energy (\(-628.75\) kcal/mol after \(1.4\times 10^{5}\) s) compared to BH (\(-626.04\) kcal/mol) and HYBRID (\(-622.86\) kcal/mol). The IGLOO curve has an almost constant slope up to \(1.25\times 10^{5}\) s, exploration time at which the average minimum energy reaches a plateau. Although its approach to low minimum energies is slower at the beginning, IGLOO surpasses the two other algorithms beyond \(8.5\times 10^{4}\) s.  
The variability of the performance of the algorithms is illustrated by their first and third quartiles shown as dotted lines in Figure 1. These quartiles were computed from 10 independent runs of the algorithms, using time frames of 650 s for Met-enkephaline and 1450 s for df-c-Myb. For the Met-enkephalin and df-c-Myb, IGLOO exhibits an interquartile mean value of \(0.7\pm 0.21\) and \(1.90\pm 0.71\), respectively, vs. \(1.34\pm 0.35\) and \(2.46\pm 1.74\), respectively, for HYBRID, and \(1.64\pm 0.64\) and \(3.03\pm 1.38\), respectively, for BH.