Bias-exchange metadynamics. BEMD 66-67 simulations were carried out adopting seven collective variables (the number of Cα -Cα contacts, Cγ -Cγ hydrophobic contacts and backbone H-bonds, dihedral correlation, α-content, antiparallel β-content and parallel β-content, as defined in Supplementary Note 2) and eight replicas, with one collective variable per replica plus the unbiased replica. One of the initial guess configurations was first equilibrated in NpT ensemble at 1 atm and 300 K for about 5 ns per replica in NpT ensemble according to the discussed protocol (vide supra); BEMD simulations were performed in NVT ensemble at 300 K, collecting 1000 ns of data for each replica; exchange of conformations between two randomly selected replicas were periodically attempted every 10000 simulation steps. CV were biased according to ordinary metadynamics scheme, adding the bias potential every 2500 simulation steps using a height value equal to 0.3 kJ mol -1 . After 160 ns, the system explored a wide region for each collective variable and we introduced loose lower and upper boundaries to improve convergence (Supplementary Note 8). The PLUMED input files required to reproduce the results of BEMD are available on PLUMED-NEST (www.plumednest.org), the public repository of the PLUMED consortium 126 .