Figure reports an analysis of the energy conservation during the NVE simulations for the two systems and for the four models (including vacuum). The energy conservation is overall good, as it remains of the same order of magnitude as the one observed for the vacuum trajectory. In terms of relative energy conservation, the energy fluctuations in the antifreeze protein MD remain in the -2-+4‰ range, whereas the ones of the peptide remain in the ±2‰ range. The usage of a tighter threshold mostly affects the short-time fluctuations, with a more pronounced effect on ddLPB due to the inner-outer linear system solver.