Figure 2.

An illustration of the HSMD reconstruction process of conformation i of a peptide consisting of three glycine residues, where for simplicity the oxygens and most of the hydrogens are discarded. At step k^′ = 6, the TPs related to the “past” atoms k^′ = 1, …, 5 (depicted by full spheres) have already been determined and these atoms are kept fixed in their positions at conformation i. At this step (6) one calculates the TPs of bond angle α_k (defined by C^′-C_α-N) and dihedral angle α_k-1 (defined by C^′-C_α-N-C^′) which are related to C^′, where k = 2k^′ and thus k = 12. The TPs are obtained from an MD simulation where the as yet unreconstructed atoms k^′ = 6, …, 10 (the “future” atoms) are moved (depicted by empty spheres connected by dashed lines) while the past atoms k^′ = 1, …, 5 are kept fixed; note that the future part should remain within the limits of the microstate and future-past interactions are taken into account. Small bins δα_k-1 and δα_k are centered at the values α_k-1 and α_k in i. The TP is calculated from the number of visits [n_visit, Eq. 11] of the future part to δα_k-1 and δα_k simultaneously during the simulation. After ρ^HS (α₁₁ α₁₂|α₁₀ ,...,α₁) [Eq. 12] has been determined, the coordinates of C^′ (and O) are fixed at their positions in i, i.e., they become “past” atoms and the process continues.