Fig. 2: Metadynamics simulations of HG cross-linking.

a Running average coordination number of Ca²⁺ with water molecules in an unbiased MD simulation. The shaded region highlights the uncertainty associated with our estimate (min–max error); the inset illustrated a six-coordinated Ca²⁺ ion. b Free energy surface relative to the formation of a single -COO⁻∥ Ca²⁺∥ -COO⁻ bridge, reported as a function of the coordination number of the Ca²⁺ ion with water molecules [CN(Ca²⁺ - H₂O)] as well as the coordination number of the Ca²⁺ ion with any of the four oxygen atoms belonging to the two -COO⁻ groups [CN(Ca²⁺ - (4)COO⁻)]. c Free energy profile relative to the interaction between a Ca²⁺ and a single COO⁻ group, reported as a function of the distance between the Ca²⁺ ion and any of the two oxygen atoms belonging to the COO⁻ group [d(Ca²⁺ - -COO⁻)]. d Representative configuration of a -COO⁻∥ Ca²⁺∥ -COO⁻ bridge. The Ca²⁺ ion and the four oxygen atoms belonging to the two -COO⁻ groups are coloured in orange and green, respectively. We also show the three water molecules the Ca²⁺ ion is coordinated to in that specific configuration. e Free energy profile relative to the interaction between two methylated carboxyl groups, reported as a function of the distance between one of the two carbon atoms within the -CH3 groups and one of the two oxygen atoms involved in the -C=O double bond; (a) typical configuration is depicted in (f), where the relevant carbon atoms are coloured in purple. g Free energy profile relative to the interaction between two carboxyl groups, reported as a function of the distance between one of the two de-protonated oxygen atoms and one of the two hydrogen atoms belonging to the carboxyl groups; a typical configuration is depicted in (h), where the relevant hydrogen atoms are coloured in lime.