Entropy-Driven Thermodynamics of Ca²⁺-Heparin Group Interactions and Implications for the Kinetics of CaCO₃ Nucleation

Sulfated and carboxylated macromolecules are abundant at sites of CaCO₃ biomineralization in diverse organisms (Knight et al., 2023, Biomacromolecules), but their roles in directing crystallization are not well-understood. Knight et al. (2024, J. Cryst. Growth Des.) found the interfacial energy (γ_net) associated with nucleating calcite (CaCO₃) is covariant with the degree of sulfate substitution (DS(SO₃^-)) on chitosan derivatives. That is, the free energy barrier to forming a new crystal-polysaccharide (PS) interface increases with increasing net charge of the polysaccharide. Analysis of the experimental data in combination with MD simulations of sulfated chitosan chains indicated greater sulfate density creates a progressively hydrophilic PS-water interface to promote water structuring around SO₃^- groups, compared to uncharged substituents. Thus γ_net becomes larger with sulfation through reductions in γ_PS-soln. MD simulations also predict Ca²⁺-SO₃^- interactions were solvent separated by distances that depended on density and position of sulfate groups.

In this study, we probe the influence of sulfate groups on water structuring and their interactions with Ca²⁺ ions by measuring the thermodynamics of Ca²⁺ binding to three characterized heparin group molecules having different sulfate group densities and regiopositions (heparosan, O-sulfated heparin, and N- and O-sulfated heparin). These biomolecules are widely found in mammalian systems and applied in biomedicine. Using isothermal titration calorimetry (ITC), we determined the free energy of binding (ΔG_rxn) and binding constant (K_b,25°C) for all materials and multiple pH and ionic strength solution conditions. For the general reaction, Ca²⁺ + heparin = Ca-heparin, we determined from heat capacity measurements that ΔG_rxn is dominated by entropic contributions (-TΔS_rxn) due to water release from polar/hydrophilic groups (Knight et al., 2024, in prep.).

Because the entropic driver of Ca²⁺-heparin interactions is directly related to changes in the macromolecule-water interface, we postulate that differences in water structuring may explain the polysaccharide-specific values of γ_net determined from the calcite nucleation experiments in Knight et al. (2024). To test this idea, we measured the rate of calcite nucleation onto the corresponding heparin materials. Comparing our estimates of γ_net and -TΔS_rxn values for the heparins and also for reported alginate materials, we found the polysaccharides associated with the largest energy barrier to CaCO₃ nucleation correlate with the greatest disruption of interfacial water (most negative -TDS) during Ca²⁺ interactions. This correlation also reconciles offsets between the interfacial energies of alginates that have the same net charge but with different M and G compositions. Thus, a consistent picture emerges when material-specific interfacial energies are viewed through the lens of how functional groups and their Ca²⁺ interactions influence solvation.

The findings reiterate the importance of understanding water structuring at macromolecule-solution interfaces and demonstrate how polysaccharide-based materials can be modified to control crystallization of a sparingly soluble salt.