Alginic acid, a naturally occurring anionic polyelectrolyte, forms strong physically cross-linked hydrogels in the presence of metal cations. The latter engage in electrostatic interactions that compete with intra- and intermolecular hydrogen bonds, determining the gel structure and properties of the system in aqueous media. In this study, we use all-atom molecular dynamics simulations to systematically analyze the interactions between alginic acid chains and Na+ and Ca2+ counterions. The formed alginates originate from the competition of intramolecular hydrogen bonding and water coordination around the polyelectrolyte. In contrast to the established interpretation, we show that calcium cations strongly bind to alginate by disrupting hydrogen bonds within (1 -> 4)-linked beta-d-mannuronate (M) residues. On the other hand, Na+ cations enhance intramolecular hydrogen bonds that stabilize a left-hand, fourfold helical chain structure in poly-M alginate, resulting in stiffer chains. Hence, the traditionally accepted flexible flat-chain model for poly-M sequence is not valid in the presence of Na+. The two cations have a distinct effect on water coordination around alginate and therefore on its solubility. While Ca+ disrupts water coordination directly around the alginate chains, mobile Na+ cations significantly disrupt the second hydration layer.