Ion-Modulated Polyelectrolyte Complexation of DNA and Polyacrylic Acid from Molecular Dynamics Simulations

Abstract: The formation of complexes between like-charged polyelectrolytes challenges conventional electrostatic intuition and highlights the central role of ions in mediating macromolecular organization. Here, we investigate the salt-dependent association of DNA with poly(acrylic acid) (PAA) using atomistic molecular dynamics simulations in NaCl, MgCl$_2$, and CaCl$_2$ solutions. A time-resolved state classification scheme, based on heavy-atom distance and hydrogen-bond formation, was applied to distinguish bound and unbound configurations, enabling quantitative analysis of how ion valency modulates complex stability and structure. The results reveal a clear hierarchy of association strength with Ca$^{2+}$ promoting persistent complex formation through direct inner-sphere coordination between DNA phosphates and PAA carboxylates, Mg$^{2+}$ mediating weaker, transient bridging interactions and Na$^+$ exhibiting only electrostatic screening action with negligible bridge formation. Structural analysis shows that multivalent ions not only enhance complex stability but also reshape the molecular organization of both macromolecules. Ca$^{2+}$ induces expansion of DNA and compaction of PAA within a strongly bridged complex characterized by directional alignment and backbone-dominated binding, whereas Mg$^{2+}$ promotes more transient groove associations and Na$^+$ supports flexible, weakly correlated contacts. Our findings provide molecular-level insight into ion-specific mechanisms underlying polyelectrolyte organization and inform the design of responsive biomaterials and nucleic acid-based assemblies in multivalent ionic environments.