Phase diagram of solution of oppositely charged polyelectrolytes

Abstract

We study a solution of long polyanions (PA) with shorter polycations (PC) and focus on the role of Coulomb interaction. A good example is solutions of DNA and PC which are widely studied for gene therapy. In the solution, each PA attracts many PCs to form a complex. When the ratio of total charges of PA and PC in the solution, x, equals to 1, complexes are neutral and they condense in a macroscopic drop. When x is far away from 1, complexes are strongly charged. The Coulomb repulsion is large and free complexes are stable. As x approaches to 1, PCs attached to PA disproportionate themselves in two competing ways. One way is inter-complex disproportionation, in which PCs make some complexes neutral and therefore condensed in a macroscopic drop while other complexes become even stronger charged and stay free. The other way is intra-complex disproportionation, in which PCs make one end of a complex neutral and condensed in a small droplet while the rest of the complex forms a strongly charged tail. Thus each complex becomes a "tadpole". These two ways can also combine together to give even lower free energy. We get a phase diagram of PA-PC solution in a plane of x and inverse screening radius of the monovalent salt, which includes phases or phase coexistence with both kinds of disproportionation.

Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and genome organization

“…Another system involves polymer-stabilized colloidal dispersions (36) or dispersions in liquid crystals (37); in the latter case, minimizing elastic distortions in the host medium induces a flocculation analogous to our cluster formation. Polycations can also induce DNA condensation through a process known as disproportionation (38); partially neutralized DNA segments aggregate into droplets (driven by short-range and Coulombic forces), surrounded by a halo of negatively charged segments (39)(40)(41). Although we do not consider Coulombic interactions, the principles are related: interstrand attraction is mediated by bridging polycations (which compacts DNA) as configurational entropy of unbound regions is maximized.…”

Entering and Exiting the Protein−Polyelectrolyte Coacervate Phase via Nonmonotonic Salt Dependence of Critical Conditions

“…While pH and ionic strength alone determine the local protein-polyelectrolyte electrostatic affinity, n follows a binding isotherm and depends on protein/polyelectrolyte bulk stoichiometry. The ability of complexes to associate even when their net charge Z T is not precisely zero increases with the molecular weight of the complex and hence with polyelectrolyte MW due to polarization and disproportionation 10 to be discussed further below. Intermediate between pH c and pH φ we may find intrapolymer soluble complexes (soluble aggregates) for which Z T was close enough to zero to allow for soluble interpolymer complexes, but further charge accumulation prevents additional aggregation to form coacervate.…”

Field‐theoretic simulations of polyelectrolyte complexation

“…17 Polyelectrolytes have been the subject of extensive theoretical and computational research for decades. [1][2][3][4][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Statistical field theory models have played a significant role in these theoretical investigations, and both mean-field and nonmean-field approaches have been employed to gain insights into the structure and thermodynamics of a wide variety of polyelectrolyte systems. [21][22][23][24][25][26][27][28] Prior to this work, however, there has been no general numerical tool for simulating a field theory model of polyelectrolytes without the use of simplifying approximations.…”