Conformation of polyions

Nishida et al., 2001] that the conformation of polyions at low ionic strength is rodlike, and hence the polyions adopt a simplified mean-field expression for g r) = g r, 9) = exp[- 7(r, 6)lkBT, where the intermolecular potential U r, 6) is a function not only of the interparticle distance, r, but the orientation angle, 6, between the rods. Computation of the intermolecular contribution to the viscosity then proceeds, using Eq. (1.80), via... 

COMPACT CONFORMATION OF POLYIONS STABILIZED BY NON-ELECTROSTATIC SHORT-RANGE INTERACTIONS... 

Thus, it is clear that the counter-ions bound by electrostatic force are different from undissociated molecules. However, the above facts do not mean that the ionbinding of the third class can always be analysed only due to electrostatic interaction. The structure of water, degree of hydration, the conformation of polyion etc., may be. 

There are two broad kinds of polyion conformation the random coil and the ordered helix. In a helix there are regularly repeated structures along the coil there are none in the case of a random coil. In this book we are concerned with the latter where there are often several conformations with approximately equal free energies and, thus, conformational changes occur readily. 

Ion binding is affected by the size and charge of the counterion, the charge and conformation of the polyion, and states of hydration. We will examine these effects in some detail. 

The conformation of macro- or polyions has been defined and discussed briefly in Section 4.1.1. The conformation of a polyion is determined by a balance between contractile forces, which depend on conformation free energy, and extension forces, which arise from electrical free energy. The extent of conformational change is determined by several factors. Changes are facilitated by the degree of flexibility of the polyion, and conformational change is greatest at low concentration of polyions. 

The most important factor determining the sensitivity of the conformation to the concentration of polyions is the change in ion activity or osmotic pressure with conformation. If the activity coeflScient of the counterions is sensitive to conformation then conformational change resulting from concentration changes of polyions becomes large. 

The main conclusion drawn from the simulations [170] is that in the presence of monovalent counterions, the charged protein-like copolymers can be soluble, even in a very poor solvent for hydrophobic units. There are three temperature regimes, which are characterized by different spatial organization of polyions and their conformational behavior. 

In the preceding section, the remarkable salt concentration effect on the acid dissociation equilibria of weak polyelectrolytes has been interpreted in a unified manner. In this treatment, the p/( ,pp values determined experimentally are believed to reflect directly the electrostatic and/or hydrophobic nature of polyelectrolyte solutions at a particular condition. It has been proposed that the nonideality term (Ap/Q corresponds to the activity ratio of H+ between the poly electrolyte phase and the bulk solution phase, and that the ion distribution equilibria between the two phases follow Donnan s law. In this section, the Gibbs-Donnan approach is extended to the equilibrium analysis of metal complexation of both weak acidic and weak basic polyelectrolytes, i.e., the ratio of the free metal ion activity or concentration in the vicinity of polyion molecules to that of bulk solution phase is expressed by the ApAT term. In Section III.A, a generalized analytical treatment of the equilibria based on the phase separation model is presented, which gives information on the intrinsic complexation equilibria at a molecular level. In Secs. B and C, which follow, two representative examples of the equilibrium analyses with weak acidic (PAA) and weak basic (PVIm) functionalities have been presented separately, in order to validate the present approach. The effect of polymer conformation on the apparent complexation equilibria has been described in Sec. III.D by exemplifying PMA. 

The Debye equation is based on the following physical description of the sample. This is a monodisperse solution of identical particles, which are in random orientations relative to the incident primary beam, and act as independent entities (i.e. there are no interparticle spatial correlations). The above derivation has presumed also that the particles are in vacuo. If they are in solution, they are required to form a two-phase system of solute and solvent. In biology, this corresponds to dilute solutions of pure proteins or glycoproteins in a low-salt buffer. Complications arise in the case of polyionic macromolecules in low-salt buffers, such as nucleic acids. Here, interparticle correlation effects can readily occur and the macromolecule is surrounded by an ion-cloud of opposite charge (i.e. a three-phase system). Other complications can arise in the cases of polydisperse distributions of macromolecules, oligomerization or dissociation phenomena, and conformational changes. Different formuhsms have to be derived for the analyses of these systems. 

Abstract Aqueous solutions of star-like polyelectrolytes (PEs) exhibit distinctive features that originate from the topological complexity of branched macromolecules. In a salt-free solution of branched PEs, mobile counterions preferentially localize in the intramolecular volume of branched macroions. Counterion localization manifests itself in a dramatic reduction of the osmotic coefficient in solutions of branched polyions as compared with those of linear PEs. The intramolecular osmotic pressure, created by entrapped counterions, imposes stretched conformations of branches and this leads to dramatic intramolecular conformational transitions upon variations in environmental conditions. In this chapter, we overview the theory of conformations and stimuli-induced conformational transitions in star-like PEs in aqueous solutions and compare these to the data from experiments and Monte Carlo and molecular dynamics simulations. 

Due to the counterion localization, conformations of branched macroions that comprise strongly dissociating groups (charge is quenched) are almost insensitive to the addition of salt, up to relatively high salt concentrations. The ability of a branched polyion to maintain a virtually constant ionic strength in its interior is of special interest for potential applications, where a controlled (buffered) microenvironment is essential (e.g., colloidal bionanoreactors, smart nanocontainers for biologically active molecules, etc.). 

---