Polyelectrolyte complex model

Fig. 3.13. (Top) An electron micrograph of an artificial chromatin model composed of T4 DNA and cationic nanoparticles of diameter 15nm. (Bottom) Typical snapshots of a model DNA (semiflexible polyelectrolyte) complexed with cationic nanoparticles. At low salt concentration (Debye screening length m/a = 1), a beads-on-a-string nucleosome-like structure is observed (left), while locally segregated clusters are formed at higher salt concentrations (rn/a = 0.3) (right) (See [46] for more details)...

The reaction between poly-4-vinylpyridine and PAA in water-ethanol (1 1 by volume) solutions has been investigated by calorimetry,2). This reaction proceeds without the release of H+ or OH- ions. As the heat of dissociation of the polyacid and the heat of formation of ionic bonds between macromolecular components are near zero, the protonation heats of PVPy at different pH both in the presence or absence of PAA have been measured. It has been found that in neutral solutions the heats of polyvinylpyridine protonation in the presence of PAA considerably exceeds the corresponding values in the absence of PAA, i.e. a considerable portion of pyridine rings is protonated in the polyelectrolyte complexes (Fig. 12). This may be caused only by the cooperative trasfer of the proton from the PAA carboxy group to the pyridine ring. Similar reactions cannot occur between low molecular model substances and neither when only one component is a polymer. 

A model of protein-polyelectrolyte complexation as the result of electrostatic binding between charged protein and multiple binding sites of opposite charge on the polyelectrolyte has proven capable of describing most features reported here up to the point of optimum precipitation (18). 

The PEC formation leads to quite different structures, depending on the characteristics of the component used and the external conditions of the reaction. As borderline cases for the resulting structures of polyelectrolyte complexes, two models (Figure 2) are discussed in the literature [23] ... 

In an attempt to estimate the energetics and kinetics of nonequilibrium transformations in metastable biopolymers the physical chemical behavior of a model system exhibiting pronounced hysteresis loops was investigated.The model hysteresis to be briefly discussed results from the acid-base titration of the polyelectrolyte complex poly(A) 2poly(U). The overall process underlying the hysteresis loop is the cyclic transition between two helical structures the triple helix poly(A) -2poly(U) and the protonated double helix poly(A) poly(A). 

Mende M, Schwarz S, Petzold G, Jaeger W (2007) Destabilization of model silica dispersions by polyelectrolyte complex particles with differoit charge excess, hydrophobicity, and particle size. J Appl Polym Sci 103 3776... 

The Introduction will give a brief description of DNA as a biopolymer (structure, conformations, topologies), some definitions in the field of polyelectrolytes (weak and strong polyelectrolytes), some generalities about DNA/ polycation complexes (factors influencing the complexation, models describing the structure of the polyplexes, methods adapted to their characterization), and a description of the parameters to take into consideration for their use in gene therapy. 

Two structural models are discussed in the literature for polyelectrolyte complex (PEC) formation, depending on the components (weak or strong polyelectrolyte, stoichiometry, molecular weight) and the external conditions (presence of salts, etc.) ladder-like (complex formation takes place on a molecular level via conformational adaptation) or scrambled egg structure (large number of chains in a particle) (Scheme 5) [65]. 

The first theory of polyelectrolyte complex formation was proposed by Voom and Overbeek [14, 15]. This mean field model was used to describe the binodal compositions, the water content and the critical salt concentration as a function of the polymer chain length. This theoretical description uses the Debye-Hiickel approximation the approximations within the derivation of the electrostatic interaction free energy are therefore only valid at low charge densities. The correlation effects at high concentrations of salt and monomeric units are neglected, and ion pairing effects such as counterion condensation are not taken into account. Despite these limitations, the experimental results could be described reasonably well [13]. 

Over the years, the theory of polyelectrolyte complex formation has been further developed. The theory of Voom and Overbeek was later extended by Nakajima and Sato, who included an interaction parameter x to account for additional interactions such as hydrophobicity [16]. Correlation effects within the dense complex phase were included in the theory by Castelnovo and Joanny, which enables prediction of a critical salt concentration [17]. Kramarenko and Khokhlov included specific ionpairing energies, but their theory ignores the formation of ion pairs between polyelectrolytes and monovalent counterions hence, they do not present a salt dependence of the complex formation [18]. Heterogenous cell models can be used to describe experimental data on polyelectrolyte complex formation. These models take the spatial structure of the complex into account [19]. In Sect. 3 on protein-protein complexation we discuss how such a model can be used to describe experimental data. 

From studies of the complexation of HSA with both anionic PVS and cationic PDMDAAC, Kokufuta [9,20] concluded that protein-polyelectrolyte complexes are stoichiometrically formed through salt linkages. However, we recently showed that the initial complexation between polyelectrolytes and proteins can even occur under conditions where the net protein charge is the same as that of the PE. This result may be attributed to non-uniform protein charge patches. These may be observed by computer modeling [47]. 

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