Donnan coefficient

Anderson, C. F., and Record, M. T. Jr. (1980). The relationship between the Poisson-Boltzmann model and the condensation hypothesis An analysis based on the low salt form of the Donnan coefficient. Biophys. Chem. 11, 353—360. 

To circumvent the above problems with mass action schemes, it is necessary to use a more general thermodynamic formalism based on parameters known as interaction coefficients, also called Donnan coefficients in some contexts (Record et al, 1998). This approach is completely general it requires no assumptions about the types of interactions the ions may make with the RNA or the kinds of environments the ions may occupy. Although interaction parameters are a fundamental concept in thermodynamics and have been widely applied to biophysical problems, the literature on this topic can be difficult to access for anyone not already familiar with the formalism, and the application of interaction coefficients to the mixed monovalent-divalent cation solutions commonly used for RNA studies has received only limited attention (Grilley et al, 2006 Misra and Draper, 1999). For these reasons, the following theory section sets out the main concepts of the preferential interaction formalism in some detail, and outlines derivations of formulas relevant to monovalent ion-RNA interactions. Section 3 presents example analyses of experimental data, and extends the preferential interaction formalism to solutions of mixed salts (i.e., KC1 and MgCl2). The section includes discussions of potential sources of error and practical considerations in data analysis for experiments with both mono- and divalent ions. 

In the definitions of T, two variables in addition to the ion chemical potential must also be specified as constant. In an equilibrium dialysis experiment, these are temperature and the chemical potential of water. This partial derivative is known as the Donnan coefficient. (Note that the hydrostatic pressure is higher in the RNA-containing solution.) In making connections between T and the Gibbs free energy, it is more convenient if temperature... 

Within the PB cell model, the counterion concentration at the outer boundary gives the osmotic pressure, which is a measure of the electrostatic repulsion between neighboring biomolecules. This pressure can also be experimentally determined. " " The Donnan coefficient, on the other hand, is strongly influenced by conditions at the macromolecular surface and can be used to provide key insight into the nature of polyelectrolyte-counterion interaction. " This interaction is important because of the salt-induced conformational changes DNA undergoes. The nature of this behavior is believed to arise from the partial collapse, or condensation. 

C. F. Anderson and M. T. Record, Jr., Biophys. Chem., 11, 353 (1980). The Relationshijp between the Poisson-Boltzmann Model and the Condensation Hypothesis An Analysis Based on the Low Salt Form of the Donnan Coefficient. 

Comparison of the concentrations of either the cation or the anion in the two phases thus has potential for evaluating the polyanion valence provided that estimates of the mean ion activity coefficient (y ) are available. Furthermore, as realized by Svensson [165], expression of the Donnan distribution of small ions in this manner has two advantages in that (i) Eq. 31 applies to each type of small ion in situations where the supporting electrolyte is not restricted to single cationic and anionic species and (ii) multivalence of a small ion is also accommodated. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

Conversely, the fundamentals for the UDL he on the coextraction of counterions into the membrane therefore, the membrane is no longer permselective (Donnan failure) [9]. Ideally, when the ionophores are saturated by ions, the ion-ionophore complex functions as an ion-exchanger and the membrane shows an anion Nernstian response. The UDL can be estimated from the membrane composition, formation constant and coextraction coefficients obtained from the so-called sandwich membrane method [73]. 

Donnan distribution coefficient phys chem A coefficient In an expression giving the distribution, on two sides of a boundary between electroiyte solutions in Donnan equilibrium, of ions which can diffuse across the boundary. dan-on, dis-tro byu-shon, kO-o,fish-ont ... 

Neglecting osmotic flow, it is possible to integrate the Nemst-Planck equations including activity coefficients (55, 142) (ref. 55, p. 338), an expression being obtained for the diffusion potential. Adding the Donnan potentials, the result is ... 

The concentration of a co ion in an ion-exchange membrane can be calculated from the Donnan equilibrium. For a monovalent salt and a dilute salt solution and assuming the activity coefficients of the salt in the membrane and the solution to be 1, the co ion concentration in the membrane is given to a first approximation by... 

Note that this treatment inherently takes into account the effect of the Donnan equilibrium. The osmotic coefficient obtained therefore is that of the polyelectrolyte with no further Donnan correction term being necessary. 

Since the preferential interaction coefficient T can be interpreted in terms of Donnan equilibrium [66, 74, 96, 97], a grand canonical Monte Carlo (GCMC) simulations could be used to determine it, from a knowledge of the slope of salt concentration c3 as a function of the polyion concentration cD [68, 73, 74]. Such an analysis was carried out by Olmsted and Hagerman for a tetrahedral four-arm DNA junction, based on the so-called primitive model of the electrolyte [74]. 

This theory of an equilibrium of one species between each side of the membrane was formulated by Donnan in 1925 and from then until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl ) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane (Hodgkin and Keynes, 1953). 

Davis SM, Donnan GA (2002) Neuroprotection establishing proof of concept in human stroke. Stroke 33 309-310 Davis SM, Donnan GA (2004) Advances in penumbra imaging with MR. Cerebrovasc Dis 17 [Suppl 3] 23-27 Desmond PM, Lovell AC, Rawlinson AA, Parsons MW, Barber PA, Yang Q, Li T, Darby DG, Gerraty RP, Davis SM, Tress BM (2001) The value of apparent diffusion coefficient maps in early cerebral ischemia. AJNR Am J Neuroradiol 22 1260-1267... 

Note that the physicochemical mechanisms that enables us to perform the chromatographic bioseparations are not always adsorption-like but can involve ion exchange, ion exclusion, or size exclusion. Even if it is generally possible to fit experimental data with a mathematical function derived from the adsorption theory, it is strongly advisable to refer to the proper physicochemical process before modeling the separation. For instance, ion exchange can be modeled with selectivity coefficients (derived from the mass action law) that can be constant or not,18,19 ion-exclusion can be modeled thanks to theories based on the Donnan exclusion, etc. 

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