Membrane transport Donnan effect

Electrophoretic elution and "switch" monoclonal antibodies are combined in a new rapid recycle method an affinity-mediated membrane transport process reported by Dall-Bauman and Ivory (8). In this modeling paper, a "switch" monoclonal antibody incorporated into a supported liquid membrane is used to facilitate the transport of human growth hormone from a high-pH to a low-pH environment. Electrochemical effects, including Donnan equilibria between the membrane and external environments, and imposition of external electrical fields, significantly affected the flux of protein across the membrane. Experimental confirmation of the simulation results could introduce affinity-mediated transport as a powerful new biospecific separation method. 

If, however, a carrier-mediated transport membrane containing charged species — in the form of either mobile ions or fixed sites — were placed between two electrolytic mixtures, significant Donnan effects could be expected. For example, consider a membrane in which the carrier is a counterion to the permeant. The permeant would be expected to be preferentially included in the membrane phase. If significant inclusion were to occur, the use of simple first-kind boundary conditions would be inappropriate and could lead to underestimation of flux. On the other hand, if the permeant and carrier were coions, the permeant could be excluded and failure to account for exclusion could lead to overprediction of flux. Further complications would arise if the complex were charged or if other charged species were present, since the net charge density inside the membrane defines Donnan equilibrium conditions. 

For membrane processes involving liquids the mass transport mechanisms can be more involved. This is because the nature of liquid mixtures currently separated by membranes is also significantly more complex they include emulsions, suspensions of solid particles, proteins, and microorganisms, and multi-component solutions of polymers, salts, acids or bases. The interactions between the species present in such liquid mixtures and the membrane materials could include not only adsorption phenomena but also electric, electrostatic, polarization, and Donnan effects. When an aqueous solution/suspension phase is treated by a MF or UF process it is generally accepted, for example, that convection and particle sieving phenomena are coupled with one or more of the phenomena noted previously. In nanofiltration processes, which typically utilize microporous membranes, the interactions with the membrane surfaces are more prevalent, and the importance of electrostatic and other effects is more significant. The conventional models utilized until now to describe liquid phase filtration are based on irreversible thermodynamics good reviews about such models have been reported in the technical literature [1.1, 1.3, 1.4]. 

Transport through nanofiltration membranes is controlled primarily by electrostatic and steric interactions. The extended Nemst-Plank equation commonly is used with Donnan and steric partitioning to predict transport rates based on effective membrane charge density, pore radius, and thickness to porosity ratio [131-132]. Inclusion of solute-pore hydrodynamic interactions and a pore size distribution improves the predictive and correlative capabilities of the models [133]. 

Electroneutrality requires that X" be transported along with M+. This again is a manifestation of the Donnan effect salt is expelled by the charged colloidal particle or polyelectrolyte. As the passage of M+X- through the membrane proceeds, c - exceeds j more and more, becoming a driving force for M+X" transport in thie reverse direction. In equilibrium and c -, < c -1,. The number of M+X"... 

An affinity-mediated system in which a switch monoclonal antibody is used to transport its antigen, human growth hormone, has been modeled. The affinity of the antibody for the hormone is dependent on local pH. In addition to the kinetic effect, maaoscopic and microscopic electrochemical effects were considered. On the larger scale, modest induced and applied electric fields were found to exert considerable influence on fluxes of antibody, hormone, and complexes. The short-range effect of Donnan potential was found to enhance the flux of hormone into the membrane. 

The mathematical model described here has illustrated that electrochemical effects can significantly influence protein flux in an affinity-mediated transport system. The system considered consists of a supported liquid membrane containing a pH-sensitive monoclonal antibody as carrier and human growth hormone as permeant. On a microscopic scale, Donnan inclusion of the hormone can increase the flux of hormone into the membrane. This allows more complex to be formed and simultaneously generates a steep hormone concentration gradient which drives a greater flux of free hormone than would occur in the absence of inclusion. 

These are both instances of what is known as active transport. Care must be taken to distinguish true active transport from certain other effects. For example, the concentration of Mg ions is much greater in most cells than in the surrounding fluid, This does not imply active transport, since the Mg " ions are strongly bound in the cells, a process which reduces the effective concentration of the ions and so disturbs the equilibrium. Another effect which can give a false impression of active transport is the Donnan equilibrium discussed in Section 7.6. We saw there that there can be an abnormal distribution of ions across a membrane because of the presence of large cations or anions to which the membrane is impermeable. 

UF and RO models may all apply to some extent to NF. Charge, however, appears to play a more important role than for other pressure driven membrane processes. The Extended-Nemst Planck Equation (equation (3.28)) is a means of describing NF behaviour. The extended Nernst Planck equation, proposed by Deen et al. (1980), includes the Donnan expression, which describes the partitioning of solutes between solution and membrane. The model can be used to calculate an effective pore size (which does not necessarily mean that pores exist), and to determine thickness and effective charge of the membrane. This information can then be used to predict the separation of mixtures (Bowen and Mukhtar (1996)). No assumptions regarding membrane morphology ate required (Peeters (1997)). The terms represent transport due to diffusion, electric field gradient and convection respectively. Jsi is the flux of an ion i, Di,i> is the ion diffusivity in the membane, R the gas constant, F the Faraday constant, y the electrical potential and Ki,c the convective hindrance factor in the membrane. 

When pore radius is in the same order of magnitude than the zeta potential barrier, transport of ionic species is affected by the flxed charge of the membrane. Ions with the same charge as the flxed ions in the membrane are excluded and cannot pass through the membrane. This effect is known as the Donnan exclusion and can be described by equilibrium thermodynamics from which the chemical potential of the ionic species can be calculated in the membrane and in the solution and then the concentration of the different species. If the concentration in the feed is low and the concentration of the fixed charge is high, the Donnan exclusion is very effective. 

Membrane phenomena cover an extremely broad field. Membranes are organized structures especially designed to perform several specific functions. They act as a barrier in living organisms to separate two regions, and they must be able to control the transport of matter. Moreover, alteration in transmembrane potentials can have a profound effect on key physiological processes such as muscle contraction and neuronal activity. In 1875, Gibbs stated the thermodynamic relations that form the basis of membrane equilibria. The theory of ionic membrane equilibrium was developed later by Donnan (1911). From theoretical considerations, Donnan obtained an expression for the electric potential difference, commonly known as the membrane potential between two phases. 

Most of the extracellular fluid is interstitial fluid (ISF) in the tissue spaces, providing the transport medium between capillaries and cells. The sodium concentration in plasma is slightly above that in ISF because plasma contains more proteins, notably albumin, which do not readily escape into ISF across the capillary membranes, and the effect of their negative charges is to hold more positively charged ions, notably sodium, in circulation (Gibbs-Donnan equilibrium). 

---