Protein adsorption Langmuir isotherm

Fig. 20. Schematic adsorption isotherms with a constant surface site concentration ([A]s in Fig. 12 is here constant), but with adsorption time as a variable. At very short times, adsorption is diffusion controlled. At short times, the protein has insufficient time to conformationally adjust to the interface, thus adsorption can be reversible and of the Langmuir type. At longer times, conformational adjustments begin leading to the commonly observed semi- orir-reversible behavior of protein adsorption. Other nomenclature same as Fig. 12...

Another correlation often employed to correlate adsorption data for proteins is the Langmuir isotherm,... 

Interpretation of the adsorption behavior of polypeptides and protein with nonporous HPLC sorbents can thus be based on Eqs. (140)—(143) in which the film mass transfer and surface interaction rates are both considered finite. Simplified cases can be derived from these two relationships for fixed-bed performance409,410,412 where the equilibrium relationship can be expressed by the Langmuir isotherm. Under these isothermal conditions, attainable adsorption capacity of the adsorbent q, which is the amount of the protein retained by the adsorbent when the column reaches saturation, can be expressed by... 

A Ithough the adsorption of polymers onto solid surfaces has been thor-oughly studied (I), relatively few studies can be found in the literature on the adsorption of proteins onto polymer surfaces. In 1905, Landsteiner and Uhliz (2) discussed the interaction of serum proteins with synthetic surfaces. Blitz and Steiner (3) showed that albumin adsorption onto solid surfaces increased with increasing albumin concentration and that adsorption was nearly irreversible. Hitchcock reported (4) that adsorption of egg albumin onto collodion membranes followed a Langmuir isotherm with maximum adsorption occurring near the isoelectric point. Later, Kemp and Rideal (5) reported that protein adsorption onto solids conforms with Langmuir adsorption. 

This isotherm model has been used successfully to accoimt for the adsorption behavior of numerous compounds, particularly (but not only) pairs of enantiomers on different chiral stationary phases. For example, Zhou et ah [28] foimd that the competitive isotherms of two homologous peptides, kallidin and bradyki-nine are well described by the bi-Langmuir model (see Figure 4.3). However, most examples of applications of the bi-Langmuir isotherm are found with enantiomers. lire N-benzoyl derivatives of several amino acids were separated on bovine serum albumin immobilized on silica [26]. Figure 4.25c compares the competitive isotherms measured by frontal analysis with the racemic (1 1) mixture of N-benzoyl-D and L-alanine, and with the single-component isotherms of these compounds determined by ECP [29]. Charton et al. foimd that the competitive adsorption isotherms of the enantiomers of ketoprofen on cellulose tris-(4-methyl benzoate) are well accounted for by a bi-Langmuir isotherm [30]. Fornstedt et al. obtained the same results for several jS-blockers (amino-alcohols) on immobilized Cel-7A, a protein [31,32]. 

Initial high slopes of adsorption isotherms indicate, usually, a high affinity of proteins for the solid/water interfaces (Fig. 6). The AG°ads values calculated from the Langmuir isotherms are usually in the range between —6 and —12 kcal/mol for various protein-adsorbent... 

Aside from the relative position of the profile, the shape of the effluent profile contains information concerning the kinetics of the adsorption process. All concentrations of protein from zero to cQ are brought into contact with the column surface as the protein solution flows through the column, as a function of the position of the profile, and therefore as a function of time. Working with small molecules, previous researchers have shown that compounds exhibiting Langmuir isotherms produce sharp fronts, and diffuse tails, if pure solvent is used to desorb the column (21,22). However, Equation 7 shows that both diffusional and adsorption effects can alter the shape of the effluent profile. The former effect includes both normal molecular diffusion, and also diffusion due to flow properties in the column (eddy diffusion), which broadens (decreases the slope) the affluent profiles. To examine the adsorption processes, apart from the diffusional effects, the following technique can be applied. 

Conventionally, cellulase adsorption onto (or accessibility for) cellulose, such as that of T. reesei cellulases onto amorphous/crystalline/lingo-cellulose, has been investigated by Langmuir-type isotherms 20, 34). They measure overall cellulase protein adsorption, assuming a uniform cellulose surface. 

A plot of r vs. Ceq is an adsorption isotherm. Data for protein adsorption are frequently modeled by the Langmuir equation, although the validity of using this equation for protein adsorption remains an open question ... 

To compute the distributions of changes in the Gibbs free energy (/(AG)) on protein adsorption, the Langmuir equation was used as the kernel of the adsorption isotherm equation in the form of Fredholm integral equation of the first kind (see Chapter 10). 

Adsorption of lipase at these adsorbents seems to be as Langmuir isotherms and data are well linearised in corresponding coordinates. In spite of that, it was of interest to evaluate the contribution of protein-protein interaction at the surface in adsorption of different proteins, including lipase. Only hpase adsorption on the surface of hydrophihc glass beads revealed the value of x distinguished from 0, in this case x=23. 

Many adsorption processes are treated thermodynamically in terms of Langmuir type of isotherms where different kinds of interactions between the surface and the molecules and the molecules themselves are incorporated. The adsorption of protein molecules is, however, often a highly dynamic phenomenon. The molecules may change orientation and conformation during or after the adsorption. The properties of the surface play an important role. Protein molecules are normally more influenced by a nonionic or hydrophobic surface than by a polar and hydrophilic surface. We have started to develop simple dynamic models for protein adsorption based on the geometrical area covered by a protein molecule in different states [1]. These models can also be extended to incorporate an energetic and geometric interaction between the adsorbed molecules [2]. 

Fig. 2. Upper diagram Illustration of the basic features of the dynamic model at low and high protein concentrations, respectively. Some different desorption time constants were used. C is the normalized concentration C C, /s,. Lang-muir-like adsorption of a molecule in two different orientations is denoted by the dashed lines. The parameters were chosen to obtain a good fit between the Langmuir case and the dynamic model at low concentrations. It is also indicated that an irreversible adsorption (dashed-dotted line) would lead to a constant adsorption at low concentrations equal to 0, + 02 = 1/ for the dynamic model. Note that (0j -I- 62) corresponds to the number of adsorbed protein molecules/per unit area. (The number is actually Afo(0, + 02)O Lower diagram 0, -t- 02 for 42 = 4 41 comparing the dynamic model with reversibility (solid line) with an irreversible adsorption (dashed-dotted line) and a Langmuir isotherm (dashed line) at intermediate concentrations. The irreversible adsorption is only approximate, given by equations (9) and (10). We have also shown schematically the packing of the protein molecules in different concentration regions...

---