Bile salts aggregation number

Szoekoe et al. (23) assume several parallel complex formation equilibria with different aggregates [the number of degrees of association is dependent on the bile salts (BS) concentration]. Each micelle with an iden-... 

Table I records the conditions of the experiment (temperature, pH, and solvent) the experimental data used to calculate the apparent micellar weights by equilibrium ultracentrifugation [V, r, C0, (dc)/ (dr)r = r, or], and the results (apparent micellar weight, M, and apparent aggregation number, Ag ), for each bile salt studied. The results are illustrated in Figures 1 to 10.

Effect of Temperature. All of the bile salts in 0.15JV NaCl at pH 8 to 9 were studied at 20°, 36°, and in some cases at 4°C. (Figure 9). Trihydroxy bile salts which form small micelles (Ag 2 to 9) are unaffected between 4° and 36°C. Further, the small micelles formed by the dihydroxy bile salts in low salt concentrations are not affected by temperature. However, the sizes of the micelles of dihydroxy bile salts having aggregation numbers greater than 10 are decreased as the temperature is increased. 

Figure 5. Apparent aggregation number vs. counterion concentration of free bile salts at 20°C., pH 8-9...

Particularly efficient solubilizing agents of the bile acid family are the salts of deoxycholic acid 6". Their complexes with water-insoluble compounds are called choleic acids . The aggregation number of deoxycholic acid (DCA) in distilled water is approximately 10-12 ( primary micelles ) and rises to about 100 ( secondary micelles ) in more concentrated solutions and/or after addition of electrolytes to primary micelles. The cmc of primary micelles lies in the range of 1-5 x 10 mol/L. Less polar cholic acids are in general much better... 

Bile salts carry extensive hydrophobic (hydrocarbon) portions in each molecule that attempt to reduce their contact with water (4). This is reflected in rapid, dynamic association-dissociation equilibrium to form self-aggregates or micelles as the total concentration of bile salt solute is increased (the CMC) [2-6]. Experimentally, micelles are undetectable in dilute solutions of the monomers, and are detected in increasing numbers and often size above the CMC [98]. Because bile salt micelles are often small (i.e., dimers) [5], and since self-aggregation continues to proceed in many cases with increasing concentration above the CMC [17,18,20,52,98], the detection of the lowest concentration at which the first aggregates form depends particularly upon the sensitivity of the experimental probes employed [98] and the physical-chemical conditions [3-5]. 

Polydispersity of simple bile salt micelles can only be assessed by modem QLS techniques employing the 2nd cumulant analysis of the time decay of the autocorrelation function [146,161]. These studies have shown, in the cases of the 4 taurine conjugates in 10 g/dl concentrations in both 0.15 M and 0.6 M NaCl, that the distribution in the polydispersity index (V) varies from 20% for small n values to 50% for large n values [6,146]. Others [112] have foimd much smaller V values (2-10%) for the unconjugated bile salts in 5% (w/v) solutions. Recently, the significance of QLS-derived polydispersities have been questioned on the basis of the rapid fluctuation in n of micellar assemblies hence V may not actually represent a micellar size distribution [167-169]. This argument is specious, since a micellar size distribution and fast fluctuations in aggregation number are identical quantities on the QLS time scale (jusec-msec) [94]. 

Fig. 13. Mean hydrodynamic radii (/ , in A) and aggregation numbers (/i) for the taurine conjugates of 4 common bile salts in 0.15 M and 0.6 M NaCl as functions of temperature. (From ref. 6 with permission.)...

There are a number of synthetic and natural surfactants where the CMC cannot be identified by an abrupt change in the solution properties. Short-chained surfactants, like as sodium octanoate, and amphiphiles with weakly pronounced hydrophobic groups, like as bile salts [202], often show a non-cooperative stepwise aggregation over a broad concentration range, so that the CMC concept is not applicable. 

Under these considerations, the analysis of the energetics of size and shape of the micelles becomes of interest. The spherical shape would be the most stable structure if the monomers aggregate with a minimum of other constraints needed to satisfy the forces as described under Chap. 2.3, because this gives the minimum surface area of contact between the micelle and the solvent. On the other hand, if large constraints exist, other possible shapes, e.g. ellipsoids, cylinders or bilayers would be present [1,4]. It is obvious that micelles as formed by non-linear surfactants, e.g. bile salts etc., can not be analyzed by these theories, because steric hinderance gives rise to rather small aggregation numbers [1,3,4, 12,32,33,34,35,36,37,38,39,40]. In the case of spherical micelles of linear alkyl chain surfactants, with aggregation numberm, the radius, R, and total volume, V, and micellar surface area, A, we have ... 

As [A ] is the concentration of bile salt anions at equilibrium, this concentration is equivalent to the CMC. If, in the case of ionic detergents, the free energy change at micellization is assumed to remain fairly constant with added counterion the whole of the left side of Eq. (7) becomes constant. Since at the CMC, [M], which is the concentration of micelles, i.e., the overall detergent concentration minus the CMC, is very small, then the micellar term —log [M]/ai is negligible irrespective of the magnitude of n, the aggregation number (Ag ). Thus, Eq. (7) becomes... 

A number of studies have been carried out to determine the aggregation number (number of molecules per micelle) of bile salt micelles. In common with results of previous studies on the critical micellar concentration (CMC) these studies have given variable results which give aggregation numbers for bile salts from 1 (that is, no micelle formation) to well over 1000 associated molecules (73, 144, 145, 120, 167-169). 

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