Determining sequential micellization steps of bile salts with multi-CMC modeling.

Hypothesis: Bile salts exhibit complex concentration-dependent micellization in aqueous solution, rooted in a long-standing hypothesis of increasing size in bile aggregation that has historically focused on the measurement of only one CMC detected by a given method, without resolving successive stepwise aggregates. Whether bile aggregation is continuous or discrete, at what concentration does the first aggregate form, and how many aggregation steps occur, all remain as open questions.

Experiments: Bile salt critical micelle concentrations (CMCs) were investigated with NMR chemical shift titrations and a multi-CMC phase separation modeling approach developed herein. The proposed strategy is to establish a correspondence of the phase separation and mass action models to treat the first CMC; subsequent micellization steps, involving larger micelles, are then treated as phase separation events.

Findings: The NMR data and the proposed multi-CMC model reveal and resolve multiple closely spaced sequential preliminary, primary, and secondary discrete CMCs in dihydroxy and trihydroxy bile salt systems in basic (pH 12) solutions with a single model of one NMR data set. Complex NMR data are closely explained by the model. Four CMCs are established in deoxycholate below 100 mM (298 K, pH 12): 3.8 ± 0.5 mM, 9.1 ± 0.3 mM, 27 ± 2 mM, and 57 ± 4 mM, while three CMCs were observed in multiple bile systems, also under basic conditions. Global fitting leverages the sensitivity of different protons to different aggregation stages. In resolving these closely spaced CMCs, the method also obtains chemical shifts of these spectroscopically inaccessible (aka dark) states of the distinct micelles.