The concept of micelles was first proposed in 1913 by McBain and has rationalized numerous experimental results of the self-aggregation of surfactants. It is generally agreed that the aggregation number (Nagg) for spherical micelles has no exact value and a certain distribution. However, our studies of calix[4]arene surfactants showed that they were monodisperse with a defined Nagg whose values are chosen from 6, 8, 12, 20, and 32. Interestingly, some of these numbers coincide with the face numbers of Platonic solids, thus we named them “Platonic micelles”. The preferred Nagg values were explained in relation to the mathematical Tammes problem: how to obtain the best coverage of a sphere surface with multiple identical circles. The coverage ratio D(N) can be calculated and produces maxima at N = 6, 12, 20, and 32, coinciding with the observed Nagg values. We presume that this “Platonic nature” may hold for any spherical micelles when Nagg is sufficiently small.

In this study, we report a preparation and an aggregate emission behavior of an amphiphilic donor-acceptor dye, which is composed of a triphenylamine-benzothiadiazole donor-acceptor chromophore and two water-soluble hexa(ethylene glycol) chains. The dye is strongly fluorescent in nonpolar solutions such as cyclohexane and toluene, whereas the emission intensity is reduced in aprotic polar solutions such as DMF and acetonitrile. This fluorescence reduction correlates with the increase in polarity, by which the transition from a local excited state to a highly polarized excited state is facilitated, leading to an increased nonradiative deactivation rate. Furthermore, significant fluorescence quenching is observed in protic polar solutions such as ethanol and methanol. Hydrogen-bonding interactions between the dye and the protic solvent molecules further accelerate the deactivation rate. In contrast, in a water solution, red light emission is achieved distinctly at 622 nm with a relatively large fluorescence quantum yield of 0.20. This red emission is related to the aggregation of the dye molecules grown in water. The kinetic analysis from the fluorescence rate constant and nonradiative rate constant indicates that the nonradiative deactivation channel is restricted in water. The formed aggregate, which was indicated by transmittance electron microscopy as a spherical aggregate morphology with a diameter of 3-4 nm, provides a less polar hydrophobic space inside the aggregate structure, by which hydrogen-bonding and the subsequent quenching are restricted, leading to the reduction of the nonradiative deactivation rate.

We synthesized new calix[4]arene-based lipids, denoted by CPCaLn, bearing the choline phosphate (CP) group which is an inverse phosphoryl choline (PC) structure. Small-angle X-ray scattering and multi-angle light scattering coupled with field flow fractionation showed that these lipids form monodisperse micelles with a fixed aggregation number and diameters of 1.9 and 2.6 nm for lipids bearing C3 and C6 alkyl tails, respectively. Furthermore, when CPCaLn was mixed with the fluorescein isothiocyanate (FITC)-bearing lipids and added to cells, strong fluorescence was observed at 37 °C, but not at 4 °C, indicating that the micelles were taken up by the cells through endocytosis. Recent studies have shown that replacement of polymer-attached PC groups with CP groups markedly promotes cellular uptake, even though the surface charge is neutral. On the basis of the idea, CPCaLn micelles interacted with cells in the same way, suggesting that the micelles bearing CP groups are expected to use as carriers in the drug delivery system.

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Micelles with perfect monodispersity in terms of the aggregation number (N agg) have recently been discovered, whose values of N agg interestingly always coincide with the vertex or face number of regular polyhedral structures (i.e., Platonic solids). Owing to the monodispersity of the micelles, named Platonic micelles, we could expect them to exhibit unprecedented aggregation behavior. In this study, the effects of alkyl chain length on micellar aggregation behavior were characterized using small-angle scattering techniques such as small-angle X-ray scattering and asymmetrical flow field-flow fractionation coupled with multi-angle light scattering, as well as analytical ultracentrifugation measurements. The N agg of Platonic micelles discretely and discontinuously increased when increasing the alkyl chain length, which differs markedly from the findings for conventional micelles. This aggregation behavior could be reasonably explained by the relationship between the thermodynamic stability of the micelles and the coverage density defined by one of the unsolved mathematical problems: the Tammes problem.

In order to characterize low affinity ATP-binding sites of renal (Na+,K+) ATPase and sarcoplasmic reticulum (Ca2+)ATPase, the effects of ATP on the splitting of the K+-sensitive phosphoenzymes were compared. ATP inactivated the dephosphorylation in the case of (Na+,K+)ATPase at relatively high concentrations, while activating it in the case of (Ca2+)ATPase. When various nucleotides were tested in place of ATP, inactivators of (Na+,K+)ATPase were found to be activators in (Ca2+)ATPase, with a few exceptions. In the absence of Mg2+, the half-maximum concentration of ATP for the inhibition or for the activation was about 0.35 mM or 0.25 mM, respectively. These values are comparable to the previously reported Km or the dissociation constant of the low affinity ATP site estimated from the steady-state kinetics of the stimulation of ATP hydrolysis or from binding measurements. By increasing the concentration of Mg2+, but not Na+, the effect of ATP on the phosphoenzyme of (Na+,K+)ATPase was reduced. On the other hand, Mg2+ did not modify the effect of ATP on the phosphoenzyme of (Ca2+)ATPase. During (Na+,K+)ATPase turnover, the low affinity ATP site appeared to be exposed in the phosphorylated form of the enzyme, but the magnesium-complexed ATP interacted poorly with the reactive K+-sensitive phosphoenzyme, which has a tightly bound magnesium, probably because of interaction between the divalent cations. In the presence of physiological levels of Mg2+ and K+, ATP appeared to bind to the (Na+,K+)ATPase only after the dephosphorylation, while it binds to the (Ca2+)-ATPase before the dephosphorylation to activate the turnover.

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