Spontaneous Formation of Ultrasmall Unilamellar Vesicles in Mixtures of an Amphiphilic Drug and a Phospholipid

We have observed ultrasmall unilamellar vesicles, with diameters of less than 20 nm, in mixtures of the tricyclic antidepressant drug amitriptyline hydrochloride (AMT) and the unsaturated zwitterionic phospholipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) in physiological saline solution. The size and shape of spontaneously formed self-assembled aggregates have been characterized using complementary techniques, i.e., small-angle neutron and X-ray scattering (SANS and SAXS) and cryo-transmission electron microscopy (cryo-TEM). We observe rodlike mixed micelles in more concentrated samples that grow considerably in length upon dilution, and a transition from micelles to vesicles is observed as the concentration approaches the critical micelle concentration of AMT. Unlike the micelles, the spontaneously formed vesicles decrease in size with each step of dilution, and ultrasmall unilamellar vesicles, with diameters as small as about 15 nm, were observed at the lowest concentrations. The spontaneously formed ultrasmall unilamellar vesicles maintain their size for as long we have investigated them (i.e., several months). To the best of our knowledge, such small vesicles have never before been reported to form spontaneously in a biocompatible phospholipid-based system. Most interestingly, the size of the vesicles was observed to be strongly dependent on the chemical structure of the phospholipid, and in mixtures of AMT and the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), the vesicles were observed to be considerably larger in size. The self-assembly behavior in the phospholipid–drug surfactant system in many ways resembles the formation of equilibrium micelles and vesicles in mixed anionic/cationic surfactant systems.


Micelles + Vesicles + Disks
The SANS data were fitted with a model for polydisperse rodlike micelles with weight-average length L, relative standard deviation /〈 〉 and elliptical cross section with half-axes a and b. In the sample [XPL= 0.20, ct = 20mM] the micelles were too large for their size distribution to be determined from the SANS data. The SAXS data were fitted with the same model with addition of core-shell layer to the cross-section. ahc and bhc are the half-axes of the hydrocarbon core of the micelles and d is the thickness of the hydrophilic head-group shell.    The differential scattering cross section as a function of scattering vector Q for a sample of noninteracting monodisperse micelles with concentration n (number of micelles per unit volume) can be written as follows [1]:

Comparison between DOPC and DMPC vesicles
where is the difference in scattering length density between aggregates and solvent and ( ) is the form factor taking into account the geometrical shape of the aggregates.
Polydisperse rods. For elongated rodlike micelles, the form factor can be factorized in one contribution from the cross-section dimensions and one contribution for infinitely thin polydisperse rods, i.e.
The form factor Pcs(q) for an homogeneous elliptical cross-section with half axes a and b, respectively, equals ( , , ) = 2 ∫ 2 ( ( , , )) /2 0 is the amplitude where B1(x) is the Bessel function of first order and ( , , ) = √ 2 sin 2 + 2 cos 2 The form factor of infinitely thin rods that are polydisperse with respect to the length L of the rods equals where Nrod(L) is the number distribution of micelles with respect to L and the form factor for an infinitely thin rod is given by [2] ( , ) = 2Si( ) − 4 sin 2 ( /2) /( ) 2 and Si( ) = ∫ sin 0 (8) In our data analysis we have assumed the number density of micelle lengths to follow a Schultz distribution in the entire range of aggregation numbers (0 < N < ), i.e.
where LN is the number-weighted average length of the micelles.
We have presented our results in Table S1 in terms of the volume-weighted average length L = (z + 2)/(z +1)LN, i.e. the mean value as calculated from the probability distribution of finding an aggregated surfactant in a micelle of length L, and the corresponding relative standard deviation L /L = 1/√ + 2. Denoting the relative standard deviation for the number-weighted distribution in Eq. (9) p, L and L /L for the volume-weighted distribution may be calculated from the relations and 〈 〉 = √1+ 2 (11) Core-and-shell cross-section of rods. The SAXS data were fitted with a core-and-shell cross-section form factor. Hence, we can calculate the cross-section form factor from Eq. 3, using the following relation for the amplitude and Δ and Δ ℎ are the differences in scattering length densities between core and shell, respectively, and solvent. Acore is the area of an elliptical core cross-section with half axes a and b. Ashell = Atot Acore is the area of the outer shell, where Atot is the total area of the cross-section with half axes a + d and b + d.
Fcore is given by Eq. (4) and he corresponding quantity for the shell may be written as where fdisk and fves = 1 − fdisk are the relative intensity-weighted fractions of bilayer disks and vesicles, respectively, and fmic = 1 -fdisk -fves is the intensity-weighted fraction of micelles. [3,4] The from factor of a homogeneous bilayer cross-section is where we have assumed disks and vesicles to have identical half bilayer thickness ξ. The form factor of infinitely thin disks with disk radius Rd equals and B1(x) is the Bessel function of first order.
The form factor of polydisperse and infinitely thin vesicles with radius R can be written as where the form factor of an infinitely thin circular shell with radius R is defined as [1,5] ( ) = ( ) 2 (20) The vesicle size distribution is assumed to follow a Schultz distribution with respect to R 2 , i.e.
where R is the average vesicle radius.
Least-squares model fitting. The reduced chi-squared used as a measure of the quality of the fits is defined as where Iexp(qi) and Imod(qi) are the experimental and model intensities, respectively, at a scattering vector modulus qi, i is the statistical uncertainties on the data points, N is the total number of data points and M is the number of parameters optimized in the model fit.

Calculations of the Surfactant Mole Fraction in aggregates
The AMT free concentration above CMC is expected to depend on the composition in the aggregates. Assuming ideal mixing behaviour in the aggregates in our samples with comparatively high electrolyte concentrations, we may write = and = (1 − ) for AMT and DOPC. Consequently, the concentrations of AMT and DOPC present in self-assembled aggregates ( ), as well as the aggregate mole fraction xPL, may be calculated for a given total surfactant concentration = + + and bulk mole fraction of DOPC = ( + )/ . [6] Taking into account that ≫ , we obtain the following relation between mole fraction in solution and mole fraction in aggregates [7] = (1 + ) We have determined the CMC of AMT in 0.154 M NaCl solution to equal = 17 mM. The critical aggregate concentration of DOPC ( ) in 0.1 M salt have been reported to be in the range 1-10 μM [8].