Model of separated form factors for unilamellar vesicles

New model of separated form factors is proposed for the evaluation of small-angle neutron scattering curves from large unilamellar vesicles. The validity of the model was checked by comparison to the model of hollow sphere. The model of separated form factors and hollow sphere model give reasonable agreement in the evaluation of vesicle parameters. PACS: 87.16.Dg, 61.12.Ex, 61.10.Eq Information about the internal membrane structure is mainly derived from X-ray diffraction experiments on multilamellar vesicles (MLVs) [1]. A single lipid bilayer possesses the structure typical of most biological membranes. Unilamellar vesicles (ULVs) appear to be more biologically appealing model of the lipid membrane than multilamellar vesicles. Moreover, vesicles are used as delivery agents of drugs, genetic materials and enzymes through living cell membrane and other hydrophobic barriers [2,3]. Today, the problem of accurate and simultaneous determination of the vesicle radius, polydispersity, and the internal membrane structure is not yet solved in SAXS and SANS experiments [5]-[9]. The information about internal membrane structure derived from the SANS experiment is based on the strip-function model of the neutron scattering length density across bilayer ρ(x) [4] and application of the hollow sphere model for the vesicle [5,7]. Important problem is to develop new approach to the evaluation of SANS and SAXS experimental curves with possibility to describe ρ(x) as an any analytical or numerical function. The purpose of present work is to propose and verify the new analytical equations for the calculation of the SANS curves from the phospholipid vesicles. Send offprint requests to: M.A. Kiselev, [email protected] 1 Experiment and Model Dipalmitoylphosphatidylcholine (DPPC) was purchased from Sigma (France), and D2O was from Isotop (S.Peterburg,Russia). LUVs were prepared by extrusion of MLVs through polycarbonate filter with pore diameter 500 Å as described in ref. [7]. The spectra from unilamellar DPPC vesicles were collected at YuMO smallangle spectrometer of IBR-2 reactor (Dubna, Russia) at T = 20◦C [10]. Incoherent background was subtracted from normalized cross section of vesicles as described in ref. [5]. DPPC concentration in sample was 1% (w/w). Macroscopic cross section of monodispersed population of vesicles [11] dΣ dΩ mon (q) = n · A(q) · S(q) (1) where n is the number of vesicles per unit volume, A(q) is scattering amplitude of vesicle, and S(q) is vesicle structure factor. S(q) ≈ 1 for 1% (w/w) DPPC concentration [12]. Scattering amplitude A(q) for the case of vesicles with spherical symmetry [11] A(q) = 4π ∫ ρ(r) sin(qr)