Dynamic light scattering

Dynamic or quasi-elastic light scattering (DLS or QLS) measurements were made on the fixed scattering angle Zetasizer Nano-S system (Malvern Instruments Ltd., Malvern, UK)^50,89, equipped with a 4 mW He-Ne laser at a wavelength of 632.8 nm. Samples in solution were measured in a quartz cuvette at 20.0 °C. A scattering angle of 173° was used, and collected in manual mode, requiring a measurement duration of 90 seconds. The resulting data were analysed using the “DTS (Version 4.2)” software (Malvern Instruments Ltd., Malvern, UK), providing a volume distribution of translational diffusion coefficients based on the CONTIN program of Provencher (1992)⁴⁸. The volume distribution was followed⁴⁹. The viscosity of the buffer used was calculated using a solvent builder interface and takes the effects of buffer salts into account.

The apparent z-average apparent hydrodynamic diameters d_z,app (nm), were evaluated from the z-average apparent translational diffusion coefficients D_z,_trans,app = by the Stokes-Einstein equation (see e.g., Harding et al.)⁸⁹:

where k_B is the Boltzmann constant, T is absolute temperature and η is the viscosity of the medium. The following assumptions were made (i) the solutions were sufficiently dilute that non-ideality effects were not significant – i.e. an extrapolation to zero concentration was not necessary. This is reasonable as the non-ideality due to the low concentration of mucin and small size of vancomycin, and also for translational diffusion the two main contributory factors to non-ideality – the hydrodynamic and thermodynamic terms - compensate for each other and can even cancel each other out^90,91. (ii) the particles (vancomycin, mucin and complex) were quasi-spheroidal and not asymmetric so there was no angular dependence of the measured D_z,trans values on anisotropic rotational diffusion effects – i.e. an extrapolation to zero angle was not necessary⁹².

The following mixing ratios were used (Fig. 5): (a) 0.5 mg/mL PGM + 0.125 mg/mL vancomycin (blue line), +1.25 mg/mL (dark green), +12.5 mg/mL (red). The 0.5 mg/mL PGM control is shown in black. (b) 0.5 mg/mL PIM + 0.125 mg/mL (blue line), +1.25 mg/mL (dark green), +12.5 mg/mL (red). The 0.5 mg/mL PIM control is shown in black and (c) 1.0 mg/mL BSM + 0.125 mg/mL (blue line), +1.25 mg/mL (dark green), +12.5 mg/mL (red). The 1.0 mg/mL BSM control is shown in black. Because free vancomycin scatters too weakly at the concentrations in the mixtures, for the vancomycin control (purple) a higher concentration of 50 mg/mL was used.