Liisa Hirvonen edited Discussion.tex  over 8 years ago

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\section{Discussion}  The radii obtained by anisotropy measurements are in the expected range and consistent with calculations based on MW, see Fig~\ref{fig:theor_radii}. While calculations based on the empirical formulas obtained from the analysis of thousands of proteins can give a  good indication of the expected size, they cannot take into account the specific propetries properties  of individual specific  molecules relating to surface roughness, shape, and the ionic charge which all affect the diffusion of the molecule. Our measured radius of 3.49$\pm$0.03~nm for the  well-characterised protein BSA is in excellent agreement with the accepted value of 3.48~nm.\cite{Axelsson1978} The cubic dependence of the radius on the rotational correlation time means that this technique is more sensitive to small changes in radius than methods where the radius depends on the measurement linearly. Anisotropy measurements can also give information about the shape of the particle. The measured anisotropies are clearly double-exponential: besides the component corresponding to the protein rotation, there is an additional fast component. This component cannot be attributed to non-spherical shape of the molecule; in case of an ellipsoid, the anisotropy decay is three-exponential, but the three exponentials are linked, and the fast component is too fast to fit this model. While it is too fast to be measured accurately with this method due to the long lifetime of the dye, the results indicate a size comparable toto  the dye molecule, and this component is most likely caused by the rotation of the dye molecule on its bond. Wilkins \textit{et.\ al.} report a similar component.\cite{Wilkins1999} Double-exponential fit taking this component into account produces excellent fit results, indicating that the proteins are approximately spherical in shape. DLS, based on the measurement of fluctuating scattered light intensity due to Brownian particles motion, motion of the particles,  is a well established method for determining the size of small particles in solution, including macromolecular drugs. Wen \textit{et al} \cite{Wen2013} report hydrodynamic radii of 4.2~nm for ranibizumab and 6.3~nm for bevacizumab using DLS, and 5.4~nm for BSA measured as a control, and Li \textit{et al} \cite{Li2011} 4.1~nm, 6.5~nm and 4.8~nm for the same molecules, respectively. These results are slightly higher than estimates based on MW, which they suspect could be due to aggregation. DLS is limited to very low particle concentrations (generally $\lesssim$1~mg/ml). SAXS and SANS are also popular methods for the size measurement of macromolecules. While they can be used with higher particle concentrations that DLS ($\sim$1-100~mg/ml) and are applicable to a large MW range from few kDa to hundreds of MDa, they have low resolution, and structural information can only be obtained through complex model building. building.\cite{Pecora_1985}  Similar to DLS, SAXS and SANS measure scattering from unlabelled molecules which simplifies sample preparation but makes the results susceptible to artefacts arising from dust and other contamination in the sample solution. The fitted rotational correlation times follow a linear increase with viscosity up to viscosity of $\sim$20~cP ($\sim$70\% volume fraction glycerol).\cite{Suhling2004} Glycerol is known to cause preferential hydration of proteins,\cite{Gekko1981} and at higher concentrations the rotational correlation times do not follow the linear model (data not shown).  %The Stokes-Einstein-Debye equation \cite{VanHolde1998} assumes that the solvent containing the rotating particles is homogeneous and continuous. Although this may not always be the case, the approximation seems to be valid for proteins which are generally much larger than the solvent molecules.\cite{Weber1953}  The measurement time interval of 5~$\mu$s used in these experiments is ideal for measuring the rotational correlation times of these proteins with this Ru dye at low viscosities. However, with the long lifetime of the dye, long pixel dwell times are needed, making scanning-based data acquisition slow. Recently developed wide-field lifetime imaging approaches \cite{Hirvonen2014_ol, Hirvonen2015_njp} that are ideally suited for measuring lifetimes at this time scale, and could image several wells containing different drugs and/or different viscosity solutions simultaneously, might benefit the size measurement of similar or higher MW drugs.