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Liisa Hirvonen deleted subsectionCalculatio.tex
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sectionIntroduction_.tex
sectionMethod___subs.tex
figures/setup3/setup3.png
subsectionCalculatio.tex
sectionResults___The.tex
figures/BSA_anisotropy2/BSA_anisotropy2.png
figures/eylea_fit/eylea_fit.png
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\subsection{Calculation of hydrodynamic radii}
The anisotropies were calculated from the intensity time decays measured in parallel and perpendicular polarisation directions with eq~\ref{eq:anisotropy} (see Fig~\ref{fig:setup}b,c). The anisotropies contain a fast component in addition of the expected longer component and were fitted with gnuplot to a double-exponential function:
\begin{equation}
y = A_1\cdot e^{-\frac{t}{\phi_1}} + A_2\cdot e^{-\frac{t}{\phi_2}} \label{eq:2expfit}
\end{equation}
where $A_1$ and $A_2$ are the amplitudes and $\phi_1$ and $\phi_2$ the rotational correlation times of the two different components.
The longer rotational correlation time for each protein obtained from the fitting was plotted against the viscosity. For each protein this yields a straight line, from which the hydrodynamic radius $R_h$ of the rotating unit can be calculated by combining the Stokes-Einstein-Debye equation (eq~\ref{eq:SED}) with the equation for the volume of a sphere:
\begin{equation}
R_h=\sqrt[3]{\frac{3kT}{4\pi}\frac{\phi}{\eta}} \label{eq:R_h}
\end{equation}
where $k$ is the Boltzmann constant, $T$ is the absolute temperature and $\phi/\eta$ is the gradient of the straight line.