Liisa Hirvonen edited sectionMethod___subs.tex  almost 9 years ago

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A simplified diagram of the data acquisition setup is shown in Fig~\ref{fig:setup}a. The anisotropy experiments were performed with Leica SP2, a standard confocal inverted microscope. A pulsed diode laser (PLP-10 470, Hamamatsu, Japan; optical pulse width 90~ps) was used as the excitation source at 200~kHz repetition rate. The beam was focussed in the middle of the well containing the sample solution with a 20$\times$ NA0.5 air objective (Leica HC PL Fluotar). The emission was collected with the same objective, through a green long-pass emission filter (550LP, details?) and completely open pinhole. Parallel and perpendicular polarization components of the fluorescence emission were separated with a polarising beam splitter (details?) and recorded simultaneously with two photomultiplier tubes (PCM-100, Hamamatsu, Japan) connected to a time-correlated single photon counting (TCSPC) acquisition card (SPC 830, Becker\&Hickl GmbH, Berlin, Germany). The measurement time window was 5~$\mu$s, with total data   acquisition time of $\sim$60~min per data set.  \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.