deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 6ecd763..0b564e8 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
\end{equation}  However, proteins have a rough surface, are often not perfectly spherical, and their charge affects the diffusion of a molecule in solution. The hydrodynamic radius $R_h$, defined as the radius of a hard sphere that diffuses at the same rate as that solute, takes these effects into account. The hydrodynamic radius is important in predicting transretinal penetration.\cite{Jackson2003,Ambati2000a} Small-angle scattering studies using X-rays (SAXS) or neutrons (SANS) \cite{Svergun_2013} as well as dynamic light scattering (DLS) \cite{Pecora_1985,Hong_2009} and nuclear magnetic resonance (NMR) techniques \cite{Wilkins1999} have been used for measuring $R_h$. Global analysis of hundreds of proteins has led to the definition of empirical Empirical  relationships have been defined  between $R_h$ and the number of amino acids $N$, related $N$ (related  to the MW by \(N = \frac{\text{MW}}{110 \text{ Da}}\). Such formulas have been defined, Da}}\)),  for example, by Wilkins \textit{et al.}\ \cite{Wilkins1999} \begin{equation}  R_h^W (\text{\AA}) = 4.75\cdot N^{0.29} \label{eq:Wilkins}  \end{equation} 
...
R_h^D (\text{\AA}) = 1.45\cdot(2.24\cdot N^{0.392}) = 3.248\cdot N^{0.392} \label{eq:Dill}  \end{equation}  These formulas were obtained by global analysis of hundreds of proteins, and fitting to a scatter plot of $R_h$ against MW. However, there is a big variance in the measured $R_h$ as a function of MW due to molecular shape, charge and surface roughness, and while these formulas give a good indication of the expected size, they do not take these effects into account.  %\subsection{Radius measurement from anisotropy}  Time-resolved fluorescence anisotropy measurements can determine the molecule's rotational mobility which depends on the molecular volume and the viscosity of the environment surrounding the molecule.\cite{Lakowicz2006} The sample solution is excited with a pulse of polarised light, and the fluorescence is collected in parallel and perpendicular polarisation directions as a function of time. The anisotropy $r(t)$ of a molecule undergoing rotational diffusion in the solution can be obtained from the measured intensities $I_\parallel$ and $I_\perp$ by