\subsection{Energy landscape frustration measurements in Ubiquitin}
\label{sec.ubiquitin}

As a test of the temperature control system, Y.\ Yang et al.\ applied the method of Hyeon and Thirmulai to calculate the frustration energy scale in octomeric Ubiquitin\cite{hyeon03}\cite{yang06}, measuring the most probable unfolding force as a function of loading rate and temperature.
Their data is presented in Figure~\ref{fig.ubiquitin_temp_depend}.
\begin{figure}[btp]
  \centering
%  \includegraphics{mp/unfolding_data.2}
  \includegraphics[width=0.5\textwidth]{ubiq_temp_ugly}
  \caption{Temperature and loading rate dependence of unfolding in Ubiquitin\cite{yang06}.
    This figure is the experimental equivalent to Hyeon and Thirmulai's simulated data in Figure~\ref{fig.const_r_sim}.
%    The $\bigtriangleup$ series was taken at 45{\dg}C, and the $\bigtriangledown$ series was taken at 5{\dg}C.
%    There are approximately {\bf$X$:p} unfolding events per point.
%    The fitting lines are {\bf:p $f^*(T=45,x) = 25.8\log(v)+4.08$ and $f^*(T=5,x) = 27.0\log(x) + 86.8$}.
    }
  \label{fig.ubiquitin_temp_depend}
\end{figure}
When the most likely unfolding force is $200\mbox{pN}$, the pulling speed is $v_1 = 66.7\mbox{nm/s}$ at $T_1 = 5\dg$C and $v_2 = 1992\mbox{nm/s}$ at $T_2 = 45\dg$C.
With a spring constant of $\kappa = 85.6\mbox{pN/nm}$ measured by thermal vibration, the loading rates are then given by
 $r_f(T_1) = \kappa v_1 = 5648\mbox{pN/s}$ and $r_f(T_2) = \kappa v_2 = 1.69\E{5}\mbox{pN/s}$.
Combined with the values from the literature of $k_0 = 5.0\E{-5}\mbox{Hz}$ and $\Delta x = 0.225\U{nm}$ \cite{yang04},
 we can calculate the unfolding energy according to Hyeon and Thirmulai's Equation 9, and extract $\varepsilon \approx 1.98\E{-20}\mbox{J} \approx 4.8 k_B T$.
Because $\varepsilon > k_BT$, this frustration is in the upper limit of frustrations for which Hyeon and Thimulai's formulation is valid.

This measurement is the first experimental measure of a protein energy landscape frustration scale, although the same technique has been used to measure the frustration of receptor-ligand binding \cite{nevo05}.
The difficulty with this experiment is a combination of the extra equipment needed to control the temperature and the large datasets required to extract $\varepsilon$.
Our streamlined system should greatly facilitate making such measurements on Titin.
%The data in Figure~\ref{fig.ubiquitin_temp_depend} is the result of $\sim$20,000 force curves, of which $\sim$4,000 were usably clean unfoldings.
%This represents roughly 100 experiment hours worth of data plus processing time.
%{\bf (Numbers reasonable, records to check against?)}
