\subsection{The supramolecular scaffold}
\label{sec:sawsim:results:scaffold}
+\begin{figure}
+ \begin{center}
+ \asyinclude{figures/order-dep/order-dep}
+ \caption{The dependence of the unfolding force on the temporal
+ unfolding order for four polymers with $4$, $8$, $12$, and $16$
+ identical protein domains. Each point in the figure is the
+ average of $400$ data points. The first point in each curve
+ represents the average of only the first peak in each of the $400$
+ simulated force curves, the second point represents the average of
+ only the second peak, and so on. The solid lines are fits of
+ \cref{eq:sawsim:order-dep} to the simulated data, with best fit
+ $\kappa_\text{WLC}=203$, $207$, $161$, and $157\U{pN/nm}$,
+ respectively, for lengths $4$ through $16$. The insets show the
+ force distributions of the first, fourth, and eighth peaks, left
+ to right, for the polymer with eight protein domains. The
+ parameters used for generating the data were the same as those
+ used for \cref{fig:sawsim:sim-sawtooth}, except for the number of
+ domains. The histogram insets were normalized in the same way as
+ in \cref{fig:sawsim:sim-hist}.\label{fig:sawsim:order-dep}}
+ \end{center}
+\end{figure}
+
Analysis of the mechanical unfolding data is complicated by the
dependence of the average unfolding force on the unfolding order due
to the serial linkage of the molecules. Under an external stretching
same protein because of the differences in unfolding order and polymer
length.
-\begin{figure}
- \begin{center}
- \asyinclude{figures/order-dep/order-dep}
- \caption{The dependence of the unfolding force on the temporal
- unfolding order for four polymers with $4$, $8$, $12$, and $16$
- identical protein domains. Each point in the figure is the
- average of $400$ data points. The first point in each curve
- represents the average of only the first peak in each of the $400$
- simulated force curves, the second point represents the average of
- only the second peak, and so on. The solid lines are fits of
- \cref{eq:sawsim:order-dep} to the simulated data, with best fit
- $\kappa_\text{WLC}=203$, $207$, $161$, and $157\U{pN/nm}$,
- respectively, for lengths $4$ through $16$. The insets show the
- force distributions of the first, fourth, and eighth peaks, left
- to right, for the polymer with eight protein domains. The
- parameters used for generating the data were the same as those
- used for \cref{fig:sawsim:sim-sawtooth}, except for the number of
- domains. The histogram insets were normalized in the same way as
- in \cref{fig:sawsim:sim-hist}.\label{fig:sawsim:order-dep}}
- \end{center}
-\end{figure}
-
\citet{benedetti11} have since proposed an alternative
parameterization for \cref{eq:kappa-system}, using
\begin{equation}