The 50 ns equilibrium simulation of ubiquitin, for example, shows the following time correlation:
Oops! There is significant rearrangement of the linker region between β3 and β4 (observed also in the previous section as a "tug of war" between R42 and D58). If we want to faithfully simulate ubiquitin, we would need to simulate "longer" (perhaps several milliseconds as we recently learned! but I digress). This kind of analysis would be very difficult with "fitting" methods, perhaps one could look at time correlations with pricipal components, but here we have direct access to a very large amount of information.
At constant velocity pulling experiments, the very first part of the unfolding trajectory sees a linear increase in force (as a "force ramp"). In that case, this Pearson correlation with time represents the force response of the protein. We examine this for the first 10 ns (of a total of 250) of "unfolding" of ubiquitin in which only minor changes in the contact map can be observed:
Residue pairs in orange get closer together as the external force increases (and could therefore be considered "force-bearing") and blue ones farther apart ("force-compliant"). More sampling than 10ns on a single frame would definitely be helpful, of course!
How about some other macroscopic variable? Let us try to explain the radius of gyration of ubiquitin. If we check how the contact map correlates with this observable, we get:
If we identify the positively correlating interactions, we find out that it is the final loop with everything else and the flexible loop with β3 that are mainly responsible for changes in the radius of gyration. This makes a lot of sense, of course.