In we show the calculated characteristic rate coefficients for the protein 4ANK as a function of the relative stability of the completely folded and completely unfolded macrobasins. At lower temperatures (more negative stabilities) the characteristic rate reflects the rate of formation of the folded state – this parallels the experimental scenario where denatured protein is rapidly equilibrated in stabilizing conditions. At higher temperatures (more positive stabilities), the unfolding process dominates the relaxation kinetics. The rates become smallest when the folding and unfolding rate eventually meet near the folding temperature. For strictly two-state folders (with a transition state that does not vary with the stability) this sort of
vs. stability plot has a sharp V-shape and is therefore called a “chevron plot”. Deviations from a strict V-shape are expected for folding mechanisms with intermediates. Experimentally, chevron plots are typically obtained by using chemical denaturant to change the relative stability of the folded and unfolded states. In computer models that lack an explicit representation of chemical denaturants, it is necessary to find other ways to change the relative stability of the folded and unfolded states, and temperature is a common choice. Although not guaranteed to behave identically, calculated thermal chevron plots have been fruitfully compared to experimental chemical denaturant chevron plots to shed light on specific questions related to real biological systems 
Thermal chevron plots obtained using two foldon definitions.
shows chevron plots calculated using the ANK and half-ANK foldon definitions. Both foldon definitions give similar chevron plots although the rates obtained using the half-ANK definitions are lower. Using either foldon definition, the plots show curvature in the unfolding arm.
For each foldon definition, we calculated the cumulative folding and unfolding fluxes using Equation 5
(, and ). The relative stabilty of the folded and unfolded macrobasins was chosen to be in the range of
in all cases, about half way up the folding or unfolding arm. The flux calculation was started with
of the population in either the folded or unfolded state, and Equation 5
was evaluated at
, yielding the equilibrium fluxes.
Flux diagrams for the full-ANK mechanism.
Folding flux diagram for the half-ANK mechanism.
Unfolding flux diagram for the half-ANK mechanism.
The mechanism inferred using ANK foldons () goes through a transition state with the third repeat folded. At high folded state stability, folding continues downhill in free energy through several competing pathways. The unfolding mechanism at high temperature is approximately the reverse of the folding process at low temperature, but it differs in that a single pathway dominates, proceeding through a broad transition state that contains both the 0010 and 0110 macrobasins. In contrast to folding conditions, relatively little flux flows through 0011.
shows the fluxes for folding according to the half-ANK foldon definition. With 46 macrobasins sampled, the half-ANK mechanisms are more elaborate. Flux goes through multiple pathways that are closely related to each other and similar to the previously discussed pathways for the ANK foldon definition. Most of the flux goes through the macrobasin 00001000, which has the N-terminal helix of repeat 3 folded, and then through 00001100 to complete the folding of the 3rd repeat. While we predict a relatively high stability for the macrobasin 01111101, the flux analysis shows that this macrobasin is not kinetically significant. The mechanism does not follow trivially from the thermodynamics; the locality of transitions matters.
The unfolding fluxes under the half-ANK foldon assignment are shown in . Unfolding is initiated at the termini. As with the ANK foldon case, the half-ANK mechanism goes through an intermediate with the center two repeats folded. For levels of global foldedness where an even number of half ANK units are folded, those macrobasins with all full ANK units either completely folded or unfolded (such as 00111100 and 00001111) are always found to be more stable than those with partially folded ANKs (such as 00011101 and 0010110). As a result, these states tend to have a larger fraction of the flux, although the exact amount of flux depends on the detailed connectivity of the model.