Figure 4. Competing thermodynamic coupling in GR produces frustration.

(a) Schematic view of the thermodynamic configuration of GR. According to this convention, the positive (+) signs between the DBD and F-domain, and the DBD and R-domain signify they are positively coupled; stabilization of one domain stabilizes the other. The negative (-) sign between the R- and the F- domains indicate they are negatively coupled; stabilization of one domain destabilizes the other. Thus, the combination of the positive coupling between DBD and R-domain, and the negative coupling between R- and F-domains produces an overall repression (red semicircle) from the effect that is mediated through the R-domain. Triplet arrows are an abbreviation to describe all the couplings in the system: first arrow indicates the coupling between DBD and F-domain, second arrow indicates coupling between R-domain and F-domain, and third arrow indicates coupling between DBD and R-domain. Green (up) arrow indicates positive coupling and red (down) arrow indicates negative coupling. Importantly for this equilibrium scheme, any permutation containing an even number of up arrows will be energetically frustrated. (b) Schematic representation of all possible thermodynamic configurations for three interacting domains (represented in the structural and spin (up or down arrows) nomenclatures). Four of the possible configurations produce frustration between the DBD and the F-domain (top), whereas four configurations do not produce frustration (bottom), representing the cases of activation and repression, respectively. Note the curved arrows connecting the domains are colored according to the overall effect on F-domain from stabilizing the DBD; this coloring scheme highlights the result that frustrated configurations result from opposing energetic couplings affecting the F-domain stability. For example, in case i (Top, Left), stabilization of the DBD destabilizes the R-domain due to the negative coupling energy, signified by the red curved arrow between domains. However, the destabilization of the R- domain has the effect of also destabilizing the F-domain, because the F- and R- domains are positively coupled. Thus, the overall effect of stabilizing the DBD is to destabilize the F-domain through its interaction with the R-domain, signified by the red curved arrow between the R- and F- domains (even though the coupling between R-F alone is positive).