120 L. G. AUGENSTINE 



jump to that adjacent macrostate by some fomi of bond rearrangement.* 

 Even without an immediate change in molecular energy due to external heat, 

 the jump will likely be followed by an instantaneous migration of the molecular 

 state locus on the new ED plane. This would be anticipated since the new locus 

 might not be the position of maximum probability for that instantaneous 

 molecular energy. A sufficient increase in temperature would eventually 

 drive the trajectory out of the fraction of the null region corresponding to an 

 active molecule: with sufficient mistreatment the locus would be driven com- 

 pletely out of the null region into the portion of configuration space representing 

 irreversibly inactivated molecules. 



Molecular energy will decrease when external heat is removed, and the 

 molecular rearrangements will be reversed or not depending upon the sym- 

 metry of the multi-dimensional surface of the well. Where denaturation is 

 reversed merely by reversing the denaturing conditions, apparently the inacti- 

 vation trajectory is retraced or else the null region is a smooth "well" with no 

 intervening metastable positions in the reversal trajectory. Thus, for reactiva- 

 tion the two trajectories would not have to be identical but need only form a 

 •closed loop. 



Asymmetry in the probability contours of even one of the ED plots traversed, 

 could cause the inactivation and reversal trajectories to diverge sufficiently 

 so that metastable, non-active configurations would result. Such situations 

 have been observed experimentally; for instance, thermal denaturation at 

 alkaline pH is not reversed upon cooling until the pH is adjusted to acidic 

 conditions (35). Since a change in pH should alter the ED contours it is easy 

 to envision how it could make the reversal of denaturation more likely by 

 changing the transition probabilities between macrostates and thus alter the 

 reversal trajectory. Such an alteration would resolve the apparent contra- 

 diction of the Second Law: a changed pH would act as a 'Maxwell Demon 

 guiding the footsteps of the reversal trajectory'. 



Considering its likely statistical nature, it is probable that much of the 

 trajectory of the locus of molecular states proceeds along essentially negligible 

 probability gradients, not only with respect to transitions from one macrostate 

 to another but more particularly with respect to instantaneous displacement 

 from the locus of arrival on a new ED plane. Such transitions should be readily 

 reversible and in general of limited consequence except as they lead to regions 

 of larger gradients. However, a 'low-gradient' region would allow considerable 

 leeway in trajectories. This would permit multiple pathways which would 

 account for the spectrum of effects often observed following physical denatura- 

 tion. In those transitions involving bonds which latch large segments of the 

 molecule together (12) (e.g. interhelical bonds) gross molecular rearrangements 

 could occur so that the trajectory would pass through regions of large probability 

 gradients. Such transitions would not be instantaneously reversible and would 

 therefore be relatively important in driving the trajectory away from the "active" 

 portion of or even out of the 'well'. 



My proposed inactivation hypothesis discussed later (37) attempts to 



* Somewhat more rigorous discussions of factors aflfecting the trajectory of the locus of 

 molecular state in similar multi-dimensional plots have been given by Teller (45) and Lumry 

 and Eyring (46). 



