118 



L. G. AUGENSTINE 



a very gross specification of the myriad degrees of freedom of macromolecules, 

 some form of multi-dimensional space will be necessary to represent their 

 stability conditions. The biologically significant portion of such a macro- 

 molecular space will also be a 'well', but in a multi-dimensional surface rather 

 than a line plot and will be centered near the locus of native structures in configu- 

 ration space. A fraction of the well will represent conditions consistent with 

 an active macromolecule and the remainder, conditions characteristic of 

 reversible inactivation. Anything outside the well will correspond to states 

 inconsistent with the restitution of a native configuration. 



The multi-dimensional space can be of sufficient dimensionahty so that 

 all configurations differing by a 'single step' are neighbors. In such a 'fine- 

 grain' specification each microstate and its probability density (as a function 

 of energy, for example) can be represented. However, such a scheme has 

 drawbacks: first, it has little novelty since any situation can be completely 

 described by a sufficient number of parameters ; second, a model dealing only 

 with microstates would be extremely diflftcult to test experimentally; and 

 third, the excessive dimensionality makes it useless as an aid in envisioning 

 possible mechanisms of macromolecular rearrangements. 



Thus, a 'coarse-grain' specification, which requires reducing the dimension- 

 ality by transforming the microstates into a more useful set of macrostates, 

 is desirable. This general operation can be schematized by the use of the follow- 

 ing contingency table : 



Table III 



■< Molecular Energy > 



^1 ^2 ^k ^n 



°'lll '''lia '^llk '^lln 



°'l21 (^122 <^12i- ^12n 



^m °'ij2 '^lik OCljn 



"'all °'212 '^21fc ^2ln 



'^iil '^iji ■ 



"■ijk 



• a,. 



A plausible specification for a multi -dimensional space is given in Table III, 

 where a sufficient number of binary digits is used so that each microstate 

 can be unequivocally identified, e.g. the two atoms involved in each bond 

 as well as the bond length and angle could be identified. Each ol^j^. represents 



