Molecular structure conflict mechanism

The immediate consequence of the theorem is that a structural instability can be established through only one of two possible mechanisms which correspond to the bifurcation and conflict catastrophes. A change in molecular structure—the making and breaking of chemical bonds—can only be caused by the formation of a degenerate critical point in the electronic charge distribution or by the attainment of an unstable intersection of the submanifolds of bond and ring critical points. 

These examples have identified two types of catastrophe points, a distinction that arises as a corollary of a theorem on structural stability. This theorem, when used to describe structural changes in a molecular system, states that the structure associated with a particular geometry X in nuclear configuration space is structurally stable if p r X) has a finite number of cps such that (i) each cp is nondegenerate (ii) the stable and unstable manifolds of any pair of cps intersect transver-sally. The immediate consequence of this theorem is that a structural instability can be established solely through either of two mechanisms in the bifurcation mechanism the charge distribution exhibits a degenerate cp, while the conflict mechanism is characterized by the nontransversal intersection of the stable and unstable manifolds of cps in p(r X). 

Each molecule (molecular weight 30000) contains one zinc(II) atom, which is (approximately) tetrahedrally coordinated to two N atoms and one O atom from amino-acid residues plus a water molecule. The structures of both the enzyme and some enzyme-substrate complexes have been carefully studied and the detailed mechanism of the hydrolysis is now quite well understood. Without going into details, a crucial factor appears to be the pronounced distortion from regular tetrahedral coordination about the Zn(II), apparently imposed by the conformational requirements of the polypeptide chain. The conflict of interest between the needs of the Zn(II) atom - which, when four-coordinate, always assumes tetrahedral coordination - and the ligands induces an entatic state, a condition of strain and tension which enhances the reactivity at the active site. The Zn atom binds the substrate peptide via the O atom of the —CONH— peptide link, and the entatic state of the free enzyme facilitates formation of the enzyme-substrate complex. 

The examples previously discussed with reference to the structure diagram demonstrated the existence of two kinds of catastrophe points, called bifurcation and conflict points. Both types of instabilities were illustrated in terms of the behaviour observed for molecular charge distributions. What we now show is that the existence of these two kinds of catastrophes and just these two, is a direct consequence of a theorem of structural stability stated by Palis and Smale in 1970. This theorem predicts what are the two basic mechanisms for structural change in a chemical system. 

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