HENRY M. SOBELL

HIGHER ENERGY KINK-ANTIKINK BOUND STATES

Bifurcations arising within premeltons having higher energy (i.e., these contain larger beta-DNA core regions that undergo more vigorous breather-motions) lead to the formation of two additional types of higher energy kink-antikink bound states in DNA. These are called branch-migratons and dislocatons. Each give rise to different types of chain-slippage events, called double- and single-stranded branch-migration.

Branch migratons arise from breathing events that cause DNA chains to come apart transiently, and to then "snap back" at nucleotide base sequences having 2-fold symmetry. Weakly hydrogen-bonded hairpin-like structures initially form. These are lengthened by a series of kinetic steps in which hydrogen-bonds connecting base-pairs within dinucleotide elements in vertical stems are broken and simultaneously reformed in horizontal stems (or vice-versa) in a concerted 2-fold symmetric process. The phenomenon is called, "cruciform-extrusion". A branch-migraton contains four stems; each stem contains kink (or antikink) boundaries connecting beta-DNA core regions with surrounding B-DNA. In three dimensions, each stem is, in all likelihood (pseudo) tetrahedrally coordinated.

Dislocatons arise at repetitive base sequences (as, for example, in poly d (G-A): poly d (C-T)). Again, these structures form as the result of particularly energetic breathing events, causing DNA chains to come apart, and then "snapping back", to form small single-stranded "bubble-like" protrusions on opposite chains. These protrusions then move apart, leaving growing regions of beta-DNA in-between. The centers of these regions modulate into kink and antikink boundaries, and these, in turn, continue to move apart to leave B-DNA. The net result is the appearance of pairs of dislocatons, each moving in opposite directions along DNA. Movement involves single-chain slippage, and is remarkably similar to the mechanism underlying moving crystal lattice dislocations. Hence the term, dislocaton.

It is easy to imagine breather motions within the dislocaton and the branch migraton that would facilitate chain-slippage. Breather motions within the dislocaton, for example, could involve kink and antikink moving together, first to the right, and then to the left, in a concerted fashion. This would facilitate single-chain slippage events (see animation). In the branch-migraton, kink and antikink within vertical stems can move in, while kink and antikink within horizontal stems move out (and vice-versa), all in a concerted fashion, to facilitate double-chain slippage events. These motions require simultaneity of movement in both horizontal and vertical stems, and this follows as a necessary consequence of the nonlinearity present in this breather soliton (see animation). We envision kinetic jump steps to involve breaking (and, after slippage, reforming) base pairs in dinucleotides between beta-elements, rather than within beta-elements. The precise details of the kinetic mechanism, however, must await further study.

The formation of these two different kinds of higher energy kink-antikink bound state structures is another example of bifurcations emanating within the centers of premeltons. The underlying source of nonlinearity that determines the path of the bifurcation is the breaking and reforming (after chain-slippage) of hydrogen bonds connecting dinucleotide base-pairs. The decision as to whether or not branch-migratons or dislocaton pairs form is determined by information coded in the nucleotide base-sequence. This information constitutes the bias.

The combined presence of torsional and writhing strain energies found in negatively superhelical circular DNA increases the probability that branch-migratons and dislocatons form at the appropriate sequences. These energies are first used to form premeltons. They are next used to form dislocatons or branch-migratons, and to propagate chain-slippage events.

The energy in negatively superhelical DNA can also be used to facilitate the B- to Z- structural phase transition. We will now discuss this.