HENRY M. SOBELL

APPENDIX A

Energies necessary for the formation of the premelton in DNA molecules come from Brownian motion, excited by solvent collisions at normal (i.e., kT) energies.

We envision DNA in solution to be continually bombarded by solvent collisions along its length. Although at first glance, one might expect the average excitation force to be zero, this is not the case in the microscopic domain, where DNA is continually experiencing unbalanced forces (i.e., the Brownian force).

Since the collision cross-sectional area of DNA is small (i.e., the diameter is about 20 Angstroms), relatively few solvent molecules impinge on its surface in short time intervals. Moreover, the flexibility of DNA is highly anisotropic. Due to this anisotropy, most solvent collisions are expected to have little effect on DNA structure, exciting only small amplitude normal mode motions in functional groups. These are expected to damp readily through solvent interactions. There are, however, small windows of collisions that deform DNA nonlinearly. We believe these collisions to hit DNA from both wide and narrow groove directions, striking DNA along dyad axes located between adjacent base pairs.

Such collisions give rise to nonlinear pulses in DNA (also called solitons, or solitary excitations), which move along the polymer chain with a velocity significantly less than the speed of sound. These contain a modulated beta-alternation in sugar puckering along both polynucleotide chains, and are nontopological -- that is, although these excitations unwind DNA, this is counterbalanced by right-handed superhelical writhing to keep the linking invariant. Energies stored and transmitted by such intrinsic locally coherent excitations can travel considerable distances along DNA with minimal dissipative loss, since they are largely internal to the polymer structure. In addition, such nonlinear pulses remain "robust", since the nonlinearity present in the sugar-pucker conformations acts to minimize dispersion effects.

The shape of the energy density profile accompanying low energy solitary excitations is expected to be sensitive to the nucleotide base sequence in DNA. This is because different DNA regions contain different base-stacking energies, and have, therefore, different intrinsic flexibilities. Energy-density profiles of traveling solitary excitations are expected to sharpen up (i.e., the leading edge of the excitation traveling more slowly than the trailing edge) within regions that start out by being more flexible than other regions. This acts to deform DNA structure, and to enhance the lifetime of these excitations. This increases the probability that, with increasing temperature, still larger excitations can form from the coalescence of additional solitary excitations that arrive in these regions. The appearance of these larger excitations deforms DNA regions still further, and gives rise to even greater flexibility in their most central regions. Eventually, with increasing temperature, premeltons arise that contain hyperflexible (liquid-like) beta-DNA cores, surrounded by phase boundaries termed "kink" and "antikink".

Premeltons have longer lifetimes, and, with increasing temperature, become nucleation centers for DNA melting. Traveling solitary excitations, originating from solvent collisions at earlier times and from more remote locations, enter the premelton, their energies being trapped within the core. This energy continues to enlarge beta-DNA core regions and increases the amplitude of breather motions, leading to DNA "breathing". Finally, with increasing temperature, permanently melted single-stranded DNA regions appear within the premelton. Their appearance signals the onset of DNA melting. We have called these larger structural solitons, "meltons".

With increasing temperature, meltons continue to trap energy from entering solitary excitations that have arisen elsewhere (and at earlier times) along B-DNA. Their energies are used to separate kink from antikink while lengthening internally melted single-stranded DNA regions. Finally, with increasing temperature, meltons coalesce and all DNA becomes single-stranded. Single-stranded DNA is extremely flexible (i.e., entropic), and can be likened to a gas-like phase.

In summary then, my thermal mechanism predicts the existence of three structural phases for DNA: the Watson-Crick A- or B- forms (solid), the hyperflexible beta-DNA form (liquid), and the entropic single-stranded melted DNA form (gas). The beta-DNA phase within the premelton is predicted to play a key role in nucleating DNA melting.