APPENDIX B - Letter for third discussion

Charles Yanofsky writes, “I just read the interesting material you sent me describing the RNA polymerase-DNA complex. Yes, it is an interesting way to look at transcription and raises several additional questions. What features of a promoter-leader sequence can influence polymerase movement and/or attachment? Are there proteins that bind near promoters that influence the polymerase-DNA interaction -- isn't this how the CAP protein acts? How are these issues related to abortive transcription?”

Henry Sobell replies, “Yes, these questions are important ones that certainly need to be answered. For the moment, however, my mechanism focuses in on answering how promoter regions undergo site-specific DNA melting by the RNA polymerase enzyme, and presents the relevant physics to help understand how this would happen. The mechanism can answer another puzzling question: The polymerase is known to bind to DNA very tightly. If this is the case, how is it possible for the polymerase to move along DNA so easily during RNA synthesis?

[Professor Yanofsky’s pioneering studies have defined how tryptophan biosynthesis is coordinately regulated in the tryp operon, a sequence of genes in E. coli that codes for the enzymes involved in tryptophan biosynthesis. Tryptophan is one of twenty amino acids found in proteins].

Panayotis Kevrekidis writes, “I am finding the discussion fascinating. However, where is the mathematical physics?”

Henry Sobell writes, “As I see it, current attempts to formulate the mathematical physics of solitary excitations in DNA have been of limited value since they have not handled DNA at the molecular level. DNA is known to have a complex molecular structure (many of us think it relatively simple, however, compared to the huge protein-DNA complexes now being visualized by X-ray crystallography), and it is not clear how to proceed using standard mathematical techniques. Asok Banerjee and I approached the problem in a completely different way, many years ago. Using nonlinear least squares energy minimization techniques, it was possible to calculate the boundaries connecting different DNA forms. The concept that such (molecular) boundaries can be calculated (preserving the canonical bond distances and angles between atoms) -- and that these correspond to the “kink” and “antikink” in the terminology of nonlinear science -- is new to many physicists and mathematicians working in the area (as well as to those in the molecular biology area), and I continue to hope that everyone will eventually come to appreciate our efforts.

While it is true that my more general theory is still conceptual, it is nevertheless compelling. Not only does the theory form a logical framework to understand a large amount of information in the molecular biology area -- it is eminently testable (we will discuss the detailed predictions it makes in a later communication).

Our audience consists of about 90 scientists. Half of these are theoretical physicists and mathematicians, while the others are molecular biologists. Al and I are trying to "breach the gap" between the two! Not an easy matter!”

[Panayotis Kevrekidis is an Associate Professor of Mathematics and Statistics at the University of Massachusetts, Amherst, Massachusetts, specializing in the understanding of the emergence and stability of solitary wave structures in optical systems and in Bose-Einstein condensates].

So -- shall we continue with our discussion?

Premeltons are examples of structural solitons. Being structural, they should be calculable. Since both DNA and double stranded RNA (the latter, incidentally, is known to be restricted to the A-form due to steric hindrance by the 2’ hydroxyl group) undergo intercalation, saturating at levels approaching “neighbor-exclusion”, this suggests that minimal energy boundaries can be calculated that connect B-DNA with beta-DNA, A-DNA with beta-DNA and A-RNA with beta-RNA. We have already discussed the structures of the three different DNA forms in the second communication.

The B-B premelton is (globally) nontopological. This is because – within each base-paired dinucleotide component -- the magnitude of torsional unwinding is counterbalanced by an equal but opposite right-handed superhelical writhing to keep the linking invariant (Linking (L), Writhing (W) and Twisting (T) are topological quantities, related to each other by the relationship, W = L – T).

There is no unwinding or right-handed superhelical writhing between emerging beta-structural elements. For these reasons, B-B premeltons have a linking number almost identical to that observed for an equivalent number of base pairs in B-DNA. This has been verified by comparing figures of 100 base pairs of B-DNA with B-B premeltons containing 50 base pairs and surrounded by 25 base pairs of B-DNA on either side. B-DNA regions can be directly superimposed in both figures.

[An excellent (simplified) discussion of linking, writhing and twisting in DNA can be found in Lubert Stryer's textbook in Biochemistry, W.H. Freeman and Company, Third Edition, page 660].

A structural feature that accompanies this interesting topology is the appearance of a modulated beta-alternation in sugar puckering along both DNA chains. The emergence of this structural feature may reflect the presence of spontaneous symmetry breaking that accompanies a nonlinear excitation, giving rise to the Peierl's distortion (i.e., the Peierl's dimerization). As one proceeds towards the center of the premelton, another source of nonlinearity appears -- the breaking of van der Waals interactions between adjacent base pairs due to the progressive (partial) unstacking of alternate base pairs. The combination of these two sources of nonlinearity leads to the appearance (i.e., the emergence) of beta-DNA –- a hyperflexible and metastable DNA form -- within the center of the premelton.

I (HS) am convinced that these concepts will eventually prove to be of key importance in understanding the nature and origin of solitary excitations in DNA.

Henry Sobell

Alwyn Scott