Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)
Chapter: Chapter 7 Unwinding the Double Helix: Using Differential Mechanics to Probe Conformational Changes...
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Chapter 7
Unwinding the Double Helix:
Using Differential Mechanics to Probe Conformational Changes in DNA
| The two strands of DNA are usually bound together in a double helix. However, many key biological processes including DNA replication and gene expression-require unwinding of the double helix. Such unwinding requires the input of energy, a large part of which is stored in the form of supercoiling of a chromosome or chromosomal region. Given a supercoiled DNA molecule, where along its sequence will unwinding occur? In this chapter, the author shows how basic principles of statistical mechanicstogether with some delicate numerical estimatescan be applied to predict the sites of supercoil-induced unwinding. The mathematical predictions are abundantly confirmed by experimental data and, when applied to new situations, they suggest novel insights about gene regulation. |
Deoxyribonucleic acid (DNA) usually occurs in the familiar Watson-Crick B-form double helix, in which the two strands of the DNA duplex are held together by hydrogen bonds between their complementary bases. Many important biological processes, however, involve separating the strands of the DNA duplex in order to gain access to the information encoded in the sequence of bases within individual strands. In transcription, the first step in gene expression, the DNA base pairing within the gene must be temporarily disrupted to allow an RNA molecule with a sequence complementary to one of the strands of the gene to be constructed. In DNA replication, the two original strands of a parent DNA molecule replicate to form two complete molecules, with each strand serving as a template for the synthesis of its complement. To
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accomplish this, the strands of the parent molecule must separate to provide access to these templates.
The regulation of important physiological processes is extremely precise and complex. In addition to many other layers of control, the strand separations required for specific functions must be carefully regulated to occur at the precise positions needed for each activity, and only at times when that activity is to be initiated. Because DNA prefers to remain in the B-form under normal conditions, strand separation requires the expenditure of (free) energy. The energy required for strand separation depends upon the sequence of base pairs being separated. Because A·T base pairs are held by only two hydrogen bonds whereas G·C pairs are held by three, it is energetically less costly to separate the former pairs than the latter. For this reason, strand separations tend to be concentrated in A+T-rich regions of the DNA. As we will see in this chapter, this provides the sequence dependence necessary to control the sites of separation.
Controlling the occurrence of separations can be accomplished by modulating the amount of energy stored in the DNA molecule itself. This is done by changing the topological constraints on the molecule. DNA in living organisms is topologically constrained into domains within which the linking number is fixed. Enzymes can change this linking number, placing the DNA in a higher energy state in which pure B-form DNA is less favored and partial strand separation is thermodynamically more achievable. (The topology and geometry of superhelicity, which is the jargon name for this process, have been described by White in Chapter 6.)
In order to illuminate the role of strand separation in DNA functions, one needs accurate theoretical methods for predicting how a particular DNA sequence will behave as its linking number is varied. This chapter describes methods that have been developed to make such predictions. The results of sample calculations are shown, and the insights that they provide regarding specific DNA activities are sketched. The global and topological nature of the constraints imposed on DNA causes behavior that exhibits many unusual and surprising features.
