National Academies Press: OpenBook
« Previous: APPLICATIONS TO DNA TOPOISOMERASE REACTIONS
Suggested Citation:"DNA ON PROTEIN COMPLEXES." National Research Council. 1995. Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology. Washington, DC: The National Academies Press. doi: 10.17226/2121.
×
Page 166

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

WINDING THE DOUBLE HELIX: USING GEOMETRY, TOPOLOGY, AND MECHANICS OF DNA 166 will be distributed to give a change of +1.44 in average writhe and a change of +0.56 in average twist. Continuing with the same example of SV40 DNA introduced in the paragraph above, if a topoisomerase of Type II were introduced into a population of SV40 with linking number difference −25, the result would be a collection of such DNA with linking number differences −25, −23, −21, . . ., −3, −1. Such enzymes in fact were discovered because of this striking difference from topoisomerase of Type I in which DNA with all negative differences, not just the odd ones, were found. Other functions of topoisomerases are to pass single-stranded DNA through itself or to pass nicked DNA-that is, DNA in which one of the backbone strands has been cut by an enzyme-through itself. This aspect of topoisomerases is dealt with in more detail in Chapter 8. DNA ON PROTEIN COMPLEXES We now turn our attention to the geometric and topological analysis of DNA whose axes are constrained to lie on surfaces (White et al., 1988). The most well-characterized example of a protein surface is the nucleosome core (Finch et al., 1977), a cylinder of height 5.04 nanometers (nm) and radius 4.3 nm. In this case the axis A of the DNA wraps nearly twice around the core as a left-handed helix of pitch 2.8 nm. The surface on which the DNA molecule lies is the so-called solvent-accessible surface (Richards, 1977). This is the surface generated by moving a water-sized spherical probe around the atomic surface of the protein at the van der Waals distance of all external atoms and is the continuous sheet defined by the locus of the center of the probe. (In general, the surface of a protein is defined in this manner.) It is this surface that comes into contact with the DNA backbone chain. Because the DNA is approximately 1 nm in radius, the DNA axis lies on a surface that is 1 nm outside of the solvent- accessible surface to account for the separation of the backbone from the axis. This latter surface is the one to which we shall refer in the rest of this section as the surface on which the DNA, meaning the DNA axis A, lies or wraps. For DNA that lies on a surface, the geometric and topological analyses are best served by dividing the linking number not into twist and writhe, which relate only to spatial properties of the DNA, but into

Next: THE SURFACE LINKING NUMBER »
Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology Get This Book
×
Buy Paperback | $80.00
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important role—in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race.

In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology.

The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences.

This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!