Calculating the Secrets of Life Contributions of the Mathematical Sciences to Molecular Biology (1995) / Chapter Skim
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Pages 167-170
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From page 167... ...
THE SURFACE LINKING NUMBER We now give a formal definition of the two quantities, surface linking number SLk and winding number, for a closed DNA on a protein surface. We assume that the surface involved has the property that at each point near the axis of the DNA, there is a well-defined surface normal vector.
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From page 168... ...
As such, SLk has three important properties. First, if the DNA axissurface combined structure is deformed in such a way that no discontinuities in the vector field v occur in the neighborhood of the DNA axis A, and A itself is not broken, then SLk remains invariant.
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From page 169... ...
Winding the Double Helix 169 , / / AREA / a At ,. ~ J / FIGURE 6.9 Examples of displacement curves and SLk.
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From page 170... ...
By the invariant properties mentioned above, SLk remains invariant even if the round torus is deformed. Examples are shown in Figure 6.
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