Rigidity, torsional

The rotational relaxation of DNA from 1 to 150 ns is due mainly to Brownian torsional (twisting) deformations of the elastic filament. Partial relaxation of the FPA on a 30-ns time scale was observed and qualitatively attributed to torsional deformations already in 1970.(15) However, our quantitative understanding of DNA motions in the 0- to 150-ns time range has come from more accurate time-resolved measurements of the FPA in conjunction with new theory and has developed entirely since 1979. In that year, the first theoretical treatments of FPA relaxation by spontaneous torsional deformations appeared. 16 171 and the first commercial synch-pump dye laser systems were delivered. Experimental confirmation of the predicted FPA decay function and determination of the torsional rigidity of DNA were first reported in 1980.(18) Other labs 19 21" subsequently reported similar results, although their anisotropy formulas were not entirely correct, and they did not so rigorously test the predicted decay function or attempt to fit likely alternatives. The development of new instrumentation, new data analysis techniques, and new theory and their application to different DNAs in various circumstances have continued to advance this field up to the present time. 

One would still like to examine the effect of ethidium on the torsional rigidity and dynamics at high binding ratios. One would also like to test the Forster theory for excitation transfer between bound ethidium molecules, since it has been questioned/65- This is possible in principle by deconvoluting the effects of depolarization by excitation transfer on the FPA, as will be shown subsequently. DLS also provides crucial information on this same question. 

Ashikawa and co-workers attempted to determine both the bending and torsional rigidities simultaneously from their FPA data by fitting a simple approximate form that was then compared with the incorrect anisotropy formula of Barkley and Zimm.(21 58,61,108) Neither their claim to distinguish the bending contribution nor their reported bending rigidities can be taken seriously. 

All torsional rigidities are uniform in the sense that a is independent of the time span of the data. b p Ionic strength. 

Figure 4.14. Torsion constant a versus channel width for 29 DNA in 0.01 M NaCl. In each of the three panels the data points correspond to the experimental time spans 0-20 ns, 0-40 ns, 0-80 ns, and 0-120 ns. The three samples differ in either spermidine concentration or pH. In the absence of spermidine, a is uniform. With the addition of spermidine, a decreases slightly on the longer time spans. The decrease probably represents zones of lower torsional rigidity. The large decrease in a on the longest two time spans when the pH is raised to 10.2 is consistent with the occurrence of occasional (isolated) major rigidity weaknesses.

A prerequisite to these calculations is the knowledge of bending and torsional rigidity coefficients (A and C, respectively) of the naked DNA. A was calculated from a persistence length a = A/kT = 50 nm [58], and C through the following equation, valid only for a naked DNA minicircle near relaxation [59]... 

Setvin. P.R- cl al.- "Torsional Rigidity of Positively and Negatively Supercoited DNA. Science. 82 iJmiiiary 3. 1992). 

When instead assemblies of helices are taken into account, it is well known that for many aspects DNA duplexes in solution can be treated as a charged anisotropic particle [2]. Accordingly, steric, electrostatic, and Van der Waals interactions, together with the mechanical properties of the helix (bending and torsional rigidity), play a major role in the formation of DNA mesophases. In addition, all these different kinds of interactions combine in a subtle and still poorly understood way to generate other forces relevant for the case of DNA. A notable example is the helix-specific, chiral interaction, whose importance for DNA assemblies will be discussed below. 

Molecular mechanics as a minimization of strain energy makes a rigid distinction between steric and electronic effects. Electronic effects are introduced in the form of empirical constants such as characteristic bond lengths and angles, the corresponding force constants, torsional rigidity of even-order bonds, planarity of aromatic systems and the coordination symmetry at transition-metal centres. These constants are accepted, without proof, to summarize the ensual of electronic interactions and used without further optimization. 

Torsional rigidity Bonds of even order are sterically rigid because of a barrier to rotation, representing the energy needed to generate the o-a-m that occurs in the twisted system, and which can be calculated directly. 

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