Torsional constants

The functional form for default torsions is the 1M+ form with th ree torsional constants VI, V2, and V3 for I -fold, 2-fold, and 3-fold contributions. I h e default values for these con stants depend on the particular chemical situatitm associated with theborid... 

Torsional Stiffness (Torsion Constant). Torsional stiffness of a body is appHed torque (N-m) divided by angle of twist (rad). Its SI unit is N-m/rad. 

The main features of this device are shown in Fig. 3.9a. The z-axis is directed along the field (the vertical), and the lever with a small mass m rotates around a horizontal axes, passing through the point 0. The length of the lever is a. The torsion spring is installed on the axis, and its torsion constant is equal fi. This is a coefficient of proportionality between the moment t and the rotation angle or. 

The effective potential governing torsional deformations could conceivably be quite anharmonic, so that overwinding is much more strongly resisted than underwinding for finite deformations. This question is addressed by examining the dependence of the torsion constant on temperature(40) and on superhelix density. 

As the torsion constant a approaches infinity, the relaxation times i, all approach 0, and the amplitude of the uniform mode, B ( oo), approaches 1.0, in which case C (t) is precisely the result for a rigid (against twist) rod. 

With respect to the torsion constants of these 43- and 69-bp restriction fragments, the fitting procedure was not robust, and acceptable precision could not be attained. 

Figure 4.10. Best-fit torsion constant a versus experimental time span for two different samples of supercoiled pUC8 dimer. The two samples are in 10 mAf Nad, 10 mAf Tris, 1 mAf EDTA, at pH 8 and T = 20°C, and differ only in their mean superhelix density (it) ,

Millar et al,(20) originally assumed that 0 = 90° and that internal motion of the dye does not affect the amplitude of the n = 0 term. Subsequent work partially remedied these deficiencies, but the resulting torsion constants are invalid due to use of the incorrect anisotropy formula of Barkley and Zimm for nonvanishing < Jx(/)2>.(19) Ashikawa and co-workers also assumed that eo = 90° and used a simple anisotropy expression that is an approximation to the incorrect formula of Barkley and Zimm.(21 52 a lt8) Consequently, absolute values of the torsion constants reported by both groups need to be corrected before any detailed comparison with results from other laboratories is possible. In principle, the relative changes in torsion constant are more reliable. 

Table 4.1. Lower-Bound and Upper-Bound Torsion Constants between Base Pairs for Various Linear DNAs at 20°C ...

An alternative method is to examine the relative rates of formation of circles and linear dimers by the ligase as a function of DNA length. Early experiments043) using this method yielded a = 7.1 x 10 12 dyn-cm.recent study using what should be a superior protocol yields a static torsion constant in the range a = (5.9 0.6) x 10 12 dyn-cm.<221)... 

Figure 4.13, Torsion constant a. versus NaCl concentration for linear DNAs. O, Linear pBR322 , calf thymus DNA x, 3300-bp Hindi fragment of pBR322.

Any anharmonicity of the torsion potential is sufficiently small that the torsion constant is unaffected by changing 7 from 273 to 351 A. 1401... 

The effect of the trivalent cation spermidine on the torsion constant of 29 DNA in 0.01 MNaCl is shown in Figure 4.14.(64) Increasing spermidine concentration induces a small CD change that saturates at 10 Between... 

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