Rigidity, bending

FIG. 15 Conformations of fluid vesicles for different values of the bending rigidity and pressure increment (a) branched polymer (b) inflated vesicle (c) prolate vesicle (d) stomatocyte. (From Gompper and Kroll [243]. Copyright 1995 APS.)... 

FIG. 16 Phase diagram of fluid vesicles as a function of pressure increment p and bending rigidity A. Solid lines denote first-order transitions, dotted lines compressibility maxima. The transition between the prolate vesicles and the stomatocytes shows strong hysteresis efifects, as indicated by the error bars. Dashed line (squares) indicates a transition from metastable prolate to metastable disk-shaped vesicles. (From Gompper and KroU 1995 [243]. Copyright 1995 APS.)... 

Den Otter, W. K. and Briels, W. J. (2003). The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics, J. Chem. Phys., 118, 4712-4720. 

The (bending) persistence length of DNA, which is proportional to its bending rigidity, has been extensively studied for well over two decades, usually via its effect on the overall dimensions of the DNA coil. This work... 

In Eqs. (4.43)—(4.47), use is made of the well-known rclation(23)P = K/kBT, where k is the bending rigidity. Equation (4.45) differs from the corresponding BZ result by the inclusion of the D L / term. Normally, this is negligible on the fluorescence time scale, but for sufficiently short filaments it could make a significant contribution. It appears with the coefficient 1.0 instead of 2.0 because the correction term from the Euler-McLaurin summation formula actually cancels out one of the two D t terms in Eq. (4.43). Equation (4.43) or (4.45) is then inserted in Eq. (4.26) to obtain the BZ tumbling correlation function for the filament. 

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. 

Top Dplu versus superhelix density. >plat is the apparent DLS diffusion coefficient at A2 = 20 x 10 ° cm 2. The lower values at a = —0.015, —0.020, and -0.025 suggest that, in this intermediate range, DNA exhibits a different secondary structure with decreased torsional and/or bending rigidity. 

Frank-Kamenetskii, M.D., Lukashin, A.V., Anshelevich, A.V., and Vologodskii, A.V. (1985) Torsional and bending rigidity of double helix from data on small DNA rings. J. Biomol. Struct. Dynam. 2, 1005-1012. 

Fig. 2 Top Freely jointed chain (FJC) model, where N bonds of length a are connected to form a flexihle chain with a certain end-to-end distance R. Bottom in the simplified model, appropriate for more advanced theoretical calculations, a continuous line is governed hy some bending rigidity or line tension. This continuous model can be used when the relevant length scales are much larger than the monomer size...

---