Straight rods

The geometrical structure of the chain in Fig. 2 is determined entirely by 6, (j), and B. The model only describes the linker geometry and does not account for excluded volume effects and other forms of nucleosome-nucleosome interaction it assumes that the core particles are point-like and that they are located at the joints of the linkers, which are straight rods. 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

Sulfur bacteria cells spherical, short or long straight rods, short spirals or filaments cells contain sulfur granules,... 

Bends and bulges. If we overlook the ridges and grooves on their surfaces the DNA structures shown in Figs. 5-3 and 5-12 are straight rods. However, real DNA rods are crooked and may contain distinct bends. The... 

While a DNA molecule may exist as a straight rod, the two ends are often covalently joined. Thus, the chromosomes of E. coli and of other bacteria are single closed circles. Circular DNA molecules are also found in mitochondria, chloroplasts, and many viruses. Further complexity arises from the fact that the circles of DNA are sometimes interlocked in chainlike fashion (catenated). An unusual example of this phenomenon is the presence of thousands of small catenated DNA circles in the single mitochondrion of a trypanosome (Fig. 5-16).183 Sometimes circular DNA is knotted as in Fig. 5-17.184-186 Knots and catenanes often appear as intermediate forms during replication and recombination, especially involving circular DNA.187 188... 

One of the most exciting biological discoveries is the recognition of DNA as a double helix (Watson and Crick, 1953) of two antiparallel polynucleotide chains with the base pairings between A and T, and between G and C (Watson and Crick s DNA structure). Thus, the nucleotide sequence in one chain is complementary to, but not identical to, that in the other chain. The diameter of the double helix measured between phosphorus atoms is 2.0 nm. The pitch is 3.4 nm. There are 10 base pairs per turn. Thus the rise per base pair is 0.34 nm, and bases are stacked in the center of the helix. This form (B form), whose base pairs lie almost normal to the helix axis, is stable under high humidity and is thought to approximate the conformation of most DNA in cells. However, the base pairs in another form (A form) of DNA, which likely occurs in complex with histone, are inclined to the helix axis by about 20° with 11 base pairs per turn. While DNA molecules may exist as straight rods, the two ends bacterial DNA are often covalently joined to form circular DNA molecules, which are frequently supercoiled. 

For a thin straight (rod-like) chain (x—+0), the left-hand side of Eq. (9) is independent of L (or of M) and close to unity. (Conversely, for a chain of finite rigidity when x (i.e. L or M) in-aeases, the left-hand side of Eq. (9) decreases and this decrease is theoretically described by the function f (x). 

Thus, if the necklace has the shape of a rigid straight rod, its rotational friction coefficient for the rotation about the central axis normal to the tod is given by... 

The intrinsic viscosity of a solution of molecules described by a kinetically rigid chain necklace that can adopt any conformation (from the straight rod to the spherically symmetrical bead distribution) is given by > 2)... 

If a worm-like chain with the conformation varying from a straight rod to a Gaussian coil (when the parameter x = 2 L/A varies from 0 to >) is used for the description of the hydro-dynamic properties of the molecule, then the following equation is also valid for it... 

The first term on the right-hand side of Eq. (27) corresponds to the expression for Dj of a thin straight rod and the second term containing L/A expresses the deviation from a straight conformation caused by fUiite flexibility of the chain. 

It follows from Eq. (29) that at x—> 0, Px— 4/x-— oo, corresponds to an infinitely thin straight rod. In the Gaussian coil conformation x tends to infinity and it follows from Eq. (29) that pj tends to unity, corresponding to a model with a spherically symmetrical segment distribution. 

The asymmetry of the shape of a worm-like chain in the conformation of a straight rod is uniquely determined by the p = L/d ratio whereas the a mmetry of the shape of a chain molecule in the Gaussian coil conformation can be characterized in various ways. 

In the same system of coordinates the asymmetry of the shape of a worm-like chain may also be evaluated over the entire range of possible conformations from a thin straight rod to a Gaussian coil ... 

Equations (39) and (40) reveal that the anisotropy of a worm-like chain in the limiting conformation of a straight rod (at x— 0) is equal to 3L, i.e. it is proportional to the contour chain length regardless of whether it is calculated in a system of coordinates of the first or the middle chain element. 

The dependence of the Kerr constant on molecular weight (reduced chain length x) during the corresponding change in tlw conformation of the molecule from the straight rod to the Gaussian coil is depicted by Eqs. (97) or (100) ... 

Let us consider a straight rod with an arbitrary cross section, as shown in Figure 17.10. If the axis of torsion coincides with the vertical axis, which... 

For proteins, a mathematical model of retention has been developed that works well for Sephadex gels.5 The solute is treated as a sphere of radius rs, while the gel is a network represented by infinitely long, straight rods of radius rx. The rods are randomly distributed, and have an average density of L units of rod length per unit volume of gel. The values of L and rx may be calculated from known dimensions of dextran chains, and then Km may be found from Eq. 14.13 ... 

The straight-rod model predicts a right-handed cholesteric helix for 96 and a left-handed one for PBLG and schizophylan, which is in agreement with experimental results.280 In the threaded EFJC model, the flexibility of the macromolecular helix can be freely chosen. The handedness of the cholesteric phase is based on entropic hard core repulsion phenomena between the helices and an enthalpic chiral dispersion force. Right-handed mesophases were predicted for solutions of 96, 97, and schizophylan. However, only for 96 this was in agreement... 

---