Virtual bond modeling

Spatial Configurations of Polynucleotide Chains. I. Steric Interactions in Polyribonucleotides A Virtual Bond Model ... 

N 121 "Configuration Statistics of Polynucleotide Chains. An Updated Virtual Bond Model to... 

Although various procedures are available for the model analysis of fibrous polymers, methods based on the virtual bond representation of the asymmetric residue may be of advantage in many cases. In the following, we describe one such method that began with simple procedures applied to polysaccharides, but has now been refined into a flexible and powerful model analysis tool that is simple to use with any class of polymer. Its use in the present case, however, is illustrated with examples drawn from the structure analysis of polysaccharides. 

The earliest attempts at model analysis of polysaccharides -typified by the x-ray crystal structure analysis of amylose triacetate - were usually conducted in three steps ( L). In the first step, a model of the chain was established which was in agreement with the fiber repeat and the lattice geometry, as obtained from diffraction data. In the second step, the invariant chain model was packed into the unit cell, subject to constraints imposed by nonbonded contacts. This was followed, in the third step, by efforts to reconcile calculated and observed structure factor amplitudes. It was quickly realized that helical models of polysaccharide chains could be easily generated and varied using the virtual bond method. Figure 1 illustrates the generation of a two-fold helical model of a (l- U)-linked polysaccharide chain. 

Figure 1. Construction of a two-fold helical model of a polysaccharide with the virtual bond method. Increasing the length VB of the virtual bond is shown by...

Model Building and Refinement with the Virtual Bond Method... 

The model of the residue can also be described by a second procedure, shown in Figure 3B. Two strings of atoms are used, beginning at separate ends of the virtual bond. The strings are not connected to one another, leaving two "open" bonds. This method is useful when the length of the virtual bond is to remain fixed during refinement. 

The model description and refinement based on the virtual bond method need not be restricted to a single monomer residue. 

The flexible helix modeled here is best described by the entire array of conformations it can assume. A comprehensive picture of this array is provided by the three-dimensional spatial probability density function Wn(r) of all possible end-to-end vectors (25, 35). This function is equal to the probability per unit volume in space that the flexible chain terminates at vector position relative to the chain origin 0,as reference. An approximate picture of this distribution function is provided by the three flexible single-stranded B-DNA chains of 128 residues in Figure 5(a). The conformations of these molecules are chosen at random by Monte Carlo methods (35, 36) from the conformations accessible to the duplex model. The three molecules are drawn in a common coordinate system defined by the initial virtual bond of each strand. For clarity, the sugar and base moieties are omitted and the segments are represented by the virtual bonds connecting successive phosphorus atoms. 

The weak bond model is useful because the distribution of formation energies can be evaluated from the known valence band and defect density of states distributions. Fig. 6.12 illustrates the distribution of formation energies, N iU). The shape is that of the valence band edge given in Fig. 3.16 and the position of the chemical potential of the defects coincides with the energy of the neutral defect gap state. Fig. 6.12 also shows that in equilibrium virtually all the band tail states which are deeper than convert into defects, while a temperatiue-dependent fraction of the states above convert. 

---