Bead-stick model

Several coarse-grained geometrical models other than the skeletal chain model are being used to predict how various physical quantities depend on the chain length, the polymer concentration, and so forth, and to perform computer simulations. Figure 1.6 illustrates a bead-stick model (a), a bead-spring model (b), and a pearl-necklace model (c). 

In the pearl-necklace model, the beads (pearls) are always in contact with the two adjacent beads. This model is essentially a bead-stick model with the stick length equal to the bead diameter. The bead always has a positive diameter. As in the bead-stick model, we can restrict the bond angle and the dihedral angle. 

Models in a Discrete Space The models described in the preceding section are in a continuous space. In the bead-stick model, for instance, the bead centers can be anywhere in the three-dimensional space, as long as the arrangement satisfies the requirement of the model. We can construct a linear chain on a discrete... 

Figure 1.20. End-to-end vector R is defined by R = fo in the bead-stick model. The...

Figure 1.21. Center of mass ro and the radius of gyration Rg in the bead-stick model.

Figure 1.23. Bond vectors in the bead-stick model with a fixed bond angle.

We consider the same model as in Section 11,2, but here we assume that all monomers = 1,..., of the /tcth chain (/r = 1,..., M) at positions x, are hydrophobic (A). The bonds between adjacent monomers are taken to be rigid (bead-stick model) and pairwise interactions among nonbonded monomers are modeled by a Lennard-Jones potential... 

Since we are interested in generic properties of such a system, we model the nanowire as an attractive Une-hke substrate and employ a coarse-grained semiflexible bead-stick model for the polymer consisting of N monomers. The chain is not grafted to this string and may move freely. The total energy of the system includes three contributions. 

Figure 11.1 Atomic resolution structure of yeast tRNAPhe (PDB accession code 1TRA), rendered as black sticks and reconstructed density (red transparent surface). The reconstructed density was generated from the filtered consensus bead model by smoothing with a Gaussian kernel. Figure adapted from Lipfert ct al. (2007b).

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