Stability of toroid and rodlike globular structures of a single stiff-chain macromolecule for different bending potentials

Abstract

We study the effect of the bending potential on the stability of toroidal and rodlike globules which are typical collapsed conformations of a single stiff-chain macromolecule. We perform numerical calculations in the framework of the bead-stick model of a polymer chain. The intrinsic structure of globules is also analyzed. It was shown that the bending potential affects the packing geometry of bundles in a toroidal globule in the ground state. This potential also influences the bends at the ends of a rodlike globule: both the shape of the loops and the number of bonds in each loop have been investigated numerically as well as by Monte Carlo computer simulations performed for a separate loop. Our main results are (1) the shape of the bending potential could be possibly seen from the geometry of a globule; (2) toroidal globules are always more favorable than the rodlike ones.

A Simple Analytical Model for Predicting the Collapsed State of Self-Attractive Semiflexible Polymers

“…However, to maintain the simplicity and generality of the model, we avoid these complexities. The more detailed model of Stukan et al [17] considered in detail the structure of the fold and beads packing, as reviewed above. Particularly, their model requires re-analysis for each specific end fold conformation, while our simple model should be quite general, although qualitative.…”

“…Moreover, the shape of an ideal “racquet” head is resolved by introducing additional parameters such as total contour length of the chain within the racquet head and the curvature of the racquet. Stukan et al [17] analyzed the stability of a bundle and a torus formed by single chain using a detailed analytical model, including bead packing energies generated by the number of bead-bead contacts. Their model was derived for collapsed structures of bead spring “pearl necklace” chains at low dimensionless temperature, where the packing order (number of bead-bead contacts) of the filaments in both torus and bundle was considered.…”

A formula for the minimal coordination number of a parallel bundle

“…( 3), and was used recently in Ref. [23]. An approximate expression was presented earlier for the average number of interactions which equals 6 − 2α N /N in our terms (see Eq.…”

“…The main purpose of this paper is to present a compact exact formula for a number of unoccupied bond sites on the surface of a tightly packed parallel bundle. This quantity commonly appears in analysis of stability of DNA toroids [2,4,13,19,20,23] and it has been computed either approximately [2,20] or by a complicated procedure [19,23] or for particular numbers of strands in the bundle [4,13]. It is reasonable to believe that the exact analytical expression will prove to be handy in the future analytical research.…”

“…Therefore, we are interested in the tightest bundle when the coordination number is minimal. The minimal coordination number enters a free energy expression that is used in studies of DNA condensation [2,4,13,19,20,23].…”