Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

A mechanical model for diversified insect wing margin shapes

The wings in different insect species are morphologically distinct with regards to their size, outer contour (margin) shape, venation, and pigmentation. The basis of the diversity of wing margin shapes remains unknown, despite the fact that gene networks governing the Drosophila wing development have been well characterised. Among the different types of wing margin shapes, smoothly curved contour is the most frequently found and implies the existence of a highly organised, multicellular mechanical structure. Here, we developed a mechanical model for diversified insect wing margin shapes, in which non-uniform bending stiffness of the wing margin is considered. We showed that a variety of spatial distribution of the bending stiffness could reproduce diverse wing margin shapes. Moreover, the inference of the distribution of the bending stiffness from experimental images indicates a common spatial profile among insects tested. We further studied the effect of the intrinsic tension of the wing blade on the margin shape and on the inferred bending stiffness. Finally, we implemented the bending stiffness of the wing margin in the cell vertex model of the wing blade, and confirmed that the hybrid model retains the essential feature of the margin model. We propose that in addition to morphogenetic processes in the wing blade, the spatial profile of the bending stiffness in the wing margin can play a pivotal role in shaping insect wings.

Effect of interaction shape on the condensed toroid of the semiflexible chain

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviors of the mean toroidal and cross sectional radii, rc and rcross, as functions of the contour length L: (rc,rcross) approximately Lnu(Nc), with nu=(1/5,2/5) for the van der Waals-type, nu=(-1/3,2/3) for the Coulomb-type, and nu=(-1,1) for the delta-function-type attractions in the asymptotic limit. For the toroids with finite winding number Nc=100-400, we find nu approximately 0 for the Yukawa interaction with screening parameter kappa=0.5-1.0 and nu=0.1-0.13 for the van der Waals-type interactions. These findings could provide a possible explanation for the experimentally well known observation nu approximately 0 of the condensed DNA toroids. Conformational transitions are also discussed.