Conformations Of Semiflexible Polymers Confined Between Two Coaxial Cylindrical Layers

In 2005, an article called Entropically Driven Helix Formation was published in Science magazine. In it, the authors Yehuda Snir and Randall D.kamien told us the chains can spontaneously form the spiral structure by avoiding overlapping of the excluded volume.We try to get a further verification of this phenomenon through theoretical computer simulation.As we all known, when placed in a crowded environment, a semi flexible tube is always forced to fold so as to make a more compact shape. And once the thickness of the tube is comparable size to the tube length, the tube may make a tight helix shape which often arises in nature. This is a common phenomenon. For example, in crowding living cells, macromolecules (such as DNA chains) are often curving themselves in order to create a better existing way. Recently, the conformation of confined biopolymers and the helix structure of polymer chains have attracted widespread attention. And many works and researches have been done by scholars in this area. Using coarse-grained Monte Carlo simulations, in which only short-ranged weakly attractive nonbonded interactions were considered between monomer and cylindrical surface, Inna Gurevitch et al. have shown that semiflexible chains adsorbed in nearly perfect helices around the cylindrical. Various factors are likely to contribute to the observed ordered helical conformations. On one hand there exist Vander wagers between polymer chains monomers and specific monomer-cylindrical interactions. On the other hand, these ordered helical conformations have brought relatively high entropy as well as changed the free energy of the whole system. Since the monomer-cylindrical attractive is very weak, whether the helical conformation can still appear if we neglect this short-ranged weakly attractive?In our work, an off-lattice Monte Carlo method is used to study the helical conformations of semiflexible polymer chains confined between two coaxial cylindrical layers. At first, we get a series of parameters which can affect the helical conformation through changing the constrained environment and the stiffness of the polymer chain. Then we study some features of the helical conformation, for example: the mean end to end distanceof the polymer chain, the persistence length lp of the chain and the helical orientation G(m)of the chain. Finally, we simply discuss the conformation differences among the polymer chains which are with different stiffnesses.1. When confined in the same environment, the stiffness of the polymer chain can affect its stable conformations. At stable state, fully flexible chain may be curled up into a ball with no order. Completely rigid chain may be pulled into a straight-chain. Only semiflexible chain can be formed spiral structure.2. The helical conformation can also be affected by the constrained condition. As confined between two coaxial cylindrical layers, helixes can only appear in proper inner and outer radius of the cylindrical layers.3. The length of the polymer chain may have to do with the stable conformation, too. This can be easily understood. Longer the chain length is, easily the helical structure can made.4. In the case of the radius of the inner cylindrical layer R1=2.0 and the radius of the outer one R2=5.0, if the chain rigid equals zero, the number of spiral and the number of monomers in spiral also equals 0. There is no helix in chain stable conformation.5. In the case of the radius of the inner cylindrical layer R1=2.0 and the radius of the outer one R2=5.0, if the chain rigid is near 20, the number of spiral is big and almost 70% of the chain monomers has involved in the helix.6. In the case of the radius of the inner cylindrical layer R1=2.0 and the radius of the outer one R2=5.0, if the chain rigid tend to equal 100, the number of spiral and the number of monomers in spiral also tends to be 0.As a vast number of biopolymers crucial to life are constrained in narrow volumes, this investigation may provide some help to the further research on biological macromolecules.