Molecular Topology Of Circular DNA Under Spherical Confinement

Confinements are widely found in biological systems.For example,DNA that the main carrier of biological genetic information confines in the cell nucleus.The topological structure of transition of DNA plays an important role for the process transcription in the confined space.Therefore,it is important to study the conformation of DNA molecules under spherical confinement.In order to further understand this biological process,based on two different models of wormlike and wormlike rod chain.we study the effect of confinement on the conformation and topological structure of circular DNA molecules by using Monte Carlo simulation method.Based on the worm-like chain model(WLC),Monte Carlo simulations are used to study the conformational behavior and topological changes of circular DNA molecules.Under the strong confinement,the distribution of the writhe number behaves as a discrete and symmetric multi-peak structure about,it is found that the conformation shows the complex entangled structure,which leads to the discrete and symmetric multi-peak distribution of the link number directly,and the number of winding turns is proportional to the number of discontinuous peaks,it's obtained from the White-Fuller topology relationship by convolution on the distribution of the twist and the writhe number.The distribution of the link number is the same as the distribution of the writhe number which also presents discrete and symmetric multi-peak distribution,and the peak increases gradually.When the confined radius exceeds the Odijk(persistence length)range,the distribution of the writhe number gradually tends to a single-peaked Gaussian distribution.Unlike the WLC model,the worm-like rod model(WLR)realizes the coupling of bend and twist.We can directly obtain the distribution of twist and writhe number of circular DNA molecules,the link number distribution is obtained by White-Fuller topology relationship on this basis.Under the strong sphere confinement,with the decrease of the confined radius,the distribution of writhe number presents the multi-peak distribution of symmetry.The twist number is not influenced significantly by the confined space,but it leads to the link number distribution to shift to the right by one order of magnitude.Due to the existence of over-twist or under-twist,the initial twist angle will also affect the distribution of link number.As the initial twist angle increases,the distribution of twist number and link number will shift to the right.By comparing the results from two models,the link number of distribution that presents multi-peaked and discrete of distribution is influenced by the writhe number,and its translation is influenced by the twist number as well as the initial twist angle.We also explored the effect of different confinement on the conformational behavior of DNA from the relative direction change of DNA molecule conformation by the fragment autocorrelation function and the structure factor from the internal structure of DNA molecule conformation,respectively.