Statistical Mechanics Properties Of Polymer Chains Under The Condition Of Free Space Or Strong Confinements

In the research area of polymer mechanics,the statistical mechanics properties of polymer chains under the condition of free space or strong confinements are very important and significant subjects,such as the technique of single-molecule genome mapping,persistence length of different DNA sequences,DNA sorting,compressing confined microtubules and so on.For several decades,the mechanical behavior of semiflexible polymer chains confined in nanochannels is a hot-spot research area.The mechanical behaviors of polymer chains confined in a nanotube have been extensively investigated:a)for the narrow tubes,polymer chains are highly extended,which lies in Odijk regime,b)for the wide channels,it lies in the classical de Gennes regime,c)between these limits,there are extended de Gennes regime,backfolded Odijk regime and so on.Under the simultaneous implementation of geometrical confinements and external force,the statistical behaviors have not fully investigated.However,there are a few exceptions.For example,Wang et al.have given a quantitatively compact formula of force-extension relation for the polymer chains in the circular or rectangular tubes.Nonetheless,all the studies are aiming to understand the mechanical behaviors in circular or rectangular tubes.Under the condition of stretching,the mechanical properties of polymer chains confined in tubes of more complex shapes are still unclear.This lack of knowledge is contradicting the increasingly using of more complicated tubes(triangular tubes etc.).Therefore,it is very urgent to develop a generalized model to describe the mechanical behaviors under the concurrent implementation of force and tubes with arbitrary cross-sections.Besides the above shortcomings of the research of polymers,the problems of polymer chains with variable persistence length also need to be emphasized.For the last several decades,the single-molecule experiments of semi-flexible polymer chains were investigated by using homogeneous polymer chains,i.e.,persistence length of polymer chains is constant(for double-strand DNA 50 nm).Because of the advanced experimental techniques,however,many experiments reveal that some mechanical behaviors can not be predicted by using the classical homogeneous polymer model,i.e.,the abnormal behaviors can not be explained through the homogenous model of polymer chains.Based on analytical derivation,numerical simulations and comparison with advanced experiments,in this PhD thesis,we have investigated:a)the mechanical behaviors of heterogeneous polymer chains(variable persistence length along the chain contour)in free space,b)the force-extension and force-compressing relations,and the dynamic properties of WLC under the simultaneous implementation of force and geometrical confinements.Specifically,it can be divided into three sections:(1)We tried to establish new mechanical models to investigate how this property of varying persistence length influences the equilibrium and dynamic behaviors.To introduce the variable persistence length into the WLC model,we modified the classically constant persistence length into variable persistence length and established a generalized formula of end-to-end distance.Note that the difficulties and cores to establish the mathematical model are calculating the diffusion equations and orientation-orientation relation function by using Green's function method.To verify the theoretical prediction,we have done the following work:a)giving a specific method to measure persistence length through advanced experimental techniques,b)by using Brownian dynamics simulations based on GBR model,we have performed extensive simulations to validate our theory and the results are in good agreement with theoretical predictions,c)based on numerical analysis,we have given the exact value of persistence length of dinucleotides steps and calculated the persistence length of DNA fragments combined by using dinucleotides steps.(2)We have investigated the mechanical behaviors under the concurrent implementation of force and tubes with arbitrary cross-sections and established a generalized formula of force-extension relation.To test our theory,we take the methods of bead-wall interaction to extend our old GBR model to simulate the behaviors of WLC confined in tubes of arbitrary cross-section.All the simulation results showed that our theory is valid and effective.(3)We have established a generalized formula of force-compressing relations and the way of applying force is straightforward force-loading.To validate our model,we have conducted extensive Brownian dynamics simulations,and the results showed that:a)in the case of a small force,our theory is in good agreement with simulation results,b)as the force gradually increases,the simulation results are slightly deviating from our theory,because the original hypothesis is not applicable,c)as the force increase to a critical forcef_c,polymer chains begin to fold.In addition,we have analyzed the factors which influence the value off_c and found that a larger tube radius and a smaller persistence length lead to a smaller value,f_c.Because of the limitation of theory and simulation methods,we have not given the quantitative formula of critical force.