Free Energy Profile Calculation And Application Of Polymer Translocation In Crowded Environment

The translocation of a polymer through a nanopore plays a crucial role in many biological processes,such as mRNA molecules passing across nuclear pores,proteins transporting through membrane channels,and so on.Moreover,the nanopore-based polymer translocation has shown potentially biotechnological applications,such as gene sequencing,controlled drug delivery.The dynamic process of translocation for polymer chains through nanopores can be explained by two key ingredients:free energy spectrum and driving force.The translocation process depends on the translocation environments,which consists of pore structure,polymer chain-pore interaction,restricted environment where the polymer is located,interaction between the polymer chain and other substances in space,and chemical potential on both sides of the nanopores.In this paper,the dynamic process of polymer translocation through nanopores in crowded environment is mainly studied.This paper mainly uses the Rosenbluth-Rosenbluth method to calculate the conformation number of the polymer chain in the presence of chaperons.The free energy profiles for the polymer chain from cis space to trans space are discussed at different chaperon concentrations.Then,we calculate translocation time by using the diffusion coefficient and Fokker-Plank equation In addition,when the interaction between chaperon and polymer chain are considered,we calculate the free energy profile for the polymer chain for the polymer chain under different conditions and obtain the translocation time.The main work of this paper is as follows:1.When the interaction between chaperon and polymer chain is not considered,we investigate the effect of chaperon concentration on translocation time and the relationship between free energy difference and chaperon concentration difference between the two sides.We find that when the chaperon concentration on both sides of the small pore are the same,the free energy profiles are symmetrical,and the value of free energy increased with the increase of chaperon concentration.However,the free energy barrier that hindered the translocation of the polymer chain decrease with the increase of chaperon concentration,which is consistent with the previous results.In addition,when the concentration of chaperons on both sides of the pores are not equal,the free energy profile is asymmetric,which will result in free energy difference ΔF.When the chaperon concentration of cis space is less than chaperon concentration in trans space,the free energy difference is less than zero,the chaperon will hinder the translocation process at this time.The polymer chain is more difficult to translocate under larger chaperon concentration difference;when the chaperon concentration of cis space is larger than chaperon concentration in trans space,the free energy difference is greater than zero,the chaperon will promote the translocation process.Larger chaperon concentration difference make the polymer chain easier to translocate.2.We also consider the influence of the interaction between chaperon and polymer chain on the translocation process.We find that when the chaperon concentration in both sides is fixed,when the interaction in trans space is repulsive,the free energy profile will increase,ΔF will decrease,and the translocation is more difficult.When the interaction in trans space is attractive,the free energy profile will decrease,ΔF will increase,and the translocation becomes very easy.In addition,We also find that when there is an attractive interaction in trans space,as the chaperon concentration increases,the free energy profile in trans space decreases,and ΔF increases accordingly,making the translocation easier.When there is a repulsive interaction in trans space,the increase of chaperon concentration leads to an increase in the free energy profile in trans space,and ΔF decreases,making the translocation more difficult.3.Without the effects of chaperon-polymer interaction,we find that the free energy difference is proportional to the chaperon concentration difference Δc（=c_c-c_t）between the cis and trans sides,as ΔF～Δc,leading to the relationships of ln（τ）～-Δc at small Δc and τ～Δc^-1 at large Δc.With the same chaperon-polymer interaction at the cis side and trans side（ε_c=ε_t=ε）,the free energy difference is also caused by the chaperon concentration difference and a proportion relationship ΔF～Δc×（ε-ε^*）is observed.Here ε^* is the critical attraction at which the attraction and volume exclusion balance each other.Therefore,there are the relationships as ln（τ）～-Δc×（ε-ε^*）and τ～[Δc×（ε-ε^*）]^-1 at ΔF<<0 and ΔF>>0,respectively.With the same chaperon concentration at the cis side and trans side（c_c=c_t）,ΔF is also found to be proportional to the interaction difference Δε（=ε_c-ε_t）between the cis side and trans side,resulting in the relationships of ln（τ）～-Δε at small Δε and τ～Δε^-1 at large Δε.4.We also study the relationship between the translocation time τ and the chaperon-polymer chain interaction.It is found find that when the chaperon concentration in one space is fixed,and the chaperon concentration of the other space changes,there is always a special interaction ε=-0.2 such that the translocation time is almost independent of the chaperon concentration difference,which is consistent with the conclusions obtained by the previous Monte Carlo simulation.In addition,when we consider the diffusion of the polymer chain,if the attractive interaction is small,the translocation time remains almost constant.When a certain threshold is reached,the translocation time begins to rise.This threshold is not the same for different chaperon concentrations.At the same time,in the same attractive interaction,if the chaperon concentration is greater,the translocation time will be longer,since the larger chaperon concentration,will make the polymer chain have bigger probability attracted by chaperons,leading to difficulty in translocation and increase the translocation time.