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Polymer translocation through a hairy channel mimicking the inner plug of a nuclear pore complex

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Abstract

A microscopic transport model of a polymer translocating through a nuclear pore complex (NPC) is presented based on self-consistent field theory (SCFT), with the NPC and its nucleoporins mimicked by a hairy channel. Multiple cell environment effects (electrolyte effect, excluded volume effect, NPC drag effect, and hydrophobic effect) are all considered in this hairy channel model. The influence of various parameters (polymer chain length, length of NPC, strength of hydrophobic effect, and excluded volume effect) on translocation time is studied through theoretical analysis and numerical calculation. Numerical simulation results show that an area of low nucleoporin number density exists in the NPC, which facilitates the translocation of the polymer. The results also show that the translocation time curves with increasing NPC length and polymer charge number are concave. In addition, there are critical values for NPC length and polymer charge number for which the translocation time has a minimal value. The translocation time decreases with the increasing strength of the hydrophobic effect and excluded volume effect.

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Abbreviations

R 1 :

Radius of cell (m)

R 2 :

Radius of nucleus (m)

l 0 :

Length of NPC (m)

M :

Dimensionless length of NPC (dimensionless)

N d :

The total number of Kuhn segments of polymer (dimensionless)

b :

Length of Kuhn segment (m)

L :

Length of polymer (m)

f(r, r 1, s):

The conformational probability function of polymer in cytoplasm and nucleus (dimensionless)

F(r, s):

The probability distribution of polymer (dimensionless)

F T(r, s):

The probability distribution of tethered polymer (dimensionless)

φ s(r):

The external potential in cytoplasm (N m)

w d :

The excluded volume parameter between chain segments (m3)

U(r):

Electrostatic potential between ions and polymer (N m)

m d :

The number of polymer groups per segments of polymer (dimensionless)

z d :

The charge number of polymer groups of polymer (dimensionless)

ɛ 0 :

Dielectric constant (C2/m2 N)

z i :

The charge number of ith kind of ions in cytoplasm (dimensionless)

ρ s(r):

Number density of segments at location r in cytoplasm and nucleus (1/m3)

n i :

The number density of ith kind of ions in cytoplasm (1/m3)

n p :

Number of nucleoporin (dimensionless)

L p :

Length of nucleoporin (m)

N p :

Number of segments of nucleoporin (dimensionless)

κ(x):

Number of protein chains per unit area at location x (1/m2)

q(r, x, s):

Distribution function of nucleoporin (dimensionless)

q +(r, x, s):

Distribution function of nucleoporin (dimensionless)

R :

Radius of NPC (m)

ω p :

Self-consistent potential field of nucleoporin chain at location (r, x) (dimensionless)

w p :

Strength of excluded volume effect of nucleoporin chain (m3)

ρ p(r, x):

Number density of segments of nucleoporin chain at location (r, x) (1/m3)

χ :

Parameters of Flory–Huggins interactions between segments (dimensionless)

βH int :

Interaction energy between nucleoporin chains (dimensionless)

ξ 0 :

Constant which is used to ensure the incompressibility (N m)

ξ(r, x):

Mean field which is used to ensure the incompressibility of nucleoporin chains (N m)

F c(x, s):

The probability distribution of polymer in NPC (dimensionless)

φ c(s):

The external potential field (N m)

φ 1(s):

The electrostatic potential of nucleoporin chain (N m)

φ 2(s):

The hydrophobic potential of nucleoporin chain (N m)

φ 3(s):

The repulsion potential of nucleoporin chain (N m)

m p :

The number of polymer groups per segments of polymer (dimensionless)

z p :

The charge number of polymer groups of nucleoporin chain (dimensionless)

ρ c(x):

Number density of segments of polymer at location x (1/m3)

λ :

The length of hydrophobic effect (m)

ɛ h :

The strength of hydrophobic effect (N m)

ɛ c :

The strength of repulsion effect (N m)

k B :

Boltzmann constant (N m/K)

T :

Absolute temperature (K)

S 1 :

The conformational entropy of polymer at first stage (dimensionless)

S 2 :

The conformational entropy of polymer at second stage (dimensionless)

S 3 :

The conformational entropy of polymer at third stage (dimensionless)

F 1 :

The free energy of polymer at first stage (dimensionless)

F 2 :

The free energy of polymer at second stage (dimensionless)

F 3 :

The free energy of polymer at third stage (dimensionless)

k 0 :

Diffusion coefficient of polymer (m2/s)

〈τ〉:

Mean translocation time (s)

〈τ 1〉:

Translocation time of first stage (s)

〈τ 2〉:

Translocation time of second stage (s)

〈τ 3〉:

Translocation time of third stage (s)

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Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant no. 51375090).

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Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, 2 Southeast Road, Jiangning District, Nanjing, 211189, China

    Chibin Zhang, Zhiwei Cheng, Xiaohui Lin & Wenquan Chu

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  1. Chibin Zhang
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Zhang, C., Cheng, Z., Lin, X. et al. Polymer translocation through a hairy channel mimicking the inner plug of a nuclear pore complex. Eur Biophys J 48, 317–327 (2019). https://doi.org/10.1007/s00249-019-01356-5

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  • DOI: https://doi.org/10.1007/s00249-019-01356-5

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