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Theoretical model of biomacromolecule through nanopore including effects of electrolyte and excluded volume

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Abstract

A theoretical model for the translocation process of biomacromolecule is developed based on the self-consistent field theory (SCFT), where the biomacromolecule is regarded as a self-avoiding polymer chain actuated by the external potential. In this theoretical model, the external potential, the Coulomb electrostatic potential of the charged ions (the electrolyte effect), and the attractive interaction between the polymer and the nanopore (the excluded volume effect) are all considered, which have effects on the free energy landscape and conformation entropy during the translocation stage. The result shows that the entropy barrier of the polymer in the solution with high valence electrolyte is much larger than that with low valence electrolyte under the same condition, leading to that the translocation time of the DNA molecules in the solution increases when the valence electrolyte increases. In addition, the attractive interaction between the polymer and the nanopore increases the free energy of the polymer, which means that the probability of the translocation through the nanopore increases. The average translocation time decreases when the excluded volume effect parameter increases. The electrolyte effect can prolong the average translocation time. The simulation results agree well with the available experimental results.

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Abbreviations

ω :

excluded volume effect parameter, m3

l 0 :

length of the nanopore, m

N :

Kuhn segment total number

b :

Kuhn segment size, m

ε :

average interaction potential between the nanopore and one chain segment, J

∆V 1,2 :

electric potential difference between two spheres, V

E 1 :

electric field intensity, V·m−1

R 1 :

radius of the donor sphere, m

R 2 :

radius of the recipient sphere, m

E 2 :

electric field intensity of the electric double layer, V·m−1

u r :

velocity of the fluid, m·s−1

r :

radial coordinate in the spherical coordinate system, m

η :

viscosity of the Newtonian fluid, N·g·s·m−2

ρ e(r):

charge density of the ions, C·m−3

R :

radius of the sphere, m

ϕ :

electric potential of the electric double layer, V

σ w :

surface charge densities of the sphere wall, C·m−2

ε f :

electrolyte permittivity, C2·m−1·J−1

v :

velocity of the ions, m·s−1

z i :

electro valence of the i-type ions, dimensionless

f ieq (r, s):

equilibrium distribution function of the i-type ions, s3·m−6

f M :

Maxwell distribution function, s3·m−6

e :

electron charge, C

t :

time, s

m i :

mass of the i-type ions, kg

f i :

distribution function of the i-type ions, s3·m−6

A :

drift coefficient of the ion in the velocity space, m·s−2

B :

diffusion coefficient of the ion in the velocity space, m2·s−3

k 1 :

constant, m6·s−5

k 2 :

constant, s−1

v 1 :

velocity of the ions, m·s−1

k 3 :

constant, m6·s−4

R i :

radius of the i-type ions, m

k B :

Boltzmann constant, J·K−1

G(r, r 1, s):

probability density function, m−3

s :

number of the chain segment, dimensionless

ϕ(r):

external potential, J

F(r, s):

probability distribution of the macromolecular, dimensionless

T :

absolute temperature, K

U(r):

external potential, J

ρ(r):

density of the chain segment, m−3

k 4 :

constant

z D :

electro valence of the polymer chain, dimensionless

F T(r, s):

probability distribution of the tethered polymer chain, dimensionless

F a :

free energy of the state of Fig. 2(a), J

S a :

entropy of the state of Fig. 2(a), J

P a :

probability of the state of Fig. 2(a), dimensionless

∆V(s):

electric potential difference at s, dimensionless

F b :

free energy of the state of Fig. 2(b), J

S b :

entropy of the state of Fig. 2(b), J

P b :

probability of the state of Fig. 2(b), dimensionless

M :

length of the nanopore, dimensionless

P T :

probability of the tethered polymer chain, dimensionless

F (b→c) :

free energy of the state from Fig. 2(b) to Fig. 2(c), J

S (b→c) :

entropy of the state from Fig. 2(b) to Fig. 2(c), J

F (c→d) :

free energy of the state from Fig. 2(c) to Fig. 2(d), J

S (c→d) :

entropy of the state from Fig. 2(c) to Fig. 2(d), J

F (d→e) :

free energy of the state from Fig. 2(e) to Fig. 2(e), J

S (d→e) :

entropy of the state from Fig. 2(d) to Fig. 2(e), J

〈τ 1〉:

average translocation time from Fig. 2(b) to Fig. 2(c), s

〈τ 2〉:

average translocation time from Fig. 2(c) to Fig. 2(d), s

〈τ 3〉:

average translocation time from Fig. 2(d) to Fig. 2(e), s

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Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, Nanjing, 211189, China

    Chibin Zhang, Xiaohui Lin & Hao Yang

Authors
  1. Chibin Zhang
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  2. Xiaohui Lin
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  3. Hao Yang
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Correspondence to Xiaohui Lin.

Additional information

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

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Zhang, C., Lin, X. & Yang, H. Theoretical model of biomacromolecule through nanopore including effects of electrolyte and excluded volume. Appl. Math. Mech.-Engl. Ed. 37, 787–802 (2016). https://doi.org/10.1007/s10483-016-2082-6

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  • DOI: https://doi.org/10.1007/s10483-016-2082-6

Keywords

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