Analyte translocation involves three phases: (i) diffusion in the loading solution, (ii) capture by the pore, and (iii) threading. The capture process remains poorly characterized because it cannot easily be visualized or inferred from indirect measurements. The capture performance of a device is often described by a capture radius generally defined as the radial distance R* at which diffusion-dominated dynamics cross over to field-induced drift. However, this definition is rather ambiguous and the related models are usually oversimplified and studied in the steady-state limit. We investigate different approaches to defining and estimating R* for a charged particle diffusing in a liquid and attracted to the nanopore by the electric field. We present a theoretical analysis of the Péclet number as well as Monte Carlo simulations with different simulation protocols. Our analysis shows that the boundary conditions, pore size, and finite experimental times all matter in the interpretation and calculation of R*.

1.
J. J.
Kasianowicz
,
E.
Brandin
,
D.
Branton
, and
D. W.
Deamer
, “
Characterization of individual polynucleotide molecules using a membrane channel
,”
Proc. Natl. Acad. Sci. U. S. A.
93
,
13770
13773
(
1996
).
2.
A.
Meller
,
L.
Nivon
, and
D.
Branton
, “
Voltage-driven DNA translocations through a nanopore
,”
Phys. Rev. Lett.
86
,
3435
3438
(
2001
).
3.
S.
Lee
,
Y.
Zhang
,
H. S.
White
,
C. C.
Harrell
, and
C. R.
Martin
, “
Electrophoretic capture and detection of nanoparticles at the opening of a membrane pore using scanning electrochemical microscopy
,”
Anal. Chem.
76
,
6108
6115
(
2004
).
4.
D.
Fologea
,
J.
Uplinger
,
B.
Thomas
,
D. S.
McNabb
, and
J.
Li
, “
Slowing DNA translocation in a solid-state nanopore
,”
Nano Lett.
5
,
1734
1737
(
2005
).
5.
Y.
He
,
M.
Tsutsui
,
C.
Fan
,
M.
Taniguchi
, and
T.
Kawai
, “
Controlling DNA translocation through gate modulation of nanopore wall surface charges
,”
ACS Nano
5
,
5509
5518
(
2011
).
6.
M.
Pastoriza-Gallego
,
L.
Rabah
,
G.
Gibrat
,
B.
Thiebot
,
F. G.
van der Goot
,
L.
Auvray
,
J.-M.
Betton
, and
J.
Pelta
, “
Dynamics of unfolded protein transport through an aerolysin pore
,”
J. Am. Chem. Soc.
133
,
2923
2931
(
2011
).
7.
M.
Mihovilovic
,
N.
Hagerty
, and
D.
Stein
, “
Statistics of DNA capture by a solid-state nanopore
,”
Phys. Rev. Lett.
110
,
028102
(
2013
).
8.
S.
Mirigian
,
Y.
Wang
, and
M.
Muthukumar
, “
Translocation of a heterogeneous polymer
,”
J. Chem. Phys.
137
,
064904
(
2012
).
9.
V. V.
Palyulin
,
T.
Ala-Nissila
, and
R.
Metzler
, “
Polymer translocation: The first two decades and the recent diversification
,”
Soft Matter
10
,
9016
9037
(
2014
).
10.
K.
Briggs
,
G.
Madejski
,
M.
Magill
,
K.
Kastritis
,
H. W.
de Haan
,
J. L.
McGrath
, and
V.
Tabard-Cossa
, “
DNA translocations through nanopores under nanoscale preconfinement
,”
Nano Lett.
18
,
660
668
(
2018
).
11.
E.
Beamish
,
V.
Tabard-Cossa
, and
M.
Godin
, “
Identifying structure in short DNA scaffolds using solid-state nanopores
,”
ACS Sens.
2
,
1814
1820
(
2017
).
12.
D.
Sean
and
G. W.
Slater
, “
Langevin dynamcis simulations of driven polymer translocation into a cross-linked gel
,”
Electrophoresis
38
,
653
658
(
2017
).
13.
M.
Charron
,
K.
Briggs
,
S.
King
,
M.
Waugh
, and
V.
Tabard-Cossa
, “
Precise DNA concentration measurements with nanopores by controlled counting
,”
Anal. Chem.
91
,
12228
12237
(
2019
).
14.
C. T. A.
Wong
and
M.
Muthukumar
, “
Polymer capture by electro-osmotic flow of oppositely charged nanopores
,”
J. Chem. Phys.
126
,
164903
(
2007
).
15.
M.
Wanunu
,
W.
Morrison
,
Y.
Rabin
,
A. Y.
Grosberg
, and
A.
Meller
, “
Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient
,”
Nat. Nanotechnol.
5
,
160
165
(
2010
).
16.
B.-j.
Jeon
and
M.
Muthukumar
, “
Polymer capture by α-hemolysin pore upon salt concentration gradient
,”
J. Chem. Phys.
140
,
015101
(
2014
).
17.
M. M.
Hatlo
,
D.
Panja
, and
R.
van Roij
, “
Translocation of DNA molecules through nanopores with salt gradients: The role of osmotic flow
,”
Phys. Rev. Lett.
107
,
068101
(
2011
).
18.
B.-j.
Jeon
and
M.
Muthukumar
, “
Electrostatic control of polymer translocation speed through α-hemolysin protein pore
,”
Macromolecules
49
,
9132
9138
(
2016
).
19.
M.
Muthukumar
, “
Theory of capture rate in polymer translocation
,”
J. Chem. Phys.
132
,
195101
(
2010
).
20.
H. H.
Katkar
and
M.
Muthukumar
, “
Role of non-equilibrium conformations on driven polymer translocation
,”
J. Chem. Phys.
148
,
024903
(
2018
).
21.
S. C.
Vollmer
and
H. W.
de Haan
, “
Translocation is a nonequilibrium process at all stages: Simulating the capture and translocation of a polymer by a nanopore
,”
J. Chem. Phys.
145
,
154902
(
2016
).
22.
F.
Farahpour
,
A.
Maleknejad
,
F.
Varnik
, and
M. R.
Ejtehadi
, “
Chain deformation in translocation phenomena
,”
Soft Matter
9
,
2750
2759
(
2013
).
23.
M.
Waugh
,
A.
Carlsen
,
D.
Sean
,
G. W.
Slater
,
K.
Briggs
,
H.
Kwok
, and
V.
Tabard-Cossa
, “
Interfacing solid-state nanopores with gel media to slow DNA translocations
,”
Electrophoresis
36
,
1759
1767
(
2015
).
24.
P.
Chen
,
J.
Gu
,
E.
Brandin
,
Y.-R.
Kim
,
Q.
Wang
, and
D.
Branton
, “
Probing single DNA molecule transport using fabricated nanopores
,”
Nano Lett.
4
,
2293
2298
(
2004
).
25.
J.
Nakane
,
M.
Akeson
, and
A.
Marziali
, “
Evaluation of nanopores as candidates for electronic analyte detection
,”
Electrophoresis
23
,
2592
2601
(
2002
).
26.
M.
Gershow
and
J. A.
Golovchenko
, “
Recapturing and trapping single molecules with a solid-state nanopore
,”
Nat. Nanotechnol.
2
,
775
779
(
2007
).
27.
A. Y.
Grosberg
and
Y.
Rabin
, “
DNA capture into a nanopore: Interplay of diffusion and electrohydrodynamics
,”
J. Chem. Phys.
133
,
165102
(
2010
).
28.
S. K.
Nomidis
,
J.
Hooyberghs
,
G.
Maglia
, and
E.
Carlon
, “
DNA capture into the ClyA nanopore: Diffusion-limited versus reaction-limited processes
,”
J. Phys.: Condens. Matter
30
,
304001
(
2018
).
29.
P.
Rowghanian
and
A. Y.
Grosberg
, “
Electrophoretic capture of a DNA chain into a nanopore
,”
Phys. Rev. E
87
,
042722
(
2013
).
30.
D.
Long
,
J.-L.
Viovy
, and
A.
Ajdari
, “
Simultaneous action of electric fields and nonelectric forces on a polyelectrolyte: Motion and deformation
,”
Phys. Rev. Lett.
76
,
3858
3861
(
1996
).
31.
A. E.
Nkodo
,
J. M.
Garnier
,
B.
Tinland
,
H.
Ren
,
C.
Desruisseaux
,
L. C.
McCormick
,
G.
Drouin
, and
G. W.
Slater
, “
Diffusion coefficient of DNA molecules during free solution electrophoresis
,”
Electrophoresis
22
,
2424
2432
(
2001
).
32.
S. W.
Kowalczyk
,
A. Y.
Grosberg
,
Y.
Rabin
, and
C.
Dekker
, “
Modeling the conductance and DNA blockade of solid-state nanopores
,”
Nanotechnology
22
,
315101
(
2011
).
33.
B. J.
Kirby
,
Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices
(
Cambridge University Press
,
2010
).
34.
S.
Redner
,
A Guide to First-Passage Processes
(
Cambridge University Press
,
Cambridge
,
2001
).
35.
H. C.
Berg
,
Random Walks in Biology
(
Princeton University Press
,
Princeton
,
1993
).
36.
A.
Szabo
,
K.
Schulten
, and
Z.
Schulten
, “
First passage time approach to diffusion controlled reactions
,”
J. Chem. Phys.
72
,
4350
4357
(
1980
).
37.
P. C.
Bressloff
,
Stochastic Processes in Cell Biology
, Interdisciplinary Applied Mathematics Vol. 410 (
Springer International Publishing
,
Cham
,
2014
).
38.
M. J.
Saxton
, “
Anomalous subdiffusion in fluorescence photobleaching recovery: A Monte Carlo study
,”
Biophys. J.
81
,
2226
2240
(
2001
).
39.
M. G.
Gauthier
and
G. W.
Slater
, “
Building reliable lattice Monte Carlo models for real drift and diffusion problems
,”
Phys. Rev. E
70
,
015103
(
2004
).
40.
S.
Hubert
, “
Theoretical study of polymers: Flow-induced deformation in nanochannels and reptation dynamics in heterogeneous gels
,” Ph.D. thesis,
University of Ottawa
,
Canada
,
2004
.
41.
J. E.
Hall
, “
Access resistance of a small circular pore
,”
J. Gen. Physiol.
66
,
531
532
(
1975
).
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