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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Phys Rev Lett. Author manuscript; available in PMC Sep 15, 2011.
Published in final edited form as:
Published online Jun 10, 2010.
PMCID: PMC3174011
NIHMSID: NIHMS320892

Base-by-base Ratcheting of Single Stranded DNA through a Solid-State Nanopore

Abstract

We investigate the base-by-base translocation dynamics of single-stranded DNA (ssDNA) confined in a solid-state nanopore dressed with an electrostatic trap, using all-atom molecular dynamics (MD) simulation. We observe on the simulation time scale of tens of nanoseconds that ssDNA can be driven through the nanopore in a ratchet-like fashion, with a step size equal to the spacing between neighboring phosphate groups in the ssDNA backbone. A 1D-Langevin-like model is derived from atomistic dynamics which can quantitatively describe simulation results and can be used to study dynamics on longer time-scales. The controlled ratcheting motion of DNA could potentially enhance the signal-to-noise ratio for nanoelectronic DNA sensing technologies.

The benefits of low-cost, high-throughput human genome sequencing to medical science has inspired extensive experimental [14] and theoretical [57] work focused on DNA translocation through solid-state nanopores. Given that microelectronic fabrication methods permit the integration of nanoelectronic devices to sense each DNA base, the genetic code (DNA sequence) could be read out during translocation by the measurement of transverse electrical current [8], voltage signal [9], ionic current [10, 11] or hydrogen-bond mediated tunneling signal [12]. One challenge is to develop a scalable and reliable method for controlling the DNA motion [3] to enhance sensing resolution.

For controlled motion of ssDNA, ideally, bases in a linear ssDNA molecule confined in a solid-state nanopore should in-turn slowly pass by or even stop in front of a sensor to allow an accurate base detection. Several methods have been suggested to control the motion of DNA including decreasing temperature [13, 14], enhancing the electro-osmotic screening of counterions [1517], increasing the viscosity of an electrolyte [14], using an alternating electric field to drive DNA back and forth [18], and applying magnetic [19] or optical [20, 21] tweezers. Alternatively, it would be useful to force DNA to adopt a “stop and go” or base-by-base ratcheting dynamics, analogous to the “stick-slip” motion of the tip of an atomic force microscope (AFM) on an atomically flat crystal surface that provides a periodic potential for the AFM tip [22].

Recently, it was proposed [23] that a solid-state nanopore consisting of a metal-insulator-metal sandwich structure [Fig. 1a], the “DNA transistor”, could generate a periodic electric potential for ssDNA. In this letter, we investigate the ratcheting dynamics of ssDNA, a linear, flexible and charged polymer, in the confined geometry provided by a solid-state nanopore in the presence of said periodic potential. Atomistic MD simulations capable of capturing the details of ssDNA motion are performed; two types of DNA driving methodologies are considered: pulled by a harmonic spring (an in-silico experiment rem iniscent of DNA pulled by an optical tweezer) as an example appropriate for high-resolution single-molecule experimental investigations [20, 21] and pushed by a biasing electric field as an example appropriate for high throughput sequencing applications [2, 3]. From the results of atomistic simulations, a 1D-Langevin-like model is constructed that quantitatively reproduces important features of the dynamics of ssDNA in the nanopore.

FIG. 1
Simulations of ssDNA driven through an electrostatic trap in a solid-state nanopore. (a) A cross-section view of the setup of MD simulations. The metal and dielectric regions are labeled with “M” and “D”, respectively. ...

Figure 1a illustrates the simulation setup. A fragment of ssDNA containing 20 adenine nucleotides poly(dA20) is submerged in a 0.1 M NaCl electrolyte confined inside a 2-nm-radius nanopore. Water molecules are explicitly included. The solid nanopore is cut from an amorphous SiO2 solid whose position is harmonically constrained in simulations. A total charge of -20 e (e the charge of an electron) is uniformly distributed to atoms on the pore surface, which can enhance the capture rate of ssDNA [6]. Periodic boundary conditions are imposed in all three axial directions. The ssDNA is covalently linked to itself over the periodic boundary of the system. As DNA inside a solid state nanopore can be electrically stretched, the ssDNA in the simulation is put under tension (about a few hundred pico-newtons [24]) by the boundary conditions such that the average spacing d between neighboring phosphate groups is 7.4 Å. Similar results as reported below are obtained in simulation when d is reduced to 6.8 Å. The center of mass of all phosphorus atoms are harmonically constrained near the center of the nanopore. This constraint prevents DNA from being attracted towards the pore surface and can be experimentally realized by polymer-coating the pore [11, 25] where we observed the similar ratchet-like dynamics of ssDNA [26]. Two opposite electric fields, ± E (E=108 mV/Å), are applied [27] in the whole layers aligned with dielectric regions, mimicking the trapping fields in the DNA transistor [Fig. 1a]. The thickness of each electrode and each dielectric field region is respectively chosen to be 2d and 2.5d , which results in the maximum energy barrier on ssDNA [23] that maximizes the trapping time of ssDNA. The simplifying assumptions given above allow the ratcheting dynamics to be ascertained clearly without sacrificing relevant details.

All-atom MD simulations are carried out in the Blue-gene supercomputers using the program NAMD [28], the Amber (parm-bsc0) force field for ssDNA [29], the TIP3P model of water [30] and the standard NVT (T =300 K) simulation procedure [15].

To obtain the mean trapping force exerted on ssDNA, we simulate the pulling of ssDNA by a harmonic spring and measure the force on the spring. An actual experiment using an optical tweezer as a spring is feasible if sub-nanometer motion of the pulling bead could be resolved [31]. In the simulations, we attach one end of a harmonic spring to the center of mass of all phosphorus atoms (hereafter called “the ssDNA position”) and fix the other end to a pulling stage that moves at a constant velocity v (1 Å/ns). With this set-up, the pulling force yields no tension between neighboring nucleotides. Figure 1 shows the pulling force F in the spring versus the ssDNA position before [Fig. 1b] and after [Fig. 1c] turning on the trapping fields E. When E=0 [Fig. 1b], the average force left angle bracket F right angle bracket in the spring, balancing the hydrodynamic drag force on the DNA, satisfies the relation γ = left angle bracket F right angle bracket/v, where the measured friction coefficient γ is about 1 pN·ns/Å. After turning on the trapping field [Fig. 1c], the pulling forces in the spring show peaks and valleys separated by a distance d, indicating uphill and downhill “motion” of ssDNA on the landscape of the trapping potential.

The dependence of the instantaneous spring force and the average force on the ssDNA position are shown in more detail in Fig. 2a. Due to thermal fluctuations, the standard deviation of forces in the spring increases with k and scales like kBTk, where kB is the Boltzmann constant, T the temperature and k the spring constant. When pulled by a stiff spring (100 pN/Å), ssDNA follows the pulling stage nearly instantaneously. Therefore, the average force in the spring balances the force of the electric trapping potential. Thus, the curve of the average force [red line in Fig. 2a] also illustrates the dependence of the trapping force on the ssDNA position. The maximum trapping force fmax on average is about a half of the theoretical prediction (eE=160 pN) in which the total charge of each nucleotide is assumed to reside at a point [23]. The resulting energy barrier (or trapping energy) is about 5 kBT.

FIG. 2
Dynamics of ssDNA when pulled using a stiff (100 pN/Å) or a weak (10 pN/Å) spring. (a) Force-position dependence when ssDNA is pulled using the stiff spring [gray line] or the weak spring [black line]. The red curve shows the averaged ...

When the spring constant is reduced to 10 pN/Å, the motion of ssDNA evinces both trapped and slip states of ssDNA [black line in Fig. 2a]. Unlike the steady sliding motion when ssDNA is pulled using the stiff spring [100 pN/Å, grey line in Fig. 2a], each slip event corresponds to a hop from an uphill potential surface to the next uphill potential surface. Hopping events are thermally activated once the force in the spring is close to fmax. Due to the dissipative hopping process, the average pulling force is nearly always positive [black line in Fig. 2a], as opposed to the positive and negative pulling forces observed in the stiff spring case [red line in Fig. 2a]. Figure 2b shows the time-dependent pulling force, indicating that ssDNA is alternatively in a trapped and a slip states. In a trapped state, ssDNA barely moves forward and the pulling force in the spring builds up. Once the pulling force is big enough for ssDNA to overcome the electric trapping force, ssDNA catches up with the pulling stage (a slip event) and the pulling force in the spring drops.

The simulated ssDNA motion under various pulling conditions is summarized in Fig. 3a. At the same pulling velocity (v=1 Å/ns), Fig. 3a shows that the motion of ssDNA changes from a steady sliding to a ratcheting motion when the spring constant is decreased. When the pulling velocity is high (v=10 Å/ns), the ratcheting motion is less obvious even when the spring constant is weak (k=10 pN/Å). Together, these results show that the ratcheting motion of ssDNA can be achieved by decreasing the loading rate kv. This is consistent with the fact that the duration, τ, of a trapped state satisfies the relation τ ~ fmax/kv.

FIG. 3
Time-position dependence of ssDNA. (a) Simulated time-position dependence of the ssDNA molecule pulled by a harmonic spring. (b) Modeled time-position dependence of the ssDNA molecule that is pulled under the same conditions. According to the pulling ...

To further characterize the ssDNA motion described above, we treat the driven motion of ssDNA along the pore in a thermal bath and on a potential of mean force [32] modeled by −Vb cos(2πz/d)/2, using

mz¨=γz.fmaxsin(2πzd)k(zz0)+2γkBTξ
(1)

where z is the ssDNA position, m the mass of ssDNA, z0 (= vt) the position of the pulling stage, and ξ the δ-correlated white noise. The external forces exerted on ssDNA are hydrodynamic friction force, electric trapping force and the pulling force from a harmonic spring. According to the measured trapping force shown in Fig. 2a, we approximate the relation between the trapping force and the ssDNA position using a sinusoidal function with fmax = Vb π/d. Note that this equation is mathematically equivalent in the limit T→0 to both the Tomlinson model for friction [33] and models for Josephson Junctions [34]. The ssDNA is in the overdamped regime, as dissipation dominates inertia (γmk).

Figure 3b shows the solution of the above model (z(0) = 0 and ż(0) = 0) without any fitting parameters, when ssDNA is pulled under the same conditions as used in the MD simulations. Predictions of the model at T = 0 [smooth lines] and T = 300 K [grey line] agree well with the simulation results shown in Fig. 3a. Because of thermally activated hops in the simulation dynamics [Fig. 3a], the duration of the trapped states is not constant at T = 300 K in contrast to T = 0 [Fig. 3b]. As this model accurately captures the dynamics of observed ssDNA motion, the slower motion of ssDNA on the experimental time scale, resulting from employing a slower pulling velocity or a larger trapping force, can be investigated simply by integrating the model (parameterized with coefficients obtained in simulations) to a long time scale.

The observed ratcheting motion of ssDNA depends on the existence of multiple meta-stable states. In a meta-stable or a trapped state, z = ż = 0, therefore −k(x − vt) = fmaxsin(2πx/d). In Fig. 2a, the left part of this equation is shown as line segments of the instantaneous force fluctuation of the spring, while the right part is shown as the curve [red line] of the averaged force, or the trapping force. When the spring constant k is bigger than the maximum slope of the curve of the trapping force [red line], each line segment of the force fluctuation intersects the curve of the trapping force only once (i.e one stable state at any time), indicating that ssDNA moves steadily through the nanopore. However, when k is smaller, some line segments may intersect the curve of the trapping force at several positions, forming several meta-stable states. A hop between meta-stable states corresponds to a slip event. Therefore, the criteria for ss-DNA to exhibit ratcheting motion is k < 2πfmax/d, i.e. not only the loading rate kv but also the spring constant k should be less than their respective thresholds.

Using the same atomistic MD simulation setup as above, we remove the pulling spring and replace it by a constant biasing electric field E across the nanopore. In Fig. 4a, we show MD trajectories of ssDNA subject to various strengths of the biasing electric field. When ssDNA is driven in the weak biasing electric field [0.6 mV/Å, red line], a ratcheting motion of ssDNA is observed. When the biasing electric field increases, these simulations demonstrate a continuous transition from a ratcheting motion to a steady sliding motion of ssDNA. A mixing of both types of motion is found at intermediate biasing electric fields. The electrically driven motion of DNA can be effectively modeled using equation (1) with the spring force replaced by the constant effective driving force feff = qeffE [15, 17], where qeff is the effective charge of ssDNA.

FIG. 4
Thermally activated ratchet-like motion of ssDNA driven by a biasing electric field. (a) Transition from a ratcheting to a steady-sliding motion of ssDNA when increasing the biasing electric field from 0.6 mV/Å to 9.4 mV/Å, or the electric ...

Figure 4b-d shows the prediction of Eq. (1) for the time-dependent force in springs with different spring constants. When the spring constant is large [1000 pN/Å, Fig. 4b], the spring force balances the modeled sinusoidal trapping force. When k=10 pN/Å [Fig 4c], we obtain similar force spikes as shown in the simulation result [Fig. 2b] and the motion of DNA is ratchet-like. Each time when the force in spring is big enough to trigger a slip event, ssDNA quickly advances a distance of d and the force in spring drops by kd. In the weak-spring limit [k=0.1 pN/Å], kd is negligible as shown in Fig. 4d and spring forces are nearly constant. Thus, electric field driving (or constant force pulling) is the limit of a weak spring pulling. Therefore, similar ratcheting motion of ss-DNA is observed when driven by a weak harmonic spring or by a biasing electric field.

In summary, we have investigated the ratcheting motion of ssDNA inside a solid-state nanopore, uncovered the basic mechanism underlying the dynamics and developed a simple 1D-Langevin-like model to describe it. Our simulations show, when driven either by a weak harmonic spring (k < 2πfmax/d) or by a biasing electric field (feff < fmax), ssDNA can be made to move through the DNA transistor such that each base in ssDNA is trapped before rapidly moving forward by one nucleotide spacing. If realized experimentally, this controlled motion of ssDNA could potentially benefit all nanopore-based ss-DNA sequencing technologies. We have investigated the effects of ion concentrations and solvent viscosity [14], different spacing d in ssDNA, friction between ssDNA and a polymer-coated pore surface as well as the predicted long-time scale ratcheting dynamics from the theoretical model; these results will be presented in a longer paper[26].

Acknowledgments

The authors acknowledge useful discussions with Mark Robbins, Ali Afzali, Yuhai Tu, Ajay Royyuru and Tom Theis. This work was supported by grant from the National Institutes of Health (R01-HG05110-01).

References

1. Li J, Gershow M, Stein D, Brandin E, Golovchenko JA. Nature Mater. 2003;2:611. [PubMed]
2. Dekker C. Nature Nanotech. 2007;2:209. [PubMed]
3. Branton D, Deamer D, Marziali A, Bayley H, Benner S, Butler T, Di Ventra M, Garaj S, Hibbs A, Huang X. e. a. Nature Biotech. 2008;26:1146. [PMC free article] [PubMed]
4. Wanunu M, Morrison W, Rabin Y, Grosberg AY, Meller A. Nature Nanotech. 2010 DOI: 10.1038/NNANO.2009.379. [PMC free article] [PubMed]
5. Luo K, Ala-Nissila T, Ying S, Bhattacharya A. Phys. Rev. Lett. 2008;100:58101.
6. Wong CTA, Muthukumar M. J. Chem. Phys. 2007;126:164903. [PubMed]
7. Lubensky D, Nelson D. Biophys. J. 1999;77:1824. [PMC free article] [PubMed]
8. Lagerqvist J, Zwolak M, Ventra MD. Nano Lett. 2006;6:779. [PMC free article] [PubMed]
9. Gracheva M, Aksimentiev A, Leburton J-P. Nanotechnology. 2006;17:3160.
10. Kasianowicz JJ, Brandin E, Branton D, Deamer DW. Proc. Natl. Acad. Sci. USA. 1996;93:13770. [PMC free article] [PubMed]
11. Iqbal S, Akin D, Bashir R. Nature Nanotech. 2007;2:243. [PubMed]
12. Chang S, He J, Kibel A, Lee M, Sankey O, Zhang P, Lindsay S. Nature Nanotech. 2009;4:297. [PMC free article] [PubMed]
13. Meller A, Nivon L, Brandin E, Golovchenko J, Branton D. Proc. Natl. Acad. Sci. USA. 2000;97:1079. [PMC free article] [PubMed]
14. Fologea D, Uplinger J, Thomas B, McNabb DS, Li J. Nano Lett. 2005;5:1734. [PMC free article] [PubMed]
15. Luan BQ, Aksimentiev A. Phys. Rev. E. 2008;78:021912. [PMC free article] [PubMed]
16. Ghosal S. Phys. Rev. E. 2007;76:061916. [PubMed]
17. van Dorp S, Keyser U, Dekker N, Dekker C, Lemay S. Nature Phys. 2009;5:347.
18. Sigalov G, Comer J, Timp G, Aksimentiev A. Nano Lett. 2008;8:56. [PMC free article] [PubMed]
19. Peng H, Ling X. Nanotechnology. 2009;20:185101. [PMC free article] [PubMed]
20. Keyser U, Koeleman B, Dorp S, Krapf D, Smeets R, Lemay S, Dekker N, Dekker C. Nature Phys. 2006;2:473.
21. Trepagnier E, Radenovic A, Sivak D, Geissler P, Liphardt J. Nano Lett. 2007;7:2824. [PubMed]
22. Schirmeisen A, Weiner D, Fuchs H. Phys. Rev. Lett. 2006;97:136101. [PubMed]
23. Polonsky S, Rossnagel S, Stolovitzky G. Appl. Phys. Lett. 2007;91:153103.
24. Ke C, Humeniuk M, S-Gracz H, Marszalek PE. Phys. Rev. Lett. 2007;99:018302. [PubMed]
25. Wanunu M, Meller A. Nano Lett. 2007;7:1580. [PubMed]
26. Luan BQ, Peng H, Polonsky S, Rossnagel S, Stolovitzky G, Martyna G. 2010. (unpublished)
27. Wells DB, Abramkina V, Aksimentiev A. J. Chem. Phys. 2007;127:125101. [PMC free article] [PubMed]
28. Phillips JC, et al. J. Comp. Chem. 2005;26:1781. [PMC free article] [PubMed]
29. Perez A, Marchan I, Svozil D, Sponer J, Cheatham TE, Laughton CA, Orozco M. Biophys. J. 2007;92:3817. [PMC free article] [PubMed]
30. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML. J. Chem. Phys. 1983;79:926.
31. Moffitt J, Chemla Y, Izhaky D, Bustamante C. Proc. Natl. Acad. Sci. USA. 2006;103:9006. [PMC free article] [PubMed]
32. Zwanzig R. Nonequilibrium Statistic Mechanics. Oxford University Press; New York: 2001.
33. Robbins MO. In: Jamming and Rheology. Liu A, Nagel S, editors. Taylor & Francis; London: 2001.
34. McCumber D. J. Appl. Phys. 1968;39:3113.
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