The effects of diffusion on an exonuclease/nanopore-based DNA sequencing engine

Abstract

Over 15 years ago, the ability to electrically detect and characterize individual polynucleotides as they are driven through a single protein ion channel was suggested as a potential method for rapidly sequencing DNA, base-by-base, in a ticker tape-like fashion. More recently, a variation of this method was proposed in which a nanopore would instead detect single nucleotides cleaved sequentially by an exonuclease enzyme in close proximity to one pore entrance. We analyze the exonuclease/nanopore-based DNA sequencing engine using analytical theory and computer simulations that describe nucleotide transport. The available data and analytical results suggest that the proposed method will be limited to reading <80 bases, imposed, in part, by the short lifetime each nucleotide spends in the vicinity of the detection element within the pore and the ability to accurately discriminate between the four mononucleotides.

FIG. 1.

Electrical discrimination between mononucleotides by a β-cyclodextrin adapter in a nanopore. (a) DNA sequencing engine based on exonuclease attached to the cap domain of the α-hemolysin ion channel. The enzyme cleaves DNA (red sphere), one base at a time, near the pore mouth. In order to correctly sequence DNA, every cleaved base has to enter the pore sequentially, reach the base discrimination site (dark blue), and transport completely through the pore. (b) A histogram of the ionic current blockades caused by dGMP, dTMP, dAMP, and dCMP binding to a β-cyclodextrin adapter in the pore are fit with four Gaussian (orange) or Voigt (indigo) functions. (c) The resultant fits demonstrate that the Voigt function better describes the data, and fully accounts for the overlap between neighboring peaks. The use of Gaussian functions overestimates the system's ability to separate the mononucleotides. The overlaps between neighboring fitted peaks for the Gaussian (d) and Voigt functions (e) are represented by their respective probability density functions on a log-linear scale. The fit of the Voigt function to the data shows that the accuracies of identifying the mononucleotides are G: 94%, T: 93%, A: 85%, and C: 95%, with an average accuracy of 92%.

FIG. 2.

A schematic of the analytical model for the exonuclease/nanopore-based DNA sequencing engine. Each base (red) is released at a point above a pore of length L. The bulk solution is assumed to be infinite and the particle is captured at z = 0.

FIG. 3.

Distributions of capture times for an individual DNA mononucleotide estimated from the inverse Laplace transform of Eq. (4) (solid lines) and numerical simulations of a three-dimensional model of the system (circles, squares) for two different applied potentials. The peak heights obtained with the analytical model were scaled to coincide with those estimated from the numerical simulations. Increasing the potential both increases the likelihood of capture and shifts the distribution to shorter capture times. A vast majority of capture events occur within the first 100 ns after cleavage of a mononucleotide. The same parameters were used in both the analytical model (Eq. (4)) and the numerical simulations. They are the mononucleotide electrophoretic mobility (μ = −2.4 × 10⁻⁴ cm²/Vs), the distance between the pore entrance and the capture point (L = 6 nm), the single nanopore ionic conductance (g = 295 pS), the number of water molecules that hydrate mobile cations and anions (N_W = 10), the molar concentration of water (c_W = 3.4 × 10²⁸ m⁻³), the electronic charge (e = 1.6 × 10⁻¹⁹ C), the ratio of the nanopore's permeabilities to cations and anions (P₊/P₋ = 0.1), the DNA base diffusion coefficient (D = 3 × 10⁻⁶ cm²/s), and the nanopore diameter (d = 2.6 nm).

FIG. 4.

The capture probability as a function of the applied voltage estimated from simulations (open circles) and the analytical model (solid line), which has no adjustable parameters and uses the same values from Fig. 3 for the radiating boundary condition κ = 8D/πd; β = 8L/πd = 5.88. A one-parameter least squares fit of Eq. (5) to the simulated results with β = 4.7 ± 0.1 is also shown (dashed line). The slight disagreement between the simulation and theoretical model may result from the analytical model's assumption that the nanopore can be represented as a one-dimensional line.

FIG. 5.

The probability of reading a single base correctly is dependent on the applied potential and the system bandwidth. At low applied potential, the capture process dominates the probability. At higher potential, the mean residence time of a base on the detector decreases exponentially, which significantly decreases the probability of identifying a given base. Increasing the system bandwidth (5 kHz blue; 30 kHz green; and 500 kHz red) increases the probability of correctly reading a base because it permits a greater potential to be used (which increases capture probability) and shorter-lived blockade events to be accurately measured. (Inset) Ignoring several sources of noise, the optimum read probability increases with increasing system bandwidth, but saturates at ∼0.75.

FIG. 6.

The probability of reading a DNA sequence correctly, P_max, as a function of the number of identical polynucleotides read, N_seq, evaluated using two algorithms described in the text. The results from the numerical simulations for the “survivor” algorithm (which discards a particular polynucleotide sequence measurement if its base assignment disagrees with that of the majority's consensus, open squares) and a “majority rules” algorithm (which makes use of the information in the minority strand sequence measurements, open circles, see text). In both cases, the probability of capturing a given nucleotide is assumed to be 0.8. The solid line is a least-square fit of Eq. (8) (with N_T = 4.3 ± 0.2) to the “survivor” algorithm simulation data. The “majority rules” simulation was performed 20 times for each N_seq to generate statistics. The error bars shown are the standard error.