Theoretical study of sequence-dependent nanopore unzipping of DNA

Abstract

We theoretically investigate the unzipping of DNA electrically driven through a nanometer-size pore. Taking the DNA base sequence explicitly into account, the unpairing and translocation process is described by a biased random walk in a one-dimensional energy landscape determined by the sequential basepair opening. Distributions of translocation times are numerically calculated as a function of applied voltage and temperature. We show that varying these two parameters changes the dynamics from a predominantly diffusive behavior to a dynamics governed by jumps over local energy barriers. The work suggests experimentally studying sequence effects, by comparing the average value and standard deviation of the statistical distribution of translocation times.

FIGURE 1

Schematic representations of a DNA duplex with a single-stranded overhang inserted into the nanopore.

FIGURE 2

Energy landscape E_j of a 1000-bp DNA fragment taken from the λ-bacteriophage sequence for three values of the bias parameter W. At j = 0 the duplex is fully closed and the single-stranded overhang is advanced as far as possible into the pore. Negative j corresponds to an entirely closed duplex diffused backward by j nucleotides relative to the j = 0 configuration. Positive j-values describe duplexes with j unzipped basepairs diffused forward by j nucleotides. T = 20°C.

FIGURE 3

Two examples of individual time evolutions of the position of a DNA duplex in a nanopore. The corresponding energy landscapes E_j are shown in Fig. 2, and zoom images into different regions of these landscapes are provided in Fig. 4. For j = j_max, the duplex is fully unzipped and the resulting single-stranded molecule can go through the pore. T = 20°C, j_max = 1000.

FIGURE 4

Detailed views on the energy landscapes E_j of a λ-phage DNA duplex in the ranges −5 ≤ j ≤ 30, 440 ≤ j ≤ 490, and 725 ≤ j ≤ 775. For j < 0, the landscapes are simply given by E_j = −Wj. They are smooth and show different slopes according to the three values of W. The corresponding base sequence is given at the top of each figure. T = 20°C.

FIGURE 5

Average value of the unzipping time as a function of the number j_max of basepairs of the DNA duplex, for different values of W. The sequence of a duplex of length j_max corresponds to the first j_max basepairs of the λ-phage DNA (GenBank accession code is NC 001416. Basepairs 1–12 correspond to the cos sequence GGGCGGCGACCT). T = 20°C.

FIGURE 6

Histograms of unzipping times obtained for the three energy landscapes of Fig. 2. Each histogram is based on 10,000 individual unzipping traces. T = 20°C, j_max = 500.

FIGURE 7

Ratio of average value 〈t_u〉 and mean-square deviation Δt_u of the unzipping time as a function of the number j_max of basepairs, for different values of W. We have for a sequence-independent energy landscape at W → ∞. This dependence is shown as a dashed line. T = 20°C. The ratio 〈t_u〉/Δt_u is evaluated over 10,000 individual runs.

FIGURE 8

Normalized square of the average/deviation ratio of the unzipping time as a function of bias W. Analytical results for duplexes with homogeneous sequences, a sequence of AT basepairs and a sequence of GC basepairs, are shown as solid lines. Corresponding Monte Carlo results (j_max = 500) are presented as diamonds. The linear regime close to threshold is the validity range of the Einstein relation (linear response regime, where tanh(x) x). Monte Carlo results for the sequence of the first 500 bp (100 bp) of the λ-phage DNA are represented by stars (circles). Monte Carlo results are computed over 10,000 runs. T = 20°C.

FIGURE 9

Temperature dependence of the average 〈t_u〉 and mean-square deviation Δt_u of the unzipping time. The average and the mean-square deviation are computed over 10,000 runs. W = 4 k_BT, j_max = 100.