Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a Nanopore Anna Stachiewicz, and Andrzej Molski J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00183 • Publication Date (Web): 28 Mar 2019 Downloaded from http://pubs.acs.org on March 28, 2019

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The Journal of Physical Chemistry

Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a Nanopore

Anna Stachiewicz∗ and Andrzej Molski Department of Chemistry, Adam Mickiewicz University, Poznan, Poland

E-mail: [email protected]

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Abstract By applying an electric eld to an insulating membrane, movement of charged particles through a nanopore can be induced. The measured ionic current reports on biomolecules passing through the nanopore. In this paper we explore the sequencedependent dynamics of DNA unzipping using our recently developed coarse-grained (CG) model. We estimated three molecular proles (the potential of mean force, position-dependent diusion coecient and position-dependent eective charge) for the DNA unzipping of four hairpins with dierent sequences. We found that the molecular proles are correlated with the ionic current and molecular events. We also explored the unzipping kinetics using Brownian dynamics. We found that the eect of hairpin structure on the unzipping/translocation times is not only energetic (weaker hairpins unzip more quickly), but also kinetic (dierent unzipping and translocation pathways play an important role).

Introduction Nanopore Force Spectroscopy (NFS) is used to study the dynamics and interactions of biomolecules (usually DNA hairpins and protein-DNA complexes) at the single-molecule level. 1,2 The pore diameter is chosen so that only the narrow part of the biomolecule can pass the pore. 3 The electric eld applied to an insulating membrane induces movement of charged particles through a nanopore and, as a result, hairpin unzipping or complex dissociation. 4 The measured ionic current reports on molecules passing through the nanopore. 5 Studies of the DNA/RNA unzipping/translocation kinetics give insight into DNA replication, DNA transcription or RNA interference. 68 The kinetic parameters describing those processes include the system lifetime, the height and position of the energy barrier, the diusion coecient and eective charge. 9,10 The DNA translocation velocity can be reduced by increasing the solvent viscosity or decreasing the temperature. 11 The translocation time decreases with the applied voltage. 12,13 2


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The electrolyte gradient can increase the translocation velocity, but at the same time decrease it by the electroosmotic drag and the electrostatic screening. 14 Pore properties (pore diameter, the interactions of analyte with the pore walls) also play an important role. 15,16 Finally, the translocation velocity depends on the DNA structure (polymer length, base pair mismatches). 17,18 The experimental information that can be recorded in NFS is limited to the unzipping time or critical voltage (the minimal voltage at which the unzipping occurs). Computer simulations help to unravel the mechanism of translocation or unzipping, e.g. eects of interactions with the pore walls, analyte conformation and unzipping sequence. 19,20 For example, Schink et al. 21 and Viasno et al. 22 studied the unzipping kinetics of dierent hairpins, modeled as motion on an eective potential surface, with the electrolyte and pore walls treated implicitly. Molecular dynamics (MD) simulations can provide detailed information on the molecular mechanism of translocation and unzipping. The coarse-grained (CG) models, where superatoms represent groups of atoms or even whole molecules, signicantly reduce the computational time. 2329 In this paper we explore the sequence-dependent dynamics of DNA unzipping using our coarse-grained (CG) model 30 that allows simulations with explicit solvent and ions. To understand how hairpin length, ratio of AT to CG base pairs and mismatch aect the unzipping kinetics at the molecular level, four dierent hairpin sequences were used. For each sequence, we estimated the potential of mean force PMF(z ), position-dependent diusion coecient

D(z) and position-dependent eective charge qe (z). Furthermore, we used these molecular proles as input in Brownian dynamics (BD) simulations of the unzipping kinetics. Both the MD and BD simulations show that not only the inter- and intra-molecular interactions but also kinetic unzipping/translocation pathways play an important role in unzipping kinetics. All molecular dynamics simulations were executed in NAMD (Scalable Molecular Dynamics). 31 VMD (Visual Molecular Dynamics) 32 and custom Tcl and Python scripts were 3



used to prepare simulations and analyze results. The paper is organized as follows: rst, we briey describe our model for electrolyte, DNA and a nanopore in inorganic membrane. Then, the protocols for the DNA unzipping and the molecular proles estimation are presented. Next, the results are compared with available experimental and all-atom (AA) simulation data. Finally, conclusions are given.

Methods CG model An overview of the models of electrolyte, DNA and nanopore used in this paper is presented below. The more detailed description of the models is given in Stachiewicz et al. 30

Electrolyte The model of electrolyte created by Marrink et al. 33 was adapted. To reproduce electrostatic interactions correctly, a few modications were applied. The particle mesh Ewald (PME) algorithm, instead of the cut-o algorithm, was used (this eliminated the abnormally high densities of ions close to the membrane surfaces observed in the nanopore conductivity simulations with the cut-o algorithm). 30 The eective dielectric constant was increased to 30. The non-bonded interactions levels were decreased: to level I (-1.195 kcal/mol) for ion-water and cation-anion and to level II (-1.076 kcal/mol) for cation-cation and anionanion. These values were chosen to reproduce the experimental scaled conductivity 34 of 1 M electrolyte at 305 K while keeping the scaling constant possibly low (3.0).

DNA Four hairpin sequences compared in the present work are denoted H10, H7, H12 and H10m: H10 :

5'-GCTCTGTTGCTCTCTCGCAACAGAGCA30 -3'

4


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H7

:

5'-TGAATGATCTCTCTCATTCAA30 -3'

H12 :

5'-GCGCGCGGCCGCTCTCTCGCGGCCGCGCGCA30 -3'

H10m:

5'-GCTATGTTGCTCTCTCGCAACAGAGCA30 -3'

Figure 1: Sequences used in the simulations. (a) Hairpin H10, (b) hairpin H12, (c) hairpin H7, (d) hairpin H10m (arrow denotes the mismatch). Gray: loop and free coil, orange: CYT, yellow: GUA, blue: ADE, purple: THY. H10 (Fig. 1a) is a hairpin consisting of 10 base pairs and 60% ratio of cytosine/guanine to thymine/adenine. Diusive dynamics of H10 were studied in Stachiewicz et al. 35 where we demonstrated that CG simulations combined with BD can unravel the mechanism of unzipping. Here we extend our work by comparing H10 to three new sequences. H7 (Fig. 1b) is a shorter system with 7 base pairs and higher content of adenine/thymine. H12 (Fig. 1c) consists of 12 base pairs and cytosine/guanine only. H10m (Fig. 1d) has the same structure as H10, but with single mismatch (marked bold in the sequence). In this way we can explore the eects of the length, ratio of AT to CG base pairs and sequence mismatch on the unzipping dynamics. The model of DNA by Dans et al. 36 was modied and extended, with original mapping left unchanged. Six superatoms represent each nucleotide: PX for the phosphate group (P), KX and KN for the sugar (C5' and C1' respectively) and three pseudoatoms for each base. The bond lengths, angles and dihedrals were taken from the canonical structure of DNA β helix generated with the program 3D-DART. 37 The force constants were set to reproduce the 5



results of the all-atom simulations with Charmm 27 force eld. 38,39 The bond force constants were xed at 40 kcal/(mol×Å2 ). The angles force constants were set at 15 kcal/(mol×rad2 ) (angles between sugar and base rings and sugar-phosphate-sugar angles), 20 kcal/(mol×rad2 ) (angles between phosphate groups and sugar rings) and 75 kcal/(mol×rad2 ) (angles inside the base rings). The dihedral force constants and multiplicities were taken from Dans et al. 36 The charges of superatoms and the parameters of Lennard-Jones interactions between DNA beads were taken from Dans et al. 36 The distance r between two superatoms at minimum energy was set as the sum of their radii and the depth ε of potential well was set as the √ geometric mean of their potential well depths εij = εi εj . The r parameter was increased to the canonical value for the sugar-sugar (KN-KN) and sugar-base interactions to prevent non-physical distortions while allowing some exibility. Other nonbonded Lennard-Jones interactions were dened as follows. The superatoms representing DNA were divided into four categories: anions (PX), hydrogen bond donors, hydrogen bond acceptors and apolar ones (KX, KN, CX). The equilibrium distance at minimum energy between the DNA and electrolyte superatoms was set as the sum of their radii (for water and ions r =2.3 Å, 50% of the optimum distance between water particles in NAMD Martini implementations). The depth of the potential well was set as the geometric mean of ε presented in Dans et al. 36 and the standard Martini value 33 for interaction level determined in simulations. More nonbonded interactions were excluded than in the original Martini due to a more detailed description, not only the directly connected atoms, but also all pairs of atoms bonded to a common third atom. The parameters were chosen to reproduce as close as possible the experimental melting temperatures 40 for the DNA helix fragments of various structures and lengths and for dierent electrolyte concentrations. Other parameters characterizing DNA, e.g. the helical parameters, RMSD, persistence length and the force-distance curves for mechanical unzipping were also shown to be consistent with experimental and AA results. 30 6


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Nanopore The membrane was modelled as uniform, electrically neutral particles with mass of 72 amu. Their positions were chosen to reproduce the hexagonal geometry of silicon nitride while keeping the superatoms as uniformly distributed as possible. Out of fourteen atoms (two elementary cells) in the all-atom model, three superatoms were left. The dimensions of the membrane were similar to those in typical experiments and all-atom simulations. The width of the membrane was 10 nm. To accelerate the simulations even more, most pore walls atoms were removed. Only the atoms closest to the solvent surface were kept and their positions xed, resulting in walls of about 10 Å thickness. The membrane particles were modeled as apolar ones (interactions with water at 0.5 kcal/mol, ions at 0.45 kcal/mol and DNA at 0.15 kcal/mol. Positions of interaction minima with DNA were calculated in a similar way as those of DNA with solvent - as the sum of radii, the radius for membrane superatoms was set at 2.6 Å. The nanopore model was reported to correctly reproduce the experimental dependence 19 of the scaled ionic current on applied voltage for voltages up to 4 V, for higher values deviations were observed. 30 To examine the inuence of the pore geometry on unzipping pathway, a number of pores was prepared by removing the atoms, which xyz coordinates of the centers satised the following equation: 41

p

x2 + y 2 < d0 /2 + |z| tan γ.

(1)

The double-conical shape was used (slope γ =10%) and 1.6 nm diameter (which corresponds to 1.3 nm all-atom).

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Unzipping protocol DNA unzipping protocol was adapted from Comer et al. 41 Each hairpin was placed inside the nanopore, with the helical part on the cis side, above the pore constriction at z =0. Then solvent and ions were added to neutralize the system and reach a desired concentration of electrolyte (1 M). The PME algorithm was applied. Each system was rst minimized for 80 ps with a timestep of 40 fs, all distances between bases were xed (additional bonds, 10 kcal/(mol×Å)) to protect the DNA structure during water equilibration. In the next steps the NPT equilibration was performed: rst for 0.5 ns (timestep 5 fs), second for 1 ns (timestep 10 fs, all additional bonds removed except those between NR, NU, NW and NZ superatoms), third for 1 ns (timestep 10 fs, only NW-NZ and NU-NR distances restrained at 5 kcal/(mol×Å)), fourth for 1 ns (timestep 5 fs, no additional restraints). Finally, the unzipping simulations were performed with the xed volume and an electric eld applied (timestep 5 fs). To prevent DNA from sticking to the pore walls observed at low voltages, additional grid potential 42 was used, constructed with radius R = 2 Å, σ = 3 Å and force constant F0 = 2 kcal/(mol×Å) (cf. Comer et al., 41 Eq. 2). Hydrogen bonds were considered as broken, when the distance between superatoms was larger than 4 Å. The KN (C1') superatom of the leading edge (base from the helical part connected directly with the coil) was chosen as the characteristic point used for measuring the translocation progress and estimation of PMF, D and qe . The model and unzipping protocol validation can be found in Stachiewicz et al. 35

PMF(z) For each system a number of unzipping simulations at dierent voltages was performed. For each system one trajectory was selected, where voltage was possibly low, but still the full translocation occurred. As a result, 2 V trajectories were selected for H10, H12 and H10m and 1 V for H7. For each unzipping trajectory the position of the leading edge KN superatom (C1') displacement along the z axis of the pore was measured and frames were selected every 8


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2 Å. Each frame was used as the starting point for simulation, with position of the KN atom harmonically restrained with spring constant k =2.5 kcal/mol. The timestep was 5 fs, the position was recorded every 100 fs. For the least stable trajectories (the R2 correlation coecient, calculated from the linear t to the Q-Q plot of the trajectory against the normal distribution, less than 0.98) simulations were repeated with k =10.0 kcal/mol. As no empty spaces between histograms are allowed in the WHAM analysis, additional simulations were performed where necessary (also with k =10.0), giving a total number of 100-180 windows. For each trajectory, the rst 25 ns were skipped, and the remaining 25 ns were taken for analysis. The WHAM program by A. Grosseld et al. 43 was used to calculate the potential of mean force. The only modication made to the original program was setting the maximum number of permitted iterations to 106 , this was required to reach the desired maximum tolerance of 10−5 . The PMF was calculated every 0.25 Å of the KN movement along the z axis of the pore, giving 350-450 classes. No signicant changes were noticed when the number of classes was increased.

D(z) The method by Hummer, 44 adapted from Woolf et al., 45 was applied to get the diusion coecient at dierent points of the trajectory (D(z)). The data analysis was performed with a custom Python script. The same data as for the PMF was taken. From the recorded KN superatom positions beyond 25 ns (out of 50 ns), the autocorrelation function corr(t) was calculated and a biexponential curve was tted:

corr(t) = p0 exp(−p1 t) + (1 − p0 ) exp(−p2 t)

9


(2)


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The tting parameters p0 , p1 , p2 were then used to estimate the autocorrelation time:

τ (z) =

p0 1 − p0 + p1 p2

(3)

The position-dependent diusion coecient D(z) was assessed by dividing the position variance var(z) for the leading edge KN superatom by the autocorrelation time: 44

D(z) =

var(z) , τ (z)

(4)

For those points, where large deviations in the diusion coecient were observed and the ts to the autocorrelation function were poor, trajectories with k =10.0 kcal/mol were used. For H10, some points required k =25.0 kcal/mol and recording the trajectories every 5 fs.

Qe (z) The protocol by Luan et al. 46 was adapted 46 to assess the eective charge along the system axis. The leading edge of the helix (the KN superatom from the helical part, adjacent to the coil) was constrained using k =2.5 kcal/mol harmonic spring. Five simulations were then performed, for 0.5, 1.0, 1.5, 2.0 and 2.5 V, in points separated by about 12 Å. The trajectories at 0.0 V, generated for computing the PMF, were also used. As previously, only the second halves of the trajectories were taken for analysis (the last 50 ns out of 100 ns). The average forces were plotted against the forces resulting from the applied voltages. From the slope of the linear t to the data the eective charge was calculated:

kq =

fe , ne∆V /l

(5)

where fe is the average force, n is the number of nucleotides, e is the elementary charge and

∆V /l is the applied electric eld. 10


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Brownian Dynamics BD simulations of nanopore unzipping were performed, using the proles PMF(z ), D(z) and qe (z) estimated in the MD simulations. The unzipping was modeled as diusion on a one-dimensional potential surface. 47 The diusive coordinate z was advanced in a time step

∆t as: z(t + ∆t) = z(t) + {[−U 0 (z) + qe (z)V˙ t]D(z)β + D0 (z)}∆t p +r 2D(t)∆t

(6)

where −U 0 (z) is the force due to the PMF U (z), qe (z)V˙ t is the force due to the positiondependent eective charge qe (z) in a voltage that is ramped up with speed V˙ , D(z) is the position dependent diusion coecient, and r-s are uncorrelated Gaussian variables of mean zero and variance one. The primes denote rst derivatives with respect to z . For each system 200 unzipping simulations were performed, for a wide range of voltage ramps, from 50 to 106 mV/s. Simulations were started close to the energy minimum and nished at the point where ionic current jump was observed in the MD unzipping simulations. This way the KN (C1') superatom movement along the z axis of the pore was reproduce. The dependence of PMF, D and qe on the position along the z axis was recovered using a splines t with a custom Python script. The python Scipy package splrep was used (http://docs.scipy.org). The resulting arrays were sampled every 0.1 nm (about 300 points) to reduce the computation time. The smoothing parameter for PMF was chosen so that the noise could be eliminated but the most distinct maxima were still present. The P 2 smoothing parameter s is dened as: z {[f (z) − g(z)]} ≤ s, where g(z) is the smoothed interpolation of (z, f (z)).

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Results and discussion Unzipping kinetics The hydrogen bond dissociation time, dened by the last moment when the distance between the two superatoms (donor and acceptor) is smaller than 4.0 Å, was used to analyze unzipping. Fig. 2 shows the unzipping times for base pairs as a function on the applied voltage. The sequence of events is similar for all four systems: the rst broken base pair is the one closest to the free coil, the last one - the base pair closest to the loop. For the medium-length (H10, see Fig. 2a) and longest hairpin (H12, see Fig. 2b) the unzipping occurs gradually. The shortest hairpin (H7, see Fig. 2d) is the least stable, the lifetime of all base pairs is similar and relatively short. The unzipping times for the hairpin with a single mismatch ((H10m, see Fig. 2c) and without mismatch (H10) are comparable. However, the rst three base pairs of H10m (located between the coil and modied base pair 4) are less stable than in H10. Fig. 3 shows the potential of mean force PMF(z ) and the mean force F (z) for the four systems. For each system, the global shape of the potential of mean force is similar. The minimum is about 50-70 Å, on the

cis

side, close to the point where the leading edge was

after the equilibration. Then, the slope is rising until the

trans

side is reached, between

-50 Å (H7) and -100 Å (H12). Beyond that point a plateau can be observed. The energy barrier height depends on the simulated system, it varies from about 50 kcal/mol for H7 (see Fig. 3c, green line), through 70 kcal/mol for H10 (see Fig. 3a,c,e, red line) and 100 kcal/mol for H10m (see Fig. 3e, yellow line), to about 120 kcal/mol for H12 (see Fig. 3a, blue line). The energy barrier for H10m is surprisingly high compared to H10, a possible explanation is that more force needs to be applied to complete the translocation due to friction or dierent nucleotide spatial arrangement. Force is dened as the negative derivative of PMF. On each of the plots at least two distinct force maxima can be observed (see Fig. 3b,d,f). The rst maximum (-20 Å for 12


70 60 50 40 30 20 10 0

1.5V 2V 2.5V 3V 4V

0

mean unzipping time [ns]

H10 a

2 4 6 8 10 basepair number

H10m 70 60 50 40 30 20 10 0

2V 2.5V 3V 4V

0



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



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c

2 4 6 8 10 basepair number

H12 70 60 50 40 30 20 10 0

2V 2.5V 3V 4V

0

b

2 4 6 8 10 12 basepair number

H7 70 60 50 40 30 20 10 0

1V 1.5V 2V 2.5V

d

0 1 2 3 4 5 6 7 8 basepair number

Figure 2: Dependence of the unzipping times for base pairs on the applied voltage. (a) Hairpin H10, (b) hairpin H12, (c) hairpin H10m, (d) hairpin H7.

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Figure 3: Comparison of the potential of mean force PMF(z ) and the mean force F (z) for the four systems. Left - PMF(z ): (a) H10 and H12, (c) H10 and H7, (e) H10 and H10m, right: F (z)

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H12, 20 Å for H10, 40 Å for H7, -10 Å for H10m) can be related to the unzipping. The second maximum (-80 Å for H12, -50 Å for H10 and H10m, -30 Å for H7) can be related to translocation, i.e. interactions with the pore walls, friction and random coil elasticity. Additionally, for H12 a third maximum can be observed about 50 Å that is related to nucleotide movement inside the pore before unzipping takes place. The most complex force prole is the one for H10m. There are two maxima, about 50 Å and -10 Å for H10m, related to unzipping, which for this system consists of two stages. First, the base pairs between the mismatched base pair (b4) and the coil are broken, then those between b4 and the loop. For translocation, there is a maximum at -50 Å and a plateau between -70 Å and -80 Å , related to changing nucleotide arrangement inside the pore. Fig. 4 shows the position-dependent diusion coecient D(z) and eective charge qe (z). On the diusion coecient prole along the z axis two ranges can be distinguished for all simulated systems (see Fig. 4a,c,e). The rst range is inside the nanopore, between -50 and 50 Å (-70 and 50 Å for H12), with D(z) about 10−6 Å2 /s. For H7 this value is slightly higher, 2 × 10−6 Å2 /s, this can be related to weaker interactions between base pairs and shorter helical part, allowing more movement inside the pore. The second area is for z less than -70 Å (-100 Å for H12), D(z) is about 4 − 5 × 10−6 Å2 /s. Paradoxically, this value is slightly lower for H7 and H10m than for H10 and H12 due to increased simulation noise, resulting from weaker interactions between base pairs and more movement inside the pore. The overall shapes of the D(z) proles are consistent with the assumptions that the diusion coecient inside the pore should be visibly lower than outside it. The eective charge prole is similar for all simulated systems (see Fig. 4b,d,f). For H10 and H10m plateau can be observed at qe = 0.4 between -10 and 50 Å. Above and below this range, qe gradually decreases until about 0.1 (in relative units) is reached. For H7 the values are slightly higher, 0.5 and 0.15 respectively. For H12 additional minimum can be observed at -12 Å. A potential explanation can be the noise eect or the fact that at this 15



Figure 4: Comparison of D(z) and qe (z) for the four systems. Left - D(z): (a) H10 and H12, (c) H10 and H7, (e) H10 and H10m, right: qe (z)

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point nucleotides are quite tightly packed on the cis side of the pore, blocking ion movement. As a result, there are more ions on the trans side, so electrostatic screening is relatively high (and eective charge relatively low). The shapes of the molecular proles F (z), D(z) and qe (z) are correlated with the translocation and unzipping events. Below an analysis is presented for each system, showing the relation between the molecular proles and the sample unzipping trajectories.

Hairpin H10 In this work the H10 hairpin is used as a reference system for comparison with H7, H12, and H10m. Therefore, for the sake of presentation, we recall the relevant characteristics of its unzipping dynamics. 35 On the force curve for H10 unzipping, four extrema (two maxima and two minima) can be distinguished (Fig. 5a). The lower maximum, located at z = 20 Å, corresponds to the beginning of unzipping, manifested as a drop in the number of intact hydrogen bonds (Fig. 5b, red line and Fig. 6a). Similarly, the local minimum at about -10 Å is related to end of the unzipping - at this point all hydrogen bonds are broken and the distance between base pairs begins to increase (see Fig. 5b, green line and Fig. 6b). The third characteristic event is when the leading edge leaves the pore (Fig. 6c), at about -55 Å. This point is slightly to the left from the highest maximum on the force curve. The diusion coecient starts to rise (Fig. 5d, red line) due to the higher possibility of mobility in the bulk solution. The increased screening provided by ions result in eective charge drop (Fig. 5d, green line and dots). Finally, at about -80 Å, a current jump is observed (Fig. 5c), when the DNA molecule is below the constriction (Fig. 6d). Free movement of the DNA molecule surrounded by ions in the bulk solution results in a plateau on the D(z) curve and stable, low qe . These results are consistent with Comer et al., 48 who explained the current jump as the quick movement of DNA and ions screening it on the trans side of the pore.

17



Figure 5: H10, correlation between a) the mean force F (z) (cf. Fig. 3b), b) number of native hydrogen bonds (red) and mean base pair separation (green), c) the ionic current, d) D(z) (red, cf. Fig. 4a) and qe (z) (green, cf. Fig. 4b,). Dashed lines denote (right to left): the beginning and end of unzipping, the leading edge of the helix leaving the pore, the current jump.

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Figure 6: The characteristic events occurring during translocation of H10, marked on the Fig. 5. a) beginning of unzipping b) end of unzipping c) edge of helix exits pore d) all DNA below constriction (current jump)

Hairpin H12 For H12, three maxima can be distinguished on the force curve (Fig. 7a). The lowest maximum can be observed about 50 Å, which may be related to nucleotide movement inside the pore before unzipping takes place, since no distinct molecular events are observed at this point. The unzipping starts at the force minimum at about z = 15 Å (Fig. 7b, red line and Fig. 8a) and nishes at the highest maximum located at z = -20 Å (Fig. 8b). This is dierent from the behavior of H10, where unzipping starts at the force maximum and ends at the minimum. A possible explanation is that for H10 the unzipping and translocation events are more clearly separated, translocation starts when most of the base pairs are already broken. For H12 these two steps happen simultaneously - the separation of base pairs begins to increase at about z = 0 Å, when half of the hydrogen bonds are still intact (see Fig. 7b, green line). The third maximum at about -80 Å can be related to the next characteristic event, when the leading edge leaves the pore (Fig. 8c). The diusion coecient rapidly increases (Fig. 7d, red line) due to the higher mobility in bulk solution. The increased screening provided by ions result in eective charge drop (Fig. 7d, green line and dots). Finally, at about -105 Å a current jump is observed (Fig. 7c), when all nucleotides are below the constriction (Fig. 8d). 19



Figure 7: H12, correlation between a) the mean force F (z) (cf. Fig. 3b), b) the number of native hydrogen bonds (red) and mean base pair separation (green), c) the ionic current, d) D(z) (red, cf. Fig. 4a) and qe (z) (green, cf. Fig. 4b,). Dashed lines denote (right to left): the beginning and end of unzipping, the leading edge of the helix leaving the pore, nucleotide spatial rearrangement in the pore, the current jump.

20


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This point is slightly to the right from the force minimum. Free movement of the DNA molecule surrounded by ions in the bulk solution results in a plateau on the D(z) curve and stable, low qe .


Hairpin H7 For H7, four extrema (two maxima and two minima) can be distinguished on the force curve (Fig. 9a). The lower maximum, located at z = 40 Å, corresponds to the beginning of unzipping, manifested as drop in the number of intact hydrogen bonds (Fig. 9b, red line and Fig. 10a). Similarly, the local minimum at about 15 Å is related to the end of the unzipping - at this point all hydrogen bonds are broken and the distance between base pairs begins to increase (see Fig. 9b, green line and Fig. 10b). The third characteristic event is when the leading edge leaves the pore (Fig. 10c), at about -35 Å. This point is slightly to the left from the highest maximum on the force curve. The diusion coecient starts to rise (Fig. 9d, red line) due to the higher possibility of movement in the bulk solution. The increased screening provided by ions result in eective charge drop Fig. 9d, green line and dots). Finally, at about -65 Å a small current jump is observed (Fig. 9c), when all DNA molecule is below the constriction (Fig. 10d). A force 21



Figure 9: H7, correlation between a) the mean force F (z) (cf. Fig. 3c), b) number of native hydrogen bonds (red) and mean base pair separation (green), c) the ionic current, d) D(z) (red, cf. Fig. 4c) and qe (z) (green, cf. Fig. 4d,). Dashed lines denote (right to left): the beginning and end of unzipping, the leading edge of the helix leaving the pore, the current jump.

22


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minimum can be observed. Free movement of the DNA molecule surrounded by ions in the bulk solution results in D(z) value over 3 × 10−6 Å2 /s and relatively stable, low qe .


Hairpin H10m On the force curve for H10m three maxima and a plateau can be observed (Fig. 11a). The rst, lowest maximum located at 50 Å is related to unzipping of the base pairs between the mismatched base pair (b4) and the coil (Fig. 11b, red line and Fig. 12a). The second unzipping stage, when the base pairs between b4 and the loop are broken, marked as force minimum, begins at z = 20 Å (Fig. 12b). At about -10 Å there are no remaining hydrogen bonds (Fig. 12c) and the base pair separation starts to grow more rapidly (Fig. 11b, green line). The next characteristic event is when the leading edge leaves the pore (Fig. 12d), at about -50 Å. This point is slightly to the left from the highest maximum on the force curve. Again, the diusion coecient starts to rise Fig. 11d, red line) and eective charge starts to decrease (Fig. 11d, green line and dots). The plateau between -70 Å and -80 AA can be related to the nucleotides rearranging inside the pore. Finally, at about -105 Å, a current jump is observed (Fig. 11c), when the DNA molecule is below the constriction. This point 23



Figure 11: H10m, correlation between a) the mean force F (z) (cf. Fig. 3b), b) number of native hydrogen bonds (red) and mean base pair separation (green), c) the ionic current, d) D(z) (red, cf. Fig. 4a) and qe (z) (green, cf. Fig. 4b,). Dashed lines denote (right to left): the end of the rst stage of unzipping, the beginning and end of the second stage of unzipping, the leading edge of the helix leaving the pore, the current jump.

24


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is halfway between the force plateau and the force minimum. From this point, a plateau on the D(z) curve and stable, low qe can be observed.

Figure 12: The characteristic events occurring during translocation of H10m, marked on the Fig. 11. a) end of the rst stage of unzipping b) beginning of the second stage of unzipping c) end of the second stage of unzipping d) edge of helix exits pore

Brownian dynamics To compare the unzipping voltage histograms simulated at dierent voltage ramp speeds from the BD with the unzipping times from the MD simulations, the former were transformed into lifetime histograms: 3

P (pk /2 + N i=k+1 pi )∆V τ [V0 + (k − 1/2)∆V ] = , V˙ (V0 + (k − 1/2)∆V )pk

(7)

where V˙ is the voltage-ramp speed, N is the number of bins, each of width ∆V , pi is the normalized number of counts in a bin, and τ is the unzipping time. For all simulated hairpin structures, the unzipping times decrease with the increasing voltage. The dierence between H12 and other systems is clearly visible (Fig. 13a), the unzipping times are signicantly longer and the critical voltage is higher, about 800 mV. The curves for the shorter structures are very similar and partially overlapping. The critical voltage is approximately 300 mV, which is consistent with Comer et al. 48 25



Page 26 of 37

The unzipping/translocation times are shorter for H7 than for H10. This is consistent with experiment 3 and mesoscopic models simulations, where the unzipping times were shown to be strongly correlated with the hairpin structure. 21 However, the unzipping/translocation times are shorter for H10 than for H10m, which is not consistent with the experiment/simulations with α-hemolysin. The possible explanation is the dierent translocation mode. H10 and H7 were rst unzipped and then translocated, these two stages were separated. For H10m and H12 these two processes happened simultaneously. As a result, the force required for translocation is higher, due to more rigid structure of the only partially unzipped hairpin, compared to the completely unzipped conformations. This eect was not observed in αhemolysin, where the pore is more narrow and the hairpin needs to be fully unzipped to start translocation. It is instructive to analyze the BD and MD simulations together (Fig. 13b). Clearly the longest unzipping times are for the longest hairpin and the shortest times for the shortest hairpin. For the two medium-length structures the unzipping times are intermediate and rather similar, which indicates that detection of a point mutation may be dicult using a wide inorganic nanopore.

DNA sequencing We have analyzed our unzipping simulations to assess the possibility of using a nanopore for DNA sequencing. To this end we have correlated two trajectories: the number of permeated nucleotides and the ionic current. This way the ionic current can be presented as a function of the nucleotide passing the pore constriction (cf. Fig. 14). Fig. 14b shows the average current for each nucleotide passing the pore constriction. The ionic current is scaled by the current for the open pore. The H12 sequence data were chosen as an example. For clarity, only the results for nucleotides 30-48 are presented. The plots show that no clear correlation can be observed between the current and the nucleotide type. Our model nanopore can reproduce the ionic current jump when DNA leaves the pore, but 26


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Figure 13: a) the results of the BD simulations b) the results of the BD and MD simulations for H10 (red), H12 (blue), H7 (green) and H10m (yellow). The voltage ramps are 0.5 V/s to 10 V/s.

27



is not detailed enough to distinguish between individual nucleotides. This is not surprising, taking into account that each superatom represents four real atoms, so not all eects of the nanopore constriction may reproduced. Moreover, the limited number of ions in the system results in a high simulation noise (Fig. 14a), so subtle ionic current changes between nucleotides are lost.

10

I / I0 [-]

5 0 −5

a

−10 A C G C G C G C C G G C G C T C T C T 1.0

/ I0 [-]

0.8 0.6

I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 37

0.4

b

0.2

0.0 A C G C G C G C C G G C G C T C T C T

Figure 14: a) dependence of ionic current on the permeated nucleotide b) dependence of average ionic current on the permeated nucleotide.

Conclusions CG MD and BD simulations were applied to study the detailed unzipping kinetics of four dierent hairpin DNA sequences in synthetic nanopores. The hairpin sequences were: H10 (10 base pairs and 60% ratio of cytosine/guanine to thymine/adenine), H7 (7 base pairs and higher content of adenine/thymine), H12 (12 base pairs and cytosine/guanine only), H10m 28


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(H10 but with single mismatch). For each system the average unzipping times for base pairs were examined. It was found that the unzipping sequence is dependent on the hairpin structure. The potential of mean force was determined for each hairpin. On each F (z) curve, the negative derivative of PMF(z ), two energy maxima were found, one of them corresponding to the unzipping, the other to the translocation barriers caused by friction and non-bonded interactions with the pore walls. The maximum related to unzipping is the highest for H12, intermediate for H10 and the lowest for H7. For H10m two unzipping-related maxima can be observed, which shows that unzipping consists of two stages. Dependence of the diusion coecient and eective charge on the DNA position along the pore axis has been determined. The proles are similar for all analyzed structures: constant value inside the pore, and sudden jump (for D(z)) or drop (for qe ) when the leading edge of the helix leaves the pore. Shape of the molecular proles F (z), D(z) and qe (z) was related to the molecular events taking place during unzipping and translocation. The current jump can be observed as clear transition on all three proles. For all structures the four characteristic points, marking: the beginning and end of unzipping, the leading edge leaving the pore and current jump can be observed on the F (z) curve. For H10 and H7 these events are clearly separated, for H12 and H10m the shape is more complex. The dierences between the F (z) prole for H12 and H10m and for H7 and H10 were related to dierent translocation modes. It was found that a higher force is required when the unzipping and translocation happen simultaneously and lower when happen consecutively. The critical voltage was estimated using the BD simulations, the value is similar to that from MD simulations and experimental results. 48 The unzipping time changes with the hairpin structure, it increases with hairpin length, similarly as in experiment 3 or mesoscopic models simulations. 21 For H10m the unzipping occurs at slightly higher voltages than for 29



Page 30 of 37

H10. This result is unexpected, because a mismatch should weaken the hairpin structure and decrease the unzipping/translocation time, as was observed in experiments with αhemolysin. 3 The possible explanation is that the eect of mismatch is not only energetic, but also kinetic - the unzipping mechanism is dierent from that for other structures (as observed on the molecular proles), so it inuences the unzipping voltage. Simplication of the MD model enables examination of kinetic properties of hairpins with dierent structure on the detail level unavailable in AA simulations or experiment. However, there are also limitations. First, the eect of the interactions with the pore walls and DNA elasticity might be overestimated in the CG MD simulations. Second, the pore of

α-hemolysin, used in experiments, is more narrow than the inorganic pores simulated in this paper, so direct comparison is not possible. Third, due to large uctuations in ionic current the model cannot be used in DNA sequencing. Nevertheless, our coarse grained model showed not only correlations between molecular proles and the unzipping/translocation events but also the presence of dierent unzipping/translocation pathways.

Acknowledgement We thank an anonymous reviewer for suggesting an assessment of the applicability of nanopore unzipping for DNA sequencing. This work was supported by intramural funds from the Department of Chemistry of Adam Mickiewicz University in PoznaÅ.

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TOC Graphic

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Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a

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