^{1}, Debayan Chakraborty

^{1,a)}, Jonathan P. K. Doye

^{1,b)}, Thomas E. Ouldridge

^{2}and Ard A. Louis

^{2}

### Abstract

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23 °C occurs at 74 pN in the model, about 6–7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.

The authors are grateful for financial support from the EPSRC and University College, and for helpful discussions with Felix Ritort.

I. INTRODUCTION

II. METHODS

A. DNA model

B. Pulling schemes

C. Thermodynamics of pulling

D. Simulation methods

III. RESULTS

IV. CONCLUSIONS

### Key Topics

- DNA
- 46.0
- Secondary structure
- 30.0
- Free energy
- 19.0
- Nucleotides
- 8.0
- Brownian dynamics
- 7.0

##### C12

## Figures

(a) Two nucleotides represented by our model, showing the rigid nucleotide unit and the backbone and base regions. (b) A short DNA duplex as represented by our model.

(a) Two nucleotides represented by our model, showing the rigid nucleotide unit and the backbone and base regions. (b) A short DNA duplex as represented by our model.

Schematic representation of the three pulling schemes used. The arrows on the DNA are in the 3′-5′ direction.

Schematic representation of the three pulling schemes used. The arrows on the DNA are in the 3′-5′ direction.

Force-extension curves for DNA at 23 °C for pulling scheme I. In (a) results from a series of Monte Carlo simulations at constant force are presented. For comparison the curve for single-stranded DNA has been added. In (b) results from dynamics simulations are presented at a number of different pulling rates. The pulling rates are given in pN/time step. These units can be converted into pN ns^{−1} by multiplying by 1.17 × 10^{5} time steps/ns, but as with any coarse-grained model absolute values of time should be treated with caution. Using this conversion, our slowest and fastest rates correspond to 0.0284 pN ns^{−1} and 5.69 pN ns^{−1}, respectively.

Force-extension curves for DNA at 23 °C for pulling scheme I. In (a) results from a series of Monte Carlo simulations at constant force are presented. For comparison the curve for single-stranded DNA has been added. In (b) results from dynamics simulations are presented at a number of different pulling rates. The pulling rates are given in pN/time step. These units can be converted into pN ns^{−1} by multiplying by 1.17 × 10^{5} time steps/ns, but as with any coarse-grained model absolute values of time should be treated with caution. Using this conversion, our slowest and fastest rates correspond to 0.0284 pN ns^{−1} and 5.69 pN ns^{−1}, respectively.

Snapshots of typical DNA configurations as the system passes through the overstretching transition at 23 °C for scheme I. The snapshots are from the dynamics run at a pulling rate of 2.43 × 10^{−7} pN/time step.

Snapshots of typical DNA configurations as the system passes through the overstretching transition at 23 °C for scheme I. The snapshots are from the dynamics run at a pulling rate of 2.43 × 10^{−7} pN/time step.

Contributions to the potential energy from (a) hydrogen bonding and (b) stacking as a function of force. In (b) the contributions from the two individual strands are included. *k* _{B} *T*/ε = 0.1 at *T* = 300 K.

Contributions to the potential energy from (a) hydrogen bonding and (b) stacking as a function of force. In (b) the contributions from the two individual strands are included. *k* _{B} *T*/ε = 0.1 at *T* = 300 K.

Free energy profiles as a function of the number of base pairs for different forces at (a) room temperature (*T* = 23 °C) and (b) *T* = 94 °C. The latter is just above the zero-force bulk melting temperature and exhibits reentrance. Note the relative flatness of the free energy profiles at this temperature.

Free energy profiles as a function of the number of base pairs for different forces at (a) room temperature (*T* = 23 °C) and (b) *T* = 94 °C. The latter is just above the zero-force bulk melting temperature and exhibits reentrance. Note the relative flatness of the free energy profiles at this temperature.

Force-extension curves for ssDNA in the presence or absence of secondary structure. As the effects of secondary structure depend on sequence, the results for four different random sequences (as well as their average) are depicted. The area of the shaded region corresponds to the average free energy of stabilization of ssDNA by secondary structure.

Force-extension curves for ssDNA in the presence or absence of secondary structure. As the effects of secondary structure depend on sequence, the results for four different random sequences (as well as their average) are depicted. The area of the shaded region corresponds to the average free energy of stabilization of ssDNA by secondary structure.

Dependence of the overstretching force on temperature. The main results for our model are from simulations where intramolecular base-pairing was turned off, but we also include results where a correction for secondary structure formation in the unpeeled chain has been applied for temperatures between 23 °C and 43 °C—above the latter temperature there is no need for a correction as the secondary structure is thermally unstable. Also included are the experimental results from Refs. ^{ 7 } and ^{ 13 } at a salt concentration of 500 mM. Note that the results of Zhang *et al.* are for the onset (not the midpoint) of the transition. The inset provides an expansion of the high temperature region where non-monotonic behaviour is observed. The horizontal line in the inset is the force at which ssDNA and dsDNA have the same extension.

Dependence of the overstretching force on temperature. The main results for our model are from simulations where intramolecular base-pairing was turned off, but we also include results where a correction for secondary structure formation in the unpeeled chain has been applied for temperatures between 23 °C and 43 °C—above the latter temperature there is no need for a correction as the secondary structure is thermally unstable. Also included are the experimental results from Refs. ^{ 7 } and ^{ 13 } at a salt concentration of 500 mM. Note that the results of Zhang *et al.* are for the onset (not the midpoint) of the transition. The inset provides an expansion of the high temperature region where non-monotonic behaviour is observed. The horizontal line in the inset is the force at which ssDNA and dsDNA have the same extension.

(a) Force-extension curves illustrating the irreversibility in our model. In all the simulations the magnitude of the pulling rate is 2.43 × 10^{−6} pN/time step. The increasing force run starts from a fully bonded duplex and provides the starting configurations for the decreasing force simulations. In case A, the force is decreased after reaching 146 pN, whereas in cases B and C the force is decreased after reaching 85.3 pN. In case C intramolecular base pairing is not allowed, preventing secondary structure formation in the unpeeled chain. (b) The final zero-force configuration for case B.

(a) Force-extension curves illustrating the irreversibility in our model. In all the simulations the magnitude of the pulling rate is 2.43 × 10^{−6} pN/time step. The increasing force run starts from a fully bonded duplex and provides the starting configurations for the decreasing force simulations. In case A, the force is decreased after reaching 146 pN, whereas in cases B and C the force is decreased after reaching 85.3 pN. In case C intramolecular base pairing is not allowed, preventing secondary structure formation in the unpeeled chain. (b) The final zero-force configuration for case B.

(a) Force-extension curve for pulling scheme II obtained from Monte Carlo simulations compared to that for scheme I. There are no points above the midpoint of overstretching because the system can no longer bear a force after dissociation. (b) Snapshot near the middle of the transition at *F* = 78 pN.

(a) Force-extension curve for pulling scheme II obtained from Monte Carlo simulations compared to that for scheme I. There are no points above the midpoint of overstretching because the system can no longer bear a force after dissociation. (b) Snapshot near the middle of the transition at *F* = 78 pN.

(a) Force-extension curves and (b) snapshots of the DNA configuration at *F* = 116 pN as it undergoes overstretching for pulling scheme III obtained from Monte Carlo simulations. For comparison, curves for pulling ssDNA and dsDNA in pulling scheme I have been added in (a).

(a) Force-extension curves and (b) snapshots of the DNA configuration at *F* = 116 pN as it undergoes overstretching for pulling scheme III obtained from Monte Carlo simulations. For comparison, curves for pulling ssDNA and dsDNA in pulling scheme I have been added in (a).

Article metrics loading...

Full text loading...

Commenting has been disabled for this content