Abstract
Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy plays a crucial role at high force. As a result, the force-temperature diagram differs significantly with the theoretical prediction.
We would like to thank S. M. Bhattacharjee, M. Prentiss, D. Mukamel, D. Marenduzzo, and Y. Kafri for their comments and suggestions. Financial supports from the CSIR, DST, India, Ministry of Science and Informatics in Poland (Grant No. 202-204-234), and the generous computer support from MPIPKS, Dresden, Germany are acknowledged.
I. INTRODUCTION
II. MODEL AND METHOD
III. RESULTS
A. Equilibrium property of dsdNA and DNA hairpin at f = 0
B. Force induced melting
IV. EFFECT OF LOOP ON THE OPENING OF HAIRPIN
V. CONCLUSIONS
Key Topics
- DNA
- 35.0
- Entropy
- 28.0
- Elasticity
- 8.0
- Biochemical reactions
- 6.0
- Elasticity theory
- 6.0
Figures
The schematic representations of the ssDNA which can form a hairpin consisting of stem (complementary nucleotides at two ends) and a loop (made up of non-complementary bases). The hairpin fluctuates between the close and open state.
The schematic representations of the ssDNA which can form a hairpin consisting of stem (complementary nucleotides at two ends) and a loop (made up of non-complementary bases). The hairpin fluctuates between the close and open state.
The schematic representations of transformation of the ssDNA to (a) the dsDNA, (b) a hairpin consisting of a loop and stem, and (c) the extended state. The loop consists of non-complementary nucleotides of the stem.
The schematic representations of transformation of the ssDNA to (a) the dsDNA, (b) a hairpin consisting of a loop and stem, and (c) the extended state. The loop consists of non-complementary nucleotides of the stem.
Variation of normalized extension(open square) and specific heat (C) (filled circle) with temperature. Solid line corresponds to the sigmoidal fit. (a) for DNA hairpin case (b) for dsDNA case.
Variation of normalized extension(open square) and specific heat (C) (filled circle) with temperature. Solid line corresponds to the sigmoidal fit. (a) for DNA hairpin case (b) for dsDNA case.
(a) f − T diagrams for a DNA hairpin obtained from LD simulations with and without the bending energy term. The arrow indicates the change in the slope which vanishes for k _{θ} = 20; (b) f − T diagrams for the dsDNA using LD simulations. The force-temperature diagram is also compared with the FJC and the mFJC models in the reduced unit. Our results are in good agreement with the FJC and the mFJC. The deviation at high force is because of the elastic energy, which is included in the mFJC; (c) and (d) The force-temperature diagrams for the DNA hairpin and the dsDNA using lattice model, which are qualitatively similar to each other. Clear differences between simulation and lattice model are visible at intermediate and high force regime of the force-temperature diagram.
(a) f − T diagrams for a DNA hairpin obtained from LD simulations with and without the bending energy term. The arrow indicates the change in the slope which vanishes for k _{θ} = 20; (b) f − T diagrams for the dsDNA using LD simulations. The force-temperature diagram is also compared with the FJC and the mFJC models in the reduced unit. Our results are in good agreement with the FJC and the mFJC. The deviation at high force is because of the elastic energy, which is included in the mFJC; (c) and (d) The force-temperature diagrams for the DNA hairpin and the dsDNA using lattice model, which are qualitatively similar to each other. Clear differences between simulation and lattice model are visible at intermediate and high force regime of the force-temperature diagram.
Temperature-extension curves at different values of the force.
Temperature-extension curves at different values of the force.
Variation of extension (up to contour length) with f at T > 0.15. The path retraces and there is no signature of hysteresis; (b) same as (a), but at T < 0.15. Path does not retrace with decreasing f and a force is required to re-zip, which is a signature of hysteresis (dotted and dotted-dashed line) .
Variation of extension (up to contour length) with f at T > 0.15. The path retraces and there is no signature of hysteresis; (b) same as (a), but at T < 0.15. Path does not retrace with decreasing f and a force is required to re-zip, which is a signature of hysteresis (dotted and dotted-dashed line) .
Variation of the applied force with loop length at high and low temperatures.
Variation of the applied force with loop length at high and low temperatures.
(a) Comparison of the probability of opening (P _{ o }) of the stem-end (solid line) and the loop-end (dotted line) with the force for different temperatures. Near the transition point (Fig. 4(a)), the probability of opening is higher for the loop-end; (b) The two probabilities are comparable, and hence, the hairpin can open from both sides; (c) It reflects that opening is always from the stem-end side.
(a) Comparison of the probability of opening (P _{ o }) of the stem-end (solid line) and the loop-end (dotted line) with the force for different temperatures. Near the transition point (Fig. 4(a)), the probability of opening is higher for the loop-end; (b) The two probabilities are comparable, and hence, the hairpin can open from both sides; (c) It reflects that opening is always from the stem-end side.
Tables
Native matrix elements (A _{ i, j }) of Eq. (1) for two conformational possibilities: a dsDNA and a DNA hairpin.
Native matrix elements (A _{ i, j }) of Eq. (1) for two conformational possibilities: a dsDNA and a DNA hairpin.
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