Folding and unfolding of a triple-branch DNA molecule with four conformational states

Abstract

Single-molecule experiments provide new insights into biological processes hitherto not accessible by measurements performed on bulk systems. We report on a study of the kinetics of a triple-branch DNA molecule with four conformational states by pulling experiments with optical tweezers and theoretical modelling. Three distinct force rips associated with different transitions between the conformational states are observed in the folding and unfolding trajectories. By applying transition rate theory to a free energy model of the molecule, probability distributions for the first rupture forces of the different transitions are calculated. Good agreement of the theoretical predictions with the experimental findings is achieved. Furthermore, due to our specific design of the molecule, we found a useful method to identify permanently frayed molecules by estimating the number of opened base-pairs from the measured force jump values.

Keywords:

• biophysics
• statistical physics
• biomolecules

Acknowledgements

S.E. thanks the Deutscher Akademischer Austauschdienst (DAAD) for providing financial support (FREE MOVER and PROMOS) for stays at the Small Biosystems Lab in Barcelona where the experiments were performed. A.A. is supported by grant AP2007-00995. F.R. is supported by the grants FIS2007-3454, Icrea Academia 2008 and HFSP (RGP55-2008).

Notes

Notes

1. In our experiments we measure the relative distance between trap and pipette, X, rather than the absolute value. The force f exerted on the molecular construct leads to a displacement f/k _b of the bead in the optical trap, where k _b = 0.08 pN/nm is the rigidity of the trap. Hence, the relative distance X is related to the relative molecular extension x _m (see Figure 2) by x _m = X − f/k _b.

2. Due to this simplification, the Δn ₁ of the first rip is likely to be slightly underestimated and the second rip's Δn ₂ overestimated. However, it will not affect the change in the total number Δn _tot of opened bps since we consider the change of x(n, f), and the contributions will cancel each other out.

3. We note that the checking of the change in the number of opened bps can be, in principle, also applied to non-permanent, reversible molecular fraying.

4. In previous publications of some of the authors, this contour length was denoted by l _n,α to emphasise the dependence on n (and, in addition, α here). This dependence is caused by the change of the contour length in the transitions. For easier reading we do not give it explicitly in the following. Further details about the contour length were already discussed in Section 4.