Dynamical modelling of molecular constructions and setups for DNA unzipping

Over the past fifteen years various single molecule experiments have investigated DNA mechanical and structural properties [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], and protein-DNA interactions [19,20,21,22,23,24,25,26,27,28,29]. These experiments provide dynamical information usually hidden in large scale bulk experiments, such as fluctuations on the scale of the individual molecule. The separation of the two strands of a DNA molecule under a mechanical stress, usually referred to as unzipping, has first been carried out by Bockelmann and Heslot in 1997 [8]. The strands are pulled apart at a constant velocity while the force necessary to the opening is measured. The average opening force for the λ phage sequence is of about 15 pN (at room temperature and standard ionic conditions), with fluctuations around this value that depend on the particular sequence content. Bockelmann, Heslot and collaborators have shown that the force signal is correlated to the average sequence on the scale of ten base-pairs but could be affected by the mutation of one base-pair adequately located along the sequence [10]. Liphart et al. and [15] and Danilowicz et al. [16,17,18] have performed an analogous experiment, using a constant force setup, on a short RNA and a long DNA molecules respectively (Figure 1B). The distance between the two strands extremities is measured as a function of the time while the molecule is submitted to a constant force. DNA strands separation has been also studied in single molecule experiments by translocation through nanopores [26,27]. The motivation underlying unzipping experiments of DNA is (at least) two-fold. First the study of unzipping aims at a better understanding of the mechanisms governing the opening of DNA during transcription and replication by proteins such as Polymerases, Helicases, and Exonucleases [20,21,28,29]. Simple theoretical models describing the opening as an unidimensional random walk on a sequence-dependent free energy landscape have been proved to describe quite well several experimental effect such as stick-slip motion in the opening at constant velocity [9,10], the long pauses at fixed position of unzipping at constant forces [16,30,31], the hopping dynamics between two or more states in unzipping at critical forces of short DNA molecules [15,31,32,33], and torsional drag effects in unzipping at large velocity [11,34]. Moreover statistical mechanical analysis have been successfully applied to extract from experimental data the sequence-dependent free energy landscape and the height of free energy barriers [35,36].

Secondly unzipping experiments could potentially be useful to extract information on the sequence itself [37]. Recently single molecule sequencing has been achieved by monitoring a DNA/RNA polymerase in the course of DNA synthesis from a ssDNA template [33,38]; such single molecule sequencing could become competitive with standard DNA sequencing because they do not require, a priori, amplification through polymerase chain reactions. A fundamental question on the possibility of extracting information on the sequence from unzipping experiments is the influence of the experimental setup on the measures and the limitations imposed by the latter [37,39]. Indeed characteristic spatio-temporal limitations are the finite rates of data acquisition, the relaxation time of the bead, the limited spatial resolution, the thermal drift, and more generally the noise in the instruments. Moreover the dynamics of the opening fork (Figure 1) is influenced by the single strands (open parts) of the molecule and the linkers, and cannot be deduced directly from the observation of the bead from which the force or the position are measured.

The accuracy of unzipping experiments at fixed velocity have improved a lot over the last decade. Initially performed with an optical fiber [8], experiments were then based on the use of simple optical traps [10]. Nowadays double optical traps [13,36] allow to reduce considerably the drift of the setup and to achieve a temporal resolution of the order of 10 KHz, a sub-nanometric spatial resolution, and a precision on measured forces of the order of fraction of pN. Unzipping at fixed force has been performed by a magnetic trap with a low temporal resolution (from 60 Hz to 200 Hz) due to the time needed to extract the position of the bead, the spatial precision being of the order of 10 nm/ √ Hz) [28,29], or by an optical trap also with a low temporal resolution (about 10 Hz) imposed by a feedback mechanism needed to keep the force constant [15]. Recently a new dumbbell dual optical trap has been developed. It operates without feedback and can maintain the force constant over distances of about 50 nm [33] with temporal resolution of 10 kHz and a spatial resolution of 0.1 nm/ √ Hz.

Limitations due to the experimental systems were first addressed in [39]. This paper stated the impossibility to infer the sequence due to ssDNA fluctuations: fluctuat

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