At this point, we want to compare the CUR size distributions obtained from the unzipping experiments with the ones obtained with the toy model. The goal is to see if the toy model is capable of reproducing the statistical properties of the unzipping mechanism, search the causes of the differences and use the model to determine the best experimental conditions to extract information from the DNA unzipping.
How much can the toy model predict the experimental results? The experimentally obtained CUR size distributions for both molecular constructs are shown in red in Fig. 4.14. The fit of these distributions to Eq. 4.10 are also shown in green in Fig. 4.14. Considering pNm (equal to the stiffness of the trap that we can measure independently) and nm (interphosphate distance for ssDNA), the parameters that best fit the experimental histograms for the 2.2 kbp sequence and their corresponding toy model parameters are
However, there are two clear differences between the experimental and the predicted CUR size distributions. First, the experimental size distributions are not smooth but have a rough shape. We already know that this is a finite size effect described in Sec. 4.2.5. The distribution is smoother for the 6.8 kbp sequence because the sequence is longer, there is more statistics and the resulting CUR size distribution is better averaged. The second difference is that the toy model predicts a large fraction of CURs of size smaller than 10 bp that are not experimentally observed. There might be two explanations to this: 1) the toy model predicts small CURs that experimentally do not exist or 2) the method to detect metastable states is not capable of discriminating CURs smaller than 10 bps.
To better understand this, we can compute the CUR size distributions (depicted in blue in Fig. 4.14) with the mesoscopic model described in Sec. 3.4.1. Again, we find that the model predicts much more small CURs than we experimentally observe. Assuming that the model is correct, we conclude that the small CURs occur but the method of analysis has a limiting resolution of about 10 bp. In other words, for every large CUR detected experimentally, the model predicts two (or more) small distributions. This limitation is due to the fact that the Bayesian analysis (Sec. 4.1) is not capable of distinguishing between force fluctuations and transitions between metastable states separated by less than 10 bp. A priori, it should be possible to do the pulling experiments at lower pulling rates and collect much more statistics. This would permit to have a better signal-to-noise ratio and discriminate the smaller metastable states. However, these experiments are much more difficult to carry out because the DNA molecule spends more time stretched and it breaks much more frequently before a whole pulling cycle can be completed.
Apart from these previous considerations, there is another issue that affects the discrimination of nearby metastable states. A quick look at Fig. 4.7 shows that histograms become smoother (i.e., the peaks are less sharp) as the molecule is progressively unzipped. The increased compliance of the molecular setup as ssDNA is released markedly decreases the resolution in discriminating intermediates (see the last paragraph of section 4.1.2 for a detailed explanation of this effect). In particular, for the 6.8 kbp construct we find that along the first 1500 bp of the hairpin only 30% of the total number of CURs smaller than 10 bp are detected, whereas beyond that limit no CUR smaller than that size is detected. If the threshold size
is defined as the size of the CUR above which of the predicted CUR are experimentally detected we find that
increases linearly with the number of open bps, establishing a limit around 10 bp for the smallest CUR size that we can detect (Fig. 4.14b, inset).
Now let us focus on the other side of the distribution (large CUR sizes). The three CUR size distributions in Fig. 4.14 are long tailed distributions, which indicate that large CURs occur with finite probability. Unfortunately, large sized CUR hinder their internal DNA sequence, limiting the possibility of unzipping one base-pair at a time, which would permit to sequence the DNA. Under what experimental conditions is it possible to break up large sized CUR into individual bps? Only by applying local force on the opening fork (thereby avoiding the large compliance of the molecular setup) and by increasing the stiffness of the probe might be possible to shrink CUR size distributions down to a single base-pair . Figs. 4.15a, 4.15b show how the CUR size distributions shrink and the largest CUR size decreases as the stiffness increases. Its value should be around 50-100 pNnm for all CUR sizes to collapse into a single bp. Remarkably enough this number is close to the stiffness value expected for an individual DNA nucleotide stretched at the unzipping force. Any probe more rigid than that will not do better.
Similarly to the problem of atomic friction we can define a parameter (defined as the ratio between the rigidities of substrate and cantilever) that controls the transition from stick-slip to continuous motion . For DNA unzipping we have
JM Huguet 2014-02-12