## 3 Validation and Results  
### Experimentally Acquired \(\cdot\)OH Data  
Time-resolved \(\cdot\)OH radical footprinting data measures the nucleotide solvent accessibility of the RNA molecule [22]. This technique can be done at multiple times during the folding process resulting in time-progress curves such as those illustrated in Figure 1 where the fraction folded is zero at \(t=0\), and one when \(t=\infty\)[18; 19]. The noise in the data is mostly a result of the subsequent analysis of the fragmentation reaction using electrophoretic separation [13; 23]. The progress curves we analyze are averaged over multiple nucleotides, which has a smoothing effect on the data, but nonetheless still results in some jaggedness, as illustrated in Figure 4A. Figure 4: Illustration of current algorithm when applied to actual experimentally obtained \(\cdot\)OH footprinting data; curve colors are consistent with Figure 1. A) Time-progress curves with experimental noise. B) Resulting state curves \(\vec{x}(t)\) determined by applying Equation 9 to the raw data and only selecting the **P** matrices that satisfy the AUC criteria. C) Optimized fit using non-linear least squares minimization of **K** of state curves. D) **K** matrices obtained using the old and new approaches to determining **P** and **K**, which yield identical results within error. Error on the rate values vary between 5 and 20%. To determine if we can still identify a single set of state curves \(\vec{x}(t)\) from this data, we performed the same analysis as that described above. When we apply Equation 9 for all **P** to the data, again a majority of the resulting \(\vec{x}(t)\) curves dip below zero. However, because of the noise in the data, even the correct state curves have a small negative component. If we define the criteria that up to 10% of the area under the curve (AUC) can be negative before we eliminate the corresponding **P** matrix as a potential model, then we identify a single set of unique state curves (Figure 4B). If we now optimize **K** using non-linear least square regression on the resulting \(\vec{x}(t)\), we are able to fit these data accurately (Figure 4C). Furthermore, the values we obtain for **K** (Figure 4D) are equivalent within error to those obtained using the original Kinfold [9] algorithm. Adjusting the AUC criteria allows us to fine tune the sensitivity of our approach. In this particular example, we chose 10% as this correctly identified the set of state curves corresponding to the folding model. Had we chosen a less stringent criteria, such as 50% negative AUC, we would have identified additional models (**P** matrices) that require testing using non-linear optimization of the **K** matrix. In essence, raising the AUC criteria results in having to test more models with least-squares optimization, and thus makes the problem more computationally intensive. When using our approach with a novel data set, an AUC criteria can be picked such that a minimal number of models need to be tested. In practice however, it will generally be more desirable to test several models to evaluate the significance in the difference in root mean square error (RMSE) of the fit. The AUC criteria allows users of the algorithm to balance computational cost and desire to comprehensively test all models with the number of models that pass the AUC criteria is highly dependent on the experimental data. As we move beyond two intermediate systems to larger and more complex molecules, one question that remains is the true information content of a series of \(\vec{C_{E}}(t)\), and whether we can always resolve a single kinetic model from them. Independent of the noise in the data, we now aim to better understand if a unique model can always be found from experimental curves(\(\vec{C_{E}}(t)\)), or if there are cases where there are degenerate models that fit the data with equivalent RMSE.