## 4 Discussion  
In this paper we propose an improved algorithm for identifying the underlying kinetic model that best describes the folding of an RNA molecule from -OH footprinting data. This new algorithm yields dramatic improvements in performance allowing us to tackle even the largest of RNA molecules. We achieved this significant improvement in efficiency by developing novel criteria for testing whether a particular kinetic model (in the form of a matrix **P**, Equation 8) produces curves that drop below zero. Since a majority of **P** matrices produce physically non-realistic state curves, we can eliminate most models without having to perform the computationally expensive non-linear least-squares optimization to determine **K**. These improvements have allowed us to test 15 three intermediate systems, and establish that in a majority of cases, it is possible to identify a single, non-degenerate kinetic model from -OH time-progress curves. Furthermore, we were able to show that the method remains robust to experimental noise, as we were able to reproduce a previously published kinetic model (Figure 4). Finally, we were able to apply our approach to very large systems (with four and five intermediates) and we determined that this approach will work and remain computationally tractable in these cases. Eliminating the need for a distributed computing solution to determine the underlying kinetic model from -OH footprinting data for medium sized systems will greatly reduce the barrier for experimental labsto performing detailed computational kinetic analysis. Fundamentally, our method offers an automated approach to determining the kinetic parameters of an RNA folding reaction, allowing an experimentalist to effectively test all possible models against their data. The kinetic model defines the identity and ultimately the structure of kinetic folding intermediates. Time-progress curves correspond to specific subdomains of the RNA (Figure 1) and intermediates are often composed of several of these domains (e.g. \(I2\) in the L-21 _T. thermophila_ is composed of the red and green curves, corresponding to the P4P6 and peripheral elements of the RNA). The structure of the \(I2\) intermediate has both the peripheral and P4P6 subdomains formed (third column, Equation 8), while the catalytic core (blue in Figure 1) is unstructured. Furthermore, once the kinetic model is known, we can compute the relative flux through the different pathways to determine the dominant folding mechanism. In the case of the L-21 _T. thermophila_ group I intron we determined that three major pathways dominate the flux (U\(\rightarrow\)I1\(\rightarrow\)F, U\(\rightarrow\)I2\(\rightarrow\)F and U\(\rightarrow\)I1\(\rightarrow\)I2\(\rightarrow\)F) [9]. Analysis of the folding of this molecule under multiple counter-ion conditions, established the relative contributions of electrostatic shielding and initial conditions on flux repartitioning in RNA folding [8]. With our new algorithm, the analysis we performed in these two papers is now feasible on a desktop computer. Our approach still tests all **P** matrices against the experimental data and this provides an equivalent level of confidence in the result as our previous implementation. It however does this in a far more computationally efficient manner. Our analysis of larger systems with up to five intermediates shows that our approach will scale and remain tractable even for the largest experimentally known systems. These results also illustrate one fundamental limitation of the approach, in that it is likely that for these large systems, it will not always be possible to identify a single combination of **P** and **K** that fits the data better than all others. This suggests that the information content of the data is not sufficient, and that other sources of data will be required. In the case of Ribosomal assembly, methods like Pulse-Chase Mass Spectrometry [4] reveal the protein's perspective on the RNA folding reaction and can provide the additional kinetic information to identify a single model.