 the Supporting Material), and if R > 1.5 Å, the residue was classed as buried. We emphasize that the results of this mobility-based analysis depend indirectly on the results of the rigidity analysis; FIRST identifies a constraint network and FRODA then explores the motion that is possible within those constraints. Therefore, it is possible for a residue to be 1) rigid but exposed, thus lying in FIR or FIR B but not in FRO; or 2) nonrigid but well protected by burial within the protein, thus lying in FRO but not in FIR or FIR B. This suggests that to predict the results of the HDX folding core, which depend upon surface exposure as well as dynamics (inherited from flexibility), a combination of the approaches employed by FIRST and FRODA may be necessary. FþF is simply the intersection of residues in FIR and FRO.
In Fig. 4, each of the five theoretical folding cores is compared with the HDX folding core for the CypA-CsA complex. In each case, folding-core residues along the protein backbone are shown as bold blocks of color.
We find that SeS consists almost entirely of slowly exchanging amino acids, although there are also many 10 20 40  50  30  70  80  60  90  100 110 120 130  140 150 160   10  20  40  50  30  70  80  60  90  100 110 120 130  140 150 160 HDX FIRST a b FIGURE 3 The HDX folding cores (blue) are given along with the FIRST folding cores (red) for the CypA-CsA complex (a) and unbound CypA (b). The residue numbers along the protein backbone are indicated above each section, with thin vertical lines added every 10 residues for clarity.
Only the residues that are part of the folding cores are colored. To see this figure in color, go online. Comparison of the experimentally determined HDX folding core for CypA-CsA (blue; shown both above and below the other folding cores), with the five folding cores computed using the theoretical approaches outlined in the text and labeled accordingly (from top to bottom, SeS (yellow), FIR (red), FIR B (orange), FRO (purple), and FþF (pink)). In each case, the folding-core residues in the primary structure of CypA are represented as colored blocks and the nonfolding core residues are white. Residue numbers along the protein backbone are indicated above the table body, with thin black vertical lines added every 10 residues for clarity. To see this figure in color, go online.
Biophysical Journal 108 (7) 1739-1746 Folding Cores in the CypA-CsA Complex slowly exchanging residues that are not part of a secondary structure unit. As expected, FIR B is smaller than FIR, since there are fewer constraints present throughout the rigidity dilution. The surface-exposed residues 12-18 and 41-47 are part of FIR but not part of FIR B. The residues in FRO are also for the most part slowly exchanging. The combined FþF folding core matches the HDX core with high specificity. Fig. 5 presents a graphical comparison between the HDX folding core and FþF on the structure of CypA. We observe that in the absence of the ligand, residues 86-90 are mostly absent from both theoretical and experimental folding cores. The relatively small number of false positives (Fig. 5, red: 10 residues in (a) and 8 in (b)) relative to false negatives (Fig. 5, blue: 36 residues in (a) and 22 in (b)) demonstrate the high ratio of specificity to sensitivity for this method.
We note that some parts of the HDX folding core, for example, residues 86-90, are poorly predicted by all of the methods. This region corresponds to a flexible, surface-exposed, unstructured region in the crystal structure ( Fig. 5 a, arrow). Our methods, based around predicting rigid, buried, and immobile regions, fall short of identifying this area as slowly exchanging. Table 2 shows the number of residues in each theoretical folding core, along with the number of true positives, T. The comparison pictured in Fig. 4 is made quantitative with the specificity, a, sensitivity, g, and enhancement factor, e, as defined in Eqs. 1-3, respectively.

Quantitative analysis of theoretical folding cores
The e values of the five theoretical folding cores, the lowest of which is 1.33 (for the previously established FIRST folding core FIR), demonstrate improvement over random selection. FþF scores highest for both the CypA-CsA complex and the unbound CypA, suggesting that the combined approach has merit. This method is highly specific (a R 0.8 in both cases), although its low g scores show that it does not capture enough of the HDX folding core to suc-cessfully capture the impact of ligand binding on HDX. SeS is highly specific (a R 0.77) and sensitive (g R 0.74), although this method of folding-core selection is clearly inappropriate for predicting changes upon ligand binding, since it does not change. The two folding cores derived solely using FIRST (FIR and FIR B ) do not reflect the experimentally observed increase in folding-core size upon ligand binding. Only when dynamics are also incorporated, i.e., in FRO and FþF, is this qualitative effect reflected.
We have also estimated the variation in a and g in Table 2, assuming a 55% error in N Ex, N Th, and T. The six proline residues in CypA do not appear in the 1 H, 15 N HSQC spectrum due to their lack of an amide proton. For this reason, HDX experiments cannot inform on whether prolines are part of a folding core. We therefore also calculated e with N ¼ 159. The ordering of the theoretical methods remains the same, and coupled with the small variation in a and g, this shows that our quantitative comparison is robust.

CONCLUSIONS
The experimental HDX folding core for the CypA-CsA complex is highly similar to that for the unbound protein, albeit with a small number of additional residues. This small change is consistent with previous observations of only subtle conformational change in CypA upon ligand binding (15,54). The FIRST folding cores differ more substantially. Ligand binding confers rigidity upon the structure but alters the pattern of rigidity loss so that the FIRST folding core in fact decreases in size. In both cases, the FIRST folding core is a reasonable match for the HDX folding core, in agreement with previous folding-core predictions using FIRST (4). The FIRST folding core is defined by the RCD at E fc, a value that decreases upon ligand binding. This means that when the folding cores are compared for the protein before and after ligand removal, we are comparing RCDs at different E cut values. As a result, there may be more FIGURE 5 Cartoon representation of a comparison of HDX folding cores with FþF folding cores for the CypA-CsA complex (a) and unbound CypA (b). In both cases, residues that are part of both folding cores are purple, those found only in the HDX folding core are blue, those in the FþF folding core only are red, and those that are not part of either folding core are red. CsA is colored black in (a). The arrow in (a) indicates residues 86-90. To see this figure in color, go online.
Biophysical Journal 108 (7) 1739-1746 constraints present in the E cut value for the unbound protein than in that for the complex, resulting in the unlikely prediction of a larger folding core in the absence of a ligand. FIRST is a tool that can be implemented rapidly, and this study complements previous studies demonstrating its utility for folding-core prediction (4,8,18,53). Nevertheless, our work also shows that the FIRST-based folding-core predictions are not yet accurate or sensitive enough to capture the impact of ligand binding for CypA. For the purpose of predicting subtle effects of ligand binding, simply analyzing patterns of rigidity, as done through FIRST, appears insufficient. The trade-off between rapid computation on the one hand, as achieved with FIRST, and the necessary accuracy of folding core prediction on the other hand needs to be more finely balanced.
As a way forward, we have introduced and discussed rapid computational methods for adding information on surface exposure and protein dynamics into a rigiditybased folding core definition. These improve markedly upon the FIRST folding core for predicting the HDX folding cores of both CypA-CsA and unliganded CypA. In addition, we show that they are less sensitive to the erroneous increase in folding-core size upon ligand removal observed using FIRST with the standard bond network. On balance, FþF, which combines rigidity and motion, appears to be the best choice for a computational determination of the folding core from a protein's structural information alone. Nevertheless, no method achieves a perfect score of a ¼ g ¼ 1, either for the uncomplexed CypA or for the CypA-CsA complex. This insensitivity to ligand binding is disappointing but unsurprising due to the scale of the challenge, both for CypA-CsA and in general.

SUPPORTING MATERIAL
Supporting Materials and Methods, seven figures, and one table are available at http://www.biophysj.org/biophysj/supplemental/S0006-3495(15) 00182-4.  Values are for CypA-CsA complex (upper) and unbound CypA (lower), with N ¼ 165. Bold numbers indicate the largest selectivity, a, sensitivity, g, and enhancement,˛, for CypA-CsA and unbound CypA. The error estimates