De310(apo), de312(apo) and E308A(apo).Figure 2. Chemical shift projection analysis (CHESPA) using mutations as perturbations. a) Schematic of CHESPA. Open circles indicate HSQC peaks of the apo forms, whereas the filled circle represents the holo form (cAMP bound) HSQC peak. The green open circle represents the apo-mutant. The compounded chemical shift between the Wt(apo) and Wt(holo) was computed as the magnitude of the vector B, |B|. Similarly the compounded chemical shift between the Wt(apo) and Mutant(apo) was calculated as |A|. The magnitude of vectors A and B define the radii of the dashed circles centered on the Wt(apo) peak (b) Representative regions of the [inhibitor 15N-1H] HSQC spectra of Wt(apo) (grey) and cAMP-bound, Wt(holo) (black) overlaid with the [15N-1H] HSQC spectra of apo-Mutants: de312 (red), de310 (blue), de305 (green). Arrows indicate the direction of shift toward activation and dashed contour lines enclose peaks of the same residues. doi:10.1371/journal.pone.0048707.gSingular Value Decomposition (SVD) Analysis of Deletion MutantsThe SVD analysis is based on previously published protocols [26], which were adapted and extended here for the application to deletion mutants. Specifically, a matrix M containing the combined chemical shifts for each assigned residue was first generated for five selected states: apo-Wt, cAMP-bound Wt, SpcAMPS-bound Wt, Rp-cAMPS-bound Wt and a 5th state that consisted of one of the deletion mutants in the apo form (i.e. de312, de310 or de310) or the inhibitor apo-L273W. The combined chemical shifts (dNH) were calculated as dNH = 0.2dN + dH, where dN and dH are the individual chemical shift (ppm) values of the backbone 15N and 1 H nuclei [26,39]. Only residues for which the frequency spread across all five states was greater than 5 and 10 Hz for the individual 1H and 15N 
23977191 nuclei, respectively, were considered. A matrix M’ was then subsequently generated 
from M in which the Rp-cAMPS-bound Wt state was used as reference for the remaining four states. Specifically, the columns of the M’ matrix were: Wt(apo) t(Rp-cAMPS), Wt(cAMP) t(Rp-cAMPS), Wt(Sp-cAMPS) t(Rp-cAMPS) and a 4th state with a deletion mutant or L273W in the apo form measured relative to Wt(RpcAMPS) (i.e. de312(apo) t(Rp-cAMPS), de310(apo) t(RpcAMPS), de305(apo) t(Rp-cAMPS) or L273W(apo) t(RpcAMPS)). The matrix 23727046 M’ was then column mean centered and factorized through SVD as previously explained [26]. The first two principal components (PCs) resulting from the SVD analyses performed here account for .93 of the total variance (Table 1) and therefore the other PCs were deemed negligible and discarded.quantum coherence (HSQC) were recorded for a total of 8 scans per t1 point. The number of digitized complex points were 256 and 1024 for the 15N and 1H dimensions, respectively, with an inter-scan delay of 1 sec. Carrier frequencies of the 15N and 1H channels were centered on water and the backbone amide region, respectively. All spectra were processed using NMRPipe [36] with linear prediction and a resolution-enhancing 60u shifted squared sine bell window function for HSQC spectra. Cross-peaks were assigned and integrated using Gaussian line-fitting in SPARKY [37]. Assignments were obtained using triple-resonance experiments [21,38]. All samples were referenced using the internal referencing compound 15N-Ac-Glycine.Chemical Shift Projection Analysis (CHESPA)The projection analysis descriptors, i.e. the cos H values, the fractional activations X and the co.De310(apo), de312(apo) and E308A(apo).Figure 2. Chemical shift projection analysis (CHESPA) using mutations as perturbations. a) Schematic of CHESPA. Open circles indicate HSQC peaks of the apo forms, whereas the filled circle represents the holo form (cAMP bound) HSQC peak. The green open circle represents the apo-mutant. The compounded chemical shift between the Wt(apo) and Wt(holo) was computed as the magnitude of the vector B, |B|. Similarly the compounded chemical shift between the Wt(apo) and Mutant(apo) was calculated as |A|. The magnitude of vectors A and B define the radii of the dashed circles centered on the Wt(apo) peak (b) Representative regions of the [15N-1H] HSQC spectra of Wt(apo) (grey) and cAMP-bound, Wt(holo) (black) overlaid with the [15N-1H] HSQC spectra of apo-Mutants: de312 (red), de310 (blue), de305 (green). Arrows indicate the direction of shift toward activation and dashed contour lines enclose peaks of the same residues. doi:10.1371/journal.pone.0048707.gSingular Value Decomposition (SVD) Analysis of Deletion MutantsThe SVD analysis is based on previously published protocols [26], which were adapted and extended here for the application to deletion mutants. Specifically, a matrix M containing the combined chemical shifts for each assigned residue was first generated for five selected states: apo-Wt, cAMP-bound Wt, SpcAMPS-bound Wt, Rp-cAMPS-bound Wt and a 5th state that consisted of one of the deletion mutants in the apo form (i.e. de312, de310 or de310) or the apo-L273W. The combined chemical shifts (dNH) were calculated as dNH = 0.2dN + dH, where dN and dH are the individual chemical shift (ppm) values of the backbone 15N and 1 H nuclei [26,39]. Only residues for which the frequency spread across all five states was greater than 5 and 10 Hz for the individual 1H and 15N 23977191 nuclei, respectively, were considered. A matrix M’ was then subsequently generated from M in which the Rp-cAMPS-bound Wt state was used as reference for the remaining four states. Specifically, the columns of the M’ matrix were: Wt(apo) t(Rp-cAMPS), Wt(cAMP) t(Rp-cAMPS), Wt(Sp-cAMPS) t(Rp-cAMPS) and a 4th state with a deletion mutant or L273W in the apo form measured relative to Wt(RpcAMPS) (i.e. de312(apo) t(Rp-cAMPS), de310(apo) t(RpcAMPS), de305(apo) t(Rp-cAMPS) or L273W(apo) t(RpcAMPS)). The matrix 23727046 M’ was then column mean centered and factorized through SVD as previously explained [26]. The first two principal components (PCs) resulting from the SVD analyses performed here account for .93 of the total variance (Table 1) and therefore the other PCs were deemed negligible and discarded.quantum coherence (HSQC) were recorded for a total of 8 scans per t1 point. The number of digitized complex points were 256 and 1024 for the 15N and 1H dimensions, respectively, with an inter-scan delay of 1 sec. Carrier frequencies of the 15N and 1H channels were centered on water and the backbone amide region, respectively. All spectra were processed using NMRPipe [36] with linear prediction and a resolution-enhancing 60u shifted squared sine bell window function for HSQC spectra. Cross-peaks were assigned and integrated using Gaussian line-fitting in SPARKY [37]. Assignments were obtained using triple-resonance experiments [21,38]. All samples were referenced using the internal referencing compound 15N-Ac-Glycine.Chemical Shift Projection Analysis (CHESPA)The projection analysis descriptors, i.e. the cos H values, the fractional activations X and the co.
