Allosteric Regulation of Glycogen Phosphorylase by Order/Disorder Transition of the 250′ and 280s Loops

Allostery is a fundamental mechanism of protein activation, yet the precise dynamic changes that underlie functional regulation of allosteric enzymes, such as glycogen phosphorylase (GlyP), remain poorly understood. Despite being the first allosteric enzyme described, its structural regulation is still a challenging problem: the key regulatory loops of the GlyP active site (250′ and 280s) are weakly stable and often missing density or have large b-factors in structural models. This led to the longstanding hypothesis that GlyP regulation is achieved through gating of the active site by (dis)order transitions, as first proposed by Barford and Johnson. However, testing this requires a quantitative measurement of weakly stable local structure which, to date, has been technically challenging in such a large protein. Hydrogen–deuterium-exchange mass spectrometry (HDX-MS) is a powerful tool for studying protein dynamics, and millisecond HDX-MS has the ability to measure site-localized stability differences in weakly stable structures, making it particularly valuable for investigating allosteric regulation in GlyP. Here, we used millisecond HDX-MS to measure the local structural perturbations of glycogen phosphorylase b (GlyPb), the phosphorylated active form (GlyPa), and the inhibited glucose-6 phosphate complex (GlyPb:G6P) at near-amino acid resolution. Our results support the Barford and Johnson hypothesis for GlyP regulation by providing insight into the dynamic changes of the key regulatory loops.

Data analysis. Subsequent data filtering, fitting, normalization, and protection factors calculation was done using in-house programs in MatLab (MathWorks).
Kinetic analysis. An in-house Matlab code was developed for automatic calculation of the segment averaged protection factors (Pf) as a measure of the reduced exchange brought by the structure of the protein. The code involves three steps: generating intrinsic uptake curves, fitting them into one-or two stretched exponentials, and plotting and fitting the experimental uptake curves in the same manner. Firstly, the intrinsic chemical amide exchange rates were calculated and simulated for each peptide according to equation 1 as demonstrated previously by Bai et all and adapted from the excel sheet provided by Englander lab (available online here http://hx2.med.upenn.edu/).
Where n is the number of residues in each peptide, k int is the intrinsic rate constant of chemical exchange for each residue and t is the labeling time. This equation uses the sum of exponentials for each amide in a peptide to provide the degree of deuterium incorporation as a function of a labeling time. At the N-terminus of the peptide the first amide becomes a primary amine after proteolysis, thus the first residue back-exchanges quickly during the LC-MS analysis. As a result, index n starts from the second residue onwards. Proline does not contain an amide hydrogen, and so its rate constant will always be zero. We adapted all the calculations from the excel spreadsheet available on W. Englander's website. From these we generated and simulated the uptake curves for each peptide, at the experimental pH and temperature 1, 2 .
The exchange kinetics were quantified as it was described previously, where the theoretical and experimental deuterium uptake were fit to a single-or double-stretched exponential function.
Where D(t) is the deuterium uptake as a function of the labelling time t, Q is the number of exchangeable amides, k represents the segment-averaged exchange constant, and β is an exponential stretching factor that accounts for the distribution of the exchange rates of the individual amides. The stretched exponential function is used when fitting the H/D kinetics, as it requires less adjustable parameters than the commonly used multiexponential one. To confirm the suitability and aptness of the stretched exponential models, we performed an F-test on the one-and two-stretched exponential models. If the more complicated (two-stretched exponential) model is correct, then the relative increase in the sum-of-squares would be greater than the relative degrees of freedom (F >1, p < .0005). Thus, only when it is statistically necessary the two-stretched exponential model will be selected. Figure S1. Flow chart of the step-by-step explanation of the in-house Matlab code developed for automatic calculation of the segment averaged protection factors (Pf).The experimental uptake curves were then fitted in the same manner as the intrinsic curves, where the starting points for the amplitudes Q1 and Q2 were restricted to be half of the previously determined Q1 and Q2 from the intrinsic fits. Also, it was necessary to add arbitrary maximum uptake data at extremely long time points to aid the fits. This facilitated the correct fit particularly for the protected regions of the protein that are exchanging predominantly slow. If the double-stretched exponential model was correct the corresponding k was calculated as an average and used for calculating protection factors.
The experimental data was afterwards filtered, thus only the peptides showing significant differences were considered 3 . Then, a t-test was performed for each time point for each peptide, between two selected states. Only when (3) or more time points showed significant difference the peptide would be accepted for further data analysis, as explained in Figure S1. The segment averaged protection factors can be then estimated by using the ratio of the intrinsic exchange rate constant (k int ) to the measured (experimental) rate constant (k exp ).

Equation S4
Where Pf = protection factor against hydrogen exchange, k int = intrinsic amide hydrogen exchange rate constant from published values 2 , k exp = fitted exchange rate constant for back-exchange corrected experimental data using Equation S2 or Equation S3.
An upper limit for the obtainable Pf had to be set, and for this data set it was determined to be 10. After analyzing the data set, 3 average peptides, with various averaged k int were chosen. The intrinsic deuterium incorporation was simulated after fitting the data acquired from the excel sheet by Bai et all according to Equation S5. Different curves were simulated with increasing Pf, Figure S2A. Only the data points corresponding to the experimental data collected in the GlyP data set were extracted, then fitted with the previously explained method (Equation S2), Figure S2B.
Where D(t) is the deuterium uptake as a function of the labelling time t, Q is the number of exchangeable amides,

S4
k represents the segment-averaged intrinsic exchange constant, β is an exponential stretching factor and Pf is idealistic protection factor ranging from 0 to 10 6 . The R 2 of all the fits using only time points equivalent to the GlyP experimental data set were plotted against the Pf (Figure 2C), and the upper limit for the obtainable Pf was determined as an average from 3 peptides with R 2 corresponding to 0.95. Figure

Equation S6
Where R = gas constant (kcal/K/mol), T = temperature (K) and Pf = protection factor from Equation S4.  GlyP:G-6-P complex in T-state (bottom). Back-exchange correction and statistical filtering were performed for the coverage map generation, made with in-house developed Matlab code for automatic calculation of protection factors. Secondary structure assignments from 1GPB.pdb are shown above. Note that these may not be precisely located where the x-axis is for assigned peptides, not linear amino acid sequence. Figure S5. Difference maps. The deuterium uptake data from GlyPa was subtracted from the data for GlyPb in order to create the deuterium uptake difference plot. Relative protection leads to a more positive value (bar on upper side); deprotection (e.g. from an exposed domain interface) results in a more negative value (bar on bottom side) (top). The deuterium uptake data from GlyPb:G6P was subtracted from the data for GlyPb in order to create the deuterium uptake difference plot. Relative protection leads to a more positive value (bar on upper side); deprotection (e.g. from an exposed domain interface) results in a more negative value (bar on bottom side) (top). Grey shaded region on Figure 4B denotes global significant difference as explained previously 3 . Figure S6. Difference in protection factors between GlyP in active R-state and apo T-state (top) and between inactive inhibitor-bound state and apo T-state (bottom). Each bar under the sequence number represents a peptide fragment monitored during the labeling experiments. Peptides colored according to the measured protection factors, where more positive value indicates more protection against hydrogen-exchange in apo GlyP. Regions of interest with coherent HDX difference are highlighted in shaded boxes. Secondary structure assignments from 1GPB.pdb are shown above. Note that these may not be precisely located where the x-axis is for assigned peptides, not linear amino acid sequence. Figure S7. Heat maps of the difference in HDX labeling between different states: active pSer14-GlyPa minus apo (top) and GlyP:G6P minus apo (bottom). The relative deuteration level summed up at each subsequent time point per peptide is color coded shown on the scale below; note different normalisation. Secondary structure assignments from 1GPB.pdb are shown above. Note that these may not be precisely located where the x-axis is for assigned peptides, not linear amino acid sequence. Figure S8. Protection factors calculated per peptide and plotted per amino acid (from mean average of overlapping peptide segments) for GlyP in three states: apo T GlyP (top), pSer14 GlyP (middle) and GlyP:G6P inactive complex (bottom). Values calculated from fitted exchange rate constants using Equation S4. Regions of interest with coherent HDX difference are highlighted in shaded boxes. Secondary structure assignments from 1GPB.pdb are shown above. Data shown is unfiltered per significance. Figure S9. Estimates of the Gibbs free energy of stability ΔG ex (HDX) calculated per peptide and plotted per amino acid (from mean average of overlapping peptide segments) in GlyP in three states: apo T-state (top), pSer14 GlyPa (middle) and GlyP:G6P inactive complex (bottom). Values calculated from fitted exchange rate constants using Equation S6. 2 kcal/mol/peptide is the upper limit of quantitation, given the very slow HDX rates of strongly protected amide protons. Regions of interest with coherent HDX difference are highlighted in shaded boxes. Secondary structure assignments from 1GPB.pdb are shown above. Data shown is unfiltered per significance.   Figure S13. HDX analysis of GlyP per peptide. Back exchange corrected data for three protein states shown (red -apo GlyPb; yellow -G6P-bound inhibited GlyPb; blue -pSer14 activated GlyPa) against theoretical intrinsic exchange rates, calculated from [1]. Peptide sequence given above the plot, amino acid number in top-left. Yaxis shows absolute % deuteration at labeling time (s) on X-axis (labels omitted for space).

S23
Table S1 Fitting parameters to multi-phase stretched exponential for hydrogen/deuterium-exchange mass spectrometry of GlyP in apo, activated and inactivated enzyme. Significantly different peptides at 3 time points are shown in the GlyPa vs GlyPb and GlyPb vs GlyP:G6P columns as red asterisk.