Supplementary Information Overlap between folding and functional energy landscapes for adenylate kinase conformational change by Ulrika Olsson & Magnus Wolf-Watz Contents: 1. Supplementary Note 2. Supplementary Figures S1-S11 3. Supplementary Table S1 4. Supplementary Methods 5. Supplementary References
Supplementary Note It might seem intuitive that the chemical shifts of the mutant AK variants should fall inbetween the chemical shifts of WT AK in open and closed states. However, a detailed consideration of the chemical shifts observed for the various states involved during the ATP binding event show that the chemical shifts of the mutants are not expected to fall in between open/closed states of WT AK. This feature is shown schematically in Supplementary Figure S11. First, the chemical shift change for WT AK in response to ATP binding is considered. WT does not populate the TS to an extent that affects the chemical shifts of either open and closed states. The blue circle representing WT AK in the apo state should be on top of the orange circle (open AK) but is shifted for clarity. When ATP is added the signal will progressively shift towards the closed conformation due to modulation of the open/closed equilibrium. Due to the ATP binding mechanism (i.e open and closed states populated equally at saturation) the signal will only move 50% of the distance expected for a fully closed ATPlid. Second, ATP binding to mutant AK is considered. Residues that have chemical shifts that are sensitive to the local unfolding/folding reaction of α6 and α7 will have a chemical shift shifted towards the TS in the apo state. When ATP is added the signal will progressively move to the closed chemical shift (due to the unity slope in Figure 6). It is clear from the figure that no correlation is expected between substrate free mutant chemical shifts and the chemical shifts of WT AK in open and closed states.
Supplementary Figures Supplementary Figure S1. Circular dichroism spectra (molar ellipticity) of AK e variants. WT AK e (filled circles), M1 (open circles) and M2 (filled triangles). The data are from measurements at 25 C with protein concentrations ranging between 9 11 µm.
Supplementary Figure S2. Isothermal titration calirometry data for binding of Ap5A to WT AK e. The upper panel show the baseline corrected instrumental response. The lower panel show the integrated data (solid squares) and the best fit to a 1:1 binding model (solid line).
Supplementary Figure S3. 1 H- 15 N HSQC spectra of M2 saturated with Ap5A. The experiment was acquired at 25 C and with 4 mm Ap5A.
Supplementary Figure S4. Chemical shift perturbations between WT and M2 AK e in complex with Ap5A at 25 C. Perturbations for non mutated residues were quantified based on combined absolute 15 N and 1 H chemical shift differences between WT and M2 calculated according to δω=0.2* 15 N + 1 H (ppm). The mutated positions (116 and 168) are indicated as red bars.
Supplementary Figure S5. M2 populates a closed state in complex with Ap5A. (a) Correlation between chemical shift perturbations in Ap5A saturated states: M2 vs. WT AK e. Chemical shift perturbations were calculated with respect to the apo states and are normalized according to δω = 0.2 15 N + 1 H (ppm). The best fitted straight line is shown in red and the slope is 0.98 ± 0.03 with an R value of 0.98. In all, 76 residues were used in the analysis. (b) The analysis in (a) is performed for residues 13-24, 23-72, 80-84, 90-98, 179-188 and 202-212, and these residues are colored in gold on the open AK e structure (4AKE.pdb).
Supplementary Figure S6. 1 H- 15 N HSQC spectra of M1 and M2 saturated with ATP. M1 is shown with blue contouring and M2 is contoured orange. The experiments were acquired at 25 C and with 20 mm ATP.
Supplementary Figure S7. Chemical shift perturbations of M1 and WT AK e in response to ATP binding. Perturbations are calculated according to: δω = 0.2 15 N + 1 H. The ATP concentrations in the experiments were 20 mm. (a) M1 (b) WT AK e (data adapted from 46 ).
Supplementary Figure S8. WT and M1 binds to ATP with overlapping binding surfaces. Residues with absolute chemical shift perturbations in ATP saturated states (relative to apo states) larger than 0.4 ppm (see Supplementary Figure S7) are colored red on the open AK e structure (4AKE). (a) M1 (b) WT AK e.
Supplementary Figure S9. Characterization of conformational exchange using chemical shifts. (a) AK e can adopt two forms: open in the absence of substrate (left) and closed when bound to the inhibitor Ap5A 46 (right). An amide proton with different chemical shifts in the open and closed states is indicated as a gray and red sphere, respectively. (b) Hypothetical 1 H- 15 N HSQC spectra highlighting the different chemical shifts for the amide proton in the open and closed states. (c, d) In the ATP saturated state, where AK e is interconverting between open and closed states, the observed chemical shift (ω OBS ) of the amide protein (yellow sphere) will be a population weighted average. The fractions open (p O ) and closed (p C ) states can be quantified from chemical shifts as indicated in the inset.
Supplementary Figure S10. Analysis of open/closed conformational equilibria. A two state conformational exchange process between open and closed states of an enzyme is assumed. Random noise, generating similar χ 2 values as in Figure 6, was added to 20 ideal data points representing equal populations of open and closed states. The observed chemical shift perturbations (δω OS ) are plotted against the open to closed (δω OC ) chemical shifts (filled circles). The red line corresponds to a linear fit of the data with random noise included. Open circles corresponds to the ideal data set with equal populations of open and closed states. A linear fit to the ideal data will give a slope of 0.5. It is clear that accurate fits of open/closed populations can be achieved with NMR data of the quality reported in Figure 6.
Supplementary Figure S11. Comparison of mutant and WT chemical shifts in open and closed states. (a) The reaction mechanism for ATP binding shown with a simplified AK representation (the AMPlid is omitted for clarity). (b) Hypothetical 1 H- 15 N HSQC spectrum illustrating the chemical shifts of the three states portrayed in (a) (orange). The closed state is in complex with Ap5A. The chemical shifts of an arbitrary amide proton (from the equivalent residue in WT and mutant and responsive to closure of the ATP lid ) for WT and mutant AK are shown as blue and green circles, respectively. The chemical shift of open WT AK has been shifted minutely from the open to state for clarity.
Supplementary Table Table S1. Thermal unfolding parameters of AK e variants Protein T m ( C) H vh (kj mol -1 ) a) Wild-type 56.6 ± 0.5 570 ± 19 M1 53.7 ± 0.5 390 ± 16 M2 50.0 ± 0.5 340 ± 10 a) Defined in the direction of unfolding
Supplementary Methods Equilibrium populations in conformational exchange from chemical shifts Equilibrium populations of proteins undergoing conformational exchange between two states can under favorable conditions be quantified with chemical shifts 46. The chemical shift is the most readily accessible NMR parameter, and can be measured with high accuracy. In the following discussion we describe how equilibrium populations of open and closed AK e can be determined in the presence of saturating amounts of the substrate ATP. Saturation of AK e with ATP results in a mixture of open and closed states in fast exchange (NMR time scale) with each other. In a two state conformational exchange process (here open and closed states) the observed chemical shift (ω OBS ) will be an average of the two interconverting states weighted by their populations if 47 ; (i) the chemical shifts of a specific probe (for instance an amide proton) differs between open and closed states, and (ii) the exchange is fast on the NMR timescale. In the fast exchange regime the rate of exchange (k ex ) is larger than the absolute difference in resonance frequency (δν) between the exchanging states, which can be formulated as k ex > δν, where k ex = k open + k close, and δν = ν C ν O (superscripts C and O refers to closed and open, respectively). In AK e the chemical shifts of the open (ω O ) and closed (ω C ) states can be measured on individual samples containing substrate-free or Ap5A saturated AK e, respectively (Supplementary Fig. S9 a, b). A hypothetical NMR spectrum explaining chemical shift averaging in the ATP saturated AK e is shown in Supplementary Figure S9c, d. The relative populations of the open (p O ) and closed states (p O ) can be calculated from measurements of three chemical shifts (ω C, ω O and ω OBS ) derived from three independent experiments, where ω OBS is measured for the ATP
saturated state (and ω C, ω O are measured as stated above) using the equations in Supplementary Figure 9d. In a protein all probes that are sensitive to the same conformational exchange process should provide converging populations of the states involved. We previously developed a robust and simple method to globally fit populations from chemical shift data of residues that are undergoing the same exchange process 46. For all residues, the chemical shift difference between the open state and a state (S) of interest (in our analysis ATP saturated states),δω OS, (Supplementary Fig. S9d) is plotted against the total chemical shift difference between open and closed states (δω OC in Supplementary Fig. S9d). The slope of the linear correlation between δω OS and δω OC provides a direct measurement of the population closed enzyme at the particular condition. The method is illustrated on a synthetic dataset in Supplementary Figure S10. Random noise was added to this dataset to show that the method is adequate for real data. With the open and closed chemical shifts available from assignments of apo and Ap5A bound AK e variants, the method can be used to accurately quantify open and closed populations of WT and mutated AK e in the presence of the natural substrate ATP. As required for this analysis, binding of ATP to WT and the M1 and M2 variants is fast on the NMR timescale as verified with nucleotide titration experiments. Ligand binding in coupled equilibrium reactions The definition of the dissociation constant for a one to one binding reaction is given by (S1). (S1)
Here, E corresponds to enzyme, S to substrate and ES to the enzyme-substrate complex. In an ITC experiment that probe ligand binding following Supplementary Equation S1 the observed dissociation constant ( ) equals K d. For AK e binding of the substrate ATP is more complex (Figure 1, main text). In addition to association the reaction involves a conformational change (i.e. closing of the ATP lid ). In this coupled equilibrium reaction, defined by (S2) depend not only on the on and off rates but also on the relative magnitudes of k close and k open. (S2) The expression in (S2) can be simplified into (S5) by insertion of (S3) and (S4) that are definitions of the equilibrium constants for association of ATP (K d ) and the subsequent conformational change (K conf ). (S3) (S4) (S5) From equation (S5) it is apparent that is modulated by K conf. Both the M1 and M2 variants bind ATP with values that are significantly lower (tighter binding) compared to WT AK e. A decrease in can depend on either an increased value of K conf or a decreased value of K d. As discussed in the main text section Mutations modulate the open-to-closed
equilibrium constant, K conf is significantly increased in the mutated variants and accounts fully for the observed reduction in. For completion, if the structural mutations in the M1 and M2 variants would stabilize a binding incompetent state as discussed in 48 must by necessity increase (weaker binding). With this model scale with the degree of ATP lid unfolding according to (S6) 48,49. (S6) k unfold /k fold. Here K u is the equilibrium constant for ATP lid unfolding and is defined as: K u =
Supplementary References 46. Ådén, J. & Wolf-Watz, M. NMR identification of transient complexes critical to adenylate kinase catalysis. J. Am. Chem. Soc. 129, 14003-14012 (2007). 47. Cavanagh, J., Fairbrother, W.J., Palmer, A.G. & Skelton, N.J. Protein NMR spectroscopy principles and practice. (Academic Press, San Diego, 1996). 48. Schrank, T.P., Bolen, D.W. & Hilser, V.J. Rational modulation of conformational fluctuations in adenylate kinase reveals a local unfolding mechanism for allostery and functional adaptation in proteins. Proc. Natl. Acad. Sci. U S A 106, 16984-16989 (2009). 49. Dincbas-Renqvist, V., Lendel, C., Dogan, J., Wahlberg, E. & Härd, T. Thermodynamics of folding, stabilization, and binding in an engineered protein-protein complex. J. Am. Chem. Soc. 126, 11220-11230 (2004).