Substrate-dependent switching of the allosteric binding mechanism of a dimeric enzyme

Supplementary Information: Substrate-dependent switching of the allosteric binding mechanism of a dimeric enzyme Lee Freiburger, 1 Teresa Miletti, 1 Siqi Zhu, 1 Oliver Baettig, Albert Berghuis, Karine Auclair, 1 Anthony Mittermaier 1 1 Department of Chemistry McGill University 801 Sherbrooke St. W. Room 3 Montreal, QC, Canada H3A 0B8 Department of Biochemistry McGill University 3655 promenade Sir William Osler, Room 905 Montreal, QC, Canada H3G 1Y6 Corresponding Author: Anthony Mittermaier Department of Chemistry McGill University 801 Sherbrooke St. W. Room 3 Montreal, QC, Canada H3A 0B8 Office: (514) 398-3085 Fax: (514) 398-3797 anthony.mittermaier@mcgill.ca Nature Chemical Biology: doi:10.1038/nchembio.166

Supplementary Results Supplementary Table 1. Extracted Model Parameters for Paromomycin K A1 ( 10 4 M -1 ) a 8.7x10 6 ±6x10 5 ΔC p,a1 (cal mol -1 K -1 ) i -1370 ±30 K A ( 10 4 M -1 ) b.73x10 7 ±5x10 5 ΔC p,a (cal mol -1 K -1 ) j -350 ±0 c K U0 0.355 ±0.1 ΔC p,u0 (cal mol -1 K -1 ) k 100 NA d K U1 0.097 ±0.008 ΔC p,u1 (cal mol -1 K -1 ) k 100 NA ΔH A1 (kcal mol -1 ) e -34.4 ±0.6 [Θ] F (deg cm dmol -1 ) l -7770 ±30 ΔH A (kcal mol -1 ) f -14.7 ±0.4 [Θ] U (deg cm dmol -1 ) m -3890 ±10 ΔH U0 (kcal mol -1 ) g -53. ±0.4 m F (deg cm dmol -1 K -1 ) n 45 ±1 ΔH U1 (kcal mol -1 ) h -73 ±1 m U (deg cm dmol -1 K -1 ) o.6 ±0.5 T =37ºC a Equilibrium association constant for the native (non-melted) enzyme and the first paromomycin molecule at T b Equilibrium association constant for the native (non- melted) enzyme and the second paromomycin molecule at T c Equilibrium constant for subunit melting in the 0-bound enzyme at T d Equilibrium constant for melting of the unbound subunit in the 1-bound enzyme at T e Enthalpy change upon binding of one molecule of paromomycin to the native (non- melted) 0-bound enzyme at T f Enthalpy change upon binding of one molecule of paromomycin to the native (non- melted) 1-bound enzyme at T g Enthalpy change upon melting of a single subunit in the 0-bound enzyme at T h Enthalpy change upon melting of the unbound subunit in the 1-bound enzyme at T i Heat capacity change upon binding of one molecule of paromomycin to the native (non- melted) 0-bound enzyme i Heat capacity change upon binding of one molecule of paromomycin to the native (non- melted) 1-bound enzyme k Heat capacity change upon subunit melting. These values were fixed at the value obtained for a monomeric mutant of AAC(6 )- Ii l CD molar ellipticity of a native (non- melted) subunit at T m CD molar ellipticity of a melted subunit at T n Temperature dependence of the molar ellipticity of a native subunit n Temperature dependence of the molar ellipticity of a melted subunit Nature Chemical Biology: doi:10.1038/nchembio.166

Supplementary Table. Extracted Model Parameters for AcCoA K A1 ( 10 4 M -1 ) a.9x10 4 ±8x10 ΔC p,a1 (cal mol -1 K -1 ) i -710 ±30 K A ( 10 4 M -1 ) b.84x10 4 ±8x10 ΔC p,a (cal mol -1 K -1 ) j -800 ±30 c K U0 0.355 ±0.1 ΔC p,u0 (cal mol -1 K -1 ) k 100 NA d K U1 0.49 ±0.04 ΔC p,u1 (cal mol -1 K -1 ) k 100 NA ΔH A1 (kcal mol -1 ) e -.5 ±0.6 [Θ] F (deg cm dmol -1 ) l -7770 ±30 ΔH A (kcal mol -1 ) f -7.9 ±0.7 [Θ] U (deg cm dmol -1 ) m -3890 ±10 ΔH U0 (kcal mol -1 ) g -53. ±0.4 m F (deg cm dmol -1 K -1 ) n 45 ±1 ΔH U1 (kcal mol -1 ) h -80 ±1 m U (deg cm dmol -1 K -1 ) o.6 ±0.5 T =37ºC a Equilibrium association constant for the native (non-melted) enzyme and the first AcCoA molecule at T b Equilibrium association constant for the native (non- melted) enzyme and the second AcCoA molecule at T c Equilibrium constant for subunit melting in the 0-bound enzyme at T d Equilibrium constant for melting of the unbound subunit in the 1-bound enzyme at T e Enthalpy change upon binding of one molecule of AcCoA to the native (non- melted) 0-bound enzyme at T f Enthalpy change upon binding of one molecule of AcCoA to the native (non- melted) 1-bound enzyme at T g Enthalpy change upon melting of a single subunit in the 0-bound enzyme at T h Enthalpy change upon melting of the unbound subunit in the 1-bound enzyme at T i Heat capacity change upon binding of one molecule of AcCoA to the native (non- melted) 0-bound enzyme i Heat capacity change upon binding of one molecule of AcCoA to the native (non- melted) 1-bound enzyme k Heat capacity change upon subunit melting. These values were fixed at the value obtained for a monomeric mutant of AAC(6 )- Ii l CD molar ellipticity of a native (non- melted) subunit at T m CD molar ellipticity of a melted subunit at T n Temperature dependence of the molar ellipticity of a native subunit n Temperature dependence of the molar ellipticity of a melted subunit Nature Chemical Biology: doi:10.1038/nchembio.166

Supplementary Note 1. Deviations from NMR titration model The intensities of 36 of the 44 AAC(6 )-Ii well-resolved holo peaks followed the simple equation holo I = fi + f (1) tot holo 1 1 throughout the titration with paromomycin, where f 1 and f are the ITC-derived fractions of 1-bound and -bound states. I 1 holo is the relative contribution of 1-bound state to the holo peak, which was fitted on a per-residue basis. Most of the fitted I 1 holo values are close to, indicating that the 1-bound form of the protein contributes approximately the equivalent signal intensity of subunits to each holo peak. However, 8 of the holo peaks built up more gradually, with I tot holo <f for points part-way through the titration, as shown in Supplementary Figure 1. Supplementary Figure 1. NMR paromomycin titration data for the holo peak of I169 in AAC(6 )- Ii. Points indicate normalized peak intensities while the dashed line indicates the buildup curve given by I holo 1 =0, I holo tot =f. (i.e. the most gradual buildup consistent with Equation (1) ). The solid line corresponds to the best fit using Equation (5) with ρ=6.5. This behaviour deviates from model described by Equation (1), as I tot holo =f (I 1 holo =0) represents the most gradual build up curve achievable. An lanation for these deviations is that they are produced by relative rapid (sub-second) exchange between the 1-bound and -bound forms, as illustrated in Supplementary Figure. Exchange between the 1-bound and -bound states is ected to be more rapid than between the 1-bound and 0-bound forms, as both 1-bound and -bound states are in the symmetrically holo conformation (xhh, HHx, and xhhx versus AA). Thus the 0-bound to 1-bound transition involves a large protein conformational change which is likely kinetically limiting while the 1- bound to -bound transition does not. We found previously that some residues produce weakened or broadened signals in the unbound subunit of the AcCoA 1-bound state (1). This situation likely holds for the paromomycin 1-bound state as well. Exchange between the 1-bound and -bound states would effectively transfer broadening to signals of the -bound state, leading to I tot holo <f. Nature Chemical Biology: doi:10.1038/nchembio.166

Supplementary Figure. Proposed kinetic scheme for paromomycin binding to AAC(6')-Ii. xhh AA HHx transitions occur more slowly than xhh xhhx HHx transitions, where x represents paromomycin and A and H represent the apo (circle) and holo (square) forms of the protein. This leads to averaging of relaxation rates for the 1-bound and -bound states. This effect can be modelled mathematically as follows: transverse relaxation rates in the 1-bound and - bound states are effectively averaged by ligand exchange so that all bound and unbound subunits in these states erience the same population-weighted mean transverse relaxation rate, R av 0.5 f 0.5 f + f R = R + R av 1 F 1 B f1+ f f1+ f, () where R F is the transverse relaxation rate of the unbound subunit in the 1-bound state and R B is the transverse relaxation rate of bound subunits in either the 1-bound or -bound states. Due to broadening, R F >>R B. The effective transverse relaxation rate thus depends on the relative populations of the 1-bound and -bound states. The intensity of each peak is proportional to {-R T}, where T is the total time magnetization is in the xy plane during the HSQC eriment. Assuming that signals for all bound and unbound subunits in the 1-and -bound states are coincident holo tot av ( 1 ) { } I f + f R T. (3) At saturating concentrations of paromomycin, R av R B, thus in order to ensure that I tot holo approaches its normalized maximum value of, Equation (3) can be modified with a constant of proportionality according to holo Itot = f + f R T This simplifies to { } ( ) { av } 1 B R T. (4) Nature Chemical Biology: doi:10.1038/nchembio.166

holo Itot = f1+ f 0.5 f f + f ( ) 1 1 ρ (5) where ρ=(r F R B )T. The value of ρ can be fitted on a per-peak basis to account for the transferred broadening. As illustrated in Supplementary Figure 1 this simple model accounts quantitatively for the erimental titration curves of these residues. We lored the possibility that rapid exchange between the 1-bound and -bound states is itself responsible for the dynamical broadening, but this inconsistent with what we observe erimentally. If these nuclei have different resonant frequencies in the 1-bound and -bound states and exchange is fast on the NMR timescale then we would ect to see gradual shifts in peak position during the titration. This is not observed. If exchange is on the intermediate-to-slow regime then an additional set of peaks corresponding to the unbound subunit in the 1-bound state should appear. This also does not occur. Thus we believe the best lanation for this phenomenon is that peak positions in the 1-bound and -bound states are coincident, but that the unbound subunit in the 1-bound state eriences dynamical broadening which is transferred to the - bound state, as described above. Supplementary Note. Thermodynamic Analysis The erimentally observable parameters, which comprise the apparent binding affinities and enthalpies for the first and second molecules of AcCoA and paromomycin as functions of temperature (K app A1, ΔH app 1, K app A, ΔH app ), were re-cast in terms of microscopic model parameters, which describe 7 thermodynamic transitions: binding of the first and second molecules of paromomycin to the native enzyme, binding of the first and second molecules of AcCoA to the native enzyme, subunit melting in the paromomycin and AcCoA 1-bound forms, and subunit melting in the 0-bound state. Each of these transitions is associated with 3 parameters: an equilibrium constant (K ) and enthalpy change (ΔH ) at an arbitrary reference temperature (T ) and the change in heat capacity (ΔC p ). The temperature dependences of microscopic equilibrium constants and enthalpies are given by and K{T} = K H R 1 1 + C p ln T T T T R T + 1 (6) T ΔH{T} = ΔH + ΔC p(t - T ). (7) The apparent equilibrium association constants for the first and second molecules of ligand are given by the ressions and K app (1+K A1 = K U1 ) A1 (8) (1+K U0 ) K app 1 A = K A (1+K U1 ), (9) Nature Chemical Biology: doi:10.1038/nchembio.166

where K A1 and K A are the intrinsic association constants of the native enzyme for the first and second molecules of ligand. K U0 = [FU]/[FF] is the equilibrium constant for partial unfolding in the 0-bound state, which is the same for both paromomycin and AcCoA calculations. K U1 =[BU ]/[BF ] is the equilibrium constant for partial unfolding in the 1-bound state, which differs for paromomycin and AcCoA. The apparent binding enthalpies for the first and second molecules of ligand are given by and H A1 H A K U1 app K = H A1 + H U1 H U0 1+K U0 (10) U1 1+K U0 K U1 app = H A H U1, (11) 1+K U1 where ΔH A1 and ΔH A are the intrinsic binding enthalpies of the native enzyme with the first and second ligand molecules. ΔH U0 is the melting enthalpy in the 0-bound form, which is the same for both paromomycin and AcCoA calculations. ΔH U1 is the melting enthalpy in the 1-bound form, which differs for paromomycin and AcCoA. The affinity and enthalpy profiles were relatively insensitive to the choices of ΔC p,u0 and ΔC p,u1. We therefore fixed both parameters equal to the value previously determined for a monomeric mutant of AAC(6 )-Ii,.1 kcal mol -1 K -1 (1, ). The molar ellipticity of the protein was fitted as the population-weighted average of those of the F and U states, which were assumed to be linear functions of temperature, according to the ression [Θ]{T} = 1 1+K U0 [Θ] F + m F (T T ) + K U0 1+K U0 [Θ] U + m U (T T ), (1) where [Θ] F and [Θ] U are the molar ellipticities of the F and U states at T and m F and m U are the corresponding temperature dependences. parameters (K A1, ΔH A1, ΔC p, A1, K A, ΔH A, ΔC p,a, K U1, ΔH U1 ) paro, (K A1, ΔH A1, ΔC p, A1, K A, ΔH A, ΔC p,a, K U1, ΔH U1 ) AcCoA, and (K U0, ΔH U0, [Θ] F, m F, [Θ] U, m U ) were adjusted to minimize the residual function: { } { } app ln{ KA } { } { } app { HA } { } { } app ln{ KA } app app app app A1, A1, calc A1, A1, calc ln K ln K ln K ln K RSS = + 1, 1, paro { } { } app { HA } app app app app A1, A1, calc A1, A1, calc H H H H + + + [ Θ] Θ [ ] [ Θ] 1, 1, paro calc AcCoA AcCoA (13) using in-house MATLAB scripts, where the sums run over all data points. Errors in the thermodynamic parameters were calculated using a Monte Carlo technique as described previously (1). Nature Chemical Biology: doi:10.1038/nchembio.166

Supplementary Note 3. Allosteric Switching Model We have described the switch between the MWC and KNF allosteric paradigms for a homodimeric system in terms of the parameters G trans, the free energy difference between the A (apo) and H (holo) conformational states, and G int, the stabilization energy for the HH interface relative to the AH and AA interfaces. Expressions for the cooperativity coefficient, α, and symmetry coefficient σ, may be derived as follows. The relative populations of all thermodynamic states are given by: [AA]=1 [AH]=[HA]=K trans (14) [HH]=K trans K int [AHx]=[xHA]=K trans K B [x] [HHx]=[xHH]= K trans K int K B [x] [xhhx]= K trans K int K B [x] where x represents the ligand, K B is the intrinsic association constant for x and the H subunit, K trans ={- G trans /(RT)}, K int ={- G int /(RT)}. The apparent affinity constants for the first and second molecules of ligand are given by A1 [ AHx ] + [ HHx] ([ ] [ ] [ ] [ ])[ ] K = AA + AH + HA + HH x (15) A [ xhhx] ([ ] [ ])[ ] K = AHx + HHx x (16) thus the cooperativity coefficient is [ xhhx] ([ AA ] + [ AH ] + [ HA ] + [ HH] ) ([ AHx ] + [ HHx] ) K α = A = K A1 [ ] ( ) ( KtransKB [ x ] +KtransKintKB [ x] ) K K K x 1+K +K K = trans int B trans trans int ( ) ( K trans +KtransKint ) K K 1+K +K K = trans int trans trans int (17) It is possible that a single molecule of paromomycin could form direct interactions with both subunits of the enzyme. If this were the case, the allosteric free energy surface would be somewhat changed, as the Nature Chemical Biology: doi:10.1038/nchembio.166

HH interface would be stabilized to a greater extent in the -bound form than it is in the 1-bound form. The model above can be modified slightly to take this into account by assigning the interaction energy between a ligand and the adjacent subunit in the H conformation a value G adj as illustrated in Supplementary Figure 3. Supplementary Figure 3. Illustration of possible inter-subunit ligand interactions for paromomycin binding to AAC(6')-Ii. A ( ) and H ( ) represent binding-incompetent and binding-competent conformations of the subunits, respectively. G int represents the stabilization of the HH ( ) interface relative to all other types subunit interfaces while G adj represents the interaction energy between a ligand (red rectangle) bound to one subunit and the adjacent H subunit. Thus the relative populations of the xhh, HHx, and xhhx states become K trans K int K adj K B [x], K trans K int K adj K B [x], and K trans K int K adj K B [x], respectively, while the other populations are unchanged. This gives ressions for the cooperativity coefficient, α, and symmetry coefficient, σ, as follows: ( ) ( K trans +KtransKintKadj ) K K K 1+K +K K α = trans int adj trans trans int (18) [ HHx] [ AHx] = =K K K σ trans int adj, (19) where K adj ={- G adj /(RT)}. This somewhat modifies the shape of the allostery free energy surface. For example, Supplementary Figure 4 shows the result if cooperativity is entirely modulated by interactions between a ligand and the adjacent subunit, i.e. G int =0 and G adj = 10 to 5 kcal mol -1. Importantly, the switch between the MWC and KNF mechanisms still occurs with a fairly small change in G adj of 3.5 kcal mol -1. Thus small changes in interface energies, mediated by either direct interactions of ligands with Nature Chemical Biology: doi:10.1038/nchembio.166

both subunits or by indirect stabilization of the protein structure, are sufficient to change the allosteric mechanism from one canonical paradigm to another. Supplementary Figure 4. Switching between the MWC and KNF allosteric paradigms mediated exclusively by interactions between a ligand bound to one subunit with the adjacent subunit. G trans corresponds to the free energy difference between the binding-incompetent A ( ) and binding-competent H ( ) states, and G adj corresponds to the free energy of the interactions formed between a ligand bound to one subunit and the adjacent H subunit, as illustrated in Supplementary Figure 3. In this case, the intrinsic stabilities of all subunit interfaces was assumed to be equal, i.e. G int =0. The KNF region corresponds to σ<.05 and the MWC corresponds to σ>0. 1. Freiburger LA, et al. (011) Competing allosteric mechanisms modulate substrate binding in a dimeric enzyme. Nature Structural & Molecular Biology 18(3):88-94.. Freiburger LA, Auclair K, & Mittermaier AK (01) Van 't Hoff global analyses of variable temperature isothermal titration calorimetry data. Thermochimica Acta 57:148-157. Nature Chemical Biology: doi:10.1038/nchembio.166