Where are the protons? Measuring and modelling proton equilibria in complex macromolecular systems.

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1 Frans Mulder PhD course Jyväskylä 2017 Where are the protons? Measuring and modelling proton equilibria in complex macromolecular systems. Frans Mulder Lecture 3 Application of NMR spectroscopy to study electrostatics 1

2 Acknowledgement Stina Lindman, Ingemar Andre and Sara Linse Biophysical hemistry, Lund University pk a values of ionizable groups in proteins are of interest as electrostatic interactions play an important role in functional aspects of proteins. The ability to assign a pk a to a specific ionizable group in a protein (based on its chemical shift) can aid in the mechanistic description of binding, catalysis, and other behaviour 2

3 net charge Asp, Glu Tyr & -term Lys N-term net charge Asp, Glu Tyr & -term Lys N-term Up- and down-shifted pka-values close to pi Up-shifted pka-values far above pi 3

4 Traditional NMR approaches to pka determination in proteins: - 1 H 1D - 1 H 2D TOSY Forman-Kay et al. (1992) Biochemistry 31, Isotope labeling for pk a values by NMR Lysine with 13-- ε Aspartate with 13-- β N O= + NH 3 N O= O O Glutamate with 13-- γ Uniform 15-N N O O N R O= O= 4

5 pk a values of lysines using 13 and 1 H 0.5 mm apo albindin D 9k (low salt) [Kesvatera et al. (1996), J Mol Biol 259, 828] The H()N experiment correlates amino 15 N chemical shift with H ε (Lys) correlates amino 15 N chemical shift with H δ (Arg) + 15 N ζ H 3 13 ζ 1 13 H ε 1 ε H ε 15 N ε 1 H ε 13 δ 1 13 H δ 1 δ H δ 5

6 The H()N experiment FKBP12, ph 7.0 [André, et al. JAS (2007).] The H()N experiment 6

7 The -TOSY(N)H experiment The -TOSY(N)H experiment 7

8 pk a values of lysines from the 15 N shift of the titrating group 15 N ζ (ppm) δ obs = (δ HA +δ A 10 (ph pk a ) ) (1+10 (ph pk a ) ) ph Henderson-Hasselbalch equation for NMR titrations of non-interacting sites [André, et al. JAS (2007).] 2 mm apo calmodulin in 100 mm Kl 8

9 pk a values of lysines from the 15 N shift of the titrating group Table 2. pk a Values of Lysine Residues in apo almodulin As Determined from N ξ or H ϵ at 25 in 100 mm Kl; K(x) Indicates That the Residue Is Not Assigned residue N ξ H ϵ N ξ + H ϵ K ( ( ( 0.02 K ( ( ( 0.04 K(3) ( ( ( 0.05 K(4) ( ( ( 0.02 K(5) ( ( ( 0.02 K(6) ( ( ( 0.02 K(7) ( ( ( 0.02 K(8) ( ( ( 0.03 remember, the model pk a = 10.4 [André, et al. JAS (2007).] ph-dependent stability to unfolding for the B1 domain of protein G PGB1-QDD β2 β1 β4 β3 Variant to ensure unprocessed protein ontains 2 extra negative charges, D8 and D37 Total of 12 side-chain carboxyl groups 9

10 olor coding according to pk a Model pk a : The H()O experiment correlates carboxyl 13 chemical shift with H β or H γ For Asp: O 13 γ OH 1 H β 1 H β 13 β N 13 α 13 [ Oda et. al, Biochemistry 33 (1994) 5275] 10

11 Spectrum at ph 5 good dispersion and sensitivity Spectra ph

12 Henderson-Hasselbalch equation: a Hill parameter is now necessary to fit the data Hill parameter to account for cooperativity δ obs = (δ HA +δ A 10 n h(ph pk a ) ) (1+10 n h(ph pk a ) ) pk a values of side-chain carboxyl groups at 0 M and 0.5 M Nal Glu pk a model =4.4 0M : M : 4.6 0M : M : 4.0 0M : M : 4.8 0M : M : 4.5 0M : M :

13 pk a values of side-chain carboxyl groups at 0 M and 0.5 M Nal: zoom in 0M : M : 3.8 pk a values continued Asp pk a model =4.0 0M : M : 4.6 0M : M : 3.2 0M : M : 4.1 0M : M : 6.1 0M : M : 4.0 0M : M : 3.8 0M : M :

14 Proton Binding apacitance (PB) Ø PB = first derivative of the titration curve with respect to ph Ø urve fitting with Hill-parameter cannot account for asymmetric titration curves PB and titration asymmetry Highly downshifted Slightly downshifted Slightly upshifted Highly upshifted 14

15 Low salt Salt dependence of Glu pka Derivative of titration curve explains cooperativity and negative-cooperativity High salt Titration behavior approaches model with addition of salt ooperativity of Asp Derivative of titration curves explain cooperativity and negative-cooperativity Low salt High salt Titration behavior approaches model with addition of salt 15

16 pk a values for Asp8 from 13 and 1 H chemical shifts Major differences between the two protons! pk a O: 4.9 pk a H β1 : 5.8 pk a H β2 : 4.7 arbonyl 13 shifts for Asp47 and Ala48 report pk a value of Asp47 carboxyl group pk a carboxyl group of D47: 3.1 pk a carbonyl group of D47: 3.2 pk a carbonyl group of A48:

17 arbonyl shifts report on hydrogen bonds pk a carboxyl group of E56: 3.8 pk a carbonyl group of K10: 3.8 How to calculate ph-dependent stability based on pk a values δδg i q U = ( ph ) = 2.3RT( q q ) δ i n (ph pk ) h 1 a i ph i q i U = i F 1 ph i n (pk ph) h a Experimental pka values for native state Denatured state treated as random coil and pk a values were calculated using a Gausssian chain model [ Zhou, PNAS 99 (2002), 3569] 17

18 pk a values explain ph-dependent stability Denaturation data ph dependent stability calculated from pk a values [ Lindman et. al, Biophys J. (2010) 99: ] onclusions -1 chemical shifts of 13 and 15 N in protein are specific and accurate reporters of side chain protonation states carefully designed NMR experiments can monitor the heteronuclear chemical shifts in 2D spectra with high sensitivity and good resolution site-specific protonation constants can be determined 18

19 onclusions -2 pk a values show that ph-dependent stability can be explained purely by electrostatics Electrostatic contributions to protein stability are small (but not to kinetics!) There is clear evidence of local electrostatic coupling between acidic side chains in PGB1, but not for basic side chains in apo am We directly detect - for the first time - asymmetry in the ph-dependent protonation of individual acidic groups in proteins as a result of the change in protein electrostatic energies with ph 19