Chemical Exchange and Ligand Binding

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1 Chemical Exchange and Ligand Binding NMR time scale Fast exchange for binding constants Slow exchange for tight binding Single vs. multiple binding mode Calcium binding process of calcium binding proteins CaM regulation of gap junctions

2 Effects of Chemical Exchange on NMR Spectra Chemical exchange refers to any process in which a nucleus exchanges between two or more environments in which its NMR parameters (e.g. chemical shift, scalar coupling, or relaxation) differ. DNMR deals with the effects in a broad sense of chemical exchange processes on NMR spectra; and conversely with the information about the changes in the environment of magnetic nuclei that can be derived from observation of NMR spectra. K ex Conformational equilibrium K B Chemical equilibrium

3 Types of Chemical Exchange Intramolecular exchange Motions of sidechains in proteins Helix-coil transitions of nucleic acids A B Unfolding of proteins Conformational equilibria Intermolecular exchange Binding of small molecules to macromolecules Protonation/deprotonation equilibria Isotope exchange processes Enzyme catalyzed reactions M+L ML Because NMR detects the molecular motion itself, rather the numbers of molecules in different states, NMR is able to detect chemical exchange even when the system is in equilibrium

4 Typical Motion Time Scale for Physical Processes

5 NMR Time Scale Time Scale Chem. Shift, d Coupling Const., J T2 relaxation Slow k << d A - d B k << J A - J B k << 1/ T 2, A - 1/ T 2, B Intermediate k = d A - d B k = J A - J B k = 1/ T 2, A - 1/ T 2, B Fast k >> d A - d B k >> J A - J B k >> 1/ T 2, A - 1/ T 2, B Sec NMR time-scale refers to the chemical shift timescale. The range of the rate can be studied s -1 for H can be extended to faster rate using 19 F, 13 C and etc.

6 2-state First Order Exchange A k1 B k -1 Lifetime of state A: t A = 1/k +1 Lifetime of state B: t B = 1/k -1 Use a single lifetime 1/ t =1/ t A + 1/t B = k +1 + k -1

7 Rationale for Chemical Exchange For slow exchange For fast exchange FT FT Bloch equation approach: dm AX /dt = -(Dω A )M AY - M AX /t A + M BX /t B dm BX /dt = -(Dω B )M BY - M BX /t B + M AX /t A

8 2-state 2nd Order Exchange M+L k +1 ML k -1 K d = [M] [L]/[ML] = k -1 /k +1 K d = M k on = k +1 ~ 10 8 M -1 s -1 (diffusion-limited) k -1 ~ s -1 Lifetime 1/ t =1/ t ML + 1/t l = k -1 (1+f ML /f L ) f ML and f L are the mole fractions of bound and free ligand, respectively

9 Slow Exchange k << δ A -δ B A k1 B k -1 Separate lines are observed for each state. The exchange rate can be readily measured from the line widths of the resonances Like the apparent spin-spin relaxation rates, 1/T 2i,obs 1/T 2A,obs = 1/T 2A + 1/t A = 1/T 2A + 1/k 1 1/T 2B,obs = 1/T 2B + 1/t B = 1/T 2B + 1/k -1 line width Lw = 1/pT 2 = 1/pT 2 + k 1 /p Each resonance is broadened by D Lw = k/p Increasing temperature increases k, line width increases

10 Slow Exchange for M+L k 1 k- 1 ML Separate resonances potentially are observable for both the free and bound states M F, M B, L F, and L B The addition of a ligand to a solution of a protein can be used to determine the stoichiometry of the complex. Once a stoichiometric mole ratio is achieved, peaks from free ligand appear with increasing intensity as the excess of free ligand increases. Obtain spectra over a range of [L]/[M] ratios from 1 to 10

11 Slow Exchange for M+L k 1 k- 1 ML For free form 1/T 2L,obs = 1/T 2L + 1/t L = 1/T 2L + k -1 f ML /f L 1/T 2M,obs = 1/T 2M + 1/t M = 1/T 2M + k -1 f ML /f M For complex form 1/T 2ML,obs = 1/T 2ML + 1/t ML = 1/T 2ML + k -1 Measurements of line width during a titration can be used to derive k -1 (k off ).

12 19 F spectra of the enzyme-inhibitor complex at various mole ratio of carbonic anhydrase:inhibitor Free inhibitor 1:4 1:3 1:2 1:1 1:0.5 Bound ligand At -6 ppm the broadened peak for the bound ligand is in slow exchange with the peak from free ligand at 0 ppm. The stoichiometry of the complex is 2:1. No signal from the free ligand is visible until more than 2 moles of inhibitor are present.

13 Coalescence Rate For A B equal concentrations, there will be a rate of interchange where the separate lines for two species are no longer discernible The coalescence rate k c = p Dd / 2 = 2.22 Dd Dd is the chemical shift difference between the two signals in the unit of Hz. Dd depends on the magnetic field

14 Coalescence Temperature Since the rate depends on the DG of the inversion, and the DG is affected by T, higher temperature will make things go faster. Tc is the temperature at which fast and slow exchange meet. T>Tc, fast exchange T<Tc, slow exchange T we can calculate the DG of the process DG = R * T C * [ ln ( T C / Dd ) ] T C

15 Fast Exchange k >> δ A -δ B A k1 k -1 B A single resonance is observed, whose chemical shift is the weight average of the chemical shifts of the two individual states δ obs = f A δ A +f B δ B, f A + f B = 1 For very fast limit 1/T 2,obs = f A /T 2A + f B /T 2B For moderately fast 1/T 2,obs = f A /T 2A + f B /T 2B + f A f B2 4p (Dd AB ) 2 / k -1 Maximal line broadening is observed when f A = f B = 0.5

16 Fast Exchange k >> δ A -δ B M+L k+1 k-1 ML For M δ M,obs = f M δ M +f ML δ ML For L δ L.obs = f L δ L +f ML δ ML 1/T 2,obs = f ML /T 2,ML + f L /T 2,L + f ML f L2 4p (d ML -d L ) 2 / k -1 A maximum in the line broadening of ligand or protein resonances occurs during the titration at a mole ratio of approx. ligand:protein 1:3 The dissociation constant for the complex can be obtained by measuring the chemical shift of the ligand resonance at a series of [L].

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19 Integration of Calcium Signaling Via CaSR LB1 LB2 Site 2 Site 1 Site 3 Site 4 site5 Identification of Ca 2+ binding sites in ECD of CaSR How can CaSR sense the change of Ca 2+ o within a narrow range? (multiple sites? cooperativity?) Identification of CaM binding region in c-tail of CaSR Y. Huang, JJ Yang, J Biol Chem. 2007; Yun Huang.. JJ Yang Biochemistry 2009; Y Hang, JJ Yang, JBC 2010

20 Subdomain Approach LB 1 LB2 site4 site3 site1 site2 site3 site2 site5 Yun Huang.. JJ Yang Biochemistry 2009

21 Fluorescence Intensity Relative change Relative change of chemical shift Two Distinct Ca 2+ -Binding Processes Revealed by NMR K d : 1.6 ± 0.1 mm n Hill : 2.3 ± [Ca 2+ ] (mm) ANS + Protein + Ca site3 site1 site ANS + Protein ANS K d1 = 0.7 ± 0.1 mm K d2 = 6.4 ± 0.8 mm n hill = 2.9 ± 1.2 Yun Huang.. JJ Yang Biochemistry 2009; wavelength (nm) [Ca 2+ ] mm

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23 Developing Calcium Sensors by Design 1. Highly targeting specificity 2. Simple stoichiometric interaction mode to ease calibration 3. Tunable affinities, selectivity & kinetics 4. Minimal perturbation on signaling without using natural calcium binding proteins JACS, 2002, 2005, 2007 Biochem, 2005, 2006, PEDS, 2007, protein science 2008 J. Zhou, A. Hofer, J.J. Yang, Biochem, 2007 A.Holder, J.J. Yang, Biotech 2009 S. Tang,.O. Delbano J.J. Yang, PNAS, 2011

24 Normalized fluorescence ormalized fluorescence (%) Normalized absorbance Normalized fluorescence H O Catcher: Ca 2+ Sensor for Detecting High Concentration E204 Y66 Neutral E223 E147 R E225 O - x - x - D202 Ca 2+ chromophore Y66 Anionic R EGFP D8 D9 D10 CatchER D Wavelength (nm) 6.0 mm Ca F488; 10 M EGTA F488; 5 mm Ca 2+ F395; 10 M EGTA F395; 5 mm Ca 2+ x - Ca x - x Designed Ca 2+ binding site 0 S. Tang,.O. Delbano J.J. Yang, PNAS, Wavelength (nm)

25 Normalized fluorescence Relative amount of Ca-bound CatchER fluorescence 3.5 CatchER: Ca 2+ binding capability F 488 Equilibrium dialysis coupled with ICP-OES F 395 A [CatchER] M Wavelength (nm) 1 H, 15 N-HSQC S. Tang,.O. Delbano J.J. Yang, PNAS, 2011

26 normalized fluorescence (%) normalized fluorescence (%) Fast Kinetics of CatchER [Ca 2+ ] µm [EGTA] µm time (s) k on = k off /K d = 3.9 x 10 6 M -1 s time (s) Fast Kinetics: k off = 700 s -1 S. Tang,.O. Delbano J.J. Yang, PNAS, 2011

27 CatchER s Ca 2+ Induced Chemical Shift Changes Y182 G228 S. Tang,.O. Delbano J.J. Yang, PNAS, 2011

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31 2:1, Ca:CaM 1:1, Ca:CaM 0:1, Ca:CaM a G113 G113 Chemical Exchange in Rat CaM G96 Fast Exchange b G59 I II G23 Slow Exchange Indicates: Initial occupancy of C- terminal domain Suggests: Temporal occupancy of N- terminal domain at low [Ca] and/or domain coupling Kirberger M, Yang JJ, JIBC, Fast Intermediate Slow II I Rat CaM I V

32 Similarities in Chemical Exchange with Ca 2+ Titration No exchange Slow exchange Fast exchange Paramecium CaM Slow then fast exchange Jaren, O.R., et al., Calcium-induced conformational switching of Paramecium calmodulin provides evidence for domain coupling. Biochemistry, (48): p Sun, H., et al., Mutation of Tyr138 disrupts the structural coupling between the opposing domains in vertebrate calmodulin. Biochemistry, (32): p I intermediate exchange II Slow exchange II I Rat CaM Fast exchange I V Kirberger M, Yang JJ, JIBC, 2013.

33 The Connexin Family Tree Söhl et al., Nat. Rev. Neurosci. 6: ,

34 Identifying CaM Binding Region in Gap Junction Connexins Score Cx50_m Cx46_h Cx44_s Cx43_h CaMKI_h CaMKII_h NH 2 COOH TKKFRLEGTLLRTYVCHI RGRVRMAGALLRTYVFNI RGKVRIAGALLRTYVFNI HGKVKMRGGLLRTYIISI FAKSKWKQAFNATAVVRH NARRKLKGAILTTMLATR 310 xxbxb#xxx#xxxx#xxx Y. Zhou. JJ Yang JBC. 2007; Zhou Y, Yang JJ. Biophys J ; Y. Chen,.. JJ Yang Biochem J. 2011

35 Dppm-H [Cx43]/[CaM] 0:1 0.4:1 0.8:1 1.2:1 Monitoring Cx Peptide and Calmodulin [Cx44]/[CaM] 0: T29 T A : : : K94 D64 G33 G61 G25 K148 A57 1.2: [Cx43]/[CaM] 2.0:1 Y. Zhou. JJ Yang JBC T29 T H (ppm) A H (ppm)

36 Strong Binding Indication by Slow Exchange CaM : Cx50p 1 : Free G CaM + Cx43p 1 : : : bound Y. Chen,.. JJ Yang Biochem J. 2011

37 HSQC Spectra of Holo-CaM with Cx50 Peptide Y. Chen,.. JJ Yang Biochem J Holo-CaM Holo-CaM + Cx50p G33 G134 T29 T117 T70 F19 A128 L116 K21 I100 I27 N137 V136 D64 I130 A57 K148 K94 A147 37