Effects of Chemical Exchange on NMR Spectra

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1 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

2 Types of Chemical Exchange Intramolecular exchange Motions of sidechains in proteins A B Helix-coil transitions of nucleic acids 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

3 2-state First Order Exchange A B k1 k -1 Lifetime of state A: τ A = 1/k +1 Lifetime of state B: τ B = 1/k -1 Use a single lifetime 1/ τ =1/ τ A + 1/τ B = k +1 + k -1

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

5 2-state 2nd Order Exchange k +1 M+L 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/ τ =1/ τ ML + 1/τ l = k -1 (1+f ML /f L ) f ML and f L are the mole fractions of bound and free ligand, respectively

6 Typical Motion Time Scale for Physical Processes SLOW very slow slow fast very fast ultrafast s ms µs ns ps fs FAST MACROSCOPIC DIFFUSION, FLOW CHEMICAL EXCHANGE MOLECULAR ROTATIONS RELAXATION TIMESCALE SPECTRAL TIMESCALE LARMOR TIMESCALE MOLECULAR VIBRATIONS

7 NMR Time Scale Time Scale Chem. Shift, δ Coupling Const., J T2 relaxation Slow k << δ Α δ Β k << J Α J Β k << 1/ T 2, Α 1/ T 2, B Intermediate k = δ Α δ Β k = J Α J Β k = 1/ T 2, Α 1/ T 2, B Fast k >> δ Α δ Β k >> J Α J Β k >> 1/ T 2, Α 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.

8 Slow Exchange k << δ A -δ B A B k1 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/τ A = 1/T 2A + 1/k 1 1/T 2B,obs = 1/T 2B + 1/τ Β = 1/T 2B + 1/k -1 line width Lw = 1/πT 2 = 1/πT 2 + k 1 /π Each resonance is broadened by Lw = k/π Increasing temperature k increases, line width increases

9 Slow Exchange for M+L ML k 1 k- 1 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

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

11 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.

12 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 = c π δ δ // 2 2 = δ δ δ is the chemical shift difference between the two signals in the unit of Hz. δ depends on the magnetic field

13 Coalescence Temperature Since the rate depends on the G of the inversion, and the G 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 G of the process G G = R ** T C * C *[[ ln ln (( T C / C / δ δ ))]] T C

14 Fast Exchange k >> δ A -δ B A B k1 k -1 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 f B, 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 4π ( δ AB ) 2 / k -1 Maximal line broadening is observed when f A = f B = 0.5

15 Line Shape Simulation

16 Fast Exchange k >> δ A -δ B k+1 M+L ML k-1 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 4π (δ ML -δ 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].

17 NMR Titration Both T6(CH3) at 1.1 ppm from DNA (A) and L(CNH 2 ) methyl from ligand (B) are in fast exchange. Expanded regions from 300 MHz 1 HNMR spectra from complexes between L(NH 2 ) and d(ggtaatacc) 2 recorded at 10 ºC (Craik)

18 Residues in the linker of Calmodulin underwent sequential phases of conformational change

19 Binding of Inhibitor to Enzyme H I * H I H * k off * k unf * H S * H * k off [protein][ligand] off K d = d = k on [protein- ligand] ligand] k on H S NMR studies are done at mm, making it difficult to determine K d with any accuracy if the binding is very tight (nm K d ).

20 Measuring Binding Constant k+1 M+L ML k-1 δ M,obs = f M δ M +f ML δ ML, The total change in δ of M δ Mo = δ ML - δ M At [L], δ M = δ M,obs - δ M If [M] is fixed, δ M= δ Mo [L]/([L]+K d ) At 0.5 δ Mo, K d = [L] Similar for A - +H + k+1 k-1 AH H=L, K d = K a δ H= δ Ho [H]/([H]+K a ) Inhibitor G-3-P binds to Triosephapte Isomerase -JMB, :319

21 NMR studies of Ca(II) Binding to cntnc [Ca]t/cTnC cntnc is the N-terminal domain of TnC from cardiac muscle with a single calcium binding site II. Peak at 10.3 ppm is G70 at the calcium binding site. Monica et al., 1997

22 Monitoring Calcium-binding by NMR CaM-CD2-III-5G Ca mm mm mm 0 mm fractional change of chemical shifts ppm K d = 144 ± 27 um [Ca(II)], (mm)

23 The Ionization of His in Oxy & DeOxyhemglobin C2H 7.7 ppm 8.7 ppm C4H 7.0 ppm 7.4 ppm Bohr effect: Hb takes up H + on releasing O2 The pka of His-β-146 changes by more than 1pH unit upon ionization due to the stabilization of the charged form by Asp94 in the deoxy structure.

24 Transferred NOE (TRNOE) Cross-relaxation (NOE) between two protons in the bound ligand is transferred to the free molecular by chemical exchange between bound and free ligand. The negative NOEs from the bound state can be detected by carrying NOE experiments on the free ligand in slow exchange, or one the averaged signals from free and bound ligand in fast exchange. irradiation H1 H2 H1 bound L free L H2 protein

25 Transferred NOE (TRNOE) free H1 k bindr k bindf bound H1 k magf k magr k magf k magr free H2 k bindr k bindf bound H2 H1 H2 H1 bound L free L For small ligands such as short peptides, the enhancement from cross-relaxation is almost 0. On the other hand, large molecules such as receptors have very efficient magnetization transfer. If the chemical exchange rate is great enough, magnetization is transferred from the free protons via the bound state. This gives distance information of the bound state. H2 protein

26 Selectively deuterated dihydrofolate reductase in the presence of 2.7 molar equivalents of trimethoprim control Irriadiation st 7.34 ppm Spectrum a-b H6 is close to H2 (or H6 ) in a folded conformation of bound trimethoprim

27 1 H(pm) Superposition of 50 energy minimized structures of FaNaCh-bound FMRFa N-terminus C-terminal amide

28 Ligand binding: Isotope editing NMR techniques exist to separate a mixture of molecules with different isotopic labels. For example, if two proteins are mixed together and one has 15N labels and the other doesn t, it is possible to only observe the amide protons of one or the other (technically it is easier to see the amides of the protein with 15N, but either is possible). This can be extended to mixtures of pools of ligands with proteins where either the ligand is labeled or the protein is labeled. More complicated mixtures can be analyzed by incorporating different types of labels (e.g. 15N on one, 13C on another)

29 Dynamic NMR to Monitor Rapid Protein Folding The intensity as a function of frequency McConnell equation I(ν) - the intensity at frequency ν C o -constants proportional to [protein] tot P N and P D - the populations of N and D The parameters needed to calculate the lineshape are C o, & ν, T 2N, T 2D, k f and k u. The first four parameters are obtained directly from the spectra using Lorentzian line shape simulation of the J-coupled multiplets. k f and k u can be obtained independently by simulating the position and shape of a given resonance. --J. Sandström, 1982

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