Chemical Exchange in NMR Spectroscopy

Transcription

1 COURSE#1022: Biochemical Applications of NMR Spectroscopy Chemical Exchange in NMR Spectroscopy LAST UPDATE: 3/28/2012 1

2 References Bain, A. D. (2003). "Chemical exchange in NMR." Progress in Nuclear Magnetic Resonance Spectroscopy 43(3-4): L. Y. Lian & G. C. K. Roberts, Chapter 6 Effects of chemical exchange on NMR spectra in NMR of Macromolecules, A Practical Approach (1993) Cavanagh, Fairbrother, Palmer, & Skelton, Chapter 5.6 Chemical Exchange Effects in NMR Spectroscopy Evans, Chapter 1.3 Kinetics Sanders & Hunter, Chapter 7 Connections through Chemical Exchange R. Freeman, Chemical Exchange from A Handbook of NMR M. H. Levitt, Chapter 15 Motion P. J. Hore, Chapter 4 Chemical Exchange in NMR, Oxford Chemistry Primer #32 2

3 Dynamics - Good or Bad for the NMR Spectrocopist? Dynamics in NMR can be a curse or rewarding its influence can cause signals to become invisible beyond detection or it can allow one to uncover a large range of motional properties at every site within a molecule 3

4 Chemical Exchange in NMR Chemical exchange in NMR refers to any process in which a nucleus exchanges between two or more environments in which its NMR parameters (chemical shift, scalar coupling, dipolar coupling, relaxation rate) differ. These may be intermolecular or intramolecular processes. Intramolecular exchange processes include: motions of protein side chains helix-coil transitions of nucleic acids unfolding of proteins conformational equilibria (conformational exchange) tautomerization Intermolecular exchange processes include: binding of ligands to macromolecules protonation/deprotonation equilibria of ionizable groups isotope exchange processes (such as the exchange of labile protons of a macromolecule with solvent) enzyme catalyzed reactions 4

5 Information From Chemical Exchange Studying chemical exchange can provide important kinetic and thermodynamic parameters such as: Kinetic Rate Constants: k on k off Thermodynamic Constants: K assoc or K d G H S G act

6 Characterizing Protein Dynamics: Parameters and Timescales Dynamic processes can be studied with a variety of NMR methods such as: Real Time NMR, RT NMR EXchange SpectroscopY, EXSY (zz-exchange) Lineshape analysis Carr Purcell Meiboom Gill Relaxation Dispersion, CPMG Rotating Frame Relaxation Dispersion, RF RD Nuclear Spin Relaxation, NSR Residual Dipolar Coupling, RDC Paramagnetic Relaxation Enhancement, PRE. Note: Multiple states are hard to detect by Xray crystallography Proteins sample a range of thermodynamically accessible conformations within a hierarchy of timescales owing to their intrinsic flexibility.. 6

7 Exchange Rates and The NMR Time Scale The NMR time scale refers to how fast an event happens relative to the NMR observables: Time Scale Chem. Shift (d) Coupling Const. (J) T 2 relaxation Slow k << A - B k << J A -J B k << 1/ T 2,A- 1/ T 2,B Intermediate k = A - B k = J A -J B k = 1/ T 2,A- 1/ T 2,B Fast k >> A - B k >> J A -J B k >> 1/ T 2,A -1/ T 2,B Range (Sec- 1 ) Two resonances (A,B) for one atom Populations ~ relative stability slow exchange k ex << (A) (B) intermediate exchange k ex ~ (A) - (B) fast exchange k ex >> (A) - (B) 7

8 Two-Site Exchange: Rotation about a partial double bond in dimethylformamide Equal Population of Exchange Sites slow 40 Hz Increasing Exchange Rate k = 0.1 s -1 k = 5 s -1 k = 10 s -1 k = 20 s -1 k = 40 s -1 coalescence k = 88.8 s -1 fast k = 200 s -1 k = 400 s -1 k = 800 s -1 k = 10,000 s -1 8

9 Unequal Population of Exchange Sites: obs = f f 2 2 f 1 + f 2 =1 where: f 1, f 2 mole fraction of each species 1, 2 chemical shift of each species 9

10 McConnell s Modification of the Bloch Equations Exchange effects on the lines can be simulated using the McConnell s Modification of the Bloch Equations. The McConnell equations combine the differential equations for a simple two-state chemical exchange process with the Bloch differential equations for a classical description of the behavior of nuclear spins in a magnetic field. This equation system provides a useful starting point for the analysis of slow, intermediate and fast chemical exchange studied using a variety of NMR experiments. Add first order kinetics terms to the Bloch equations for the change in magnetization over time. Can obtain a general equation for the real part of the frequency domain signal arising from symmetric chemical exchange. McConnell, H. M. (1958). "Reaction rates by nuclear magnetic resonance." Journal Of Chemical Physics 28: Idiyatullin, D., S. Michaeli and M. Garwood (2004). "Product operator analysis of the influence of chemical exchange on relaxation rates." Journal of Magnetic Resonance 171(2):

11 Symmetric Two-Site Exchange: Measuring the Exchange Rate k = o2 /2(h e -h o ) k = o / 2 1/2 k = ( o2 - e2 ) 1/2 /2 1/2 k = (h e -h o ) k exchange rate peak frequency h peak-width at half-height e with exchange o no exchange 11

12 Asymmetric Two-Site Exchange If the populations of A and B are different the position of the averaged peak is a population-weighted average: average = p A A + p B B If the chemical shifts of the two species are known, then the position of the peak in the fast exchange spectrum may be used to derive the equilibrium constant of the reaction. (h e -h o ) = 4 p A p B o2 /(k A +k B ) Fast Exchange Coalescence Slow exchange δ calculation of a two-site exchange system for the ratio between the chemical shift difference δ and the rate constant 1/τ varying between 40 and 0.1 k A = (h e -h o ) A k B = (h e -h o ) B k exchange rate peak frequency h peak-width at half-height e with exchange 12 o no exchange

13 Diagnosis of the exchange regime 13

14 Scenario: Two-Site Exchange in Fast Exchange Limit Extra term is due to exchange broadening 14

15 Scenario: Two-Site Exchange in Limit of Slow Exchange If see plot like this, exchange is present: as increase temp, LW will initially decrease then increase 15

16 Scenario: Two-Site Exchange at Coalescence 16

17 Two-Site Exchange: Coalescence Temperature and Measurement of Thermodynamic Parameters for Interconversion Eyring relation used to determine ΔG from the temperature dependence of k: Arrhenius plot of ln( LW) vs 1/T will give G act 17

18 The NMR Advantage for Studying Dynamics NMR is able to detect chemical exchange even when the system is in equilibrium we can perturb the magnetization in one state to study rates without perturbing the chemical system. Almost all other spectroscopic methods of measuring rates involve displacing the system from equilibrium and following its return to equilibrium. Timescale of UV/Vis/IR spectroscopy is very small because lifetime of excited state is short spectrum of mixture is a sum of its individual components B A C In NMR, spectrum of mix is not necessarily a sum of spectra of its individual components depends on timescale of process. A B C Binding of a lanthanide complex to an oligonucleotide by UV/Vis Proton NMR selective inversion experiment on dimethylacetamide 18

19 NMR Methods To Study Exchange: RT NMR First and foremost, NMR provides access to site-specific probes of local structure and dynamics with unmatched coverage across almost every atom in the protein In this powerful yet simple approach, dynamic processes on the ~s timescale are directly detected by quantifying the time-dependence of NMR signal intensities. Physical processes on this timescale include: protein folding solvent hydrogen-exchange relatively slow conformational changes cis-trans proline isomerization domain movements The real-time (RT) NMR experiment is performed by initiating the physical process of interest then rapidly acquiring a sequence of NMR spectra. A special injection apparatus or application of laser light can streamline the initiation process within the NMR tube to study protein folding, ligand binding or conformational changes. The signal intensities from a series of spectra as a function of the time of acquisition are then fitted to an appropriate model such as exponential conversion from A B. 19

20 RT NMR Example: Hydrogen Exchange (HX) vs. Protein Structure Hydrogen exchange (HX) is used to measure the exchange rate of the labile protons in a macromolecule. For example, if a protein is placed in D 2 O, the amide signals due to 1 H nuclei will disappear over time due to chemical exchange. The observed NH intensity loss can usually be fit to a simple exponential to measure a exchange rate (k ex ): The amide exchange rate usually correlates with the secondary structure in proteins. Can also use to determine sites that are protected after complexation. 20

21 RT NMR Example: Folding of Protein Upon ph Change Study folding of the protein α-lactalbumin upon ph jump using a rapid-mixing apparatus.. After a post-mixing dead time of 2 s, each 2D spectrum was acquired in a mere 10 s, revealing distinct signals from both the molten globule state and the folded state of the protein: Time-dependent intensities of 92 signals from the folded state and 5 signals from the molten globule state fit well to a single-exponential with τex=109±5 s, consistent with a global two-state folding pathway: 21

22 NMR Methods To Study Exchange: Exchange Spectroscopy EXchange SpectroscopY (EXSY), also known as the zz-exchange experiment, is used to quantify dynamic processes in the ms time window. Physical processes in this time window include slow conformational changes such as domain movement, ligand binding and release, topological interconversion of secondary structure and cis-trans isomerization. EXSY requires that the dynamic process is in the slow exchange regime where each structural probe reveals a unique set of signals (kex Δν ). Typically, a series of 2D spectra are acquired with different values of t mix to generate build-up curves from the four measured intensities. These data are fit to an exchange model to extract kinetic rates of interconversion. For two-state exchange, three equations describe the three unique build-up curves: 22

23 EXSY Example: Catalytic Mechanism within the Proteasome Practically though, many EXSY studies only require a few structural probes to address the questions of interest. For example, in studies of the α7 annulus of the 20 S proteasome core particle, two crucial methionine methyl probes were sufficient to provide unique insight into motions vital to its catalytic mechanism. Studying this massive 180 kda complex was made possible via special methyl group labeling. The authors concluded that the gating of this proteasome is controlled through highly dynamic N- termini that interconvert between conformations that place them either outside or well inside the antechamber, with rates of proteolysis that depend on the relative populations of termini in the in and out states. 23

24 Saturation Transfer: A Method to Measure Kinetics Under Slow Exchange Saturation of PCr signal causes the - phosphate of ATP to decrease in intensity and vice versa during metabolic flux 24

25 Inversion Transfer: A Method to Measure Kinetics Under Slow Exchange 25

26 NMR Methods To Study Exchange: Lineshape Analysis Lineshape analysis is a relatively straightforward approach to interpretation of NMR spectra reporting exchange in the ms time window. Physical processes in this time window include: binding events and slow intermediate conformational changes such as small domain movements that could affect catalytic turnover rate and allostery. Typically, a series of spectra are acquired along a titration coordinate such as ligand concentration, temperature or ph to observe their incremental effect upon the NMR spectrum. The spectra in the series may differ depending on the timescale of chemical exchange: 26

27 Measuring the Binding Constant Under Fast Exchange Titration of ligand binding to protein monitored by 2D 15 N- 1 H HSQC Ligand Concentration Plot chemical shift as a function of ligand concentration to get K d really only accurate under conditions of very fast exchange (see Lian & Roberts) 27

28 Ligand Binding Under Slow Exchange (k << A - B) Generally more difficult to measure K d under conditions of slow exchange but can use intensity changes 28

29 Measuring Binding Using NMR: Chemical Shift Mapping (CSP-NMR) Monitor the binding of ligands can be small molecules, drugs, inhibitors, peptides, proteins, etc. Determine binding constants Site-specific Spatial distribution of responses can be mapped on structure 29

30 Chemical shift, ph and Measurement of pk a HOOC-CH-CH - 3 OOC-CH-CH3 NH 2 NH 2 = p 1 p 2 ph = pk a + log max - min max shift under acidic conditions min shift under basic conditions Observed shift 30

31 More to come. Ligand conformations - Transferred noe Drug discovery/ Ligand screening based on STD (Saturation Transfer Difference) and other methods pka s Exchange Influences NMR Spectroscopy In Many Ways Enzyme kinetics Protein folding/unfolding Binding sites H-bonding and Hydration 31