Millisecond Time-scale Protein Dynamics by Relaxation Dispersion NMR Dmitry M. Korzhnev Department of Molecular, Microbial and Structural Biology University of Connecticut Health Center 263 Farmington Ave, Farmington, CT, 06032-3305, U.S.A. June 202 (tutorial Introduction NMR Tools for Studies of Protein Dynamics From Wang & Palmer, (2003 Magn. Reson. Chem. 4, 866
Introduction Conformational Exchange: Processes Accompanied by Changes in NMR Chemical Shifts ω s No Exchange Slow Exchange (k ex < ω µs Intermediate Exchange (k ex ~ ω Fast Exchange (k ex > ω Major techniques are based on modulation of the exchange line broadening - CPMG modulation by CPMG-type refocusing sequences -R ρ modulation by on- or off-resonance RF irradiation Introduction Conformational Exchange in Proteins Energy landscape of a protein: Processes involving high-energy protein states: High-energy state - protein recognition and binding - enzyme catalysis - protein folding Ground state ms Multi-dimensional! Ground state Invisible excited state p > 0.5% 2
Introduction Conformational Exchange in Proteins Cavity creating mutant L99A T4 lysozyme Processes involving high-energy protein states: - protein recognition and binding Open? - protein folding - enzyme catalysis Closed Bound cavity mutant T4 lysozyme (µs-ms, CPMG: Mulder et al (200 Nature Struct. Biol. 8, 932 935 Bouvignies et al (20 Nature 477, -4 pkid / KIX complex (µs-ms, CPMG Sugase, Dyson, Wright (2007 Nature 447, 02-025. CIN85 SH3 domain / ubiquitin (µs-ms, CPMG: Korzhnev et al (2009 J. Mol. Biol. 386, 39 405 In general: ms - k on =0 6-0 7 M - s -, k D =0-00 µm Introduction Conformational Exchange in Proteins Processes involving high-energy protein states: - protein recognition and binding - protein folding - enzyme catalysis DHFR - dihydrofolate reductase (µs-ms, CPMG: Boehr, McElheny, Dyson,Wright (2006 Science 33, 638-642 cyclophilin A (µs-ms, CPMG Eisenmesser et al (2005 Nature 438, 7-2 RNase A (µs-ms, CPMG: Kovrigin, Loria (2006 Biochemistry 45, 2636-2647 3
Introduction Conformational Exchange in Proteins Unfolded Processes involving high-energy protein states: - protein recognition and binding Intermediate? Misfolded? - protein folding - enzyme catalysis Folded Oligomer Aggregate villin headpiece (µs, R ρ : Grey et al (2006 J. Mol. Biol 355, 078-094 Fyn SH3 domain (µs-ms, CPMG, R ρ Korzhnev et al (2004 Nature 430, 526-590 Korzhnev et al (2005 JACS 27, 73-72 FF domain (µs-ms, CPMG: Korzhnev et al (200 Science 329, 32-36 Introduction Lecture Outline. Introduction 2. CPMG-type relaxation dispersion measurements - basic principles - theory (R 2,eff CPMG as a function of exchange parameters - 5 N CPMG experiments (R 2, relaxation-compensated, decoupled, TROSY/anti-TROSY - CPMG-type experiments for different nuclei and spin-coherences 3. CPMG data interpretation and analysis - discrimination between 2-state and multiple-state exchange models - characterization of transition/intermediate states from kinetic/thermodynamic parameters - extraction of chemical shifts and RDCs in excited protein states 4. Protein structure determination from limited NMR data - structure of excited states from chemical shifts and RDCs 4
CPMG Principles Principle of CPMG Experiment - Spin-Echo Spin-echo 90 o ±y 80 o x Hahn (950, Phys. Rev. 80, 580 NMR spectrum of a nucleus Ω A ω = Ω B -Ω A exchange M A M A exp(-2r 2,eff R 2,eff effective transverse relaxation rate Exchange A B Ω B CPMG: multiple-echo pulse sequence Carr & Purcell (954 Phys. Rev. 4, 630 Meiboom, & Gill (958, Rev. Sci. Instrum. 29, 688 90 o ±y 80 o x Exchange is studied via modulation of R 2,eff by CPMG n CPMG Principles What are CPMG-type Relaxation Dispersions? Relaxation Dispersion - the dependence of R 2,eff on CPMG frequency ν CPMG = /(4 R 2,eff Exchange A B π 2 delay between pulses CPMG pulse-sequence π π π π 2 2 2 M A M A exp(-r 2,eff T T π π π π π π ν CPMG M A - transverse magnetization π - 80 o pulse 2 - delay between 80 o pulses 5
CPMG Principles What are CPMG-type Relaxation Dispersions? Relaxation Dispersion - the dependence of R 2,eff on CPMG frequency ν CPMG = /(4 R 2,eff Exchange A B π 2 delay between pulses R 2,eff (ν CPMG = f (p B, k ex, ϖ π π π π π π ν CPMG p B populations - thermodynamics k ex exchange rates - kinetics ϖ chemical shift - structure differences CPMG Principles What is measured in CPMG-type relaxation dispersion experiments? Regular approach: - For each ν CPMG peak intensities are measured at different length of relaxation period T - R 2,eff is obtained by exponential fit of peak intensities A exp(-r 2,eff T Problem: Excessively time-consuming Constant relaxation time approach: - For each value of ν CPMG a single spectrum is recorded at given T - one reference spectrum is recorded at T = 0. * - peak intensities Rare ( ν CPMG converted = to inr anti + 2 2,eff as: R eff 2 ( R + R R ( ν 2 ex CPMG I( ν CPMG ( ν CPMG = ln T I 0 R 2 ν CPMG ν CPMG 6
CPMG Principles CPMG Data Analysis To extract conformational exchange parameters ζ experimental data R 2,eff are least-square fit by model values R 2,eff clc (ζ : 2 χ ( ζ = clc ( R2, eff ( ζ R2, eff 2 ( R2, eff 2 Done by minimization of χ 2 (ζ ζ = {k ex, p B, ω, R 2,inf } Experimental data: Model data: R 2, eff I ( ν CPMG = ln T I 0 R clc 2, eff M A (4 n ( ζ = ln 4 n M (0 A M A (0 initial magnetization of ground state A M A (4n magnetization after( 80 80 n sequence CPMG Theory R 2,eff as a Function of Exchange Parameters Model data: R clc 2, eff M A (4 n ( ζ = ln 4 n M (0 A ζ = {k ex, p B, ω, R 2,inf } CPMG pulse-sequence (-80---80- n π π π π M(0 2 2 2 M(4n=M(0exp(-R 2,eff T??? T To derive expression for R 2,eff (ζ one has to calculate M(4n by modeling magnetization evolution during CPMG sequence Next slides expressions for R 2,eff (ζ 7
CPMG Theory Chemical exchange A B d [ A ] = k AB[ A ] + k BA[ B ] dt d [ B ] = k AB[ A ] k BA[ B ] dt [A], [B] - concentrations of reactant and product k AB, k BA - rates of forward and reverse processes d [ A] kab kba [ A] dt [ B] = kab k BA [ B] Exchange CPMG Theory Bloch-McConnell Equation Evolution of magnetization under free precession in 2-state exchange case d dt M M A± B± ( t R2 k = ( t k AB AB k BA ± i ω R 2 k BA M M A± B± ( t ( t M A±, M B± - magnetization of states A and B M + = M x +im y M - = M x -im y relaxation CS evolution exchange d!! M dt ( t = Rˆ M ( t ± ± ± R + and R - are evolution matrices for M + and M - magnetization vectors 8
CPMG Theory Solution of Bloch-McConnell Equation d!! M dt ( t = RM ˆ ( t M! R M! ( t = exp{ ˆ t} ( 0 matrix exponential can be calculated numerically e.g. in Mathematica or MATLAB software. CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n M! M! M! ( 0 = ( 0 + ( 0 + Consider magnetization evolution starting from M + = M x +im y 9
CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n M! R M! ( = exp{ ˆ } ( 0 + + + In the first period magnetization M + evolves under the influence of R + CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n M! R M! ( 80 = exp{ ˆ } ( 0 + + 80 o pulse interconvert M + and M - 0
CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n M! R R M! ( 80 = exp{ ˆ } exp{ ˆ } ( 0 + + In the second period magnetization M - evolves under the influence of R - CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n M! R R R R M! ( 80 80 = exp{ ˆ } exp{ ˆ } exp{ ˆ } exp{ ˆ } ( 0 + + + + Second -80- is considered similarly to the first one but magnetization evolution starts from M -
CPMG Theory Magnetization Evolution in CPMG Sequence 80 2n n ( 4n = ( exp{ ˆ } exp{ ˆ } exp{ ˆ } exp{ ˆ } ( 0 M! R R R R M! + + + + or in compact form! "! M S M ( 4n = exp{ 4n} ( 0 General equation for magnetization evolution during CPMG sequence (obtained by taking power n of evolution matrix for -80---80- block CPMG Theory Generalization to Multiple-State Exchange Case n ( 4n = ( exp{ ˆ } exp{ ˆ } exp{ ˆ } exp{ ˆ } ( 0 M! R R R R M! + + + + A k p ex B ω BA 2 states - R + and R - are 2x2 matrices A k ex p C A B k ex p B C B k ex ω CA ω BA D F C G E 3 states - R + and R - are 3x3 matrices n states - R + and R - are nxn matrices H R clc 2, eff R 2 M A (4 n = ln 4 n M A (0 v CPMG 2
CPMG Theory Analytical expressions for R 2,eff in case of 2-state exchange! "! M S M ( 4n = exp{ 4n} ( 0 M A (4n = C exp(λ T+C 2 exp(λ 2 T λ and λ 2 - eigenvalues of S In most cases of interest λ << λ 2 so that one exponential term dominates: M A (4n = C exp(λ T In some cases λ can be calculated analytically CPMG Theory Fast Exchange Regime Luz-Meiboom and Bloom Equations Luz-Meiboom formula: Luz, Meiboom, J. Chem. Phys. 39 (963 366 R 2, eff 2 ( k 2 p tanh ApB ω ex = R + kex kex Valid in: Fast exchange limit: High field limit: k ex >> ω ν CPMG >> ω Bloom formula: Bloom et al (965 J. Chem. Phys. 42 65 kex k 2, 2 sinh ex eff sinh R = R + ( ξ 2 2 ξ ξ = k 4 p p ω 2 2 ex A B Extracted parameters: k ex and p a p b ω 2 3
CPMG Theory Intermediate Exchange Regime Carver-Richards Equation Carver, Richards (972, J. Magn. Reson., 6, 89-05 Davis et al (994, J. Magn. Reson B 04, 266 275 eff kex R2 = R2 + D D 2 4 cosh + cosh + cos ( η η D 2 ψ + 2 ω = ± 2 2 2 ψ + ζ ± ζ = 2 ω( p p k A B ex 2 2 η 2 ψ ζ ψ ± = + ± ψ = 2 2 2 ( p p k ω + 4 p p k ( A B ex A B ex General equation Valid at: k ex >> R 2 p B << Extracted parameters: k ex, p B (p A, ω CPMG Theory Slow Exchange Regime Tollinger-Skrynnikov-Kay Equation Tollinger et. al. (200 J. Am. Chem. Soc., 23, 34. ( ω sin R2, eff = R2 + kab ω Valid in: Slow exchange limit: k ex << ω Extracted parameters: k AB, (but not k BA, ω 4
CPMG 5 N experiments Regular 5 N R 2 CPMG Experiment Farrow et al. (994 Biochemistry, 33, 5984-6003 Problem: Mixing of inphase N x and antiphase 2N y H z magnetization due to scalar coupling lead to undesirable dispersions. R2, eff ( νcpmg = εrin + ( ε Ranti + Rex ( νcpmg sin( πj ε 2 πj / 2ν = NH CPMG NH / 2ν CPMG Range of validity: ν CPMG >πj NH /2 i.e. at ν CPMG from 400-500 Hz and higher CPMG dispersion profiles must be flat in the absence of exchange! 5
CPMG 5 N experiments Relaxation-Compensated 5 N CPMG Scheme (RC-CPMG Loria, Rance, Palmer (999 J. Am. Chem. Soc. 2, 233-2332 -N x 2N y H z N x 2N y H z 2N y H z N x Flatness enforced: R2, eff ( νcpmg = ( Rin + Ranti + Rex ( νcpmg 2 T/2 T/2 Accessible ν CPMG range: from 50 to 000 Hz with 50 Hz step (at T=40ms CPMG 5 N experiments Decoupled 5 N CPMG Scheme (CW-CPMG Hansen, Vallurupalli, Kay (2008 J. Phys. Chem. B 2, 5898-5904 Advantages over RC-CPMG: - Improved sensitivity in-phase magnetization N x evolves during relaxation period T, instead of the mix of N x and 2N y H z which relaxes faster than pure N x. - Better sampling of ν CPMG Minimal number of π pulses in CW- CPMG is 2 instead of 4 in RC-CPMG, which allows sample ν CPMG with 2-times smaller step N x N x Accessible ν CPMG range: from 25 to 000 Hz with 25Hz step (at T=40ms 6
CPMG 5 N experiments 5 N TROSY and anti-trosy CPMG Schemes Loria, Rance, Palmer (999 J. Biomol. NMR 5, 5-55 Vallurupalli et al (2007 PNAS 04, 8473 8477 Red TROSY Blue anti-trosy N x -2N x H z N x +2N x H z N x -2N x H z N x +2N x H z TROSY anti-trosy Element in the middle is to suppress cross-relaxation between TROSY and anti-trosy components (selectively inverts sign of anti-trosy relative to TROSY, and vice versa TROSY-CPMG - beneficial for large proteins TROSY-CPMG and anti-trosy-cpmg allow measurements of HN RDCs in excited states CPMG Experiments for Different Nuclei: Isotope Labeling Schemes CPMG Experiments for different nuclei / coherences Backbone Nuclei: 5 N Loria et al., (999 JACS 2, 233 Loria et al., (999 JBNMR, 5, 5 (TROSY H N Ishima, Torchia (2003 J. Biomol. NMR 25, 243. Orekhov, Korzhnev, Kay (2004 JACS 26, 886 (TROSY 3 C α Hansen et al (2008 JACS 30, 2667 3 H α Lundstrom et al (2009 JACS 3, 95 3 C O Ishima et al (2004 JBNMR 29, 87. Lundstrom, Hansen, Kay (2008 JBNMR 42, 35 Minimal labeling: reviewed in Lundstrom et al. (2009 Nat. Protocols 4, 64 5 N, 3 C O 5 N/U- 3 C 3 C-glucose, 5 NH 4 Cl, grown in H 2 O H N 5 N/U- 2 H 2 H-glucose, 5 NH 4 Cl, grown in 2 H 2 O 3 C α selective- 3 C (- 3 C-glucose, grown in H 2 O H α U- 3 C/partially- 2 H 3 C/ 2 H- glucose, grown in : 2 H 2 O:H 2 O 7
CPMG Experiments for different nuclei / coherences CPMG Experiments for Different Coherences: Six CPMG-type Schemes for the Backbone Amide Groups H- 5 N energy level diagram Six CPMG-type experiments H SQ H single-quantum (H + +H - Ishima, Torchia (2003 J. Biomol. NMR 25, 243. Orekhov, Korzhnev, Kay (2004 JACS 26, 886 (TROSY H 5 N 5 N SQ 5 N single-quantum (N + +N - Loria et al., (999 JACS 2, 233 Loria et al., (999 JBNMR, 5, 5 (TROSY H 5 N H- 5 N DQ double-quantum (N + H + +N - H - H- 5 N ZQ zero-quantum (N + H - +N - H + H 5 N Orekhov, Korzhnev, Kay (2004 JACS 26, 886 H H MQ H multiple-quantum (N X H X 5 N MQ 5 N multiple-quantum (N X H X Korzhnev et al. (2004 JACS 26, 7320 5 N H 5 N Six experiments allow accurate characterization of a multi-state exchange! CPMG Experiments for different nuclei / coherences CPMG Experiments for Different Coherences: Six CPMG-type Schemes for the Backbone Amide Groups H- 5 N energy level diagram Six CPMG-type experiments G48M Fyn SH3 Six experiments allow accurate characterization of a multi-state exchange! 8
CPMG Experiments for different nuclei / coherences 3 C MQ-CPMG Experiment for Side-Chain Methyl Groups: Methyl-TROSY 3 C SQ CPMG single-quantum Skrynnikov et al., (200 J. Am. Chem. Soc. 23, 4556 3 C MQ CPMG multiple-quantum (methyl TROSY Korzhnev et al., (2004 J. Am. Chem. Soc. 26, 3964 Malate Synthase G, 723 residues (82 kda 20S Proteasome CP (670 kda 3 C MQ Sprangers, Kay (2007 Nature, 445, 68 CPMG - data analysis and interpretation 2-State vs Multiple-state Exchange Inconsistency of 2-state parameters obtained from local fits (e.g. on a per-residue basis more complex process more than 2-states involved Intermediates! Global fit of CPMG data Multiple: - Resiudes -Nuclei - Spin coherences - Magnetic fields - Temperatures - Pressures - Denaturent - Solvent viscosities Discrimination between 2-state and multi-state exchange models Global 3-state fit multiple minimum problem χ 2 model parameters 9
CPMG - data analysis and interpretation Kinetics and Thermodynamics of Exchange Processes p i populations - thermodynamics of exchanging states k ex,ij exchange rates - thermodynamics of transition state ensembles Example: Temperature dependence of exchange rates Variables: Temperature entropy, enthalpy Pressure volume Denaturant m-values etc CPMG - data analysis and interpretation Obtaining Signs of Chemical Shift Differences Parameters extracted from CPMG data: k ex p B ω Signs of ω need to be determined from additional experiments. From changes in peak position in HSQC or HMQC spectra recorded at different magnetic fields : Skrynnikov, Dahlquist, Kay JACS. 2002 24 2352 5 N direction in HSQC 5 N ppm 800 MHz 5 N HSQC 500 MHz minor peak invisible ± ω? ( up to ~20 ppb 5 N H ppm 2. From R ρ measurements at low spin-lock field strength: Korzhnev et al (2005 JACS 27, 73 Auer et al (2009 JACS 3, 0832 Auer et al (200 J. Biomol. NMR 46, 205 20
CPMG - data analysis and interpretation Chemical Shifts and RDCs Report on Structure of Excited States ϖ chemical shift differences - local backbone and side-chain structure D RDC differences - orientation of secondary and tertiary structure elements Ground state Invisible high-energy state - 0.5 0 % population - millisecond life-time ϖ B? D B CHESHIRE Cavalli et al (2007, PNAS 04, 965 ϖ B D B Structure of excited states CS-ROSETTA Shen et al (2008, PNAS 05, 4685 Structure calculation of excited states Example Structure of Transient Folding Intermediate of the FF domain FF domain from human HYPA/FBP - Folds via an on-pathway intermediate F I U - Folds in two phases fast U I - microsecond ~0 5 /s slow I F - millisecond ~0 3 /s - 7 amino acids - α-α-3 0 -α topology - Wild-type FF domain Intermediate state: p I ~ -5% at 20-35 o C millisecond life-time Unfolded state: p U << p I undetectable Jemth et al (2004 Proc. Natl. Acad. Sci. 0, 6450 Jemth et al (2005 J. Mol. Biol., 350, 363 Korzhnev et al (2007 J. Mol. Biol., 372, 497 - Detection of intermediate; 3-state kinetics - Φ-value analysis of F I transition state - NMR relaxation dispersion; HD exchange 2
Structure calculation of excited states Example Relaxation Dispersion Measurements for the WT FF Domain 5 NSQ CPMG 5 N/ 2 H protein H 2 O 30 o C Backbone chemical shifts: Relaxation dispersion experiments 3 C α SQ CPMG 5 N/selective- 3 C α protein H 2 O 30 o C H N SQ CPMG 5 N/ 2 H protein H 2 O 30 o C 3 C O SQ CPMG 5 N/ 3 C/ 2 H protein H 2 O 30 o C H α SQ CPMG 5 N/ 3 C/partial- 2 H protein 2 H 2 O 35 o C 5 N- H RDCs: Relaxation dispersion experiments 5 N SQ CPMG (single-quantum 5 N TR CPMG (TROSY 5 N AT CPMG (anti-trosy 5 N/ 2 H protein PEG(C 2 E 5 /hexanol mixture H 2 O 30 o C Chemical shift differences ϖ IF RDC differences D IF ϖ I =ϖ F + ϖ IF 93% backbone resonance assignment of the I state D I =D F + D IF 92% of 5 N- H RDCs of the I state Structure calculation of excited states Example Secondary Structure and Flexibility of the Folding Intermediate from NMR Chemical Shifts Secondary structure: Flexibility: TALOS+ Shen et al (2009 J. Biomol. NMR 44, 23 RCI Berjanskii et al (2005 JACS 27, 4970 non-native S 2 = - rigid S 2 = 0 - dynamic Intermediate has a well defined core: S 2 > 0.6: 2-30, 33-54, 58-65 (46 residues Intermediate has a well structured core with non-native C-terminal part 22
Structure calculation of excited states Example Structure Determination of the Folding Intermediate by CS-Rosetta Flow chart of CS-Rosetta calculations: Structure generation step by step: From http://spin.niddk.nih.gov/bax/software/csrosetta/. Select residue frame -66 cut off flexible tails -0, 67-7 (RCI S2<0.6 2. Run CS-ROSETTA calculations input data: N HN 3Cα Hα 3CO chemical shifts 5 0,000 models 3. Re-score generated models according Rosetta score + CS score + RDC score input data: chemical shifts, 5N-H RDCs RDCs input 0 best structures Structure Calculations for the Folding Intermediate Converged! Convergence: Experimental vs. predicted data: Chemical shifts: Funnel-like CS-Rosetta score vs. RMSD to best structure Residual Dipolar Couplings: (over residues with S2 > 0.7 Structural ensemble of the folding intermediate is in good agreement with experimental data 23
Structure calculation of excited states Example Structure of the Intermediate Reveals Details of the Folding Pathway Folded (native: Korzhnev et al (200 Science 329, 32-36 Intermediate: Breaking non-native structure upon I F transition causes two orders of magnitude slowing folding rate Summary of Material Introduced. Principles of CPMG relaxation dispersion measurements 2. Theoretical consideration CPMG-type experiments 3. Pulse-sequences for 5 N CPMG dispersion measurements 4. Analysis and interpretation of CPMG dispersion data 5. Structure calculation of excited states with CS-Rosetta 24
Deadline: Dec 20 TOEFL/GRE korzhniev@uchc.edu 25