Protein Dynamics by NMR Why NMR is the best!
Key Points NMR dynamics divided into 2 regimes: fast and slow. How protein mobons affect NMR parameters depend on whether they are faster or slower than the rotabonal correlabon Bme Fast Bmescale dynamics (ps ns) limited by rotabonal correlabon Bme of protein parameters describe distribubon of states Slower Bmescale dynamics (µs ms) require chemical shil difference measured more directly
Protein Dynamics by NMR H N Relaxation T1, T2, heteronuclear NOE Relaxation T1ρ, CPMG Lineshape analysis ZZ-exchange, NOESY H/D exchange
NMR Timescales Transport, catalysis, many interesbng biological processes.. ps ns µs ms sec >hrs Relaxa&on T1, T2, HETNOE Relaxa>on T1ρ, CPMG Satura>on transfer ZZ exchange, NOESY Line shape analysis H/D exchange
Slow Timescale Exchange Great for characterizing a 2 state process: Open vs closed conformabon of a protein Free vs bound state Folded vs unfolded 3 or more state More challenging to analyze quanbtabvely Strength of NMR Simultaneously measure exchange rate (kinebcs) populabons (thermodynamics) chemical shils (structural informabon) Site specific resolubon. Is the process global or local? If global, all residues should have the same exchange rate and populabons **Fast and slow regimes within the slow >mescale limit!!!**
Characterizing a 2 state processes G (k AB ) G p A,ω A State A: Structural info embedded in chemical shil, ω A p B,ω B G (k BA ) State B: Structural info embedded in chemical shil, ω B k A AB B k BA k ex = k BA + k AB Thermo: G= RTlnK eq K eq =p B /p A KineBcs: k ex =k BA +k AB k AB =p A k ex p A +p B =1 p A >p B k BA >k AB
Basic NMR reminders Chemical shil depends on the environment of the nucleus Hydrogen bonding, secondary structure, ring currents, electrostabcs, side chain torsion angles, etc. Two different states have two different chemical shils Integrate to determine populabons Just like organic chemistry integrate peaks to see which correspond to 1,2, or 3 protons. If two peaks correspond to the same nucleus in two states, then the integrals give the relabve populabons If peaks are of similar width, can use peak height instead of volume. z (B o ) Net magnebc moment Precession at chemical shil frequency
Basic NMR reminders Chemical shil is a precession frequency. Serves as a reference point for measuring protein dynamics. Slow Bmescale dynamics are described as fast or slow depending on the relabve values of k ex and ω (chemical shil difference between the two states). To convert from ν in ppm to ν in Hz: use ν=γb o /2π (ν=ω/2π ) ppm is parts per million, so 1ppm=600Hz on a 600MHz spectrometer. z (B o ) Net magnebc moment Precession at chemical shil frequency
TheoreBcal NMR line shapes for fast k ex >> ν two site exchange k ex (s 1 ) 10000 2000 900 k A AB B k BA k ex = k BA + k AB 200 slow k ex << ν 20 < 0.1 Remember: Chemical shil difference ( ν) is a frequency. Popula>on 0.5 0.5 0.75 0.25 Palmer, et al, Methods in Enzymology, 2001
Lineshape Analysis Requires a BtraBon TheoreBcal equabons for lineshape (including peak width, intensity, separabon) Parameters: intrinsic relaxabon rates (R 2o ), exchange rate (k ex ), populabons (p A ), chemical shil difference ( ν) Change condibons so that the values of the parameters change in disbnct ways so they can be deconvoluted Fit the lineshape as a funcbon of BtraBon Adding ligand (free vs bound) Adding denaturant (folded vs unfolded) Changing ph (pka determinabon) Changing temperature (folding, conformabonal change, almost any process)
Fast Exchange k ex >> ν Observe a single peak at the weighted average posibon. What happens upon BtraBon? As populabon shils, peak posibons shils Ex. ShiLing 2 state equilibrium State A=free State B=bound State A=folded State B=unfolded State A=open conformabon State B=closed conformabon If 600 MHz spectrometer, Then ν=1200 Hz k ex?
Slow Exchange k ex << ν Peaks don t shil. What happens upon BtraBon of a 2 state system? As populabon shils, peaks corresponding to each state appear/ disappear Ex. ShiLing 2 state equilibrium State A=free State B=bound State A=folded State B=unfolded State A=open conformabon State B=closed conformabon If 600 MHz spectrometer, Then ν=1200 Hz k ex?
OLen somewhere in the middle k ex and ω both influence the peak posibon/lineshape. Careful analysis can determine p A, k ex, and ω. ω will not be the same for all residues in a protein might have some in slow exchange, some in fast exchange, some in intermediate. Wolf Watz, et al. Nat. Struct. Mol. Biol. 11, 945 949. a 4.0 mm 1.4 mm 0.8 mm 0 mm 7.1 7.0 6.9 1 H (p.p.m) 106 107 108 15 N (p.p.m) TitraBon of ligand (concentrabon indicated) into protein. A) shows a peak from the protein HSQC undergoing the transibon from free to bound. B) shows the 1D lineshape simulabon of the spectrum. b 108.0 107.0 15 N (p.p.m) 106.0 105.0
Hidden exchange Skewed populabons what if you can t see the second state because it s only 2% populated? ex. Slow exchange but second peak so much less intense it s not observable) What if you can t Btrate something to reveal the exchange, but suspect that your protein is undergoing exchange? Or you want to quanbfy the exchange? Fast exchange: only see an average peak. Do you have a single state or is there an equilibrium? Slow exchange: 2 sets of peaks. Is it slow exchange or no exchange? NOESY, ZZ exchange helpful for ms s exchange (ms s) CPMG helpful for µs ms exchange
NOESY/ZZ analysis Basic strategy: Record inibal chemical shil, wait (mixing Bme), record final chemical shil No exchange: inibal and final states are the same (ω 1 =ω 2 ) observe diagonal/auto peak With exchange: chemical shil of final state is different than the inibal state observe crosspeak (ω 1 ω 2 ) NOTE: chemical shil of the two states must be different in order to observe the exchange Ex. regions close to binding interface will show the effect of binding, regions far away will not. By chance, even if there is a conformabonal change, an individual residue within that region may have the same chemical shil in both states. Useful for Slow exchange, 2sets of peaks already visible in spectrum Exchange rates 10s 100s of milliseconds Direct kinebc measurement vary mixing Bme and see how much conformabonal change occurs
NOESY Analysis 1 H Encode chemical shil (ω1) Mixing Bme Acquire data (chemical shil, ω2) Crosspeaks arise when: H B H B N 2 protons are close in space ω1 (ppm) H A H C2 H C1 State 1 State 2 H C1 H C2 ω2 (ppm) H A H B Slow conformabonal exchange between 2 states with different chemical shils
ZZ exchange Insert mixing >me (spins along z, hence the name ZZ exchange) Transfer magnebzabon from 1H to 15N Transfer magnebzabon from 15N to 1H HSQC Record chemical shil in indirect dimension (t 1 ), 15 N frequency in this case Record chemical shil in directly detected dimension (t 2 ), 1 H frequency in this case HSQC 15 N HSQC+ ZZ 15 N 2A 2B 1B (If no exchange, no addifonal peaks will be observed) 1A 1 H 1 H
NOESY/ZZ analysis Record ω 1, mixing Bme, record ω 2 Vary mixing Bme (10s 100s of milliseconds) Monitor build up of cross peaks and decay of auto peaks to determine exchange rate Since it s slow exchange da dt = R A 1 A k AB A + k BA B db dt = R B 1 B k BA B + k AB A R 1 is intrinsic relaxabon rate, k ex =k AB +k BA get populabons from relabve heights/volumes of inibal peaks Get chemical shil of inibal states from inibal peaks
ZZ exchange example 105.0 15N (ppm) 110.0 115.0 120.0 125.0 130.0 In this example, the two peaks corresponding to a single amide in the HSQC have equal volumes, thus the two states are equally populated. 135.0 11.0 10.0 9.0 1H (ppm) 8.0 7.0
ZZ exchange example da dt = R A 1 A k AB A + k BA B db dt = R B 1 B k BA B + k AB A Equal populabons means: da dt db = R A 1 k k k R B 1 k dt [ A] B
Characterizing a 2 state processes G (k AB )= G (k BA ) Thermo: G= RTlnK eq =0 K eq =p B /p A =1 G=0 p A,ω A p B,ω B State A: Structural info embedded in chemical shil, ω A State B: Structural info embedded in chemical shil, ω B KineBcs: k ex =k BA +k AB k AB =p A k ex p A +p B =1 p A =p B =0.5 k BA =k AB k AB A B k BA k BA = k AB
CPMG: Transverse RelaxaBon & ConformaBonal Exchange z z z 90 y T 2 delay B 0 x B 1 on x B 1 off x ω A y y y Chemical shil evolubon
CPMG z z z 90 y T 2 delay B 0 y x B 1 on y x B 1 off y x ω A Chemical shil evolubon + transverse relaxabon ω A Intrinsic linewidth R 2 0
CPMG z z z 90 y T 2 delay B 0 x B 1 on x B 1 off x ω A y y y ω B (Ignoring transverse relaxabon) 180 x z z x T 2 delay B 1 off ω B ω A x y No exchange, spins refocused, same linewidth. y
CPMG z z z B 0 y k AB A B k BA k BA = k AB exchange contributes to line broadening x 90 y B 1 on y y z addibonal dephasing x x T 2 delay B 1 off T 2 delay B 1 off y y z ω B 180 x x ω A AND exchange ω A ω B x Note: need a chemical shil difference!
CPMG: Transverse RelaxaBon & ConformaBonal Exchange R 2 (ν CPMG ) = R 2 0 + (p A p B ω 2 /k ex )(1 (4ν CPMG /k ex )tanh(k ex /4ν CPMG )) R 2 eff (Hz) R ex k ex =1660 s 1 ν CPMG (Hz) R 20 R ex = p A p B ω 2 /k ex What would a residue with no exchange look like? Relate ω to known chemical shil differences to assign exchanging states Use different field strength data to separate p A and ω. More frequent 180 pulses
CPMG example: Lid mobon is the rate limibng step in Adk catalysis T = 20 C mesoadk k close 1380 s 1 k open 282 s 1 k cat = 261 s 1 k cat Note the power of NMR: we can easily see that this is a global conformabonal exchange process. Residues all across the protein report the same populabons and exchange rate. Not all remote residues sense the change ( ω too small). Wolf Watz, et al. Nat. Struct. Mol. Biol. 11, 945 949.
CPMG Notes Can see invisible states Detect presence of a second state by its effect on the linewidth of the first state. For slower exchange rates, can detect low populabons where signal isn t strong enough to observe directly. For faster exchange rates, can detect that a single peak actually reflects a populabon weighted average of exchanging states, not a single state. Can detect minor species with popula>ons as low as 0.5% Can reconstruct structures of these minor states Measure chemical shil difference, know chemical shil of major state, can calculate chemical shil of minor state. This predicts secondary structure of minor state Can also detect RDC of minor state and use that to orient structure elements. Can determine structure of a state that is too lowly populated for direct structure determinabon or is only transiently populated! (ex. Folding intermediates)
NtrC: ParBally AcBve Mutants Gardino, et al, Methods Enzymology (2007) 423:149 165. The NMR structures of NtrCr (blue) and P NtrCr (orange) are superimposed. PhosphorylaBon causes a conformabonal change from the inacbve (blue) to the acbve (orange) state.
NtrC: ParBally AcBve Mutants Gardino, et al, Methods Enzymology (2007) 423:149 165. Two state model for NtrC. WT More acbve mutants k ex >10000 Hz, fast exchange unphosphorylated I A 85% ParBally acbve mutant, unphosphorylated P NtrC I A Changes in peak posibon are shown for the backbone amide of D88. The pa~ern reflects the equilibrium between the two states. More acbve mutants have a higher percentage in the acbve conformabon, even in the absence of phosphorylabon. Phosphorylated I A 99% Note: ω values indicate the unphosphorylated and phosphorylated states are not the endpoints. Exchange is detectable in both phosphorylated and unphosphorylated states. Phosphoryla>on is not a perfect on/off switch!
Fast Timescale Dynamics Less intuibve than slow Bmescale dynamics Measure ps ns mobons Faster fluctuabons Small mobons Large number of states Reflect entropy of system, although exact calculabon is not parbcularly helpful Reflects re orientabonal mobon only, not affected by mobons along an internuclear vector Only observing a small subset of protein nuclei Ignores rest of protein, water, etc
Fast Timescale Dynamics Measure R 1, R 2, and heternuclear NOE Molecular tumbling (global) and protein mobon (local) cause fluctuabons in local magnebc field that lead to relaxabon. CorrelaBon between macroscopic relaxabon and microscopic fluctuabons follows the fluctuabon dissipabon theorem. Anisotropic interacbons (chemical shil anisotropy and dipolar coupling) depend on orientabon of molecule in magnebc field. As the protein moves, the local field due to these interacbons fluctuates, this causes loss of coherence (T2 relaxabon) and return to equilibrium (T1 relaxabon). SomeBmes the field has the right frequency to cause spin flips. This leads to NOE. RelaxaBon depends on the spectral density, J(ω) the probability of field fluctuabons of each frequency/energy within the thermal fluctuabons of the molecue. Only certain frequencies cause energy transfer between spins or between spins and la ce
Spectral Density Grzesiek, EMBO course 2007
Fast Timescale Dynamics Measure R 1, R 2, and heternuclear NOE Molecular tumbling (global) and protein mobon (local) cause fluctuabons in local magnebc field that lead to relaxabon. Model free analysis leads to fi ng of several parameters (per residue) as well as parameters describing overall tumbling of the molecule: S 2, order parameter, correla>on func>on at infinite >me Most robust, well determined. Ranges from 0 1 0=0 probability that you will sbll be in the same orientabon. Isotropic mobon 1=completely rigid. You will sbll be in the same orientabon at any Bme High (0.85) in secondary structure. Low (0.4 0.6) in unstructured regions or intrinsically disordered proteins. τ, internal correlabon Bme, not very accurate. Only sensi&ve to local mo&on faster than global tumbling
Fast Bmescale dynamics τ c T1 T2 B o H N S 2, τ e NOE N H S 2 0.9 Increasing flexibility S 2 0.65
Fast Timescale Dynamics Order parameters reflect fast Bmescale, small amplitude bond fluctuabons Can calculate from MD trajectories Higher order parameters in regions of secondary structure Reflect local packing can calculate order parameters reasonably well just by looking at local packing (# interacbons around a given residue) Reasonable agreement with B factors from crystal structure, if regions affected by crystal packing between molecules are avoided. S 2 1.0 0.8 0.6 0.4 0.2 0.0 0 50 100 150 Residue 200