Protein dynamics from NMR Relaxation data Clubb 3/15/17 (S f2 ) ( e )
Nitrogen-15 relaxation ZZ-exchange R 1 = 1/T 1 Longitudinal relaxation (decay back to z-axis) R 2 = 1/T 2 Spin-spin relaxation (dephasing in transverse plane) 15N{H} heteronuclear NOEs Heteronuclear steady state NOE (saturate amide proton and measure NOE effect on directly bonded nitrogen atom))
Measure 15 N T1, 15 N T2 and { 1 H- 15 N} NOE 15 N T2 (R2) dephasing 15 N T1 (R1) Recovery of magnetization to Z-axis Steady state {1H-15N} NOE saturation H f N {H} = (I Io)/Io Where I and Io are the intensity of the 15 N resonance with and without saturation of the attached hydrogen atom -CO-N-C -- 3
15 N Relaxation backbone motion Record series of HSQC-type experiments in which peak intensity depends on rate of relaxation = 138ms Extract rates of decay by fitting peak intensity as a function of delay time in each experiment = 86ms = 17ms Model Fitting Fit relaxation data to motional model of protein or nucleic acid. (typically the model free model) Longitudinal (R1) Transverse (R2) 1H-15 NOEs Dynamics 10-12 to 10-3 sec 4 Model free analysis yields: S 2, e, c and R ex
Relaxation rates sample motions described by the spectral density function The relaxation rate constants for dipolar, CSA and quadrupolar interactions are linear combinations of spectral density functions, J( ). For example, one can derive the following equations for dipolar relaxation of a heteronucleus (i.e. 15 N or 13 C) by a proton R 1,N = 1/T 1,N = (d 2 /4)[J( H - N ) + 3J( N ) + 6J( H + N )] R 2,N = 1/T 2,N = (d 2 /8)[4J(0) + J( H - N ) + 3J( N ) + 6J( H ) + 6J( H + N )] NOE 15N{1H} = 1 + (d 2 /4)( H / N ) [6J( H + N ) - J( H - N )] x T 1,N where d = ( H N (h/8 )/r HN3 ) The J( ) terms are spectral density terms that tell us what frequency of motions are going to contribute to relaxation. They have the form J( ) = c /(1+ 2 c2 ) and allow the motional characteristics of the system (the correlation time c ) to be expressed in terms of the power available for relaxation at frequency : 6
Recall: Spectral Density Function (J( )): Power available from the lattice (molecular motions) to bring about relaxation via transition probablities. It is a function of frequency ( ). All measurable relaxation properties of a protein (T1, T2, NOE) can be expressed in terms of the spectral density function. J( ) depends on how fast the macromolecule tumbles in solution. It therefore depends on the size and shape of the macromolecule, and the temperature and viscosity of the solution. For spherically shaped macromolecule ( isotropically tumbling) J( ) = c /(1+ 2 c2 ) Relaxation rates sample motions described by the spectral density function R 1,N = 1/T 1,N = (d 2 /4)[J( H - N ) + 3J( N ) + 6J( H + N )] On a 500MHz spectrometer: ~450MHz ~50MHz ~550MHz 7
Longitudinal (T1) Transverse (T2) 15N{1H}-NOEs Liparo-Szabo method to model fast time scale motions from NMR data Fit relaxation data to obtain parameters that define the motion of the amide bond. Simplest case: (isotropic diffusion) S f2 and e Order parameter (S 2 ). Ranges from 0 to 1, with 0 meaning the N- H bond vector is completely flexible and 1 indicating that the bond vector is rigid. Time constant associated with fast motions ( e): Normally in the picosceond range as proteins studied by NMR tumble much more slowly with tc values in the nanosecond range 8
rotational diffusion ( c ) translational diffusion (D). In the above figure the protein is shown as an ellipsoid with distinct diffusion tensors that are parallel and perpendicular to the long axis of the protein 9
Longitudinal (T1) Transverse (T2) 1H-15 NOEs Fitting of relaxation data S f2 and e For some residues the relaxation data is not fit well by assuming only fast motions. For these residues an additional fitting parameter is used to account for slow timescale motions (Rex) S f2 and e + R ex Slow motions ( s to ms) conformational exchange (R ex ) reveals the presence of exchange process between different conformers that have distinct chemical environments. (chemical shifts). This additional fitting parameter has units of sec -1. It is the additional broadening of the 15N resonance caused by exchange. Newer techniques are now available to measure Rex directly 12 (relaxation compensated CPMG expts).
Simplest Case: Rex caused by two site exchange A k 1 k -1 B p 1 : population of A p 2 ; population of B : frequency difference between A and B cp: delay between pulses in cpmg expt. k ex : k 1 /p 1 = k -1 /p 2 13
NtrC (inactive) His kinase P NtrC-P (active) Structural changes NtrC protein becomes active when it is phosphorylated. The two forms of the protein have different structures 14
Question: Does phosphorylation induce a structural change in NtrC? or Is there a pre-existing equilibrium between the different protein confomers that is shifted towards the phosphorylated form upon phosphorylation? (allosteric activation also called population model) Induced fit NtrC (inactive) or P NtrC-P (active) Population model NtrC (inactive) NtrC (active) Pre-existing equilibrium That is shifted upon phosphorylation 15
Measured relaxation parameters 16
Differences in slow-time scale dynamics Apo-form inactive D86N/A98T (partially active) Phosphorylated active Structural differences Apo-form vs. phosphorylated 17
The two conformers are in fast exchange Single set of resonances observed for apo and phosphorylated forms. Therefore the two forms must be in fast exchange with one another. Rex values are a measure of the broadening caused by the exchange process. 18
Mutations that activate the protein shift the equilibrium towards the active conformation Superimposed HSQC spectra Unphosphorylated D86N mutant that shows intermediate activity Apo-form Phosphorylated form 19
P NtrC (inactive) or NtrC-P (active) P NtrC (inactive) NtrC (active) Pre-existing equilibrium That is shifted upon phosphorylation Structural changes Changes in Rex values NtrC NtrC-P 20
Free Energy ZZ-exchange
Measuring Slow Chemical Exchange Processes (ligand binding, cis/trans proline isomerization) Two-site exchange A IsdC:heme k a k b koff kon B IsdC + heme Slow exchange. k << >> 1/
1H-15N HSQC 15N ppm 1H ppm 1H-15N ZZ-Exchange HSQC 15N ppm 1H ppm
Heme binding kinetics from ZZ-exchange NMR IsdC:heme (holo) koff kon IsdC + heme (apo) Robson SA, Peterson R, Bouchard LS, Villareal VA, Clubb RT.J Am Chem Soc. 2010; 132:9522-