Time Domain EPR: Membrane-binding Proteins Using R 1 from EPR as a probe of the Structure-function and the Dynamics- function relation in biology Graduate Students: Tamara Okonogi Robert Nielsen Faculty: Michael Gelb Kate Pratt Post Docs: Andy Ball Ying Lin Stephane Canaan Kepeng Che Supported by NSF and NIH

Time Domain EPR: Outline Time Domain: Saturation Recovery and Pulsed Electron Double Resonance Methods –Comparison with CW methods –Spectrometer, experiment, data Theory of relaxation Rates Application to the Spin Relaxant Method Using site directed mutagenesis –Orienting a Membrane-binding Protein –Determine an Oxygen gradient in a membrane

CW Power Saturation The method to obtain spin-lattice relaxation rates using CW methods. Plot the Peak to Peak height as a function of microwave power (or really amplitude).

Details of CW Power Saturation Peak-to-Peak height A product of spin-spin and spin-lattice relaxation rates.

CW Field (Gauss)

TD ESR Spectrometer

Pulsed Bridge

Free Induction Decay Measures spin-spin dephasing

Pulsed Saturation Recovery Measures relaxation to equilibrium

Pulsed Electron-Electron Double Resonance

pSR; the effect of a relaxant

Collision with Oxygen

Redfield Theory (or BWRT) Relaxation rate theory began with Bloch and Wangness, and was amplified by Alfred Redfield to be a complete theory for the effects of dynamics and stochastic processes on spins in condensed matter. Relaxation theory is often called BWRT (Bloch Wangness and Redfield Theory). BWRT Predicts Spin-Lattice (R 1 ) and Spin- Spin (R 2 ) relaxation rates. Relaxation Rates are related to Relaxation times:

What Redfield Theory (BWRT) Uses There is a system Hamiltonian BWRT requires a bilinear operator, which couples the spin system (S) to the lattice (or bath), F –The Hamiltonian is: F is the fluctuating variable that causes the spins to have a fluctuating environment The fluctuation of the lattice, coupled to the spin system, then causes the spins to relax or dissipate the absorbed (microwave or r.f.) energy, non- radiatively.

A problem: R 2 diverges The coupling Hamiltonian (e.n.d.) is: The orientation variable,, is a stochastic function of time. The correlation function (at high temperature) is: This shows the statistical origin of the rotational correlation time. Exponential decay of the correlation function with time is typical of such functions. Nielsen, R. D. and Robinson, B. H. "A Novel Relaxation Equation of Motion". J. Physical Chemistry 2004; 108:

CW Spectra CTPO

R 2 from BWRT, diverging R 2 rates from Kubo Theory R 2 rates from modified BWRT Relaxation Rates (MHz) D.A.Haas, C. Mailer, and B.H. Robinson, Biophysical J. (1993) 64, 594

R 1 does not diverge R 1 for the electron and R 1 for the nitrogen nucleus in a nitroxide spin label as a function of rotational correlation times can be computed from BWRT. If R 2 diverges for correlation times longer than a few nanoseconds how can we rely on the theory to give us R 1 values out to milliseconds and beyond? The Problem: Why does the theory fail for R 2 rates but not for R 1 rates? It is important to understand why R 1 works and to understand why R 2 fails.

Nitroxide Nitrogen Spin Lattice Relaxation Rates Electron spin-lattice relaxation rates: With O 2 and Without O 2 Correlation Time (sec) Relaxation Rates (sec -1 ) B.H. Robinson, D. A. Haas and C. Mailer (1994). Science 263(5146):

Mechanisms of R 1 Sum the rates from statistically independent processes –Spin-Rotation, rate goes as –Electron-Nuclear Dipolar Coupling Electron rate peaks at the spectrometer frequency Nuclear rate Peaks at coupling –Oxygen relaxation (used later) –Empirical “Spin-Diffusion” process Just a catch-all effect, goes at Partially due to spins local to the nitroxide

The ideal form of the solution is: The actual form of the solution is a bit more complicated: The two rates are: The slower rate dominates. Time (sec) Solution (Signal) Black: two rate solution Blue: rate Green: BWRT rate

Dominant Rate in all limits In the fast motion limit: In the slow motion limit: BWRT gives only the fast motion limit, which predicts that the rate goes to infinity as the correlation time goes to infinity. The new theory avoids this and correctly predicts coherent oscillations of (at frequency ) as the interaction becomes coherent, in the no motion limit. The rates in the two limits may be “combined” into a rate that does cover both motional regimes (for both R 1 and R 2 ): New Term in both R 2 and R 1 rates

Spin Labeled-Fatty Acids in DOPC Different spectrometer frequencies (from 2 to 35 GHz) with the best possible single effective correlation time. A poor fit. The frequency dependence of simple isotropic rotational motion is incomplete. Spin-Lattice Relaxation rates for varied Doxyl-Steric Acids in DOPC. Data from Jin and Hyde SL at 5 position SL at 12 position SL at 16 position

Same Data Different Model Improving the model to include anisotropic dynamics. For simplicity the anisotropy ratio was kept constant. Improved agreement indicates the need to improve the model, and the frequency dependence of the relaxation rates can rule- out some incorrect models.

Relaxation rates from 60 different experiments Correlation among all the data and the model. Model has 1 adjustable parameter (the mean rotational correlation time) for each sample at all 5 different frequencies and two different isotopic forms.

Bee venom phospholipase Oriented on a membrane surface by Site Directed Mutagenesis EPR spin relaxant method Lin, Y., Nielsen, R., Murray, D., Hubbell, W. L., Mailer, C., Robinson, B. H. and Gelb, M. H. Science 1998; 279 (5358): Membrane Binding Proteins

Labeling a protein (PLA2) with a Spin Probe Use site directed mutagenesis techniques to prepare proteins with a single properly placed cytsteine. General Reaction for adding relaxants The protein should contain only one cysteine for labeling. Protein labeled at only one site at a time per experiment.

Relaxant Method: Nitroxide Spectra depend on concentration of relaxants Spin-Lattice: T 1 -1 or R 1 Spin-Spin: T 2 -1 or R 2 Rates are increased by the same amount due to additional relaxing agents (relaxants).

Human (HGIIA) Secretory Phospholipase sPLA2 A highly charged (+20 residues) lipase, 14kDa protein And a highly charged (-70 mV) membrane All exposure data was determined by SR and pELDOR directly measuring spin-lattice relaxation rates.

CW Spectra of hGIIA on Micelles hGIIACTPO

CW Spectrum of site N70C with CROX

Probing the hGIIA protein surface potential using CW and TD EPR

rates from pSR and pELDOR for CTPO solvent accessibility Spin Lattice Relaxation Rates for sl-sPLA2

Power Saturation Curves site S120C

O 2 Relaxant: hGIIA on LUV TD CW

Compare O 2 Relaxant Effects from TD-SR and CW

Summary of Vesicle data Large protein surface charge determined by CW and TD data Complete protection from Crox for all EPR data Oxygen effect reduced relative to solution Light scattering occurs

Aggregation model ~50 enzymes (36 Angstrom diameter) LUV of DOPM (100 nm diameter)

TD data, Vesicles vs. Mixed Micelles Vesicle (DTPM) Mixed Micelles

hGIIA-sPLA2 on mixed micelles NiEDDA Crox

sPLA2 on Membrane View from membrane Yellow: Hydrophobic Residues Blue: Charged (pos) residues Orientation perpendicular to that predicted by M. Jain. Anchored by hydrophobic residues. Charges not essential

sPLA2 Conclusions sPLA2 causes the vesicles to aggregate. Explains much other data and misconceptions about the kinetics and processive nature of sPLA2 action. sPLA2 was oriented on micelles (instead) using spin- lattice relaxation rates alone. Orientation different from that of another model. Hydrophobic residues are the main points of contact. Charges provide a general, non-specific attraction. Substrate binding site identified by orientation on the mixed micelles

The WALP Proteins WALP proteins are single alpha helical membrane-spanning proteins. The sequence is 23 residues long: HCO-NH-G-WW-L-(AL) 8 -WW-A-CO-NH 2 Leucine and Alanine are both hydrophobic. In a membrane this forms a single turn alpha helix. The membrane, di-oleic (DO) PC, is about Ang thick. The two outer Tryptophans (W) are about 30 Angs apart. The membrane will stretch (or shrink) to accommodate the protein. Demmers et al: J. Biol. Chem., 276, , 2001

WALP23 The sequence is 23 residues long: HCO-NH-G-WW-L-(AL) 8 -WW-A-CO-NH 2 Subcyznski et al. Biochemistry, 2003, 42, 3939

WALP23-sl CW spectra CW EPR spectra of spin labeled WALP23 at various positions.

Oxygen Transport Parameter The Oxygen transport parameter is the change in the spin-lattice relaxation rate due to oxygen collision-relaxation, where Depends on transport properties (e.g. Diffusion) of Oxygen in the local environment of the spin label

Typical WALP/DOPC Saturation Recovery EPR CW With Oxygen Without Oxygen

Walp23 in DOPM: Oxygen Transport Parameter From SR Estimated from the CW line width

From SR Walp23 in DOPC: Oxygen Transport Parameter

Ratio Parameter* * Altenbach, C. et al. PNAS (1994) 91 (5),

Conclusions The gradient of the oxygen transport parameter, measured on WALP 23, is ideal as a ruler for determination of spin label position in membranes. The spin-lattice and spin-spin relaxation rates show dependence on local mobility of the spin label in the bi-layer. The oxygen transport parameter cannot be separated into its two components: the oxygen concentration and transport-dependent coefficient. The ratio parameter, designed to cancel out transport effects, provides a profile of relative relaxant concentration. Ratio parameter can be used to position nitroxide in the membrane.