Relaxation of methyl groups in large proteins

Relaxation of methyl groups in large proteins

Bachelorproject Niek van Staveren

Supervised by Renee Otten and Frans Mulder

Contents:

1. Introduction 2

2. NMR spectroscopy of large proteins 2

3. DhlA 3

4. Theory 3

4.1 Methyl experiment 3

4.2 Relaxation Experiment 6

4.3 Relaxation period 9

4.4 Processing and FuDA program 10

5. Results and Discussion 11

5.1 Methyl Experiment 11

5.2 Relaxation Experiment 12

6. Conclusion 13

1. Introduction

Protein dynamics play an important role in the biological function of enzymes. Relaxation experiments in NMR (Nuclear Magnetic Resonance) spectroscopy can give a lot of information about protein dynamics. In this report a method is described that uses the conformational transitions (chemical exchange) of side chain methyl groups to find dynamic parts of large proteins. This experiment measures relaxation rates of the carbon nucleus in the presence of continuous wave off-resonance irradiation. The protein haloalkane dehalogenase (DhlA) of Xanthobacter Autotrophicus GJ10 was used to test these experiments. DhlA is able to catalyze the hydrolysis of halogen-carbon bonds in different small haloalkane molecules.

2. NMR spectroscopy of large proteins

Nuclear Magnetic Resonance (NMR) spectroscopy is a very popular technique to determine the structure of small organic molecules. It uses the magnetic properties of nuclei that posses a spin angular momentum, also called spin. Most commonly used in protein NMR are nuclei with spin ½.

When such a nucleus is placed in a magnetic field, and its orientation in the field is measured, only two outcomes are possible: the nuclear magnetic moment is aligned either with the field or against it. These two spin states are called α and β. Since they differ slightly in energy, there will be a preference for the low-energy orientation of the nucleus. Hence, all nuclear spin orientations combined lead to a net macroscopic magnetisation of the sample in the magnet (diamagnetism), which can be represented by a vector pointing along the direction of the magnetic field (z-direction). When during a NMR experiment a radio frequency (RF) pulse of the right frequency (see below) is applied to the sample in the magnet, it will disturb the alignment of the nuclear magnets with the static magnetic field, causing it to tilt away from the z-direction. To obtain the highest NMR signal strength the magnetisation vector should

become perpendicular to the static magnetic field after this RF pulse. As soon as the magnetization vector is tilted away from the z-axis into the xy-plane, it will start to precess around the z-axis. This precession frequency (also called Larmor frequency) is proportional to the strength of the magnetic field and the proportionality constant is characteristic for the type of nucleus:

The RF frequency that is needed to tilt the nuclear magnetisation vector away from the z-axis must be very close to this nuclear precession frequency.

The chemical environment of the nucleus will have a small effect on its precession frequency and this difference is called chemical shift. The chemical shift expressed in ppm (parts per million) can be used to obtain some information on the structure of the molecule(s) in a sample. In larger molecules like proteins there are a lot of nuclei which all will have their own chemical shift. In a normal 1H experiment this will lead to a huge overlap in peaks and no information can be obtained from this.

Therefore multi-dimensional experiments are necessary for proteins, in which not only the chemical shift of protons is measured but also those of carbon (13C) and nitrogen (15N) nuclei. To obtain even more dispersion in peaks, methyl groups can be used. The rapid three-fold rotation of methyl groups results in small line widths and will therefore produce high-resolution spectra even for larger proteins.

These qualities are used in the methyl experiment and relaxation experiment discussed in following sections.

2 γ B υ = π

3. DhlA

To test the relaxation experiment the protein haloalkane dehalogenase (DhlA) of Xanthobacter

Autotrophicus GJ10 was used. This protein consisting of 310 amino acids is capable of catalyzing the hydrolysis of halogen-carbon bonds in different haloalkane molecules such as 1,2-dichloroethane, 1,3- chloropropane and 1,2-dibromoethane. The protein DhlA was chosen for the relaxation experiment because of its kinetic properties¹. These kinetic properties indicate a possibility that DhlA might have conformational (chemical) exchange in the timescale we measure with the methyl relaxation

experiment. Chemical exchange information can also give more insight into the reaction pathway of DhlA, and point out which residues are involved in a conformational change of the protein. A ¹³C/¹⁵N/

2H-labeled sample was prepared by growing in [¹H,¹³C]-glucose, D20 and ¹⁵N-ammonium sulphate.

Such a sample is necessary to obtain high resolution and high signal to noise ratio in NMR-experiments on large proteins, as will be discussed in the next chapters. Figure 1 shows the structure and secondary structure elements of DhlA retrieved from the RCSB protein data bank (PDB) with accession number 1CIJ. This x-ray structure was determined in the presence of bromide. The purple arrows represent β- sheets and the light-blue turns represent α-helices.

4. Theory

4.1 Methyl experiment

For the assignment of the methyl groups of DhlA the C-TOCSY-CHD2-se experiment was used. This three-dimensional experiment correlates site chain methyl groups and backbone carbon groups (Cα and Cβ). Together with previously done backbone experiments, which gave backbone chemical shifts, the methyl peaks could be assigned to a specific residue. Figure 2 shows the pulse sequence of the C- 1 G.H. Krooshof, R. Floris, A.W.J.W. Tepper, and D.B. Janssen, Thermodynamic analysis of halide binding to haloalkane dehalogenase suggests the occurrence of large conformational changes. Protein Science (1999), 8:355–360.

Figure 1: Structure of DhlA of the PDB-file 1CIJ

TOCSY-CHD2-se experiment.

The first proton and nitrogen pulses followed by a gradient are to make sure that we start only with ¹³C magnetization. After the first carbon pulse the carbon magnetization is transferred from z to -y.

Then the first evolution period t1 starts. Because of proton decoupling (WALTZ-16) during the evolution periods and mixing period no coupling with ¹H will arise. In this evolution period we measure the chemical shift of the carbons we start on (Ω1C).

The t1 evolution period is followed with an 90-degree carbon x-pulse. The symbol σ will stand for the previously obtained terms.

In the next period the magnetization is mixed over the different carbon groups within an amino acid.

For this a FLOPSY-8 mixing period was used. The FLOPSY-8 pulse sequence is designed for mixing along the z-axis in TOCSY experiments. It is efficient over large bandwidths and therefore useful in ¹³C mixing.

2C^x

z y

C C

  → −π

1

1 1

cos( 1) sin( 1)

t

y C y C x

C t C t C

−  → − Ω + Ω

2

1 1

cos( 1) sin( 1)

Cx

Ct Cz Ct Cx

σ   →⁻π Ω + Ω

Figure 2: Pulse sequence of the C-TOCSY-CHD2-se experiment. The delays that were used are: CT =14 ms and τ =1.98 ms. More details follow in 3.2 results and discussion.

( 8)

cos( 1 1)

Mixing FLOPSY

ct Cz

σ       →⁻ Ω

After the mixing period a second evolution period takes place. During this period we measure the chemical shift of the carbons that now posses magnetization that was obtained in the mixing period (Ω2C). This evolution period is a constant time evolution period. Evolution time is varied by moving the refocusing 180º carbon pulse to the beginning of the period.

Proton decoupling is switched off 2τ before the end of the CT-period to obtain anti-phase coherence terms between proton and carbon.

Only the antiphase terms remain because τ is set to be:

To detect these terms we need to get back to in-phase proton terms. To get in-phase proton terms we make use of the INEPT. A first INEPT converts the HzCy term into an observable Hy. During the INEPT the coupling between proton and carbon will allow the anti-phase terms to get into a in-phase prorton term. Chemical shift is refocused during the period due to the 180º pulse in the middle of the period.

After the first 90º pulse the HzCx term is transferred to a HxCx term. This means that coupling will not affect this term during this period.

1 4J_HC τ =

2^Cx cos( 1_ct C1) _y σ   → −⁻π Ω

2

2 1 2 1

cos( 2)cos( 1) sin( 2)cos( 1)

t

ct ct Cy ct ct Cy

σ  → − Ω Ω + Ω Ω

2 1 2 1

2*2

2 1 2 1

cos(2 )cos( 2)cos( 1) 2sin(2 )cos( 2)cos( 1)

cos(2 )sin( 2)cos( 1) 2sin(2 )sin( 2)cos( 1)

HC z z HC c c y HC c c z x

J H C

HC c c x HC c c z y

J t t C J t t H C

J t t C J t t H C

π τ π τ π τ

σ π τ π τ

− Ω Ω + Ω Ω

     → + Ω Ω − Ω Ω

2 1 2 1

2cos( _ct2)cos( _ct H C1) _{z x} 2sin( _ct2)cos( _ct H C1) _{z y}

σ → Ω Ω − Ω Ω

2 2

2 1 2 1

2cos( 2)cos( 1) 2sin( 2)cos( 1)

y x

H C

ct ct H Cx x ct ct H Cx z

π π

σ     →⁺ Ω Ω − Ω Ω

2 1

2

2 1 2 1

2cos( 2)cos( 1)

2cos( )sin( 2)cos( 1) 2sin( )sin( 2)cos( 1)

HC z z c c x x

J H C

HC c c x z HC c c y

t t H C

J t t H C J t t H

π τ

σ π τ π τ

Ω Ω

    → − Ω Ω − Ω Ω

2 1

2 1 2 1

2cos( 2)cos( 1)

2cos( )sin( 2)cos( 1) 2sin( )sin( 2)cos( 1)

x x c c x x

H C

HC c c x z HC c c y

t t H C

J t t H C J t t H

π π

σ ⁺ π τ π τ

Ω Ω

   → + Ω Ω + Ω Ω

2 1

2

2 1 2 1

2 1

2cos( 2)cos( 1)

2cos( )cos( )sin( 2)cos( 1) sin( )cos( )sin( 2)cos( 1)

cos( )sin( )sin( 2)cos( 1) 2sin( )sin( )sin(

HC z z

c c x x

J H C

HC HC c c x z HC HC c c y

HC HC c c y HC HC

t t H C

J J t t H C J J t t H

J J t t H J J

π τ

σ π τ π τ π τ π τ

π τ π τ π τ π τ

Ω Ω

    → + Ω Ω + Ω Ω

+ Ω Ω − Ω 2_ct2)cos(Ω1_ct H C1) _{x z}

If we look at the beginning of the first INEPT (after the two 90º pulses) we can see that we now arrived at a comparable situation. In the second INEPT the HxCz term will undergo the same process as in the first INEPT. The Hz term will remain the same because they observe no coupling or chemical shift evolution, it will only change sign because of the 180° pulse.

The last period was built into the sequence to make some time for gradient g3. Together with gradient 2 it is used to select for the measured magnetization.

4.2 Relaxation Experiment

Figure 3 shows the pulse sequence of the methyl relaxation experiment.

The experiment starts on proton, and the first carbon pulse is only to ensure that we start with proton magnetization only. In a first INEPT proton magnetization is transferred to HzCy. In the middle of the INEPT we see two shaped 180° pulses. The carbon shaped pulse is optimized for the methyl region, the proton 180º pulse is shifted to the methyl region.

2 1 2 1

2cos( _ct2)cos( _ct H C1) _{x x} sin( _ct2)cos( _ct H1) _y

σ → Ω Ω + Ω Ω

2 2

2 1 2 1

2cos( 2)cos( 1) sin( 2)cos( 1)

x y

H C

ct ct H Cx z ct ct Hz

π π

σ     → −⁺ Ω Ω + Ω Ω

2 1 2 1

cos( 2)cos( 1) sin( 2)cos( 1)

INEPT

ct ct Hy ct ct Hz

σ   → Ω Ω − Ω Ω

2^Hy cos( 2_ct2)cos( 1_ct H1) _y sin( 2_ct2)cos( 1_ct H1) _x

σ   →π Ω Ω − Ω Ω

Figure 3: Pulse sequence methyl relaxation experiment. With τa= 1.98 ms and TC=14.0 ms. More details in 4.3 results and discussion.

The second INEPT then transfers the HzCy magnetization to Cz. After this the relaxation delay starts.

The section relaxation period will explain further what goes on during this period.

The carbon magnetization is then transferred back into the rotating frame to obtain chemical shift evolution. Because of proton decoupling no coupling will occur during this period. A constant time is used for chemical shift evolution. The refocusing shaped carbon pulse will be moved by varying tau1 to obtain chemical shift evolution t1.

2H^x

z y

H H

  → −π

2 ^{JHC H Cz z} cos( ) 2sin( )

y HC y HC x z

H ^{π τ} π J τ H π J τ H C

−     → − +

cos( ) 2sin( )

x x

H C

HC y HC x z

J H J H C

π π

σ    →⁺ π τ − π τ

2^{πJHCτH Cz z} cos( J_HC )cos( J_HC )H_y 2sin( J_HC )cos( J_HC )H C_{x z} 2cos( J_HC )sin( J_HC )H C_{x z} sin( J_HC )sin( J_HC )H_y

σ     → π τ π τ − π τ π τ − π τ π τ − π τ π τ

2^Hy 2^Cx cos( J_HC )cos( J_HC )H_y 2sin( J_HC )cos( J_HC )H C_{z y} 2cos( J_HC )sin( J_HC )H C_{z y} sin( J_HC )sin( J_HC )H_y

π π

σ     →⁺ π τ π τ − π τ π τ − π τ π τ − π τ π τ

cos(2 J_HC )H_y 2sin(2 J_HC )H C_{z y}

σ → π τ − π τ

Relaxation delay

2H C_{z y}    →2^{πJHCH Cz z} 2cos(π J_HCτ )H C_{z y} − sin(π J_HCτ)C_x

2cos( ) sin( )

x x

H C

HC z y HC x

J H C J C

π π

σ    →⁺ π τ − π τ

2 2cos( )cos( ) cos( )sin( )

sin( )cos( ) 2sin( )sin( )

HC z z HC HC z y HC HC x

J H C

HC HC x HC HC z y

J J H C J J C

J J C J J H C

π τ π τ π τ π τ π τ

σ π τ π τ π τ π τ

    → −

− −

2cos(2 J_HC )H C_{z y} sin(2 J_HC )C_x

σ → π τ − π τ

2^Hx 2^Cy 2cos(2 J_HC )H C_{y y} sin(2 J_HC )C_z

π π

σ     → −⁺ π τ − π τ

Cz

σ → −

2C^x

Cy

σ   → −π

1

1 1

cos( 1) sin( 1)

tau

ct Cy ct Cx

σ   → − Ω + Ω

At the end of the evolution period the proton decoupling is switched off. This will lead to two anti phase carbon-proton terms. In two INEPT periods these two terms will both be transferred to in-phase proton terms.

1 1

2cos( _Ct H C1) _{z x} 2sin( _Ct H C1) _{z y}

σ → Ω + Ω

2 2

1 1

2cos( 1) 2sin( 1)

x y

H C

Ct H Cy z Ct H Cy y

π π

σ     →⁺ Ω − Ω

1 1

2*2

1 1

cos(2 )cos( 1) 2sin(2 )cos( 1)

cos(2 )sin( 1) 2sin(2 )sin( 1)

HC z z HC c y HC c z x

J H C

HC c x HC c z y

J t C J t H C

J t C J t H C

π τ π τ π τ

σ π τ π τ

− Ω + Ω

     → + Ω + Ω

2

1 1 1

2cos( )cos( 1) sin( )cos( 1) 2sin( 1)

HC z z

J H C

HC c y z HC c x c y y

J t H C J t H t H C

π τ

σ     → π τ Ω − π τ Ω − Ω

1 1 1

2cos( )cos( 1) sin( )cos( 1) 2sin( 1)

x x

H C

HC c y z HC c x c y y

J t H C J t H t H C

π π

σ    →⁺ π τ Ω − π τ Ω − Ω

1 1

2

1 1

1

2cos( )cos( )cos( 1) sin( )cos( )cos( 1)

cos( )sin( )cos( 1) 2sin( )sin( )cos( 1)

2sin( 1)

HC z z

HC HC c y z HC HC c x

J H C

HC HC c x HC HC c y z

c y y

J J t H C J J t H

J J t H J J t H C

t H C

π τ

π τ π τ π τ π τ

σ π τ π τ π τ π τ

Ω − Ω

    → Ω − Ω

− Ω

1 1

cos( _ct H1) _x 2sin( _ct H C1) _{y y}

σ → − Ω − Ω

2 2

1 1

cos( 1) 2sin( 1)

y x

H C

ct Hz ct H Cy z

π π

σ     →⁺ Ω − Ω

2

1 1 1

cos( 1) 2cos( )sin( 1) sin( )sin( 1)

HC z z

J H C

ct Hz JHC ct H Cy z JHC ct Hx

π τ

σ     → Ω − π τ Ω + π τ Ω

1 1 1

cos( 1) 2cos( )sin( 1) sin( )sin( 1)

x x

H C

ct Hz JHC ct H Cy z JHC ct Hx

π π

σ    → −⁺ Ω − π τ Ω + π τ Ω

1 1

sin( _ct H1) _x cos( _ct H1) _z

σ → Ω − Ω

2

1 1

sin( 1) cos( 1)

Hx

Ct Hx Ct Hy

σ   →π Ω + Ω

1 2

1 1

1 1

cos( 1)

2cos( )cos( )sin( 1) sin( )cos( )sin( 1)

cos( )sin( )sin( 1) 2sin( )sin( )sin( 1)

HC z z

c z

J H C

HC HC c y z HC HC c x

HC HC c x HC HC c y z

t H

J J t H C J J t H

J J t H J J t H C

π τ

σ π τ π τ π τ π τ

π τ π τ π τ π τ

− Ω

    → − Ω + Ω

+ Ω + Ω

4.3 Relaxation period

The relaxation period is the most important period in this experiment. During this period we measure relaxation at different offsets and with different relaxation times. Relaxation can be divided into three different parts:

R1 is the relaxation due to longitudinal relaxation. R2,0 and Rex are the transverse relaxation rates, in which Rex is the contribution due to exchange. Exchange is the switch between two states A and B, with different resonance frequencies ωA and ωB, and with populations pA and pB. The rate of exchange is the sum of the two individual exchange rates kex = kAB + kBA. When an RF field is switched on (with strength ω1 = -γB1), the magnetization will be aligned with the effective field:

In which Ω is the population weighted offset from the carrier frequency (Ω = pAωA + pBωB – ωcarrier).

The nuclear spin magnetization will be oriented at a certain angle from the static magnetic field:

When the offset is varied also the tilt angle θ will be varied. By doing this the relaxation rate of exchange can be determined. Measured here are exchange rates in the fast exchange region. Kinetic properties and large conformational changes suggest that there might be exchange in this region¹. Fast exchange means that the rate of exchange between the two states kex is far greater then the difference in resonance frequency between the two states (Δω). The exchange relaxation rate can be given by the following formula.

Where φ = pApB(Δω)². The used offsets are shown in table 1. Proteins used for this experiment should be highly deuterated and carbon enriched to obtain ¹³CHD2 groups. This is necessary to obtain single exponential relaxation delays. ¹³CH3 groups will have multi exponential relaxation delays due to more interactions between ¹H and ¹³C.²

2 U. Brath, M. Akke, D. Yang, L.E. Kay, and F.A.A. Mulder, Functional Dynamics of Human FKBP12 Revealed by Methyl ¹³C Rotating Frame Relaxation Dispersion NMR Spectroscopy, J. Am. Chem. Soc., 2006, 128 (17), 5718-5727

2 2 2

1 1cos 2,0sin _exsin

R_ρ = R θ + R θ + R θ

2 2

ex ex

ex eff

R k ϕ k

= ω

+

2 2

1

ω eff = Ω + ω

arctan( / )1

θ = ω Ω

Table 1: Different offsets used in the relaxations experiment

B1 Offset (Hz)

700 0, 700, -700

988 0. 900, -900

1395 0, 1500, -1500

1971 0, 2000, -2000

2784 0, 2500, -2500

3932 0, 3500, -3500

4.4 Processing and FuDA program

The relaxation experiment was performed on a 600 MHz proton frequency Varian NMR spectrometer.

The data was processed with the programs NMRPipe and NMRDraw. The relaxation experiment gives the HSQC-spectrum of DhlA at different relaxation times. The data consisted of 106 x 512 complex points (F1 x F2). Acquisition time of one spectrum was approximately 25 min. Peak positions and labels from the methyl experiment were copied to the relaxation experiment using Sparky. The

relaxation rates were determined using the program FuDA (Function and Data Analysis), written by D.

Flemming Hansen³. Instead of using peak heights this program fits line shapes of peaks using a mixture of Lorentzian and Gaussian functions (see figure 4). Using only peak heights can be inaccurate. The FuDA program is also able to fit overlapping peaks, but these overlapping peaks should be specified in the input file.

3 The program can be found at: http://pound.med.utoronto.ca/~flemming/fuda/

Figure 4: Two peaks are fit with the FuDA program

5. Results and Discussion 5.1 Methyl Experiment

The methyl experiment was performed on a 600 MHz proton frequency Varian NMR spectrometer.

The NMRPipe/NMRDraw software package was used to process the data. Forward backward linear prediction was used in the direct domain. In the indirect domain mirror image linear prediction was used. The data consisted of 49 x 200 x 512 complex points (F1(C) x F2(Cmethyl) x F3(H)). The

experiment was done three times: two times a mixing time of 17 ms, and once a mixing time of 12 ms, to make sure that the magnetization was mixed in all the different amino acids. The total acquisition time was 48 h. Then data of the methyl experiment were read into the Sparky program. This program was used to keep track of all the assignments that were done. It is capable of coupling the backbone experiment to the methyl experiment and making a assignment in this way. It shows the HSQC- spectrum of DhlA (5) with in the third domain the correlation to the other carbon groups of the amino acids.

The signals of the methyl groups of the protein can now be assigned to a specific residue number because of the specific Cα and Cβ chemical shifts given from varies other NMR experiments. DhlA contains 102 methyl containing amino acids groups. Table 2 sums up all the methyl containing amino acids in DhlA and shows if they could be assigned in the backbone and methyl experiment.

Figure 5: HSQC- projection of the C-TOCSY-CHD2-se experiment on DhlA

Table 2: Assignment DhlA

Backbone experiment Methyl experiment Total

Isoleucine 13 14 14

Alanine 28 27 30

Threonine 13 13 16

Leucine 24 11 28

Valine 10 7 14

88 72 102

For all the isoleucines and most of the alanines and threonines the assignment could be done.

Assignment of leucine and valine is more complex due to overlap and less specific chemical shifts.

5.2 Relaxation Experiment

First the relaxation time T1 was determined by applying different relaxation times in the relaxation delay. Relaxation times varied from 0 to 1 second. Then the T1ρ relaxation times were measured using different offsets and different relaxation times. Figure 6 shows the relaxation curves that were obtained with the curve fitting of the Sparky program.

A Matlab script was used to produce relaxation dispersion profiles as shown in figure 8. The script uses two different models two fit the dispersion profiles. The first model uses two parameters (R1 and R2,0) and the second model uses four parameters (R1, R2,0, φ and kex). The first model will fit the data best in the absence of exchange, the second model fits data best in the presence of exchange. Figure 7 shows the relaxation rates (vertical axis) plotted against the tilt angle.

Figure 6: Relaxation curves

Figure 8 shows the relaxation dispersion profiles. On the vertical axis the R2 relaxation rates are plotted against the effective field ωeff. In the absence of exchange R2 will remain constant over different

effective fields as shown in the dispersion profiles in figure 8. No exchange was observed for the residues of the DhlA protein studied under the chosen conditions. This could be due to the absence of an ligand. Adding a ligand like bromine could be necessary in order to observe exchange of the DhlA protein.

6. Conclusion

The C-TOCSY-CHD2-se experiment is a very useful experiment in combination with backbone

experiments. Most of the methyl containing residues could be assigned using the chemical shifts of the backbone experiments. The assignment of the DhlA methyl groups was used in the relaxation

experiments. A relaxation experiment using methyl groups was successfully designed. Because of the use of methyl groups the experiment is also able to measure relaxation on larger proteins like DhlA (310 amino acids). The protein DhlA showed no chemical exchange under the conditions which were used here. Further studies on DhlA with incorporation of ligands should be done, in order to gain more information in the conformational changes of the DhlA protein.

Figure 7: Relaxation rates as a function of the tilt angle. Blue data points were included in the fits. Red and green data points were excluded due to Hartman-Hahn matching (red) and violation of the adiabatic condition (green)

Valine 77 CG2 Threonine 197 CG2 Isoleucine 241 CG2

Figure 8: Relaxation dispersion profiles.

Valine 77 CG2 Threonine 197 CG2 Isoleucine 241 CG2