1 Introduction to Biomolecular NMR. 2 Nuclear Magnetic Resonance Spectroscopy Certain isotopes ( 1 H, 13 C, 15 N, 31 P ) have intrinsic magnetic moment.

1

Introduction to Biomolecular NMR

2

Nuclear Magnetic Resonance Spectroscopy

• Certain isotopes (1H, 13C, 15N, 31P ) have intrinsic magnetic moment

• Precess like tops in magnetic field B0

• In a 600 MHz spectrometer– protons precess at 600 MHz– 15N nuclei precess at ~60 MHz– 13C nuclei precess at ~125 MHz

Bo

= Bo

3

Creating coherence

• Unless the spins are aligned (coherent), their nett effect will be zero

• B0 field aligns spins M0

• B1 field rotates M0 into x-y plane

• M0 rotates at speed in x-y plane

• Coils in x-y plane record fluctuating magnetic field

• B1 field must rotate about z-axis at precession frequency

Mo

z

x

i

B1

yBo

4

1D NMR experiment

z

x

Mxyy

z

x

y

Mo

Free Induction Decay(FID)

90y

pulse

5

Free Induction Decay

t

M

M(t) = cos( t) exp(- t/T)

FT

6

Fourier transform spectroscopy

• System resonates at many different frequencies (c.f. church bell)

• Excite all frequencies simultaneously using a ‘hard’ pulse

• Frequency analyse (Fourier transform) to yield component frequencies

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

t

7

Two major causes of decay of signal

• Spin-lattice relaxation (T1 decay)– loss of energy by spins leads to return of M

to z axis

– happens with time constant T1

• Loss of coherence due to dephasing (T decay)

• T1 >> T2

• T2 inversely related to homogeneity of B0

• No energy is lost during dephasing signal may be refocused

M(t) = M(0) e-t / T1

M(t) = M(0) e-t / T2

Mz

x

y

M

z

x

y

8

NMR of proteins

• A sample of protein contains many protons– HN proton attached to N on backbone

– H proton attached to C on backbone

– H proton attached to C on backbone (typically 2)

– H proton attached to C on backbone

– Protons in H2O molecules (concentration 110 M as compared to ~1mM for protein)

• Different protons precess at different frequencies, depending on their chemical environment

– depends on the chemical shielding; e.g. how exposed the nucleus is to the solvent or how close it is to a heavy atom such as C or N

– protons in water correspond to =0 (no chemical shielding)

– protons in the protein may have >0 (to the right of the water peak) or <0 (to the left)

• Define a B0-independent scale:

– known as ppm’s

= - B0

= H2O - ) / ( 106 H2O ) = / 106

9

1D NMR spectrum of a protein

• In terms of ppm scale, peaks appear at same place irrespective of the strength of B0

larger proteins have more overlapping peaks

• But line width is independent of B0

– roughly T2-1

– increases with size of protein

less overlap at higher field• Also strength of signal increases

with B0

• Conclusion: going to higher field increases sensitivity and resolution

10

Interactions between nuclei (couplings)

• Coupled springs– transfer of energy back and forth

• Scalar coupling– mediated through overlap of electronic orbitals– “through bond” coupling– useful for assigning particular peaks to particular protons– determine covalent structure of the protein molecule

• Dipolar coupling– results from interaction of dipolar fields of nuclei– “through space” coupling – useful for determining non-covalent structure (folded shape) of molecule

11

Simplest 2D experimentCorrelation spectrOScopY experiment

• Pair of coupled nuclei s1 and s2

• Record whole series of 1D experiments, each with a different value of t1

• Second 90 pulse transfers magnetization from s1 to s2

• Data acquired during t2 tells us the precession frequency (2) of s2

• During t1 magnetization is on s1 and therefore precesses at frequency 1

– initial magnitude at beginning of t2 depends on t1 and 1

S(t2) = cos(2t2)

S(t1,t2) = cos(1t1) cos(2t2)

COSY pulse sequence

90x90y

t1

t2

12

The amplitiude of the 1D spectrum acquired during t2 varies sinusoidally with a different frequency as a function of the interval t1, indicating that during t1 the magnetization is on a spin with the corresponding frequency

13

2D NMR spectrum

Fourier transform in both t1and t2 gives S(1, 2), which when plotted as contour function gives a peak at coordinates 1 and 2

1

2

14

2D COSY spectrum

• Magnetization which stays on same nucleus during t1and t2 has the same frequency in both dimensions along the diagonal

• Magnetisation which jumps from a nucleus with frequency 1 during t1 to one with frequency 2 during t2 is represented by a cross-peak at cooordinates (1,2)

• The furthest that magnetisation is able to jump is the distance of 3 bonds; i.e

– HN - H

– H - H

– H - H

15

COSY spectrum of a small molecule

• COSY spectrum directly confirms covalent structure of molecules

16

TOCSYTOtal Correlation SpectroscopY

• TOCSY is an ‘relayed’ extension of COSY– uses scalar coupling

• Cross-peaks appear between all spins which can be connected by relaying

• Magnetisation still can’t be transferred across peptide bond (3-bond limit still applies) amino acids still form isolated spin

systems

• Useful for recognising particular amino acids

17

Heteronuclear NMR

• 3-bond limit means that cross-peaks are never observed between protons in different amino acids; i.e. there is no magnetization transfer across the peptide bond

• Magnetization can be transferred if the intervening nuclei are magnetic; i.e. 13C and 15N.

• This is achieved by producing the protein recombinantly in bacteria grown with 15N-ammonium chloride and 13C-glucose as the sole nitrogen and carbon sources respectively

Peptide bond

18

3D experiments• The previous experiments can be

extended to two indirect dimensions, t1 and t2

• The real time interval during which all the FID’s are recorded is called t3, or the direct dimension.

• S is a function of t1, t2, and t3; to get the spectrum it must be Fourier transformed inall three time dimensions.

• If the magnetization is on a nucleus with frequency 1 in t1, 2 in t2 and 3 in t3, the spectrum will have a ‘peak’ centred at coordinates (1, 2, 3)

• In 3D a peak is more like a ball

C

HN

N

19

Heteronuclear assignment experiments• 3D HNCA experiment

– protein must be isotopically enriched with 1H, 13C and 15N

• Peaks represented as balls in 3D space at coordinates corresponding to:– 1H shift of an amide proton (HN)

– 15N shift of attached N

– 13C shift of attached C

• At same 1H and 15N values, another peak corresponding to 13C shift of Cof preceding residue

makes it possible to walk along sequence to assign entire backbone

residue i-1 residue i

20

1

2

3

4

5

Assignment of all HN, N and C resonances of a pentapeptide in a HNCA spectrum by ‘walking’ along the backbone. In each case the black sphere represents the in-residue C , the grey sphere the C of the preceding residue

HN

N

C

21

NOE effect provides structural information

• Nuclear Overhauser Effect produces coupling between protons which are close in space (though not necessarily covalently bonded)

• NOE cross-peaks R-6

only observed for R < 5 Å• NOESY is 2D experiment in

which cross peak intensities are proportional to NOE between corresponding protons

NOESY spectrum of lysozyme

22

Basic method for protein structure determination by NMR

• ASSIGN all peaks using COSY-type spectra

• Identify all cross peaks between assigned diagonal peaks on NOESY spectra

• Convert NOESY cross-peaks to distance constraints between corresponding protons

• Find 3D structure which optimally satisfies distance constraints as well as protein stereochemistry

23

Structure determination

• Molecular modelling with energy function

Etotal = Ecovalent geometry + ENOE restraints

• Use optimisation algorithm to find molecular structure with lowest value of Etotal which still satisfies all NMR-derived distance constraints

• Generate family of structures

• Resolution generally not as good as X-ray, but may be better reflection of molecules in-vivo