SEMINARProtein NMR spectroscopy

Author: Jan PremruUniversity of Ljubljana

Faculty of mathematics and physicsDepartment of physics

Mentor: dr.Janez �trancarJoµzef �tefan InstituteLaboratory of biophysics

13th January 2008

Abstract

This seminar brie�y presents protein biochemical description and structure characterization.The main emphasis of the seminar is on basic theory as well as basic experimental aspects ofnuclear magnetic resonance(NMR) spectroscopy of proteins in solution. Theoretical part providesreader with enough theoretical background necessary for understanding experimental techniquesof one-dimensional and multi-dimensional NMR spectroscopy, explained latter in the seminar.Also discussed is an outline of protein structure determination.

Contents

1 Protein basics 11.1 Biochemical description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Structure characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Protein structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Nuclear magnetic resonance(NMR) spectroscopy 32.1 NMR basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 NMR spectral properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Chemical shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 J-coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Dipolar coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 Nuclear Overhauser e¤ect . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 1D-NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 2D-NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 COSY(COrrelation SpectroscopY) . . . . . . . . . . . . . . . . . . . . . . 112.4.2 TOCSY(TOtal Correlation SpectroscopY) . . . . . . . . . . . . . . . . . . 122.4.3 NOESY(Nuclear OvErhauser SpectroscopY) . . . . . . . . . . . . . . . . 122.4.4 HSQC(Heteronuclear Single Quantum Correlation) . . . . . . . . . . . . . 12

2.5 3D NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5.1 HNCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Protein structure determination outline 163.1 Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Constraints for structure calculation . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Structure calculation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Conclusion 17

1 Protein basics

1.1 Biochemical description

Proteins are organic, linear chain polymeres, built from 20 natural amino acids (�-amino acids).All amino acids(except proline) posses common structural features, that is � carbon(C�) towhich an amino group(NH2), a carboxyl group(COOH), a hydrogen atom(H) and a variableside chain(R) are bonded. Amino acids in chain(called residues) link with peptide bonds, formedwith dehydration proces (�gure 1). The linked chain of central C� and its adjacent C and Natoms of each amino acid residue de�ne the protein main chain or backbone. The two unbondedamino and carboxyl groups left after the formation of the protein are known as the N -terminaland C-terminal ends, respectively.

1.2 Structure characterization

To succesfully reproduce protein stucture, one must know atom sizes, bond lengths and dihedralangles for each residue in backbone and all the sidechains. Especially dihedral angles have thegreatest impact on protein folding into its unique 3D shape, i.e. a small rotation can re�ect ina notable change in structure. Dihedral angle is the angle between two planes, �rst of which isdetermined by �rst 3 of 4 succeeding atoms of the backbone, and second determined by the last

1

Figure 1: Amino acids forming a peptide bond

3 of the same 4 atoms of the backbone. There are three angles �i(sequence C �N � C� � C), i(sequence N�C��C�N) and i(sequence C��C�N�C�) per residue i. These de�ne localstructure assumed by the backbone. The double bond of the C = O group of a single amino acidis delocalised into the C�N bond, giving each of these bonds a partial double bonded character.This has the e¤ect of restricting the sequence C� �N �CO�C� to lie in a single plane, calledamide plane(�gure 2) and also locks i to values 0 or �. The �i and i angles are de�ned asclockwise rotations about the C� �N and C� � C bonds, respectively, looking along the bondsaway from the atom. The conformation is de�ned as �i = i = 0 when all main chain atoms arecoplanar.

Figure 2: Protein backbone dihedral angles

1.3 Protein structure

Proteins structure is often described at 4 distinct levels:

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1.Primary structure - amino acid sequence2.Secondary structure - regularly repeating local structures stabilized by hydrogen bonds.

The most common examples are the alpha helix and beta sheet(�gure 3). Because secondarystructures are local, many regions of di¤erent secondary structure can be present in the sameprotein molecule.3.Tertiary structure - overall shape of a single protein molecule including the spatial rela-

tionship of the secondary structures to one another. Tertiary structure is generally stabilizedby nonlocal interactions, most commonly the formation of a hydrophobic core, hydrogen bonds,disul�de bonds,...4.Quaternary structure - shape or structure that results from the interaction between multiple

proteins, each as part of the larger assembly called protein complex

Figure 3: Protein secondary structure is often beta pleated sheet or ��helix

Succesful determination of protein tertiary or quaternary structure can provide importantinsight into the relation between protein structure and its function. There are two most commonlyused techniques of protein structure determination, namely nuclear magnetic resonance(NMR)spectroscopy(protein in solution) and X-ray crystallography(protein form crystals in solid state),both of which are able to produce information at atomic level resolution. In this seminar I willfocus on protein NMR spectroscopy in solution.

2 Nuclear magnetic resonance(NMR) spectroscopy

It is a technique which exploits the magnetic properties of certain nuclei. It is in principleapplicable to any nucleus possessing spin. The NMR spectrum provides us with information onthe number and type of chemical entities in investigated sample, i.e. protein. Protein NMR isperformed on aqueous samples of highly puri�ed protein. Usually the sample consist of 300�600microlitres with a protein concentration in the range 0:1� 3 millimolar(N � 1020 protein units).The source of the protein can be either natural or produced in an expression system usingrecombinant DNA techniques through genetic engineering. Recombinantly expressed proteinsare usually easier to produce in su¢ cient quantity, and makes isotopic labelling possible(i.e.nuclei of 12C with no net nuclear spin are replaced with isotope 13C with net spin s = 1

2 ). Most

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commonly used isotops are 13C and 15N . When using proton NMR, solvent is heavy water,in order to remove large proton signal from water molecules(1H with net nuclear spin s = 1

2replaced with 2H with net nuclear spin s = 1).

2.1 NMR basics

Let us denote overall spin of the nucleus by the spin quantum number I. A non-zero spin isassociated with a non-zero magnetic moment ~�

~� = ~I (1)

For nuclei, the gyromagnetic ratio is a characteristic value that is speci�c to the nucleus inquestion. The nuclear magnetic moment ~� in external magnetic �eld ~B0 experiences a torque~N , given by

~N = ~�� ~B0 (2)

Torque has orientation perpendicular to both ~� and ~B0, therefore it means that ~� will precessabout ~B0. Since ~N = d~I

dt equation(2) rewrites to

d~I

dt= ~I � ~B0 (3)

and we get frequency of precession called Larmor frequency

!L = � B0 (4)

Since spin is both value and orientation quantized, so is magnetic moment. The z componentof spin is

Iz = m~ (5)

and z component of magnetic moment is

�z = m ~ (6)

Thus the nucleus with I = 12 has two possible z components of spin states, namely m = 1

2 andm = � 1

2 . The energies of these states are degenerate, they are the same. Hence the populationsof the two states will be exactly equal at thermal equilibrium.If a nucleus is placed in a magnetic �eld, however, the interaction between the nuclear mag-

netic moment ~� and the external magnetic �eld ~B0 causes the two states to no longer have thesame energy. The energy of a magnetic moment ~� in a magnetic �eld ~B0 = B0(0; 0; 1) is givenby

Em = � ~B0 � ~� = �m ~B0 (7)

The energy splitting for the nucleus with I = 12 (m = 1

2 or m = � 12 ) is

�E = E 12� E� 1

2= � ~B0 (8)

The ratio of populations of energy levels is given by Boltzmann distribution as

P 12

P� 12

= e��EkT = e

~B0kT (9)

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At normal temperature the argument ~B0

kT << 1 and the excess of population in lower energylevel is very small(typically 0:1%), but su¢ cient for the magnetization, de�ned as

~M =1

V

X~�i (10)

to be macroscopic and detectable. Since all ~�i precess with di¤erent phases around ~B0(around zaxis in our case), projections on xy plane average to 0, hence the total equilibrium magnetizationwill point along the z axis. In nonequilibrium state magnetization precesses around ~B0 (�gure4). If all ~�i have equal frequency !L of precession(in general this is not the case), they are called

Figure 4: In equilibrium state magnetization points along B0, while in nonequilibrium statemagnetization precesses around B0, in our case z axis direction.

on-resonance.If we introduce an radiofrequency(RF) pulse with Larmor frequency along x-axis ~Brf =

Brf (1; 0; 0) cos!Lt, magnetization begins to precess around x-axis and z-axis. This can be seenif we move into coordinate sistem which rotates around ~B0 with !L. The initial magnetizationpoints along the z0 = z axis. The �eld ~Brf transforms as

~B0rf = Brf

0@ cos!Lt sin!Lt 0� sin!Lt cos!Lt 0

0 0 1

1A0@ cos!Lt00

1A = Brf

0@ cos2 !Lt� sin!Lt cos!Lt

0

1A =

=Brf2

0@ (1� cos 2!Lt)� sin 2!Lt

0

1A =Brf2

240@ 100

1A�0@ cos 2!Ltsin 2!Lt

0

1A35 (11)

and we see that �rst term �eld appears static and second term �eld rotates around z0 with twicethe Larmor frequency. Because of this fast rotating second term �eld e¤ect on magnetizationaverages to 0. First term �eld acts as a static �eld in rotating frame and thus the magnetizationprecesses around x0 axis. If we apply the pulse just long enough, the magnetization can berotated into xy plane. In laboratory frame, magnetization precesses around z axis, because ofthe static ~B0 �eld. The RF pulse which rotates magnetization for angle �

2 around axis x is called�2 xpulse(�gure 5). On the same principle, we have �x, �y, etc. pulses. If we have a receiver coil

with its symmetry axis lying in xy plane, we measure sinusoidal signal of induced current in thecoil, the frequency of which is exactly !L. Typical NMR experiment setup is shown in �gure 6.Due to spin-spin interaction, the phase correlation between the spins is lost in time, this is

known as spin-spin relaxation time. It causes the signal of the magnetization in xy plane to

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Figure 5: RF pulse which rotates magnetization for angle �2 around axis x is called

�2 xpulse

Figure 6: Typical NMR experiment setup[2]

decay exponentially with characteristic time T2 as given in equation(12).

Mxy(t) =Mxy;0e� tT2 (12)

Also the inhomogeneity of �eld ~B0 causes magnetic moments at di¤erent places to precess withdi¤erent !i. In rotating frame there is a frequency o¤set of ! = !i�!L with which the magneticmoments precess around z0 axis and are thus called o¤-resonance. This causes the dephasing oftotal magnetization with time. The total relaxation time is denoted T �2 and is determined byequation(13).

1

T �2=1

T2+

1

Tinh:(13)

Another characteristic time is T1, named spin-lattice relaxation time due to interaction of nuclearmagnetic moments with electron magnetic moments. Magnetization therefore relaxes into itstermodinamical equilibrium state along z axis, as given in equation(14).

Mz =Mz;0(1� e�tT1 ) (14)

Both relaxation times depend on the strength of magnetic �elds pressed. Typically the T2 isnotably smaller than T1 so the signal decays almost exclusively due to spin-spin interaction and�eld inhomogeneity. This is called free induction decay(FID).

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2.2 NMR spectral properties

The NMR signal decays exponentially. The stronger the decay of the signal the broader the char-acteristic lines of chemical entities in Fourier power spectrum, obtained with Fourier transformof the signal [4]. This is NMR spectrum and its general features and shape can be explainedwith some physical background.

2.2.1 Chemical shift

The acctual magnetic �eld present at the nucleus is attenuated, shielded, by the presence ofelectrons that surround the nucleus(thought of as moving charges), giving a modi�ed �eld at thenucleus B = (1 � �)B0, where � represents the degree of shielding and B0 is the strength ofthe applied magnetic �eld. The degree of shielding of speci�c nucleus is dependent on surround-ing electron density, in other words, on its chemical environment. Nuclei in di¤erent environ-ment(binding partners, bond lengths, angles, presence of electronegative atoms) thus experiencedi¤erent e¤ective magnetic �elds and, in turn, have di¤erent resonance frequencies. They areseparated in the NMR spectrum. Instead of frequency, NMR spectrum axes denote chemicalshift �

�i =!i � !ref!ref

106ppm (15)

where !i is the frequency of observed nuclei and !ref is a reference frequency of some chosensubstance(i.e. in protein NMR spectroscopy 2,2-dimethyl-2-silapentane-5-sulfonic acid is used).Chemical shift � of this substance is chosen to be 0 and it is the origin of the ppm scale(partsper milion). Chemical shift(�gure 7) is thus important for identi�cation of compounds and alsofor determining protein secondary structure, since it varies with dihedral angles(it can reverselybe used to predict local dihedral angles)[4][2].

Figure 7: Chemical shift �, measured in ppm(parts per milion) units, relative to that of referencesubstance(i.e. TMS), which is de�ned to be 0[1]

2.2.2 J-coupling

The J-coupling is a scalar interaction which arises between two di¤erent nuclear spins, I1 and I2,and is mediated by the electrons surrounding these two spins(via chemical bonds not throughspace). The electrons are polarised in the opposite direction to the nucleus they are interactingwith. This polarisation in turn has an e¤ect on the other electrons in close proximity, which at theend a¤ects the neighbouring nuclei. J-coupling does not depend on orientation but it does dependon the number of bonds between I1 and I2. Only coupling through one(1J � 100 � 250 Hz),two(2J � 10 � 15 Hz, geminal) or three(3J � 5 � 8 Hz, vicinal) chemical bonds is normallyobservable. Coupling can not be described classically, but rather quantum-mechanically with

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interaction hamiltonian of the form

HJ =Xj;kk<j

2�Jjk Ij � Ik (16)

The e¤ect of this coupling is splitting of energy levels and consequently separation of spectrallines(�gure 8). The coupling of nuclear spin I1 with n equivalent nuclear spins I2 causes spec-

Figure 8: E¤ect of J-coupling is splitting of energy levels and consequently separation of spectrallines

tral line of I1 nuclei to split into n + 1 multiplet with intensity ratios following the Pascal�striangle. Note that the coupling with identical spins does not cause splitting. Thus J-couplingcombined with chemical shift tells us not only about chemical environment, but also the numberof neighboring NMR active nuclei(through chemical bonds). 3J coupling depends on dihedralangle(through equation(17) known as Karplus equation) and can therefore be used for determ-ination of dihedral angle � if 3J is known.

3J = A+B cos�+ C cos 2� (17)

J-coupling is resolved in 2D and 3D-NMR to determine correlation between nuclei (COSY,TOCSY spectrometry)[3].

2.2.3 Dipolar coupling

Between two spins I and S there is direct dipole-dipole magnetic interaction, called dipolarcoupling. We consider a two spin system(�gure 9) with inter-nuclear radius ~r for which thedipolar interaction is given by equation(18).

Hdipolar =�0~2 I S

4�[I � Sr3

� 3 (I � ~r)(S � ~r)r5

] (18)

8

Figure 9: Two spin system

This can be expanded and rewritten in terms of lowering and raising operators for the two spins

Hdipolar =�0~2 I S4�r3

[A+B + C +D + E + F ] (19)

A = IzSz(1� 3 cos2 �)

B = �14[I+S� + I�S+](1� 3 cos2 �)

C = �32[I+Sz + IzS

+] sin � cos �e�i�

D = �32[I�Sz + IzS

�] sin � cos �ei�

E = �34I+S+ sin2 �e�2i�

F = �34I�S� sin2 �e2i�

with energy levels presented in �gure 10. � represents angle between direction of applied magnetic�eld ~B0(in our case z axis) and direction of inter-nuclear radius vector ~r, ' represents azimuthangle between x axis and xy projection of inter-nuclear radius vector ~r. � state represents paralleland � anti-parallel spin orientation(relative to the external �eld ~B0). Note that in general statesj��i and j��i do not have equal energies. The notations W I;S

0;1;2 corresponds to zero, single- ordouble quantum transition of spins I or S, respectively. The term A cannot cause transition

Figure 10: Energy levels of dipolar coupled two spin system

between states, it only a¤ects the amplitude of the state(returns product of eigenvalues of both

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spins and is orientation dependent). It would cause splitting in much the same manner as J-coupling. All other terms include raising or lowering operators and will therefore contributeto transitions between states. In solutions, which allow isotropic tumbling of molecules(rateof rotational motion is normally signi�cantly higher than the transitional rates, typical valuesare !~108=s for former and !~103=s far latter), the splitting of resonance lines due to dipolarcoupling is not observed. This is beacuse the contibution of dipolar interaction is averaged tozero by isotropic rotation of molecules in solution[4].

2.2.4 Nuclear Overhauser e¤ect

For the transitions W I;S0;1;2 to occur the stimulating electromagnetic �eld with wide range of

frequencies(W0 � !I�!S , W I;S1 � !I or !S , W2 � !I+!S) must be present. Although there is

no e¤ect on the resonance frequency from dipolar coupling, the tumbling of the molecule generatesa �uctuating electromagnetic �eld(e¤ective �eld strength changes with rotation due to orientationdependent dipolar coupling with neighboring spins) that can stimulate zero-quantum, single-quantum, and double-quantum transitions, providing a mechanism for nuclear spin relaxation.The relaxation rates are independent of the relative orientation of the coupled spins. Resonanceline intensity changes caused by dipolar cross-relaxation from neighbouring spins(typically within5�A radius) with perturbed energy level populations(via RF pulses) is called nuclear Overhausere¤ect or NOE. We will not go into further detail about transitional rates because it is beyond thescope of this seminar, but bear in mind that it is possible to obtain information on inter-protondistances(geometrical restraints in protein structure calculation) from the measurements of theserates. For further reading on NOE the reader is kindly directed to [4].

2.3 1D-NMR

Peak in 1D spectrum is considered the collection of all lines which originate from a single chemicalshift line due to splitting(via any of before mentioned phenomena). Integration over each peak isproportional to the number of active nuclei at that chemical shift. In case of proteins 1D-NMRspectrum is often very populated with spectral lines(mostly multiplets) and there is unavoidablecoincidental overlap of spectral lines(�gure 11). Therefore one usually must apply 2D or 3D-NMRspectroscopy to get more clear information.

2.4 2D-NMR

Two dimesional NMR principles are exactly the same as in 1D NMR. The basic pulse scheme(�gure12), after equilibrium state with magnetization along z-axis ~M = M0(0; 0; 1) is achieved, is asfollows:1.Non-selective pulse �

2 ywhich turns magnetization along the x-axis ~M = M0(1; 0; 0). This

phase is called preparation.2.Before the next pulse the magnetization precesses freely in xy plane for time t1. This phase

is called evolution.3.Next phase is called mixing and consists of one or more pulses. In this phase the cross-

relaxation can occur(transfer of magnetization from 1-type spins with !1 to 2-type spins !2 dueto NOE or J-coupling).4.The last pulse in mixing phase is always such that rotates magnetization in xy plane and

makes it observable. The time after the last pulse is labeled t2.This gives signal at one value of t1. We repeat the process at multiple t1. The 2D signal

on domain [t1; t2] is then 2D fourier transformed into domain [!1; !2] and we get a 2D NMR

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Figure 11: 1D spectrum is often very populated with spectral lines and there is accidentaloverlap[4]

Figure 12: 2D NMR phases scheme

spectrum, which is then interpreted. Typical 2D spectrum is shown in (�gure 13). In general thereare two types of NMR experiments, namely homo-nuclear(each axis in 2D spectrum representsproton 1H nuclear spin) and hetero-nuclear(one axis in 2D spectrum represents 1H and theother some di¤erent nuclear spin, i.e. 13C or 15N). We will give examples of some of the basicexperiments.

2.4.1 COSY(COrrelation SpectroscopY)

COSY is a homonuclear chemical shift correlation experiment via J-coupling. The pulse sequenceis shown in �gure 14. The magnetization M1 (of nuclei at site 1) after the �rst �

2 pulse isin xy plane. This labels magnetization M1 with chemical shift of site 1 type protons. Aftersecond �

2 pulse, the z component of magnetization M1 is nonzero(the amplitude depends onphase !1t1), which in turn has the e¤ect on magnetization M2 of site 2 type protons. Theinteraction is transfered via J-coupling. The e¤ect on M2 is proportional to z component ofmagnetization M1 and thus dependent on !1t1. The e¤ect goes equally vice versa. Thereforethe FT of signal on domain [t1; t2] will give spectrum with peaks on diagonal, corresponding tonon-transfered magnetization, and peaks simetrically above and below diagonal, correspondingto transfered magnetization. The o¤-diagonal peak expresses coupling between proton, which has!1 represented on horizontal line, and proton with !2 represented on vertical line.The splittingdue to J-coupling occurs in every dimension and again only for neighbours no more than 3 bondsaway. Typical COSY spectrum is presented in �gure 14. From COSY spectrum one can thereforeextract the conectivity of protons and also information about dihedral angles �i(subsection J-coupling).

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Figure 13: 2D NMR spectrum[3]

2.4.2 TOCSY(TOtal Correlation SpectroscopY)

TOCSY is a homonuclear chemical shift correlation experiment via successive J-coupling, whichmeans that mixing is a sequence of several � pulses as shown in �gure 15. In contrast to COSYit correlates all protons of a spin system(amino acid residue). Therefore, we have the signalswhich also appear in a COSY spectrum, but also additional signals which originate from theinteraction of all protons of a spin system that are connected with more than 3 chemical bonds.Consequently there exists a characteristic pattern of signals for each amino acid from which theamino acid can be identi�ed. It does not yield sequential connectivity though. Typical TOCSYspectrum is presented in �gure 15.

2.4.3 NOESY(Nuclear OvErhauser SpectroscopY)

NOESY is a homonuclear chemical shift correlation experiment via nuclear Overhauser ef-fect(dipolar interaction). The pulse sequence is shown in �gure 16. The magnetization M1

(of nuclei at site 1) after the �rst �2 pulse is in xy plane. This labels magnetization M1 with

chemical shift of site 1 type protons. After second �2 pulse, the z component of magnetizationM1

is nonzero(the amplitude depends on phase !1t1). The system is then left for �m(mixing time) inwhich the magnetization cross-relaxation due to NOE occurs. The e¤ect on M2 is proportionalto z component of magnetization M1 and thus dependent on !1t1. The spectrum is similarto TOCSY. The intensity of the NOE is in �rst approximation propotional to 1

r6 , with ~r beingthe inter-nuclear vector. It correlates all protons which are close enough in space, regardless ofthe chemical bonding and can therefore provide geometrical restraints on protein secondary andtertiary structure.

2.4.4 HSQC(Heteronuclear Single Quantum Correlation)

HSQC is a heteronuclear chemical shift correlation experiment. Let us look at 15N�HSQC wherethe heteronucleus is 15N . It is one of the most important 2D NMR experiments. It correlates

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Figure 14: Typical COSY spectrum and pulse sequence. Splitting due to J-coupling is visible in1d spectrum plotted along each axis. In 2d spectrum the splitting occurs in each dimension, sothe oval or rectangular areas are acctually numerous peaks[4]

the nitrogen atom of an NH group with the directly attached proton, and each signal in aHSQC spectrum represents a proton that is bound to a nitrogen atom. Since every residue hasa unique HN �15 N pair on the protein backbone and ideally has distinct frequency signals,the HSQC spectrum can serve as the identi�cation of each residue(therefore 15N�HSQC is alsocalled �ngerprint). The HSQC spectrum also contains signals from the NH groups of the sidechains. Example of the HSQC spectrum and pulse sequence is shown in �gure 17. The HSQCspectrum has no diagonal peaks like a homonuclear spectrum. This can be achieved by properpulse sequence, which we will not discuss in detail.There exists numerous derivatives of mentioned experiments, i.e. instead of homonuclear

COSY, TOCSY, NOESY, we can have heteronuclear with di¤erent isotopes, most frequentlyused are 13C and 15N [1].

2.5 3D NMR

2D spectra (like NOESY or TOCSY) of larger proteins are often crowded with signals. Therefore,these spectra are spreading out in a third dimension (usually 13C and 15N), so that the signalsare distributed in a cube instead of a plane. A three dimensional NMR experiment can easily beconstructed from a two dimensional one by inserting an additional indirect evolution time anda second mixing period between the �rst mixing period and the direct data acqusition. Eachof the di¤erent indirect time periods t1, t2 is incremented separately. There are two principalclasses of 3D experiments:-experiments that consist of two 2D experiments, one after another, like NOESY-HSQC and

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Figure 15: Typical TOCSY spectrum and pulse sequence. As in COSY, there is splitting ineach area in 2d spectrum. But in comparison with COSY, we notice additional cross-peak areaswhich emerge from successive J-coupling through whole spin system[4]

Figure 16: NOESY pulse sequence

TOCSY-HSQC-triple resonance experimentsTriple resonance experiments are the method of choice for the sequential assignment of larger

proteins (> 150 amino acids). These experiments are called triple resonance because threedi¤erent nuclei (1H, 13C and 15N) are correlated. The experiments are performed on doublylabelled (13C, 15N) proteins. Therefore pulse sequence for each nuclei type is needed, but itis always such that the magnetization is transferred through all three nuclei types. The mostimportant advantage of the triple resonance spectra is their simplicity: They contain only a fewsignals on each frequency - often only one. The problem of spectral overlap is therefore markedlyreduced. The magnetization in triple resonance experiments is transfered via 1J and 2J-coupling.There is a whole bunch of triple resonance experiments which can not be covered in this shortseminar. Therefore, I will explain only the general nomenclature of triple resonance experimentsand I will deal with the HNCA which is the prototype for all these experiments.

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Figure 17: Typical HSQC spectrum and pulse sequence for each nucleus. Note that it has nodiagonal peaks[3]

2.5.1 HNCA

In each step magnetization is transferred via strong 1J-couplings between the nuclei(�gure 18).The coupling which connects the nitrogen atom with the C� carbon of the preceeding amino

Figure 18: 1J and 2J-coupling in HNCA experiment[2]

acid (2J = 7Hz) is only marginally smaller than the coupling to the directly attached C�atom (1J = 11Hz). Thus, the nitrogen atom of a given amino acid is correlated with bothC� - its own and the one of the preceeding amino acid. Therefore, it is possible to assignthe protein backbone exclusively with an HNCA spectrum. But usually more triple resonanceexperiments are needed because the cross signal of the preceeding amino acid has to be identi�edand degenerate resonance frequencies, which can incidentally still occur, have to be resolved.The pulse sequence and spectrum are pretty complex and will not be given here, but reader isdirected to [4] for further information.

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3 Protein structure determination outline

The aim of the analysis of NMR spectra is to extract all available information about interatomicdistances and torsion angles. In the initial stage of investigation by NMR spectroscopy eachresonance must be associated with a speci�c nucleus in the investigated protein. This process iscalled assignment. The strategies for assignment depend on type of experiment employed.

3.1 Assignment

In 2D NMR, experiments like COSY, TOCSY and HSQC are employed for identi�cation of aminoacids in the backbone. The sequential assignment of the amino acids in the protein backboneis done by NOESY(because the distances between Hi

N , Hi�, H

i� , H

i and H

i+1N is smaller than

5�A in almost every case). Interresidual cross signals(from HiN ;,H

i�, H

i� , H

i dipolar coupling to

Hi+1N as shown in �gure19) can be distinguished from the intraresidual ones by comparing the

NOESY with the TOCSY spectrum(J-coupling in i-th spin system). A series of these sequentialcross signals between Hi

� and Hi+1N determines the order of the amino acid spin systems in the

protein.

Figure 19: In NOESY we get cross peaks of Hi+1N with Hi

N , Hi�, H

i� , H

i , because distances

between are smaller than 5�A and NOE e¤ect is observable

In 3D triple resonance NMR we do not need any knowledge about spin systems. A HNCAspectrum has three frequency axes: 1H, 15N and 13C. It correlates an amide proton with the C�atom of the own and in most cases also with the C� of the preceeding amino acid. A projectionof a HNCA on 1H15N looks like an HSQC, thus each signal represents a single amino acid. Atthe frequency of each amide proton there are two cross signals in the C� dimension, one fromthe intraresidual and one from the interresidual C� atom. Using these cross signals a chain ofcorrelations through the whole amino acid sequence can be established, just like building a chainof dominoes. The assignment can be sped up by other 3D triple resonance NMR experiments[4].

3.2 Constraints for structure calculation

Of special importance for structure calculation are proton-proton distances, which can be es-timated from the signal intensities in NOESY spectra. The intensity of the NOE is in �rstapproximation propotional to 1

r6 , with ~r being the inter-nuclear vector. Distances are derivedfrom the spectra after calibration against NOE signals for known distances (such as distancesin elements of secondary structure) and grouped into few classes(table). An upper and a lowerbound are assigned to each class. The lowest bound is often set to the sum of the van der Waals

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radii(radius of atom aproximated by a hard sphere, which is determined as half the distancebetween equal nonbonded atoms when there is force equilibrium) of the two protons.

NOE lower bound(�A) upper bound(�A)very strong 2.3 2.5strong 2.8 3.1medium 3.1 3.4weak 3.5 3.9very weak 4.2 5.0

It is distinguished between cross peaks of protons no more than �ve amino acids apart in theprotein sequence (medium range NOE�s) and those which are more than �ve amino acids apart(long range NOE�s). The former are mainly indicative of the protein backbone conformation andare used for secondary structure determination, whereas the latter are an expression of the globalstructure of the protein and therefore contain the main information used for tertiary structurecalculation. The torsional angles �i are derived from COSY spectra.

3.3 Structure calculation methods

There are various computer programs, employing two in principle di¤erent methods for calculat-ing a protein structure in solution:1.Distance geometry (DG): This method is based on a calculation of matrices of distance

constraints for each pair of atoms from all available distance constraints, bond and torsion anglesas well as van der Waals radii. This set of distances is then projected from the n-dimensionaldistance space into the three-dimensional space of a cartesian coordinate system, in which itdetermines the coordinates of all atoms of the proteins.2.Simulated Annealing (SA): This is a molecular dynamics method, which takes place directly

in the cartesian coordinate system. In this method, a starting structure is heated to a hightemperature in a simulation (i.e. the atoms of the starting structure get a high thermal mobility).During many discrete cooling steps the starting structure can evolve towards the energeticallyfavourable �nal structure under the in�uence of a force �eld derived from the constraints.After some iterations of assignment, constraining and calculating, the result of the structure

calculation is a family of possible protein structures as in �gure 20, rather than one de�nedstructure. The family adequately satis�es all experimental data acquired. The quality of a NMRstructure can be de�ned by the mean deviation of each structure of this family from an energyminimized mean structure which has to be calculated previously. The smaller the deviation fromthis mean structure the narrower the conformational space[2].

4 Conclusion

NMR spectroscopy is an important technique of acquiring experimental data for structure calcu-lation of proteins in solution. It can produce atomic resolution results, it is done in solution(nocrystallization needed, however, high concentrations are still needed), it can provide informationon local dynamics of protein parts and through structure calculation provides an important in-sight into protein function. The protein structure calculation is a fairly complex and di¢ cult,many times also a very time consuming, process. Even though, the number of yearly announcedsuccesfully determined protein structures is increasing, which is important in many areas ofscience such as biophysics, biotech industry, medicine and others, including academic research.There has been a considerable interest in automating the process of structure calculation. Several

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Figure 20: The result of structure determination is a family of structures on the left, rather thanone structure on the right.

di¤erent computer programs have been published that do this processes automatically. E¤ortshave also been made to standardize the structure calculation protocol to make it quicker andmore amenable to automation.

References

[1] James Keeler. Understanding nmr spectroscopy, 2002.

[2] Joseph B. Lambert and Eugene P. Mazzola. Nuclear Magnetic Resonance Spectroscopy: AnIntroduction to Principles, Applications, and Experimental Methods. Prentice Hall, NewJersey, 2004.

[3] David G. Reid. Protein nmr techniques. Methods in molecular biology, 1997.

[4] Gordon S. Rule and T.Kevin Hitchens. Fundamentals of NMR spectroscopy. Springer, 2006.

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