SEMINAR Protein NMR spectroscopy

Transcription

1 SEMINAR Protein NMR spectroscopy Author: Jan Premru University of Ljubljana Faculty of mathematics and physics Department of physics Mentor: dr.janez Štrancar Joµzef Štefan Institute Laboratory of biophysics 13th January 2008

2 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 of nuclear magnetic resonance(nmr) spectroscopy of proteins in solution. Theoretical part provides reader with enough theoretical background necessary for understanding experimental techniques of one-dimensional and multi-dimensional NMR spectroscopy, explained latter in the seminar. Also discussed is an outline of protein structure determination.

3 Contents 1 Protein basics Biochemical description Structure characterization Protein structure Nuclear magnetic resonance(nmr) spectroscopy NMR basics NMR spectral properties Chemical shift J-coupling Dipolar coupling Nuclear Overhauser e ect D-NMR D-NMR COSY(COrrelation SpectroscopY) TOCSY(TOtal Correlation SpectroscopY) NOESY(Nuclear OvErhauser SpectroscopY) HSQC(Heteronuclear Single Quantum Correlation) D NMR HNCA Protein structure determination outline Assignment Constraints for structure calculation Structure calculation methods 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 ) to which an amino group(nh 2 ), a carboxyl group(cooh), a hydrogen atom(h) and a variable side chain(r) are bonded. Amino acids in chain(called residues) link with peptide bonds, formed with dehydration proces ( gure 1). The linked chain of central C and its adjacent C and N atoms of each amino acid residue de ne the protein main chain or backbone. The two unbonded amino and carboxyl groups left after the formation of the protein are known as the N-terminal and C-terminal ends, respectively. 1.2 Structure characterization To succesfully reproduce protein stucture, one must know atom sizes, bond lengths and dihedral angles for each residue in backbone and all the sidechains. Especially dihedral angles have the greatest impact on protein folding into its unique 3D shape, i.e. a small rotation can re ect in a notable change in structure. Dihedral angle is the angle between two planes, rst of which is determined by rst 3 of 4 succeeding atoms of the backbone, and second determined by the last 1

4 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 local structure assumed by the backbone. The double bond of the C = O group of a single amino acid is 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, called amide plane( gure 2) and also locks i to values 0 or. The i and i angles are de ned as clockwise rotations about the C N and C C bonds, respectively, looking along the bonds away from the atom. The conformation is de ned as i = i = 0 when all main chain atoms are coplanar. Figure 2: Protein backbone dihedral angles 1.3 Protein structure Proteins structure is often described at 4 distinct levels: 2

5 1.Primary structure - amino acid sequence 2.Secondary structure - regularly repeating local structures stabilized by hydrogen bonds. The most common examples are the alpha helix and beta sheet( gure 3). Because secondary structures are local, many regions of di erent secondary structure can be present in the same protein molecule. 3.Tertiary structure - overall shape of a single protein molecule including the spatial relationship of the secondary structures to one another. Tertiary structure is generally stabilized by 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 important insight into the relation between protein structure and its function. There are two most commonly used 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 will focus 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 principle applicable to any nucleus possessing spin. The NMR spectrum provides us with information on the number and type of chemical entities in investigated sample, i.e. protein. Protein NMR is performed on aqueous samples of highly puri ed protein. Usually the sample consist of microlitres with a protein concentration in the range 0:1 3 millimolar(n protein units). The source of the protein can be either natural or produced in an expression system using recombinant DNA techniques through genetic engineering. Recombinantly expressed proteins are usually easier to produce in su cient quantity, and makes isotopic labelling possible(i.e. nuclei of 12 C with no net nuclear spin are replaced with isotope 13 C with net spin s = 1 2 ). Most 3

6 commonly used isotops are 13 C and 15 N. When using proton NMR, solvent is heavy water, in order to remove large proton signal from water molecules( 1 H with net nuclear spin s = 1 2 replaced with 2 H 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 is associated with a non-zero magnetic moment ~ ~ = ~ I (1) For nuclei, the gyromagnetic ratio is a characteristic value that is speci c to the nucleus in question. The nuclear magnetic moment ~ in external magnetic eld ~ B 0 experiences a torque ~N, given by ~N = ~ ~ B 0 (2) Torque has orientation perpendicular to both ~ and B ~ 0, therefore it means that ~ will precess about B ~ 0. Since N ~ = d~ I dt equation(2) rewrites to and we get frequency of precession called Larmor frequency d ~ I dt = ~ I ~ B 0 (3)! L = B 0 (4) Since spin is both value and orientation quantized, so is magnetic moment. The z component of spin is I z = m~ (5) and z component of magnetic moment is z = m~ (6) Thus the nucleus with I = 1 2 has two possible z components of spin states, namely m = 1 2 and m = 1 2. The energies of these states are degenerate, they are the same. Hence the populations of 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 magnetic moment ~ and the external magnetic eld B ~ 0 causes the two states to no longer have the same energy. The energy of a magnetic moment ~ in a magnetic eld B ~ 0 = B 0 (0; 0; 1) is given by E m = B ~ 0 ~ = m~b 0 (7) The energy splitting for the nucleus with I = 1 2 (m = 1 2 or m = E = E ) is E 1 2 = ~B 0 (8) The ratio of populations of energy levels is given by Boltzmann distribution as P 1 2 P 1 2 = e E kt = e ~B 0 kt (9) 4

7 At normal temperature the argument ~B0 kt << 1 and the excess of population in lower energy level is very small(typically 0:1%), but su cient for the magnetization, de ned as ~M = 1 X ~i (10) V to be macroscopic and detectable. Since all ~ i precess with di erent phases around ~ B 0 (around z axis in our case), projections on xy plane average to 0, hence the total equilibrium magnetization will point along the z axis. In nonequilibrium state magnetization precesses around ~ B 0 ( gure 4). 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 B 0, while in nonequilibrium state magnetization precesses around B 0, in our case z axis direction. on-resonance. If we introduce an radiofrequency(rf) pulse with Larmor frequency along x-axis ~ B rf = B rf (1; 0; 0) cos! L t, magnetization begins to precess around x-axis and z-axis. This can be seen if we move into coordinate sistem which rotates around ~ B 0 with! L. The initial magnetization points along the z 0 = z axis. The eld ~ B rf transforms as 0 ~B rf 0 = B = B rf 2 cos! L t sin! L t 0 sin! L t cos! L t (1 cos 2! Lt) sin 2! L t A = B rf 2 cos! L t A = B 1 4@ 1 0 A 0 cos 2! Lt sin 2! L t 0 cos 2! L t sin! L t cos! L t A = A5 (11) and we see that rst term eld appears static and second term eld rotates around z 0 with twice the Larmor frequency. Because of this fast rotating second term eld e ect on magnetization averages to 0. First term eld acts as a static eld in rotating frame and thus the magnetization precesses around x 0 axis. If we apply the pulse just long enough, the magnetization can be rotated into xy plane. In laboratory frame, magnetization precesses around z axis, because of the static B ~ 0 eld. The RF pulse which rotates magnetization for angle 2 around axis x is called 2 x pulse( 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 the coil, 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 5

8 Figure 5: RF pulse which rotates magnetization for angle 2 around axis x is called 2 x pulse Figure 6: Typical NMR experiment setup[2] decay exponentially with characteristic time T 2 as given in equation(12). M xy (t) = M xy;0 e t T 2 (12) Also the inhomogeneity of eld B ~ 0 causes magnetic moments at di erent places to precess with di erent! i. In rotating frame there is a frequency o set of! =! i! L with which the magnetic moments precess around z 0 axis and are thus called o -resonance. This causes the dephasing of total magnetization with time. The total relaxation time is denoted T2 and is determined by equation(13). 1 = (13) T 2 T inh: T 2 Another characteristic time is T 1, named spin-lattice relaxation time due to interaction of nuclear magnetic moments with electron magnetic moments. Magnetization therefore relaxes into its termodinamical equilibrium state along z axis, as given in equation(14). M z = M z;0 (1 e t T 1 ) (14) Both relaxation times depend on the strength of magnetic elds pressed. Typically the T 2 is notably smaller than T 1 so the signal decays almost exclusively due to spin-spin interaction and eld inhomogeneity. This is called free induction decay(fid). 6

9 2.2 NMR spectral properties The NMR signal decays exponentially. The stronger the decay of the signal the broader the characteristic lines of chemical entities in Fourier power spectrum, obtained with Fourier transform of the signal [4]. This is NMR spectrum and its general features and shape can be explained with some physical background Chemical shift The acctual magnetic eld present at the nucleus is attenuated, shielded, by the presence of electrons that surround the nucleus(thought of as moving charges), giving a modi ed eld at the nucleus B = (1 )B 0, where represents the degree of shielding and B 0 is the strength of the applied magnetic eld. The degree of shielding of speci c nucleus is dependent on surrounding electron density, in other words, on its chemical environment. Nuclei in di erent environment(binding partners, bond lengths, angles, presence of electronegative atoms) thus experience di erent e ective magnetic elds and, in turn, have di erent resonance frequencies. They are separated in the NMR spectrum. Instead of frequency, NMR spectrum axes denote chemical shift i =! i! ref 10 6 ppm (15)! ref where! i is the frequency of observed nuclei and! ref is a reference frequency of some chosen substance(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(parts per milion). Chemical shift( gure 7) is thus important for identi cation of compounds and also for determining protein secondary structure, since it varies with dihedral angles(it can reversely be used to predict local dihedral angles)[4][2]. Figure 7: Chemical shift, measured in ppm(parts per milion) units, relative to that of reference substance(i.e. TMS), which is de ned to be 0[1] J-coupling The J-coupling is a scalar interaction which arises between two di erent nuclear spins, I 1 and I 2, and is mediated by the electrons surrounding these two spins(via chemical bonds not through space). The electrons are polarised in the opposite direction to the nucleus they are interacting with. This polarisation in turn has an e ect on the other electrons in close proximity, which at the end a ects the neighbouring nuclei. J-coupling does not depend on orientation but it does depend on the number of bonds between I 1 and I 2. Only coupling through one( 1 J Hz), two( 2 J Hz, geminal) or three( 3 J 5 8 Hz, vicinal) chemical bonds is normally observable. Coupling can not be described classically, but rather quantum-mechanically with 7

10 interaction hamiltonian of the form ^H J = X j;k k<j 2J jk^i j ^I k (16) The e ect of this coupling is splitting of energy levels and consequently separation of spectral lines( gure 8). The coupling of nuclear spin I 1 with n equivalent nuclear spins I 2 causes spec- Figure 8: E ect of J-coupling is splitting of energy levels and consequently separation of spectral lines tral line of I 1 nuclei to split into n + 1 multiplet with intensity ratios following the Pascal s triangle. Note that the coupling with identical spins does not cause splitting. Thus J-coupling combined with chemical shift tells us not only about chemical environment, but also the number of neighboring NMR active nuclei(through chemical bonds). 3 J coupling depends on dihedral angle(through equation(17) known as Karplus equation) and can therefore be used for determination of dihedral angle if 3 J is known. 3 J = 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] Dipolar coupling Between two spins I and S there is direct dipole-dipole magnetic interaction, called dipolar coupling. We consider a two spin system( gure 9) with inter-nuclear radius ~r for which the dipolar interaction is given by equation(18). ^H dipolar = 0~ 2 I S ^S [^I 4 r 3 3 (^I ~r)(^s ~r) r 5 ] (18) 8

11 Figure 9: Two spin system This can be expanded and rewritten in terms of lowering and raising operators for the two spins ^H dipolar = 0~ 2 I S 4r 3 [A + B + C + D + E + F ] (19) A = ^I z ^Sz (1 3 cos 2 ) 1 B = 4 [^I + ^S + ^I ^S+ ](1 3 cos 2 ) 3 C = 2 [^I + ^Sz + ^I ^S+ z ] sin cos e i 3 D = 2 [^I ^Sz + ^I z ^S ] sin cos e i 3 E = 4 ^I + ^S+ sin 2 e 2i 3 F = 4 ^I ^S sin 2 e 2i with energy levels presented in gure 10. represents angle between direction of applied magnetic eld B ~ 0 (in our case z axis) and direction of inter-nuclear radius vector ~r, ' represents azimuth angle between x axis and xy projection of inter-nuclear radius vector ~r. state represents parallel and anti-parallel spin orientation(relative to the external eld B ~ 0 ). Note that in general states ji and ji do not have equal energies. The notations W I;S 0;1;2 corresponds to zero, single- or double 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 9

12 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 contribute to transitions between states. In solutions, which allow isotropic tumbling of molecules(rate of rotational motion is normally signi cantly higher than the transitional rates, typical values are!~10 8 =s for former and!~10 3 =s far latter), the splitting of resonance lines due to dipolar coupling is not observed. This is beacuse the contibution of dipolar interaction is averaged to zero by isotropic rotation of molecules in solution[4] Nuclear Overhauser e ect For the transitions W I;S 0;1;2 frequencies(w 0! I to occur the stimulating electromagnetic eld with wide range of! S, W I;S 1! I or! S, W 2! I +! S ) must be present. Although there is no e ect on the resonance frequency from dipolar coupling, the tumbling of the molecule generates a uctuating electromagnetic eld(e ective eld strength changes with rotation due to orientation dependent dipolar coupling with neighboring spins) that can stimulate zero-quantum, singlequantum, and double-quantum transitions, providing a mechanism for nuclear spin relaxation. The relaxation rates are independent of the relative orientation of the coupled spins. Resonance line intensity changes caused by dipolar cross-relaxation from neighbouring spins(typically within 5 A radius) with perturbed energy level populations(via RF pulses) is called nuclear Overhauser e ect or NOE. We will not go into further detail about transitional rates because it is beyond the scope of this seminar, but bear in mind that it is possible to obtain information on inter-proton distances(geometrical restraints in protein structure calculation) from the measurements of these rates. For further reading on NOE the reader is kindly directed to [4] D-NMR Peak in 1D spectrum is considered the collection of all lines which originate from a single chemical shift line due to splitting(via any of before mentioned phenomena). Integration over each peak is proportional to the number of active nuclei at that chemical shift. In case of proteins 1D-NMR spectrum is often very populated with spectral lines(mostly multiplets) and there is unavoidable coincidental overlap of spectral lines( gure 11). Therefore one usually must apply 2D or 3D-NMR spectroscopy to get more clear information D-NMR Two dimesional NMR principles are exactly the same as in 1D NMR. The basic pulse scheme( gure 12), after equilibrium state with magnetization along z-axis ~ M = M 0 (0; 0; 1) is achieved, is as follows: 1.Non-selective pulse 2 y which turns magnetization along the x-axis ~ M = M 0 (1; 0; 0). This phase is called preparation. 2.Before the next pulse the magnetization precesses freely in xy plane for time t 1. This phase is called evolution. 3.Next phase is called mixing and consists of one or more pulses. In this phase the crossrelaxation can occur(transfer of magnetization from 1-type spins with! 1 to 2-type spins! 2 due to 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 t 2. This gives signal at one value of t 1. We repeat the process at multiple t 1. The 2D signal on domain [t 1 ; t 2 ] is then 2D fourier transformed into domain [! 1 ;! 2 ] and we get a 2D NMR 10

13 Figure 11: overlap[4] 1D spectrum is often very populated with spectral lines and there is accidental Figure 12: 2D NMR phases scheme spectrum, which is then interpreted. Typical 2D spectrum is shown in ( gure 13). In general there are two types of NMR experiments, namely homo-nuclear(each axis in 2D spectrum represents proton 1 H nuclear spin) and hetero-nuclear(one axis in 2D spectrum represents 1 H and the other some di erent nuclear spin, i.e. 13 C or 15 N). We will give examples of some of the basic experiments COSY(COrrelation SpectroscopY) COSY is a homonuclear chemical shift correlation experiment via J-coupling. The pulse sequence is shown in gure 14. The magnetization M 1 (of nuclei at site 1) after the rst 2 pulse is in xy plane. This labels magnetization M 1 with chemical shift of site 1 type protons. After second 2 pulse, the z component of magnetization M 1 is nonzero(the amplitude depends on phase! 1 t 1 ), which in turn has the e ect on magnetization M 2 of site 2 type protons. The interaction is transfered via J-coupling. The e ect on M 2 is proportional to z component of magnetization M 1 and thus dependent on! 1 t 1. The e ect goes equally vice versa. Therefore the FT of signal on domain [t 1 ; t 2 ] will give spectrum with peaks on diagonal, corresponding to non-transfered magnetization, and peaks simetrically above and below diagonal, corresponding to 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 splitting due to J-coupling occurs in every dimension and again only for neighbours no more than 3 bonds away. Typical COSY spectrum is presented in gure 14. From COSY spectrum one can therefore extract the conectivity of protons and also information about dihedral angles i (subsection J- coupling). 11

14 Figure 13: 2D NMR spectrum[3] TOCSY(TOtal Correlation SpectroscopY) TOCSY is a homonuclear chemical shift correlation experiment via successive J-coupling, which means that mixing is a sequence of several pulses as shown in gure 15. In contrast to COSY it correlates all protons of a spin system(amino acid residue). Therefore, we have the signals which also appear in a COSY spectrum, but also additional signals which originate from the interaction 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 the amino acid can be identi ed. It does not yield sequential connectivity though. Typical TOCSY spectrum is presented in gure NOESY(Nuclear OvErhauser SpectroscopY) NOESY is a homonuclear chemical shift correlation experiment via nuclear Overhauser effect(dipolar interaction). The pulse sequence is shown in gure 16. The magnetization M 1 (of nuclei at site 1) after the rst 2 pulse is in xy plane. This labels magnetization M 1 with chemical shift of site 1 type protons. After second 2 pulse, the z component of magnetization M 1 is nonzero(the amplitude depends on phase! 1 t 1 ). The system is then left for m (mixing time) in which the magnetization cross-relaxation due to NOE occurs. The e ect on M 2 is proportional to z component of magnetization M 1 and thus dependent on! 1 t 1. The spectrum is similar to TOCSY. The intensity of the NOE is in rst approximation propotional to 1 r, with ~r being 6 the inter-nuclear vector. It correlates all protons which are close enough in space, regardless of the chemical bonding and can therefore provide geometrical restraints on protein secondary and tertiary structure HSQC(Heteronuclear Single Quantum Correlation) HSQC is a heteronuclear chemical shift correlation experiment. Let us look at 15 N HSQC where the heteronucleus is 15 N. It is one of the most important 2D NMR experiments. It correlates 12

15 Figure 14: Typical COSY spectrum and pulse sequence. Splitting due to J-coupling is visible in 1d spectrum plotted along each axis. In 2d spectrum the splitting occurs in each dimension, so the 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 a HSQC spectrum represents a proton that is bound to a nitrogen atom. Since every residue has a unique H 15 N 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 15 N HSQC is also called ngerprint). The HSQC spectrum also contains signals from the N H groups of the side chains. Example of the HSQC spectrum and pulse sequence is shown in gure 17. The HSQC spectrum has no diagonal peaks like a homonuclear spectrum. This can be achieved by proper pulse 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 frequently used are 13 C and 15 N[1] D 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 13 C and 15 N), so that the signals are distributed in a cube instead of a plane. A three dimensional NMR experiment can easily be constructed from a two dimensional one by inserting an additional indirect evolution time and a second mixing period between the rst mixing period and the direct data acqusition. Each of the di erent indirect time periods t 1, t 2 is incremented separately. There are two principal classes of 3D experiments: -experiments that consist of two 2D experiments, one after another, like NOESY-HSQC and 13

16 Figure 15: Typical TOCSY spectrum and pulse sequence. As in COSY, there is splitting in each area in 2d spectrum. But in comparison with COSY, we notice additional cross-peak areas which emerge from successive J-coupling through whole spin system[4] Figure 16: NOESY pulse sequence TOCSY-HSQC -triple resonance experiments Triple resonance experiments are the method of choice for the sequential assignment of larger proteins (> 150 amino acids). These experiments are called triple resonance because three di erent nuclei ( 1 H, 13 C and 15 N) are correlated. The experiments are performed on doubly labelled ( 13 C, 15 N) proteins. Therefore pulse sequence for each nuclei type is needed, but it is always such that the magnetization is transferred through all three nuclei types. The most important advantage of the triple resonance spectra is their simplicity: They contain only a few signals on each frequency - often only one. The problem of spectral overlap is therefore markedly reduced. The magnetization in triple resonance experiments is transfered via 1 J and 2 J-coupling. There is a whole bunch of triple resonance experiments which can not be covered in this short seminar. Therefore, I will explain only the general nomenclature of triple resonance experiments and I will deal with the HNCA which is the prototype for all these experiments. 14

17 Figure 17: Typical HSQC spectrum and pulse sequence for each nucleus. Note that it has no diagonal peaks[3] HNCA In each step magnetization is transferred via strong 1 J-couplings between the nuclei( gure 18). The coupling which connects the nitrogen atom with the C carbon of the preceeding amino Figure 18: 1 J and 2 J-coupling in HNCA experiment[2] acid ( 2 J = 7Hz) is only marginally smaller than the coupling to the directly attached C atom ( 1 J = 11Hz). Thus, the nitrogen atom of a given amino acid is correlated with both C - its own and the one of the preceeding amino acid. Therefore, it is possible to assign the protein backbone exclusively with an HNCA spectrum. But usually more triple resonance experiments are needed because the cross signal of the preceeding amino acid has to be identi ed and 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 is directed to [4] for further information. 15

18 3 Protein structure determination outline The aim of the analysis of NMR spectra is to extract all available information about interatomic distances and torsion angles. In the initial stage of investigation by NMR spectroscopy each resonance must be associated with a speci c nucleus in the investigated protein. This process is called 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 amino acids in the backbone. The sequential assignment of the amino acids in the protein backbone is done by NOESY(because the distances between HN i, Hi, H i, Hi and H i+1 N is smaller than 5A in almost every case). Interresidual cross signals(from HN i ;,Hi, H i, Hi dipolar coupling to H i+1 N 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 sequential cross signals between H i and H i+1 N determines the order of the amino acid spin systems in the protein. Figure 19: In NOESY we get cross peaks of H i+1 N with Hi N, Hi, H i, Hi, because distances between are smaller than 5A and NOE e ect is observable In 3D triple resonance NMR we do not need any knowledge about spin systems. A HNCA spectrum has three frequency axes: 1 H, 15 N and 13 C. 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 projection of a HNCA on 1 H 15 N looks like an HSQC, thus each signal represents a single amino acid. At the frequency of each amide proton there are two cross signals in the C dimension, one from the intraresidual and one from the interresidual C atom. Using these cross signals a chain of correlations through the whole amino acid sequence can be established, just like building a chain of 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 estimated from the signal intensities in NOESY spectra. The intensity of the NOE is in rst approximation propotional to 1 r, with ~r being the inter-nuclear vector. Distances are derived 6 from the spectra after calibration against NOE signals for known distances (such as distances in elements of secondary structure) and grouped into few classes(table). An upper and a lower bound are assigned to each class. The lowest bound is often set to the sum of the van der Waals 16

19 radii(radius of atom aproximated by a hard sphere, which is determined as half the distance between equal nonbonded atoms when there is force equilibrium) of the two protons. NOE lower bound( A) upper bound( A) very strong strong medium weak very weak It is distinguished between cross peaks of protons no more than ve amino acids apart in the protein 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 and are used for secondary structure determination, whereas the latter are an expression of the global structure of the protein and therefore contain the main information used for tertiary structure calculation. 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 calculating 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 angles as well as van der Waals radii. This set of distances is then projected from the n-dimensional distance space into the three-dimensional space of a cartesian coordinate system, in which it determines 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 high temperature 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 energetically favourable 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 ned structure. The family adequately satis es all experimental data acquired. The quality of a NMR structure can be de ned by the mean deviation of each structure of this family from an energy minimized mean structure which has to be calculated previously. The smaller the deviation from this mean structure the narrower the conformational space[2]. 4 Conclusion NMR spectroscopy is an important technique of acquiring experimental data for structure calculation of proteins in solution. It can produce atomic resolution results, it is done in solution(no crystallization needed, however, high concentrations are still needed), it can provide information on local dynamics of protein parts and through structure calculation provides an important insight 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 announced succesfully determined protein structures is increasing, which is important in many areas of science 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 17

20 Figure 20: The result of structure determination is a family of structures on the left, rather than one structure on the right. di erent computer programs have been published that do this processes automatically. E orts have also been made to standardize the structure calculation protocol to make it quicker and more amenable to automation. References [1] James Keeler. Understanding nmr spectroscopy, [2] Joseph B. Lambert and Eugene P. Mazzola. Nuclear Magnetic Resonance Spectroscopy: An Introduction to Principles, Applications, and Experimental Methods. Prentice Hall, New Jersey, [3] David G. Reid. Protein nmr techniques. Methods in molecular biology, [4] Gordon S. Rule and T.Kevin Hitchens. Fundamentals of NMR spectroscopy. Springer,