Structure determination of ribosomal proteins and …8914/FULLTEXT01.pdfKeywords: nuclear magnetic resonance, structure determination, ribosomal proteins, NMR simulations, NMR theory,

Structure determination of ribosomal proteins and development of new methods in

biomolecular NMR

Magnus Helgstrand

Department of Biotechnology Royal Institute of Technology

Stockholm 2001

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ISBN 91-7283-083-2 Stockholm 2001 Universitetsservice US AB

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Contents

Contents ..................................................................................................................................... iii Abstract ...................................................................................................................................... iv Main References.........................................................................................................................v Preface ........................................................................................................................................vi Acknowledgements .................................................................................................................vii Abbreviations ..........................................................................................................................viii 1 Introduction .......................................................................................................................1

1.1 Nuclear Magnetic Resonance for nonscientists ...................................................1 1.2 NMR Theory .............................................................................................................1 1.3 The assignment procedure.......................................................................................4 1.4 Structure determination using NMR......................................................................4

2 Development of formalism for simulation of NMR experiments ............................7 2.1 Simulations in NMR.................................................................................................7 2.2 Theory.........................................................................................................................7 2.3 Homonuclear case...................................................................................................16 2.4 Heteronuclear case..................................................................................................16 2.5 Simulations during chemical exchange ................................................................17 2.6 Future perspective...................................................................................................17

3 Structure determination of ribosomal proteins S16 and S19 ...................................18 3.1 The Ribosome .........................................................................................................18 3.2 S16 .............................................................................................................................19 3.3 S19 .............................................................................................................................20 3.4 Structures of ribosomal subunits..........................................................................20 3.5 Future perspective...................................................................................................23

4 Development of a computer program for semiautomatic assignment...................24 4.1 Tools to aid assignment of NMR spectra ...........................................................24 4.2 Ansig for Windows.................................................................................................24 4.3 Future perspective...................................................................................................25

5 References.........................................................................................................................27

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Magnus Helgstrand (2001): Structure determination of ribosomal proteins and development of new methods in biomolecular NMR. Department of Biotechnology, Royal Institute of Technology (KTH), Stockholm, Sweden.

Abstract

This thesis concerns different areas of biomolecular nuclear magnetic resonance spectroscopy (NMR). In the first part of the thesis a new formalism for simulations of NMR pulse sequences is introduced. The formalism is derived both from classical mechanics and quantum mechanics and is presented for homonuclear and heteronuclear spin systems. The formalism has also been adapted to systems in chemical exchange. Simulations of pulse sequences should be more straightforward using the new formalism.

In the second part of the thesis the NMR solution structures of two ribosomal proteins are described. The ribosome is responsible for protein production in all living cells and to understand the mechanism of the ribosome it is important to know the three dimensional structure. In this thesis the structures of S16 and S19, two of the proteins in the small ribosomal subunit, are presented. S16 is a mixed α/β protein with a five-stranded parallel-antiparallel β-sheet and two α-helices. S19 is s mixed α/β protein with a three-stranded parallel-antiparallel β-sheet, one α-helix and a short 310-helix.

In the third part of the thesis a program for semiautomatic assignment of NMR-spectra is presented. Assigning resonances in the NMR spectrum is a labor-intensive process, which can take long time. In semiautomatic assignment a computer program aids the user in finding assignments but leaves all decisions to the user, thus speeding up the process. The program described in this thesis is a new version of ANSIG, called Ansig for Windows. The program runs on PCs under Windows and has several tools for semiautomatic assignment.

Keywords: nuclear magnetic resonance, structure determination, ribosomal proteins, NMR simulations, NMR theory, NMR assignment software, semiautomatic assignment

©Magnus Helgstrand, 2001

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Main References

This thesis is based on the following papers, referred to in the text by their Roman numerals.

I. Allard, P., Helgstrand, M. and Härd, T. (1997). A method for simulation of NOESY, ROESY and off-resonance ROESY spectra. J. Magn. Reson. 129, 19-29A.

II. Allard, P., Helgstrand, M. and Härd, T. (1998). The complete

homogenous master equation for a heteronuclear two-spin system in the basis of Cartesian product operators. J. Magn. Reson. 134, 7-16A.

III. Helgstrand, M., Härd, T. and Allard, P. (2000). Simulations of NMR

pulse sequences during equilibrium and non-equilibrium chemical exchange. J. Biomol. NMR 18, 49-63B.

IV. Allard, P., Rak, A. V., Wimberly, B. T., Clemons Jr, W. M., Kalinin, A.,

Helgstrand, M., Garber, M. B., Ramakrishnan, V. and Härd, T. (2000). Another piece of the ribosome: solution structure of S16 and its location in the 30S subunit. Structure 8, 875-882C.

V. Helgstrand, M., Rak, A. V., Allard, P., Davydova, N., Garber, M. B. and

Härd, T. (1999). Solution structure of the ribosomal protein S19 from Thermus thermophilus. J. Mol. Biol. 292, 1071-1081B.

VI. Helgstrand, M., Kraulis, P., Allard, P. and Härd, T. (2000). Ansig for

Windows: An interactive computer program for semiautomatic assignment of protein NMR spectra. J. Biomol. NMR 18, 329-336B.

All papers are reproduced with permission from the copyright holders: ©Academic PressA, ©Kluwer Academic PressB, ©Elsevier Science Ltd.C

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Preface

During the four years I have been a graduate student I have worked with projects from a wide area of biomolecular NMR. Consequently this thesis spans projects as diverse as structure determination, software development and NMR theory.

My graduate studies started with the structure determination of the ribosomal protein S19. Structure determination of proteins using NMR is a quite tedious process of looking at different spectra on a computer screen. Since this process sometimes bored me, I started to do simulations of NMR-experiments using the Bloch equations, as described below. The simulations lead to the study of NMR-theory and a new formalism for easy simulation of different NMR pulse sequences was developed together with one of my supervisors, Peter Allard. The project with simulations and development of NMR formalism then continued throughout my entire graduate studies (Papers I-III). When the structure of S19 was finished (Paper V) I was not happy with the program I had used for assignment of spectra. At that time my other supervisor, Torleif Härd, asked me if I wanted to rewrite the excellent program ANSIG1,2 for PCs running Windows. While rewriting the program I added more and more assignment routines and the idea of semiautomatic assignment was born (Paper VI).

During my graduate studies I have learnt a lot, had a lot of fun and hopefully made a small contribution to the collective human knowledge in the form of this thesis.

Magnus Helgstrand April, 2001

vii

Acknowledgements

I would like to thank several people for making my time as a graduate student interesting and pleasant:

Först och främst Torleif för att jag fått möjlighet att arbeta i din grupp, trots att jag envetet har hållit mig borta från allt laborativt arbete. Jag uppskattar mycket att du har gett mig så fria händer att göra det jag tycker är intressant. Peter för att du alltid har funnits till hands för att svara på mina, ibland inte helt genomtänkta, frågor. Jag har också uppskattat alla långa och mycket trevliga diskussioner rörande allt från evolution till NMR-teori. Tack också för lånet av datorn! De doktorander som har varit i gruppen under stor del av den tid jag varit där, Henrik, Anja och Magnus. Henke för trevliga turer på isar och i fjällen. Anja för trevligt sällskap och för din entusiasm. Mange för att du är positiv och säger vad du tycker. Övriga medlemmar i NMR gruppen: Alexandra, Anders, Christofer, Elisabet, Esmeralda, Helena, Lotta, Martin, Niklas, Susanne och Vildan. Även de som varit en del av NMR-gruppen, men som slutat: Peter, Anders och Annika. Gudrun, Micke, Peter H, Peter A, Philip, Henrik och alla andra som brukar äta vid CSB-bordet i lunchrummet för trevliga lunchstunder och livliga diskussioner. Everyone who works/has worked at CSB, especially Erik, Lennart, Pekka, Johan and Matthew. Co-authors not already mentioned above. Vänner och bekanta för att ni har hjälpt mig att tänka på något annat än forskning, speciellt Kicki, Niklas, Eva, Dennis, Per och Camilla för trevligt umgänge och (för det mesta) mycket god mat. Mattias för att du försöker lära mig något om musik. Morrs, Farrs, Brorr, Syrr, Anna och Andreas för att ni alltid finns där. Än har jag inte fastnat i magneten! Tack även till farmor, farfar, Börje, Lena, Knusarna, Siv, Bill och Lina. Axel för att du alltid är glad och busig. Sist men inte minst Lotta. Jag älskar dig.

viii

Abbreviations

1D One-dimensional 2D Two-dimensional 3D Three-dimensional ANSIG Assignment of NMR spectra by interactive graphics API Application programming interface CSA Chemical shift anisotropy GL Graphics language GNU GNU's not Unix HSQC Heteronuclear single quantum coherence spectroscopy I/O Input/output mRNA Messenger RNA NMR Nuclear magnetic resonance NOE Nuclear Overhauser enhancement NOESY NOE spectroscopy PC Personal computer RMSD Root mean square deviation RNA Ribonucleic acid RF Radio frequency ROESY Rotating frame nuclear Overhauser effect spectroscopy rRNA Ribosomal RNA SA Simulated annealing TOCSY Total correlation spectroscopy TROSY Transverse relaxation optimized spectroscopy

Introduction 1

1 Introduction

1.1 Nuclear Magnetic Resonance for nonscientists

Nuclear Magnetic Resonance (NMR) is a method that can be used to study structure and behavior of molecules. A sample containing the molecule under study is inserted into a strong magnetic field. Some nuclei in the molecule then react as small magnets. Small magnets in a large magnetic field orient themselves; like the needle of a compass. Unlike compasses the small nucleic magnets can be oriented in two ways, along the magnetic field or opposite the magnetic field. There is only a small energy difference between the two orientations, which means that only slightly more nuclei will be in the lower energy orientation. Adding up the contributions from all the small magnets give a small bulk magnetization parallel to the strong external magnetic field. When studying molecular structure and/or behavior with NMR this bulk magnetization is manipulated with radio frequency (RF) pulses and then studied with a RF-receiver (radio). The manipulations of bulk magnetization in NMR can be compared to using a hammer, the pulse, on a church bell, the bulk magnetization. The response from the bell is a sound of a specific frequency and from the bulk magnetization the response is a radio transmission of a specific frequency, the resonance frequency. Depending on the internal location of the magnetically active nuclei within the molecule, the resonance frequency received from the nuclei will be slightly modified. The modifications are interpreted as different physical properties, like distances and chemical bonds between atoms in a molecule.

1.2 NMR Theory

NMR is a spectroscopic phenomenon. To completely describe what is going on in the NMR spectrometer a quantum mechanical description is necessary. Such a description is presented in section 2.2. The theoretical description in this section is a simplified semiclassical description adapted from Cavanagh 19963. The theory in this section aims at presenting some basic NMR concepts mentioned in the text and in Papers I-VI, such as Larmor frequency, chemical shift and relaxation.

1.2.11.2.11.2.11.2.1 Nuclear magnetic momentNuclear magnetic momentNuclear magnetic momentNuclear magnetic moment

The spin of the nucleus is an intrinsic property. The nuclear spin angular momentum is a quantum mechanical vector property with a magnitude given by

( )[ ]122

+=⋅= IIIII h (1)

in which ħ is Planck’s constant divided by 2π, and I is the angular momentum quantum number. The laws of quantum mechanics only allow for specification of one component of the vector together with the magnitude. In NMR Iz is usually specified.

2 Ribosomal proteins and new methods in NMR

mIz h= , in which ( )IIIIm ,1,,1, −+−−= K . (2)

The nuclear magnetic moment is directly proportional to the spin angular momentum and is given by

Iγµ = (3)

in which µ is the magnetic moment and γ, the gyromagnetic ratio, is a constant dependent on the nucleus. The energy for a magnetic moment in an external magnetic field is given by

BE ⋅−= µ (4)

in which B is the external magnetic field. In NMR the external magnetic field is defined to be parallel to the z-axis, which means that

00 BmBIE zm γγ h−=−= (5)

in which B0 is the static magnetic field strength. In a sample at equilibrium the number of spins in one energy level divided by the number of spins in all energy levels is given by the Boltzmann distribution.

≈

−

−= ∑

−=

I

Im B

m

B

mm

TkE

TkE

NN expexp

( )121 0 +

+≈ I

TkBm

B

γh (6)

in which T is the temperature and kB is the Boltzmann constant. The bulk magnetization is then given by

( )TkIIBNmNM

B

I

Imm 3

1022

0+

≈= ∑−=

hh

γγ . (7)

The quantum mechanical selection rule for magnetic dipole transitions is ∆m = ±1, which, using Equation 5, gives the energy difference between two levels

0BE γh=∆ (8)

which corresponds to the Larmor frequency

00 Bγω −= . (9)

The magnetic field strength of NMR spectrometers is usually given as the frequency corresponding to the Larmor frequency for 1H. A magnetic field of 11.74 T corresponds to a 1H Larmor frequency of 500 MHz.

Introduction 3

1.2.21.2.21.2.21.2.2 Bloch equationsBloch equationsBloch equationsBloch equations

A formalism to describe the evolution of the bulk magnetization using classical mechanics was first proposed by Bloch 19464. The foundation is the equation of motion for a magnetic dipole in an external magnetic field

( ) ( ) ( )tBtMtMdtd γ×= (10)

in which B is an external magnetic field. The equation for bulk magnetization in the laboratory frame can be transformed to a frame rotating with the frequency ωRF around the z-axis of the laboratory frame. This equation can be written

( ) ( ) ( )tBtMtMdtd rrr

γ×= (11)

in which

rrrrkjBiBB

γϕϕ Ω

++= sincos 11 (12)

and r denotes a rotating frame. The vectors i, j and k are unit vectors in the rotating frame, φ is the phase of an applied RF field with frequency ωRF and magnitude B1 and Ω is given by

RFωω −=Ω 0 . (13)

The local magnetic field for a nucleus is given by the combined effect of the external magnetic field and the environment in which the nucleus is located. If ωRF is chosen to be γB0, in which B0 is the external magnetic field, Ω is the chemical shift. The chemical shift gives a value on how much the local magnetic field differs from the external magnetic field.

The Bloch differential equation can be written in matrix form as

( )( )( )

( )( )( )

−Ω

−Ω−=

tMtMtM

BBBB

tMtMtM

dtd

z

y

x

rx

ry

rx

ry

z

y

x

00

0

γγγγ

. (14)

This equation does not take into account the return of the bulk magnetization back to thermal equilibrium; this will be discussed in the next section.

1.2.31.2.31.2.31.2.3 RelaxationRelaxationRelaxationRelaxation

After a perturbation of the bulk magnetization by an external RF-field the magnetization returns back to the equilibrium value over time. This process is called relaxation and can be incorporated into the Bloch equations. Relaxation is divided into two mechanisms. The first mechanism, spin-lattice relaxation, accounts for the return


of the population difference between the energy levels of the spins to equilibrium. The second mechanism, spin-spin relaxation, accounts for the disappearance of magnetization from the x-y plane in the rotating frame. The spin-lattice relaxation rate is denoted R1 and the spin-spin relaxation rate is denoted R2. The Bloch equations including relaxation are written

( )( )( )

( )( )( )

+

−−Ω−

Ω−=

101

2

2

00

RMtMtMtM

RBBBRBR

tMtMtM

dtd

z

y

x

rx

ry

rx

ry

z

y

x

γγγγ

(15)

in which M0 is the equilibrium magnetization given by the Boltzmann distribution (Equation 7). The Bloch equations can be made homogenous and solved numerically; this is done in Paper I.

1.3 The assignment procedure

After acquiring NMR-spectra on a protein sample, the peaks of the spectra have to be identified. In 1D spectra every peak usually corresponds to one nucleus in the protein. Spectra with two or more dimensions usually have off-diagonal peaks, called crosspeaks, which correspond to an interaction between two or more nuclei. The interactions are mainly of two different types: through space interactions and interactions through chemical bonds. During the assignment process these two types of interactions are used to assign chemical shifts to hydrogen nuclei, and in some cases also to nitrogen and carbon nuclei in the protein.

Assignment usually starts with identification of hydrogen-nitrogen (HN-N) pairs in the backbone of the amino acid residue sequence of the protein. After identification of these pairs, spectra from different sequential experiments (such as the HNCA5/HN(CO)CA6 pair) are used to sequentially connect the HN-N pairs to each other. During this process usually also the Cα, Hα, Cβ and Hβ nuclei are identified. After amino acid residues have been connected into chains of different lengths, the chains are placed in the protein amino acid sequence. Placing the chains in the protein amino acid sequence is usually done based on the chemical shifts of Cα, Hα, Cβ and Hβ, which are dependent on amino acid type. Assignment of sidechain nuclei starts after identification of most of the amino acid residues in the spectra. Sidechain nuclei are usually identified using different TOCSY7 experiments, correlating the nuclei of the sidechains with the already known backbone nuclei in the same residue. It should in principle be possible to assign chemical shifts to all nuclei in the protein in this way. In practice this is almost never the case, there are almost always some nuclei with too similar chemical shifts to be told apart. Missing peaks due to motion and/or chemical exchange is also a problem.

1.4 Structure determination using NMR

Structure determination of biomolecules using NMR is mostly based on local distance and angle information (for an overview of protein and DNA/RNA structure determination using NMR see Wüthrich, 19868). Distance information is obtained

Introduction 5

from the nuclear Overhauser effect (NOE)9. Angle information is mainly obtained from spin-spin interactions through chemical bonds10,11. From the information obtained a model of the molecule under study is calculated using numerical methods.

New methods to acquire structural information have recently been developed. These methods are based on residual dipole-dipole couplings in dilute macroscopically ordered media12, which give information on the orientation of bonds within the molecule. This information is thus not local. Residual dipole-dipole couplings were not used in the study of ribosomal proteins in this thesis.

1.4.11.4.11.4.11.4.1 Distance restraintsDistance restraintsDistance restraintsDistance restraints

Distance restraints are acquired from NOE spectroscopy (NOESY)13. In NOESY the dipole-dipole cross relaxation mechanism is utilized to extract distances between interacting nuclei. Crosspeaks between interacting nuclei are obtained in a spectrum from a NOESY experiment. The intensities of the crosspeaks are mainly proportional to the distances between nuclei to the power of minus six. Distance information is quickly lost for larger distances and distances larger than about 6 Å can usually not be detected. Cross peak intensities can also depend on other mechanisms, such as relaxation and chemical exchange. Distance restraints are therefore usually divided into classes, e.g. 1.8-2.7 Å, 1.8-3.5 Å, 1.8-5.0 Å and 1.8-6.0 Å3. No energy penalties are given in the structure calculation if the distances in the model structure are within the distance intervals.

1.4.21.4.21.4.21.4.2 Angle restraintsAngle restraintsAngle restraintsAngle restraints

Magnetization cannot only be transferred through space but also over chemical bonds. The mechanism for transfer of magnetization over chemical bonds is called scalar coupling or J-coupling. The transfer rate of magnetization over a chemical bond depends on the local conformation of atoms. Magnetization can be transferred over more than one bond. For example the 3-bond scalar couplings between HN and Hα in the peptide backbone, as measured by a HNHA-experiment14, give information about the dihedral angle between NH and Cα. Information obtained can be translated to an angle by the Karplus equation10,11. The Karplus equation is periodic, and thus more than one angle is possible for a certain scalar coupling. Angular information is therefore included in the structure calculations as favored and less favored regions instead of specific angles3.

1.4.31.4.31.4.31.4.3 Structure calculationStructure calculationStructure calculationStructure calculation

Structure calculations are usually done with either one of two methods; simulated annealing or distance geometry. The method used in this thesis is simulated annealing.

A model of the protein is constructed using the amino acid sequence as a template before calculating the structure of the protein using simulated annealing. Atoms in the model of the molecule are restricted in motion according to a force field and the restraints obtained by NMR. The force field parameterizes known physical properties like bond distances and atom radii. NMR restraints are included as described above. The model is then heated to a high temperature by increasing the amount of energy


distributed in it, both as kinetic energy and potential energy. The model is allowed to change conformation at the high temperature and because the energy is high, many conformations are allowed. In the next step lowering the amount of energy in the model by small amounts slowly cools it. During cooling the molecule is allowed to change conformation and if the cooling process is slow enough the molecule will at the end reach the lowest possible potential energy conformation. Low energy models should have the same structure as the native protein. In practice the procedure is repeated and many structures are calculated to yield an ensemble of slightly different conformations. Low energy structures from an ensemble of many model structures with low potential energies and similar conformations are believed to be correct.

Structure calculations are usually performed with the programs CNS15 or X-PLOR16.

1.4.41.4.41.4.41.4.4 Structure validationStructure validationStructure validationStructure validation

After a protein structure has been calculated the structure must be validated. Structures are validated by studying the geometry of the molecule, the potential energy in the molecule and the overall fold. The geometry of the molecule is for example studied using Ramachandran plots, comparing backbone angles in the protein with backbone angles in other well-defined protein structures. If the calculated structures have abnormal backbone angles it might be due to a special interaction in the protein, but more likely it is due to an erroneous structure. The potential energy is calculated using force fields, parameterizing intramolecular forces. If the potential energy is too high the calculated structure of the protein may be wrong. The overall fold is studied visually to see that the protein looks like a well-folded protein.

The reason for an erroneous structure could for example be misassigned nuclei, misassigned NOE crosspeaks or insufficient number of restraints. The reason could also be too fast cooling in the simulated annealing step during structure calculation. If the structure seems to be wrong, assignment of NMR spectra is verified and/or new restraints added. New structures are then calculated.

Development of formalism for simulation of NMR experiments 7

2 Development of formalism for simulation of NMR experiments

2.1 Simulations in NMR

Pulse sequences in modern liquid state NMR are often very complex. The outcome of a pulse sequence cannot readily be understood without an involved analysis, using for example Cartesian product operators17. For complicated pulse sequences such analytical approaches can get overwhelming, and in these cases numerical simulation can be used18-20.

The aim in constructing the new formalism presented in Papers I-III was to combine the Cartesian product operator formalism, used in analytical calculations, with numerical simulations. The magnitude of different Cartesian product operators can in this way be followed throughout the simulation of a pulse sequence. The formalism allows for simulation of complex pulse sequences for homonuclear spin systems taking relaxation into account (Paper I). The formalism was also developed for heteronuclear spin systems (Paper II) and for systems in chemical exchange (Paper III).

2.2 Theory

In this section NMR theory will be described in more detail than in previous sections. The theory in this section is a basis for the formalism introduced in Papers I-III and has been adapted from Abragam 196121, Ernst et al. 198722 and Cavanagh 19963.

2.2.12.2.12.2.12.2.1 The Density operatorThe Density operatorThe Density operatorThe Density operator

The state of a quantum mechanical system is given by the state function ( )tψ . The evolution of the state function over time is described by the time-dependent Schrödinger equation, which may be written

( ) ( ) ( )tttt

ψψ idd

Η−= , (16)

in which H(t) is the time-dependent Hamiltonian for the system. The state function can be expanded in an orthonormal basis

,...,2,1 , nii = , (17)

( ) ( )∑=

=n

ii itct

1 ψ (18)


in which the time dependence of ( )tψ is expressed by the time dependence of the complex coefficients ci(t) and n is the dimensionality of the space. State vectors may represent the bases of the space; it is then called Hilbert space.

Spins in an ensemble, for example an NMR sample, are usually not in the same quantum mechanical state, i.e. they do not have the same state function. For an ensemble of spins the average density operator is defined as

( ) ( ) ( )∑=k

kkk ttpt ψψρ (19)

in which pk is the probability that a spin system of the ensemble is in the state ( )tkψ . The density operator is very useful, if the density operator is known at a specific time t, any observable property can be calculated according to

( ) tObsObs ρ tr= , (20)

in which † denotes the adjoint. The density operator may be expanded in Hilbert space using Equation 18 above

( ) ( ) ( )∑∑ ∗=i j

ji jitctct ρ , (21)

in which the bar denotes an ensemble average and * denotes the complex conjugate. The equation of motion for the density operator can be derived from the time-

dependent Schrödinger equation, according to Equation 16:

( ) ( ) ( )[ ]tttt

ρρ , Hidd

−= . (22)

So far no restrictions have been imposed on the density operator; it describes the entire quantum mechanical system. In NMR this is not really necessary, the quantum mechanical system can be limited to only include the nuclear spins and let other interactions be part of the surrounding, often called the lattice. The equation of motion for the spin density operator σ(t) in the quantum mechanical master equation is defined as:

( ) ( ) ( )[ ] ( )( )0ˆ , i

dd σσσσ −Γ−Η−= ttttt

S (23)

in which SΗ is the reduced Hamiltonian. The reduced Hamiltonian only includes nuclear spin interactions; all other interactions are included in the superoperator Γ , the relaxation superoperator. A superoperator is defined as an operator acting on other operators, in this case the density operator. The relaxation superoperator accounts for the return of the system to thermal equilibrium. For convenience the suffix S will be dropped from now on.


2.2.22.2.22.2.22.2.2 The Liouville space of Cartesian spin operatorsThe Liouville space of Cartesian spin operatorsThe Liouville space of Cartesian spin operatorsThe Liouville space of Cartesian spin operators

As well as operators in Hilbert space can be written as a linear combination of an orthogonal set of basis functions, the superoperators in super space, or Liouville space, can be written as a linear combination of orthogonal operators from Hilbert space.

For a Hilbert space of dimension n there are n2 operators. If, for example, an isolated spin ½ is considered, the Hilbert space state functions can be represented by the vectors

=

01

α and

=

10

β . (24)

In this vector space there are 22 = 4 operators represented by a set of four 2 by 2 matrices. One set of operators is the Cartesian spin operators

=

1001

21

21 E ,

=

0110

21

xI ,

−=

0ii0

21

yI and

−

=10

0121

zI . (25)

The matrices are transformed into vectors by adding rows after each other. The result is an orthogonal basis:

[ ]100121

21

=E , [ ]011021

=xI ,

[ ]0ii021

−=yI and [ ]100121

−=zI . (26)

It is now evident that a superoperator in Liouville space must be of the dimensionality n2*n2, in which n is the dimensionality of the Hilbert space.

In Equation 23, the quantum mechanical master equation, there is a commutator superoperator

[ ] Η−Η=Η≡Η σσσσ , ˆ . (27)

In matrix form Η can be written as

Ε⊗Η−Ε⊗Η=Η ~~ˆ (28)

in which E is the unity matrix, ~ denotes the transpose of a matrix and ⊗ denotes the direct product. The direct product between two matrices is given by (illustrated for 2 by 2 matrices):


=

=

⊗

=⊗

BBBB

BA2221

1211

2221

1211

2221

1211

AAAA

BBBB

AAAA

=

2222212222212121

1222112212211121

2212211222112111

1212111212111111

BABABABABABABABABABABABABABABABA

(29)

Considering the example above, the spin Hamiltonian, in rad/s, for an isolated spin ½ can be written (in the rotating frame) as

yyxxz III ωω ++Ω=Η , (30)

in which Ω is the chemical shift, ωx and ωy are the applied magnetic fields along the x and y axis respectively. ωx and ωy are given by

ϕγω cos1r

x B−= and ϕγω sin1r

y B−= (31)

in which B1r is the strength of the applied RF field and φ is the phase. Using the

matrix representation in Equation 25, H may be written

=

−+

+

−

Ω=Η0ii0

21

0110

21

1001

21

yx ωω

Ω−+−Ω

=yx

yx

ωωωω

ii

21

. (32)

The commutator superoperator may then be constructed according to

−

⊗

Ω−+−Ω

=Η1001

ii

21ˆ

yx

yx

ωωωω

=

Ω−−+Ω

⊗

−

yx

yx

ωωωω

ii

21

1001

−

Ω−+Ω−+

−Ω−Ω

=

0i000i

i000i0

21

yx

yx

yx

yx

ωωωω

ωωωω


=

Ω−−+Ω

Ω−−+Ω

−

yx

yx

yx

yx

ωωωω

ωωωω

i00i00

00i00i

21

+−+−−Ω−+−Ω+−

−−−

=

0ii0i20i

i02i0ii0

21

yxyx

yxyx

yxyx

yxyx

ωωωωωωωωωωωω

ωωωω

. (33)

The Hamiltonian is now expressed in the basis of Cartesian spin operators using

rr

srrs BB

BB ˆ Η=Η (34)

in which r and s represent the coordinate of the matrix element and Br and Bs are the Cartesian spin operators in vector form (Equation 26). As an example the matrix element r = 2 and s = 3 is calculated using the base B1 = ½E, B2 = Ix, B3 = Iy and B4 = Iz.

=Η

=Η22

3223

ˆ BBBB

[ ] =

−

+−+−−Ω−+−Ω+−

−−−

=

0ii

0

0ii0i20i

i02i0ii0

011041

yxyx

yxyx

yxyx

yxyx

ωωωωωωωωωωωω

ωωωω

[ ] Ω−=

−

−Ω−Ω= i

0ii

0

i222i241

yy ωω (35)


Performing the calculation for all elements in the superoperator matrix, the result is

−Ω−

−Ω−=Η

0000

000000

iˆ

y x

x

y

ωωωω

. (36)

The lower right 3 by 3 submatrix is recognized as the matrix representation of the Bloch equations without relaxation.

2.2.32.2.32.2.32.2.3 RelaxatiRelaxatiRelaxatiRelaxation theoryon theoryon theoryon theory

The relaxation superoperator in the quantum mechanical master equation (Equation 23) has to be evaluated using perturbation theory. The theory discussed below is adapted from a book by Abragam, 196121 and is a semiclassical approach to relaxation.

First the master equation is rewritten in the form:

( ) ( ) ( )[ ]tttt

σσ , idd

10 Η+Η−= (37)

in which H0 is the ordinary spin Hamiltonian and H1(t) is a perturbing time-dependent Hamiltonian responsible for the interaction between the spins (described by H0) and the environment. If the following transformation is made

ttT ee 00 -ii ΗΗ= σσ and ( ) ( ) ttT etet 00 -i1

i1 ΗΗ Η=Η (38)

H0 is eliminated from Equation 37. Equation 37 can then be written

( ) ( ) ( )[ ]tttt

TTT σσ , idd

1Η−= . (39)

Using the Magnus expansion23 up to the second order, the transformed density operator may be written as

( ) ( ) ( ) ( )[ ]∫ −′′Η−=t

TTTT tdtt0

1 0 , i0 σσσ

( ) ( ) ( )[ ][ ]∫∫′

′′Η′Η′′′−t

TTTt

tttdtd0

110

0 , , σ . (40)


Taking the time derivative of the expansion (Equation 40) the result is

( ) ( ) ( )[ ]−Η−= 0 , idd

1TTT tt

tσσ

( ) ( ) ( )[ ][ ]0 , , 110

TTTT

tttd σ′ΗΗ′−∫ . (41)

Taking the ensemble average of the transformed density operator and assuming that other criteria are fulfilled (see Abragam, p. 276 for a discussion of these criteria) the time evolution of the density operator can be written:

( ) ( ) ( ) ( )[ ][ ]tttdtt

TTTT σττσ ,,dd

110

−ΗΗ−= ∫∞

. (42)

The form of the random Hamiltonian H1 will now be discussed. In the semiclassical approach to relaxation theory the Hamiltonian can be expressed as:

( ) ( )( ) ( )∑=Ηq

qq AtFt1 (43)

in which F(q) are random functions of time and A(q) are operators acting on the system of spins under study. The correlation function, describing the “randomness” of the random functions F is written as

( ) ( )( ) ( ) ( )ττ += ′′ tFtFg qqqq

* . (44)

Fourier transformation of the correlation function gives the spectral density functions:

( ) ( )∫∞

∞−

−′′ = ττω ωτdegJ qqqq

i and ( ) ( )∫∞

−′′ =

0

i ττω ωτdegj qqqq . (45)

Substituting Equations 43-45 into Equation 42 and assuming that ( ) ( )*qq FF =− and ( ) ( )†qq AA =− , in which * denotes the complex conjugate and † the adjoint of a matrix,

the evolution of the transformed density operator can be written

( )( ) ( )( ) ( ) ( ) ( )[ ][ ] ×−= ∑

′′

′′

+ ′′

ppqq

Tqp

qp

tT tAAett

qp

qp

,,,

i ,,dd σσ ωω

( )( )

∫∞

−′−×

0

i, ττ

τω degqp

qq . (46)


Assuming that gqq’(τ) = δqq’gq(t)

( )( ) ( )( ) ( )( )∫

∞− −=

0

i i21 q

pqqpqq kJdeg

qp ωωττ τω . (47)

If only spin ½ are considered the function k represents a very small shift in the energy of the system, k may be included in H0. The final result is:

( ) ( )( ) ( ) ( ) ( )[ ][ ]∑ −−=pq

Tqp

qp

qpq

T tAAJtt ,

,,21

dd σωσ . (48)

This equation may be transformed back to the normal master equation

( ) ( )[ ] ( )( )00ˆ , i

dd σσσσ −Γ−Η−= tttt

(49)

in which Γ is defined as

( )( ) ( ) ( )[ ][ ]∑ −=Γpq

qp

qp

qpq AAJ

,

, , ˆ ω . (50)

This equation is used in Papers I-III to calculate the relaxation elements in the matrix representation of the homogenous master equation. In the papers the equation is used with Wigner 3-J symbols to denote interacting operators.

2.2.42.2.42.2.42.2.4 Inhomogeneous to homogenousInhomogeneous to homogenousInhomogeneous to homogenousInhomogeneous to homogenous

The quantum mechanical master equation (Equation 23), is inhomogeneous but can be transformed in to an homogenous form24-26. The equation may be written in matrix form

+

×

=

nnnnn

n

n C

C

I

I

xx

xx

I

I

dtd

MM

K

MOM

K

M11

1

1111

. (51)

This system of differential equations may be made homogenous by increasing the dimensionality. In the quantum mechanical master equation the unity operator, E/2, is added. The equation system is then written as

+

×

=

nnnnn

n

n C

C

I

IE

xx

xx

I

IE

dtd

MM

L

MOMM

L

L

M11

1

1111

02/

0

00002/

. (52)


The vector with constants, C1 to Cn, may be transferred to the first column of the matrix

×

=

nnnnn

n

n I

IE

xxC

xxC

I

IE

dtd

M

L

MOMM

L

L

M1

1

11111

2/

2

20002/

. (53)

The only difference between Equations 51 and 53, except that 53 is homogenous, is the addition of a new differential equation stating that

02/ =Edtd

(54)

which is trivial.

2.2.52.2.52.2.52.2.5 NumeNumeNumeNumerical calculationsrical calculationsrical calculationsrical calculations

To calculate the outcome of an NMR experiment, the density operator is used. The homogenous form of the master equation may be written as

( ) ( )tPtdtd σσ ˆ−= (55)

in which σ(t) is the vector representation of the density operator in the basis of Cartesian product operators and P is the homogenous form of the combined commutator superoperator of the Hamiltonian and the relaxation superoperator. The solution to this system of differential equations is

( ) ( )0êxp =

−= ttPt σσ (56)

in which the exponential of a matrix is defined according to the Taylor expansion. During a pulse sequence the density operator evolves under different

Hamiltonians and therefore also under different P . Calculation of the outcome of a pulse sequence can be performed according to

( ) ( )01122êxpêxpêxp tPPPt nnn στττσ

−

−××

−= K (57)

in which σ(t0) is the density operator at the beginning of the pulse sequence and P1 to Pn are the pulses/delays of the pulse sequence and τ1 to τn their respective length.

The expectation value of an observable is calculated according to

( )t†σObsObs = (58)

in which Obs for an NMR experiment is Ix or Iy.


In numerical simulations, using the formalism, the most computational intensive part is to calculate the exponential of a matrix. The simulations in Papers I-III are performed using the mathematical program Matlab, which utilizes the Padé approximation with scaling and squaring (method 3 described in the paper by Moler and van Loan, 197827).

2.3 Homonuclear case

In Paper I formalism for simulation of homonuclear pulse sequences, using homogenous equations, is introduced. The formalism is presented both in a classical version and a quantum mechanical version. The classical version utilizes the Bloch equations4 and Solomon equations9 extended to a system of N spins. The quantum mechanical version is based on the theory described in section 2.2. Chemical shift anisotropy (CSA) is not included in the quantum mechanical formalism in Paper I.

The formalism derived from classical mechanics is suitable for simulations of NOESY13, ROESY28,29 and off resonance ROESY30,31 experiments. These experiments usually involve many spins, which do not interact through scalar couplings, and can thus be simulated without the need for an extensive quantum mechanical analysis. For N interacting spin ½ the matrix needed for simulations has (3N+1)*(3N+1) elements.

The formalism derived from quantum mechanics is useful for simulation of experiments in which scalar couplings cannot be ignored, for example the TOCSY7 experiment. The matrix needed for simulations of N spin ½ has 4N*4N elements and is thus not practical to use for large spin systems.

2.4 Heteronuclear case

In Paper II formalism for simulation of heteronuclear pulse sequences is introduced. The formalism is presented as the complete homogenous master equation in the basis of Cartesian product operators for spin ½. The formalism in Paper II is a direct continuation of the formalism in Paper I. In the heteronuclear version CSA effects on the relaxation constants are included for one of the spins.

The formalism introduced in Paper II should be useful for simulations of heteronuclear experiments such as HSQC32 and heteronuclear cross-polarization33 type experiments.

In Paper II a method for simulation of pulsed field gradients is described. The incorporation of pulsed field gradients are accomplished by dividing the NMR sample into a discrete number of planes. An extra external magnetic field with field strength dependent on the location in the sample is included in the propagator and density operators calculated for each plane. After the last pulsed field gradient all planes are added together and the resulting density operator will be filtered according to the pulsed field gradients. A high number of planes yield a better approximation, but takes longer time to simulate. This method of gradient simulation has later been published by Meresi et al., 199934.


2.5 Simulations during chemical exchange

In Paper III formalism for simulation of NMR pulse sequences during chemical exchange is introduced. Both classical and a quantum mechanical formalisms are described.

The classical formalism builds on the McConnell equations35.The McConnell equations are obtained by combining the Bloch equations with the differential equations for chemical exchange. To get an extended basis for the combined differential equations the direct product space is used, as described in Paper III.

The quantum mechanical description is based on the construction of an extended basis in the same way as for the classical formalism. The complete homogenous master equation in the basis of Cartesian product operators is used instead of the Bloch equations. The result for a 2-spin and 2-state system is a 31 by 31 matrix, describing 31 differential equations. Since the formalism includes cross-correlation between dipole-dipole and CSA relaxation for all spins, TROSY36 type experiments may be simulated.

In Paper III formalism for simulation of chemical exchange at non-equilibrium is presented. The McConnell equations have been extended with differential equations describing the time dependence of chemical exchange. These equations are included as a submatrix in the larger matrix, feeding the time dependence of the chemical exchange back into the rest of the matrix. Only first order kinetics can be simulated. The formalism should be useful for simulations of stop-flow NMR experiments37. Stop-flow NMR experiments may, for example, be used to study protein folding38,39.

2.6 Future perspective

The formalism described in Papers I-III should be useful in the construction of new, complicated composite pulses or pulse sequences. Using average Liouvillian theory25,26 the formalism may be used for the optimization of pulse sequences in which certain relaxation pathways should be closed and others open during a time interval. In this new formalism the matrix elements in the average Liouvillian can be interpreted as transfer rates between different Cartesian product operators, which is a very intuitive way at looking at pulse sequences. A modified form of average Liouvillian theory may be used to optimize pulse sequences for the study of chemical exchange.

It should be possible to extract exchange rates from an experiment by simulating the known pulse sequence. Depending on the experiment and amount of information available either a classical or quantum mechanical approach could be used. The experimental result is used in a target function and simulated annealing, or some other optimization method, is used to extract the exchange rates. This method could in principle also be used to extract other parameters in the propagator superoperator in Liouville space, such as dipole-dipole cross relaxation rates.


3 Structure determination of ribosomal proteins S16 and S19

3.1 The Ribosome

The ribosome is responsible for protein production in all living cells. In the ribosome an mRNA template is read and a peptide is produced. The ribosome is a large nucleoprotein complex consisting of rRNA molecules and proteins.

Proteins from the prokaryotic ribosome were studied in this thesis and thus the prokaryotic ribosome will be discussed below. The eukaryotic ribosome has the same functionality, but is somewhat larger and has another naming convention.

In prokaryotes the ribosome consists of 3 nucleic acid molecules and more than 50 proteins, to a total mass of about 2.5 MDa40. The ribosome may be divided into two subunits, the large subunit, called 50S, and the small subunit, called 30S. The role of the ribosomal proteins is to support and stabilize the proper folding of the rRNAs.

The 30S subunit of the prokaryotic ribosome consists of 21 proteins and one molecule of rRNA. The 30S subunit is responsible for monitoring the decoding of mRNA. Several antibiotics are known to interact with the small subunit41.

To be able to understand the mechanism of protein synthesis in detail the structure of the ribosome and its components must be known. Structural studies, such

Figure 3.1 The NMR solution structure of S16 from Thermus thermophilus. Figure prepared with MOLMOL44.

Structure determination of ribosomal proteins S16 and S19 19

as cross-linking, affinity labeling, electron microscopy, neutron scattering and x-ray crystallography, have been performed over a period of more than 25 years (for a review see Al-Karadaghi, 200040). Until recently no atomic resolution structure of the ribosome was available, and the structural work aimed at placing individual proteins and protein-RNA complexes in low-resolution electron density maps obtained by electron microscopy and/or x-ray crystallography. The structure determination of S16 and S19 should be viewed in this context.

3.2 S16

The ribosomal protein S16 from Thermus thermophilus42 consists of 88 amino acid residues and is located in the small ribosomal subunit. The protein is known to be a secondary binder to rRNA; proteins S4 and S20 must bind to rRNA prior to S1643.

The solution structure of S16 was determined using NMR as described in Paper IV. The structure of S16 is depicted in Figure 3.1. S16 consists of two α-helices (residues 53 to 61 and 70 to 76) and a parallel-antiparallel β-sheet consisting of five strands (3 to 9, 16 to 22, 37 to 40, 49 to 51 and the parallel strand, residues 65 and 66). S16 adopts a folding topology that has not previously been observed.

The S16 protein was modeled into a 5.5 Å resolution electron density map of the 30S ribosomal subunit from Thermus thermophilus. S16 binds the rRNA at helix 21. This is 70 Å from the location predicted by neutron scattering experiments45 but it agrees well with hydroxyl radical protection data46.

Figure 3.2 The NMR solution structure of S19 from Thermus thermophilus. Figure prepared with MOLMOL44.


Figure 3.3 The S16 structures as determined by NMR (black) and x-ray crystallography by the group of Ramakrishnan (gray). The backbone trace of residues 2 to 81 is shown. The orientation is the same as in Figure 3.1. Figure prepared with MOLMOL44.

3.3 S19

The ribosomal protein S19 from Thermus thermophilus consists of 93 amino acid residues and is located in the small ribosomal subunit. The protein is known to be a secondary binder of rRNA; S7 has to bind before S19 can bind to the subunit43. It has been suggested that S19 influences tetracycline binding to the 30S subunit47, this will be discussed further below.

The solution structure of S19 was determined using NMR as described in Paper V. The structure of S19 is shown in Figure 3.1. Residues 1 to 8 and 79 to 93 are unstructured and exposed to water when S19 is not bound to the 30S subunit. The structured part of S19 consists of an α-helix (residues 13 to 25), a 310-helix (residues 42 to 44) and a parallel-antiparallel β-sheet consisting of three strands (residues 30 to 32, 47 to 52 and 57 to 62). S19 represents a new folding topology.

3.4 Structures of ribosomal subunits

After the structures of S16 and S19 were published, atomic resolution structures of both subunits in the prokaryotic ribosome were published. The x-ray structure of the large subunit from Haloarcula marismortui was published by Ban et al. 200048. The x-ray structure of the small subunit from Thermus thermophilus was published simultaneously by the groups of Yonath49 and Ramakrishnan50. So far there is no atomic resolution


Figure 3.4 Superposition of the S19 structures as determined by NMR (black) and x-ray crystallography by the groups of Ramakrishnan (dark gray) and Yonath (light gray). The orientation is the same as in Figure 3.2. Figure prepared with MOLMOL44.

structure of the entire ribosome available but a 7.8 Å resolution structure has been published51.

While determining the structure of the small subunit from Thermus thermophilus the NMR structures of S16 and S19 were used. The group of Yonath modeled the NMR structure of S19 into the electron density map. The group of Ramakrishnan used the S16 and S19 structures to identify electron densities for the proteins. For S16, this was done already in an electron density map with lower resolution (5.5 Å)52 as described in Paper IV.

The structure of S16 in the structure of the 30S subunit, agrees well with the structure determined by NMR. The RMSD of backbone heavy atoms in residues 2 to 81 to the structure determined by the group of Ramakrishnan is 2.21 Å. The group of Yonath only includes a Cα-trace and RMSD values can therefore not be calculated. A superposition of the NMR structure and x-ray structure from the group of Ramakrishnan of S16 is shown in Figure 3.3.

The NMR structure of S19 agrees well with the structures from the small subunit determined by the groups of Ramakrishnan and Yonath. The RMSD values are 2.15 Å and 2.12 Å respectively, calculated for heavy backbone atoms of residues 12 through 71. The RMSD between the x-ray structures is 2.25 Å. A superposition of the three S19 structures is depicted in Figure 3.4. It is striking how different the structure from the group of Yonath (light gray in Figure 3.4) is in the loop between the two strands in the antiparallel β-sheet.


Figure 3.5 S19 (white) and S13 (dark gray) bound to rRNA (gray). Only rRNA in the vicinity of S19 and S13 is shown. Figure prepared with MOLMOL44.

Studies of the structures of the small subunit show that S19 has contacts to helices 30, 32, 33b and 42 of the rRNA50 and that in addition to rRNA, S19 also has contacts to S13 when bound to the ribosome (Figure 3.5). These findings agree well with prior biochemical studies46,53.

In Paper V two different binding areas were suggested on the surface of S19; the loop 34 to 38 was predicted to interact with rRNA and residues 67 to 77 was predicted to interact with ribosomal protein S13. Both these binding areas seem to agree well with the structure of the small ribosomal subunit. For example the sidechain of Arg 36 interacts with the sidechain of Cytosine 1320 through a putative hydrogen bond (Figure 3.6 right) and the sidechain of Trp 34 is stacked on the base of Adenine 1014 (Figure 3.6 left). The carbonyl oxygen of residue Glu 73 in S19 seems to form a hydrogen bond to the backbone amide of Tyr 87 in S13. There are also other putative interactions in this region, mostly through sidechains.


Figure 3.6 The left panel shows the stacking of the sidechain of Trp 34 in S19 and the base of A1014in rRNA. The right panel shows a putative hydrogen bond between Arg 36 in S19 and C1320 in rRNA. Figure prepared with MOLMOL44.

A structure of tetracycline bound to the 30S subunit is available54. The primary binding site of Tetracycline is between helices H31 and H34. This is the same part of the subunit, the head, as S19 but far from S19. There is no obvious way in which S19 could influence binding of tetracycline to the small ribosomal subunit.


The structures of the large and small subunits of the prokaryotic ribosome are now known, but the function of the ribosome is not yet fully understood. The difference between the crystal structures of the small ribosomal subunit calls for structures with even higher resolution before the mechanism of the ribosome can be understood on an atomic level.

Besides understanding the function of the ribosome, studies will in the future aim at the development of new antibiotics targeting the prokaryotic ribosome. To aid the development of new antibiotics, a structure of the eukaryotic (preferably human) ribosome should be known. Comparisons between the two structures may then lead to development of antibiotics targeting the prokaryotic but not the eukaryotic ribosome.

In the process of developing new antibiotics the structures of single proteins from the ribosome might be used as targets. If the binding of a vital ribosomal protein can be inhibited protein synthesis will be interrupted, leading to cell death. Binding areas on ribosomal proteins are now known and thus potential target sites on the proteins are also known. NMR is an excellent method for screening for new compounds interacting with proteins. With known NMR structures and assignments, methods like SAR by NMR55 might be used to develop molecules inhibiting protein-protein or protein-rRNA interactions. The NMR structures presented in this thesis, together with other NMR structures of ribosomal proteins, are potential targets for such studies.


4 Development of a computer program for semiautomatic assignment

4.1 Tools to aid assignment of NMR spectra

Assignment of NMR spectra, as described in section 1.3, can be performed manually using paper and pencil, but nowadays computer programs are usually used. Computer programs for assignment can roughly be divided into two groups: programs for manual assignment and programs for automatic assignment.

Programs for manual assignment aid the user by showing NMR-spectra graphically and by keeping track of crosspeaks and assignments, much the same way as paper and pencil would have been used. Programs that belong to this class are for example Pronto56, ANSIG1,2 and XEASY57. These programs are usually good at presenting graphical data to the user but often lack good tools to aid the user in the process of finding new assignments.

Programs for automatic assignment of spectra usually do not show graphics but do assignment of spectra automatically. Programs in this group are for example AUTOASSIGN58, GARANT59 and ARIA60. The automatic assignment processes in these programs are much faster than the manual assignment process but the programs do not utilize the expertise of the user and the resulting assignments must be validated manually.

4.2 Ansig for Windows

Ansig for Windows, introduced in Paper VI, is a program for semiautomatic assignment of NMR spectra. Semiautomatic assignment is a mix between the capabilities of the programs in the groups described above. Interactive graphics capabilities are combined with tools to find new assignments. All decisions in semiautomatic assignment should be left to the user. Decisions should be based on the users experience as well as suggestions from the program, thus speeding up the assignment process as well as increasing the accuracy of the final result.

Ansig for Windows is built on ANSIG (version 3.3)2, and thus has the same graphics capabilities. A series of new tools have been included in Ansig for Windows to allow for semiautomatic assignment. These tools were built as pop-up windows (dialog boxes) and allow the user to search for assignments and update the assignment database. The tools are connected to the graphics display in order for the user to display the suggested assignments graphically. The tools are described in detail in Paper VI.

4.2.14.2.14.2.14.2.1 Software developmentSoftware developmentSoftware developmentSoftware development

ANSIG is written in Fortran 77. To be able to reuse as much program code as possible from ANSIG, Ansig for Windows was also written in Fortran, but using a slightly modernized version, Fortran 95. To be able to keep the excellent graphics

Development of a computer program for semiautomatic assignment 25

capabilities of ANSIG in the new program, the graphics routines written in the Silicon Graphics Graphics Language (GL) was translated to the open graphics standard OpenGL61. The decision to write the new program for PCs running Windows was based on the recent fast development of PC graphics cards supporting OpenGL. A decent PC system also has a more attractive price than a Unix based system. The reason for not choosing Linux as the operating system was the lack of standard for window managers running under this operating system. It is also more difficult for the end user to administrate a Linux based system than a Windows based system.

There are several disadvantages using Fortran when programming for Windows. First of all the Windows API is not written with Fortran in mind. All calls to the Windows API demand C-style variables and pointers. Pointers being especially complicated, since they are not available in Fortran 95. Utilization of the Windows API in Ansig for Windows was enabled by a package distributed with the compiler (Lahey Fortran 95). This package puts an extra layer between the C-style interface of the Windows API and the Fortran code. A second problem with Fortran is the lack of dynamic memory allocation. This leads to software demanding large amounts of, mostly unused, memory. A third problem with Fortran is that it is not object oriented, which makes the source code unnecessarily complicated and difficult to update.

Ansig for Windows is fully compatible with ANSIG; i.e. files used together with ANSIG can directly be used with Ansig for Windows. To achieve this compatibility the I/O part of Ansig for Windows had to be rewritten to store binary files in the format used on Silicon Graphics computers. The problem was the endianity, or the way 32-bit numbers are stored. To be able to read files from Silicon Graphics computers the byte-order of 32-bit numbers have to be rearranged.

Although there were problems in making Ansig for Windows the result is fully compatible with ANSIG at the same time as Ansig for Windows is a genuine Windows program. Ansig for Windows utilizes known windows features such as menus, multiple windows and dialog boxes. The interactive graphics is as fast, or even faster, on PCs with good graphics cards than on Silicon Graphics O2 workstations. Several users in the group now use Ansig for Windows on their desktop PCs instead of Silicon Graphics workstations. Comments on Ansig for Windows have arrived from other groups, indicating that the program is used in other laboratories around the world.


Ansig for Windows is distributed under a GNU license62, which makes the source code available for anyone to change. The idea being that those interested can make additions to the program and re-compile it.

New features to include are, for example, an interface to ARIA60, a program for automatic assignment of NOE crosspeaks, and more tools for semiautomatic assignment. It would also be nice to include help routines for first time users, giving them hints on what typical crosspeak patterns look like for different amino acid sidechains. An interactive window for showing typical structures of α-helices, β-sheets and other secondary structure elements should also be implemented in a future version of Ansig for Windows.


In retrospect it would probably have been better to write Ansig for Windows in an object-oriented language, for example C++. This would have made Ansig for Windows a great platform for additions of new features.

References 27

5 References 1. Kraulis, P. J. (1989). ANSIG: A program for the assignment of protein 1H

2D NMR spectra by interactive computer graphics. J. Magn. Reson. 84, 627-633.

2. Kraulis, P. J., Domaille, P. J., Campbell-Burk, S. L., Van Aken, T. & Laue, E. D. (1994). Solution structure and dynamics of ras p21.GDP determined by heteronuclear three- and four-dimensional NMR spectroscopy. Biochemistry 33, 3515-3531.

3. Cavanagh, J., Fairbrother, W. J., Palmer III, A. G. & Skelton, N. J. (1996) Protein NMR spectroscopy, Academic Press, San Diego

4. Bloch, F. (1946). Nuclear Induction. Phys. Rev. 70, 460-474. 5. Ikura, M., Kay, L. E. & Bax, A. (1990). A novel approach for sequential

assignment of 1H, 13C, and 15N spectra of larger proteins: heteronuclear triple-resonance three-dimensional NMR spectroscopy. Application to calmodulin. Biochemistry 29, 4659-4667.

6. Yamazaki, T., Lee, W., Arrowsmith, C. H., Muhandiram, D. R. & Kay, L. E. (1994). A suite of triple resonance NMR experiments for the backbone assignment of 15N, 13C, 2H labeled proteins with high sensitivity. J. Am. Chem. Soc. 116, 11655-11666.

7. Griesinger, C., Otting, G., Wüthrich, K. & Ernst, R. R. (1988). Clean TOCSY for 1H spin system identification in macromolecules. J. Am. Chem. Soc. 110, 7870-7872.

8. Wüthrich, K. (1986) NMR of proteins and nucleic acids, John Wiley & Sons, New York

9. Solomon, I. (1955). Relaxation processes in a system of two spins. Phys. Rev. 99, 559-565.

10. Karplus, M. (1959). Contact electron-spin coupling of nuclear magnetic moments. J. Chem. Phys. 30, 11-15.

11. Karplus, M. (1963). Vicinal proton coupling in nuclear magnetic resonance. J. Am. Chem. Soc. 85, 2870-2871.

12. Tjandra, N. & Bax, A. (1997). Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium. Science 278, 1111-1114.

13. Macura, S. & Ernst , R. R. (1980). Elucidation of cross relaxation in liquids by two-dimensional N.M.R. spectroscopy. Mol. Phys. 41, 95-117.

14. Vuister, G. W. & Bax, A. (1993). Quantitative J correlation: A new approach for measuring homonuclear three-bond J(HNHα) coupling constants in 15N-enriched proteins. J. Am. Chem. Soc. 115, 7772-7777.

15. Brünger, A. T. et al. (1998). Crystallography & NMR system: A new software suite for macromolecular structure determination. Acta Cryst. D 54, 905-921.

16. Brünger, A. T. (1992) X-PLOR version 3.1. A system for X-ray crystallography and NMR, Yale University Press, New Haven, CT


17. Sørensen, O. W., Eich, G. W., Levitt, M. H., Bodenhausen, G. & Ernst, R. R. (1983). Product operator formalism for the description of NMR pulse experiments. Prog. NMR Spectrosc. 16, 163-192.

18. Smith, S. A., Levante, T. O., Meier, B. H. & Ernst, R. R. (1994). Computer simulations in magnetic resonance. An object-oriented programming approach. J. Magn. Reson. A 106, 75-105.

19. Allman, T., Bain, A. D. & Garbow, J. R. (1996). SIMPLTN, a program for the simulation of pulse NMR spectra. J. Magn. Reson. A 123, 26-31.

20. Nicholas, P., Fushman, D., Ruchinsky, V. & Cowburn, D. (2000). The Virtual NMR Spectrometer: A computer program for efficient simulation of NMR experiments involving pulsed field gradients. J. Magn. Reson. 145, 262-275.

21. Abragam, A. (1961) Principles of nuclear magnetism, Oxford University Press, Oxford

22. Ernst, R. R., Bodenhausen, G. & Wokaun, A. (1987) Principles of nuclear magnetic resonance in one and two dimensions, Oxford University Press, Oxford

23. Magnus, W. (1954). On the exponential solution of differential equations for a linear operator. Comm. Pure Appl. Math. VII, 649-673.

24. Jeener, J. (1982). Superoperators in magnetic resonance. Adv. Magn. Reson. 10, 2-51.

25. Levitt, M. H. & Di Bari, L. (1992). Steady state in magnetic resonance pulse experiments. Phys. Rev. Lett. 69, 3124-3127.

26. Levitt, M. H. & Di Bari, L. (1994). The homogenous master equation and the manipulation of relaxation networks. Bull. Magn. Reson. 16, 94-114.

27. Moler, C. & van Loan, C. (1978). Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20, 801-836.

28. Bothner-By, A. A., Stephens, R. L. & Lee, J. (1984). Structure determination of a tetrasaccharide: Transient nuclear Overhauser effects in the rotating frame. J. Am. Chem. Soc. 106, 811-813.

29. Bax, A. & Davis, D. G. (1985). Practical aspects of two-dimensional transverse NOE spectroscopy. J. Magn. Reson. 63, 207-213.

30. Desvaux, H., Berthault, P., Birlirakis, N. & Goldman, M. (1994). Off-resonance ROESY for the study of dynamic processes. J. Magn. Reson. A 108, 219-229.

31. Kuwata, K. & Schleich, T. (1994). Off-resonance rotating-frame nuclear Overhauser effect spectroscopy. J. Magn. Reson. A 111, 43-49.

32. Bodenhausen, G. & Ruben, D. J. (1980). Natural abundance nitrogen-15 NMR by enhanced heteronuclear spectroscopy. Chem. Phys. Lett. 69, 185-189.

33. Ernst, M., Griesinger, C., Ernst, R. R. & Bermel, W. (1991). Optimized heteronuclear cross polarization in liquids. Mol. Phys. 74, 219-252.

34. Meresi, G. H., Cuperlovic, M., Palke, W. E. & Gerig, J. T. (1999). Pulsed field gradients in simulations of one- and two-dimensional NMR spectra. J. Magn. Reson. 137, 186-195.

35. McConnell, H. M. (1958). Reaction rates by nuclear magnetic resonance. J. Chem. Phys. 28, 430-431.

36. Pervushin, K., Riek, R., Wider, G. & Wüthrich, K. (1997). Attenuated T2 relaxation by mutual cancellation of dipole-dipole coupling and chemical shift

References 29

anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution. Proc. Natl. Acad. Sci. USA 94, 12366-12371.

37. Kühne, R. O., Schaffhauser, T., Wokaun, A. & Ernst, R. R. (1979). Study of transient chemical reactions by NMR. Fast stopped-flow Fourier transform experiments. J. Magn. Reson. 35, 39-67.

38. Balbach, J. et al. (1995). Following protein folding in real time using NMR spectroscopy. Nature Struct. Biol. 2, 865-870.

39. Balbach, J. et al. (1996). Protein folding monitored at individual residues during a two-dimensional NMR experiment. Science 274, 1161-1163.

40. Al-Karadaghi, S., Kristensen, O. & Liljas, A. (2000). A decade of progress in understanding the structural basis of protein synthesis. Prog. Biophys. Mol. Biol. 73, 167-193.

41. Gale, E. F., Cundliffe, E., Reynolds, P. E., Richmond, M. H. & Waring, M. J. (1981) The molecular basis of antibiotic action, John Wiley & Sons, London

42. Oshima, T. & Imahori, K. (1974). Description of Thermus thermophilus (Yoshida and Oshima) comb. nov., a nonsporulating thermophilic bacterium fron Japanese thermal spa. Int. J. Syst. Bacteriol. 24, 102-112.

43. Mizushima, S. & Nomura, M. (1970). Assembly mapping of 30S ribosomal proteins from E. coli. Nature 226, 1214-1218.

44. Koradi, R., Billeter, M. & Wüthrich, K. (1996). MOLMOL: a program for display and analysis of macromolecular structures. J. Mol. Graphics 14, 51-55.

45. Capel, M. S. et al. (1987). A complete mapping of the proteins in the small ribosomal subunit of Escherichia coli. Science 238, 1403-1406.

46. Powers, T. & Noller, H. F. (1995). Hydroxyl radical footprinting of ribosomal proteins on 16S rRNA. RNA 1, 194-209.

47. Buck, M. A. & Cooperman, B. S. (1990). Single protein omission reconstitution studies of tetracycline binding to the 30S subunit of Escherichia coli ribosomes. Biochemistry 29, 5374-5379.

48. Ban, N., Nissen, P., Hansen, J., Moore, P. B. & Steitz, T. A. (2000). The complete atomic structure of the large ribosomal subunit at 2.4 Å resolution. Science 289, 905-920.

49. Schluenzen, F. et al. (2000). Structure of functionally activated small ribosomal subunit at 3.3 Å resolution. Cell 102, 615-623.

50. Wimberly, B. T. et al. (2000). Structure of the 30S ribosomal subunit. Nature 407, 327-339.

51. Cate, J. H., Yusupov, M. M., Yusupova, G. Z., Earnest, T. N. & Noller, H. F. (1999). X-ray crystal structures of 70S ribosome functional complexes. Science 285, 2095-2104.

52. Clemons, W. M. et al. (1999). Structure of a bacterial 30S ribosomal subunit at 5.5 Å resolution. Nature 400, 833-840.

53. Pohl, T. & Wittmann-Liebold, B. (1988). Identification of a cross-link in the Escherichia coli ribosomal protein pair S13-S19 at the amino acid level. J. Biol. Chem. 263, 4293-4301.

54. Brodersen, D. E. et al. (2000). The structural basis for the action of the antibiotics tetracycline, pactamycin, and hygromycin B on the 30S ribosomal subunit. Cell 103, 1143-1154.


55. Shuker, S. B., Hajduk, P. J., Meadows, R. P. & Fesik, S. W. (1996). Discovering high-affinity ligands for proteins: SAR by NMR. Science 274, 1531-1534.

56. Kjaer, M., Andersen, K. V. & Poulsen, F. M. (1994). Automated and semiautomated analysis of homo- and heteronuclear multidimensional nuclear magnetic resonance spectra of proteins: the program Pronto. Methods Enzymol. 239, 288-307.

57. Bartels, C., Xia, T., Billeter, M., Güntert, P. & Wüthrich, K. (1995). The program XEASY for computer-supported NMR spectral analysis of biological macromolecules. J. Biomol. NMR 5, 1-10.

58. Zimmerman, D., Kulikowski, C., Wang, L., Lyons, B. & Montelione, G. T. (1994). Automated sequencing of amino acid spin systems in proteins using multidimensional HCC(CO)NH-TOCSY spectroscopy and constraint propagation methods from artificial intelligence. J. Biomol. NMR 4, 241-256.

59. Bartels, C., Güntert, P., Billeter, M. & Wüthrich, K. (1997). GARANT - A general algorithm for resonance assignment of multidimensional nuclear magnetic resonance spectra. J. Comput. Chem. 18, 139-149.

60. Nilges, M., Macias, M. J., O'Donoghue, S. I. & Oschkinat, H. (1997). Automated NOESY interpretation with ambiguous distance restraints: the refined NMR solution structure of the pleckstrin homology domain from β-spectrin. J. Mol. Biol. 269, 408-422.

61. http://www.opengl.org/ 62. http://www.gnu.org/copyleft/gpl.html

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