Protein dynamics [Elektronische Ressource] : comparison of incoherent neutron scattering and molecular dynamics simulation / presented by Torsten Becker

Informations

• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2005
• Nombre de lectures: 60
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Science
presented by
Diplom-Physiker: Torsten Becker
born in: Schongau
Oral examination: 17. November 2004Protein Dynamics
Comparison of Incoherent Neutron
Scattering and Molecular Dynamics
Simulation
Referees: Prof. Dr. Jeremy C. Smith
PD Dr. Ilme SchlichtingThe city really ain’t no bigger than the friendly people that you meet.
Bill Withers: Lonely town, lonely street
Acknowledgments
This thesis would not have been possible without the help of many people. At this
point i want to say thank you to all of them.
I want to especially thank my supervisor Jeremy C. Smith for letting me work on
this interesting subject and for guiding the progress of this thesis with ideas and
discussions.
Andrea Vaiana and Alexander Tournier shared with me the joy and pain of getting
started in research. Thanks a lot for all the interesting discussions about science,
politics and all the rest...
My special thanks to Erika Balog for working with me on the dimerization project
and discovering the universal scaling law of errorbars.
I am grateful to Jennifer Hayward for providing me with trajectories to test my ideas
about the dynamical transition.
If this thesis is written in a language approximating English it is due to the great
e ort Durba Sengupta, Lars Meinhold and Vandana Kurkal put into proof reading.
This thesis would lack its nicest graphics without the help of Sabine Radl. Thank
you very much.
Finally, a special thank you to my parents who encouraged and supported me through-
out my long education.Zusammenfassung
Proteindynamik und deren Beziehung zur biologischen Funktion von Proteinen ist Gegenstand
zahlreicher experimenteller und theoretischer Untersuchungen. In der vorgelegten Arbeit werden
Aspekte der Proteindynamik im Pico- und Nanosekundenbereich untersucht. Experimentelle Unter-
suchungen haben eine Abhaengigkeit zwischen enzymatischer Aktivit at und atomaren Fluktuationen
auf diesen Zeitskalen aufgezeigt. Inkoherente Neutronenstreuung sowie Molekulardynamiksimula-
tionen stellen geeignete Instrumente zur Untersuchung atomarer Dynamik auf diesen Zeitskalen zur
Verfugung.
Ein interessantes Ph anomen im Hinblick auf den Zusammenhang zwischen Flexibilit at und Ak-
tivit at ist die Dynamical Transition, d.h. ein nicht-linearer Anstieg atomarer Fluktuationen bei
einer charakteristischen Temperatur T 200K. Die explizite Einbeziehung des instrumentellen0
Au osungsverm ogens eines Neutronenstreuspektrometers in die theoretische Analyse der Dynami-
cal Transition fuhrt zu einer neuen Interpretation dieses Uberganges. Mittels Molekulardynamik-
simulationen wird die quantitative Ubereinstimmung dieser alternativen Interpretation mit der
Zeitskalen- wie auch der Temperaturab angigkeit der mittleren quadratischen Auslenkung eines Pro-
teins in L osung gezeigt. Darub erhinaus bietet diese Interpretation eine Erkl arung der experimentell
beobachteten Verschiebung der Ubergangstemperatur, T , in Abh angigkeit der instrumentellen0
Au osung.
Die Gauss’sche N aherung, grundlegend fur die experimentelle Bestimmung der mittleren quadra-
2tischen Auslenkung,hr i, wird untersucht und Korrekturen hierzu diskutiert. Abweichungen von
2dieser N aherung werden fur Q 6A auf die Heterogenit at atomarer Bewegungen zuruc kgefuhrt.
Abschliessend wird eine Methode vorgeschlagen, um aus der inkoherenten inelastischen Streufunk-
tion die Schwingungsdichte des Systems abzuleiten. Mittels dieser Methode werden Anderungen der
Schwingungsdichte des Proteins Dihydrofolate Reduktase bei Bindung des Liganden Metho-
trexate bestimmt. Es wird gezeigt, dass die Anderungen im Spektrum dieser internen Freiheitsgrade
einen signi k anten Beitrag zur freien Bindungsenergie dieses Systems beitragen.
Summary
Protein dynamics and its relation to protein function is the subject of various studies using both,
theoretical and experimental techniques. In this thesis, several aspects of protein dynamics on short
timescales are addressed. Motions in the pico- to nanosecond timescale have been experimentally
shown to be intimately related to enzyme activity. Incoherent neutron scattering and molecular
dynamics simulation are well suited and widely used to study motions on the above timescales.
A prominent phenomenon in the context of this observed exibilit y-activity relationship is the dy-
namical transition, i.e. a non-linear increase in atomic uctuations at a characteristic transition
temperature of T 200K. By explicitly incorporating nite resolution of neutron spectrometers0
in the theoretical analysis of neutron scattering experiments, a novel interpretation of the dynami-
cal transition arises. This alternative ’frequency window’ interpretation is shown to reproduce the
timescale and temperature dependence of mean-square displacements calculated from MD simula-
tions of a protein in solution. The frequency window interpretation, furthermore, o ers an explana-
tion of the experimentally observed shift of T with instrumental resolution. Implications of the new0
interpretation for the relation between the dynamical transition and enzyme activity are discussed.
Molecular dynamics simulations are further used to test the Gaussian approximation implicit in
experimental data analysis. Deviations from Gaussian scattering in the calculated spectra for
22 2Q 6A are shown to be dominated by the distribution ofhr i.
Finally, a method to derive the vibrational density of states on an absolute scale from low-temperature
inelastic incoherent neutron scattering is suggested. The change in the vibrational density of states
of the protein dihydrofolate reductase on binding the ligand methotrexate is determined. The vi-
brations of the complex soften signi can tly relative to the unbound protein. The resulting free
energy change, which is directly determined by the density of states change, is found to contribute
signi can tly to the binding equilibrium.Publication list
Balog, E., Becker, T., Oettl, M., Lechner, R., Daniel, R., Finney, J. & Smith, J. (2004).
Direct determination of vibrational density of states change on ligand binding to a protein.
Phys. Rev. Lett., 93, 028103.
Becker, T. & Smith, J.C. (2003). Energy resolution and dynamical heterogeneity e ects on
elastic incoherent neutron scattering from molecular systems. Phys. Rev. E, 67, 021904.
Becker, T., Fischer, S., Noe, F., Tournier, A., Ullmann, M. & Smith, J. (2003). Protein
dynamics: Glass transition and mechanical function. In B. Kramer, ed., Advances in
Solid State Physics, vol. 43, 677{694, Springer.
Becker, T., Hayward, J., Daniel, R., Finney, J. & Smith, J. (2004). Neutron frequency
windows and the protein dynamical transition. Bioph. J., 87, 1{9.
Hayward, J., Becker, T. & Smith, J. (2002). The glass transition in proteins. In Krause, E. &
J ager, W., eds., High Performance Computing in Science and Engineering’02, 503{511,
Springer.
Meinhold, L., Lammers, S., Becker, T. & Smith, J.C. (2004). Convergence properties of
x-ray scattering calculated from protein crystal molecular dynamics simulations. Physica
B, 350, 127{131.
1Contents
0 About the thesis 1
1 Protein dynamics 3
1.1 Structural diversity of proteins . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Flexibility-activity relationship . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The energy landscape of proteins . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 The dynamical transition in proteins . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Protein association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Neutron scattering from proteins 15
2.1 Theory of neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Response function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Coherent and incoherent scattering . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Elastic, quasielastic and inelastic scattering . . . . . . . . . . . . . . . . . . 22
2.5 Separation of motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 The Gaussian approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Computer simulations of proteins 27
3.1 Molecular dynamics force eld . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Time evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Analysis of molecular dynamics simulations . . . . . . . . . . . . . . . . . . 35
4 Protein dynamics and neutron scattering 39
4.1 Internal protein dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Energy landscapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
iii CONTENTS
4.3 Stretched exponential relaxation . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Single exponential relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 The dynamical transition in proteins 59
5.1 Equilibrium and frequency window scenario . . . . . . . . . . . . . . . . . . 60
5.2 Dynamical transition in MD Simulations . . . . . . . . . . . . . . . . . . . . 64
5.3