Chemomechanical coupling and motor cycles of the molecular motor myosin V [Elektronische Ressource] / Veronika Bierbaum. Betreuer: Reinhard Lipowsky

Veronika Bierbaum

Sujets

• Physik

Informations

• Publié par: universitat_potsdam
• Publié le: 01 janvier 2011
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

Universitat Potsdam
Chemomechanical coupling and motor cycles of the molecular
motor myosin V
von
Veronika Bierbaum
Dissertation
zur Erlangung des akademischen Grades
"doctor rerum naturalium"
(Dr. rer. nat.)
in der Wissenschaftsdisziplin Physik
Max-Planck-Institut fur Kolloid- und Grenz achenforschung
Theorie und Bio-Systeme
Potsdam, Februar 2011This work is licensed under a Creative Commons License:
Attribution - Noncommercial - Share Alike 3.0 Germany
To view a copy of this license visit
http://creativecommons.org/licenses/by-nc-sa/3.0/de/










































Published online at the
Institutional Repository of the University of Potsdam:
URL http://opus.kobv.de/ubp/volltexte/2011/5361/
URN urn:nbn:de:kobv:517-opus-53614
http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-53614 Erklarung
Hiermit versichere ich, dass ich die vorliegende Arbeit selbstst andig verfasst und keine
anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.
Potsdam, den 15. Januar 2011blafaselContents
1 Introduction 5
1.1 A rst glance at molecular motors . . . . . . . . . . . . . . . . . . . . . . 5
1.2 The physics of molecular motors . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Experimental characterization of the molecular motor myosin V . . . . . 9
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Networks 15
2.1 Enzymatic networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Elements of graph theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Network cycles and probability uxes . . . . . . . . . . . . . . . . . . . . 20
2.4 Nonequilibrium thermodynamics . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Networks with absorbing states . . . . . . . . . . . . . . . . . . . . . . . 27
3 Motors in continuous space 33
3.1 Brownian motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Chemical and mechanical transitions . . . . . . . . . . . . . . . . . . . . 35
3.3 From continous to discrete space . . . . . . . . . . . . . . . . . . . . . . 36
4 The molecular motor myosin V 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Network representations . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Motor dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Cyclic uxes and balance conditions . . . . . . . . . . . . . . . . . . . . . 47
4.5 Functional form of mechanical stepping rates . . . . . . . . . . . . . . . . 49
4.6 Specication of transition rates . . . . . . . . . . . . . . . . . . . . . . . 50
5 Stepping dynamics 55
5.1 Motor velocity in the absence of load . . . . . . . . . . . . . . . . . . . . 55
5.2 Motor velocity and step ratio in the presence of load . . . . . . . . . . . 57
5.3 Run length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Aspects of chemomechanical coupling . . . . . . . . . . . . . . . . . . . 63
6 Dwell time distributions 71
1Contents
6.1 Reduced network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Conditional dwell time distributions . . . . . . . . . . . . . . . . . . . . . 74
6.3 Absence of load: the gating e ect . . . . . . . . . . . . . . . . . . . . . . 77
6.4 Presence of load: backward stepping . . . . . . . . . . . . . . . . . . . . 78
7 Summary and further perspectives 83
7.1 Chemical kinetics of myosin V . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Dwell time distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.3 Power stroke and collective behaviour of molecular motors . . . . . . . . 85
7.4 The world outside the test tube . . . . . . . . . . . . . . . . . . . . . . . 86
A Spanning trees for the chemomechanical network 89
B Network properties and additional experimental information 95
B.1 Additional pathways and properties of F . . . . . . . . . . . . . . . . . . 95s
B.2 The e ect of load force on nucleotide binding . . . . . . . . . . . . . . . . 98
B.3 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
C The Gillespie algorithm 103
D Explicit solutions of the dwell time distributions 107
E List of symbols 109
Bibliography 115
2Abstract
In the living cell, the organization of the complex internal structure relies to a large
extent on molecular motors. Molecular motors are proteins that are able to convert
chemical energy from the hydrolysis of adenosine triphosphate (ATP) into mechanical
work. Being about 10 to 100 nanometers in size, the molecules act on a length scale,
for which thermal collisions have a considerable impact onto their motion. In this way,
they constitute paradigmatic examples of thermodynamic machines out of equilibrium.
This study develops a theoretical description for the energy conversion by the molec-
ular motor myosin V, using many di erent aspects of theoretical physics. Myosin V
has been studied extensively in both bulk and single molecule experiments. Its stepping
velocity has been characterized as a function of external control parameters such as nu-
cleotide concentration and applied forces. In addition, numerous kinetic rates involved
in the enzymatic reaction of the molecule have been determined. For forces that exceed
the stall force of the motor, myosin V exhibits a ’ratcheting’ behaviour: For loads in the
direction of forward stepping, the velocity depends on the concentration of ATP, while
for backward loads there is no such inuence.
Based on the chemical states of the motor, we construct a general network theory that
incorporates experimental observations about the stepping behaviour of myosin V. The
motor’s motion is captured through the network description supplemented by a Markov
process to describe the motor dynamics. This approach has the advantage of directly ad-
dressing the chemical kinetics of the molecule, and treating the mechanical and chemical
processes on equal grounds. We utilize constraints arising from nonequilibrium thermo-
dynamics to determine motor parameters and demonstrate that the motor behaviour
is governed by several chemomechanical motor cycles. In addition, we investigate the
functional dependence of stepping rates on force by deducing the motor’s response to
external loads via an appropriate Fokker-Planck equation. For substall forces, the dom-
inant pathway of the motor network is profoundly dierent from the one for superstall
forces, which leads to a stepping behaviour that is in agreement with the experimental
observations. The extension of our analysis to Markov processes with absorbing bound-
aries allows for the calculation of the motor’s dwell time distributions. These reveal
aspects of the coordination of the motor’s heads and contain direct information about
the backsteps of the motor. Our theory provides a unied description for the myosin V
motor as studied in single motor experiments.
3