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Stochastic modeling of motor proteins
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Motor proteins are microscopic biological machines that convert chemical energy into mechanical motion and work. They power a diverse range of biological processes, for example the swimming and crawling motion of bacteria, intracellular transport, and muscle contraction. Understanding the physical basis of these processes is interesting in its own right, but also has an interesting potential for applications in medicine and nanotechnology.

The ongoing rapid developments in single molecule experimental techniques make it possible to probe these systems on the single molecule level, with increasing temporal and spatial resolution. The work presented in this thesis is concerned with physical modeling of motor proteins on the molecular scale, and with theoretical challenges in the interpretation of single molecule experiments.

First, we have investigated how a small groups of elastically coupled motors collaborate, or fail to do so, when producing strong forces. Using a simple model inspired by the motor protein PilT, we find that the motors counteract each other if the density becomes higher than a certain threshold, which depends on the asymmetry of the system.

Second, we have contributed to the interpretation of experiments in which the stepwise motion of a motor protein is followed in real time. Such data is naturally interpreted in terms of first passage processes. Our main conclusions are (1) Contrary to some earlier suggestions, the stepping events do not correspond to the cycle completion events associated with the work of Hill and co-workers. We have given a correct formulation. (2) Simple kinetic models predict a generic mechanism that gives rise to correlations in step directions and waiting times. Analysis of stepping data from a chimaeric flagellar motor was consistent with this prediction. (3) In the special case of a reversible motor, the chemical driving force can be extracted from statistical analysis of stepping trajectories.

Place, publisher, year, edition, pages
Stockholm: KTH , 2008. , vii, 71 p.
Series
Trita-FYS, ISSN 0280-316X ; 2008:9
Keyword [en]
molecular motor, motor protein, Markov process, fluctuations, statistical mechanics, microscopic reversibility
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-4664ISBN: 978-91-7178-897-9 (print)OAI: oai:DiVA.org:kth-4664DiVA: diva2:13313
Public defence
2008-03-28, FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100820Available from: 2008-03-07 Created: 2008-03-07 Last updated: 2010-08-20Bibliographically approved
List of papers
1. Force generation in small ensembles of Brownian motors
Open this publication in new window or tab >>Force generation in small ensembles of Brownian motors
2006 (English)In: Physical Review E, ISSN 1539-3755, Vol. 74, no 2, 021908-1-021908-8 p.Article in journal (Refereed) Published
Abstract [en]

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed 150 pN. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration.

Keyword
molecular motors, pilus-retraction, twitching motility, ratchet model, iv pilus, transport, protein
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-15963 (URN)10.1103/PhysRevE.74.021908 (DOI)000240238100094 ()2-s2.0-33746882496 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-08-20Bibliographically approved
2. Back-stepping, hidden substeps, and conditional dwell times in molecular motors
Open this publication in new window or tab >>Back-stepping, hidden substeps, and conditional dwell times in molecular motors
2007 (English)In: Physical Review E, ISSN 1539-3755, Vol. 75, no 2, 021909-1-021909-16 p.Article in journal (Refereed) Published
Abstract [en]

Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one knows biochemically that one or more mechanochemical substeps remain hidden in each enzymatic cycle. In order to properly interpret experimental data for back-to-forward step ratios, mean conditional step-to-step dwell times, etc., a first-passage analysis has been developed that takes account of hidden substeps in N-state sequential models. The explicit, general results differ significantly from previous treatments that identify the observed steps with complete mechanochemical cycles; e.g., the mean dwell times tau(+) and tau(-) prior to forward and back steps, respectively, are normally unequal although the dwell times tau(++) and tau(- -) between successive forward and back steps are equal. Illustrative (N=2)-state examples display a wide range of behavior. The formulation extends to the case of two or more detectable transitions in a multistate cycle with hidden substeps.

Keyword
Biochemistry; Enzymes; Mathematical models; Molecular structure; Back-to-forward step ratios; Conditional dwell times; First-passage analysis; Molecular motors
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-8083 (URN)10.1103/PhysRevE.75.021909 (DOI)000244531900070 ()
Note
QC 20100820Available from: 2008-03-07 Created: 2008-03-07 Last updated: 2010-08-20Bibliographically approved
3. Dwell Time Symmetry in Random Walks and Molecular Motors
Open this publication in new window or tab >>Dwell Time Symmetry in Random Walks and Molecular Motors
2007 (English)In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 92, no 11, 3804-3816 p.Article in journal (Refereed) Published
Abstract [en]

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.

Keyword
MYOSIN-V PROCESSIVITY; FLUCTUATION ANALYSIS; KINESIN MOLECULES; FLAGELLAR MOTOR; KINETIC-MODELS; ROTARY MOTOR; F-1-ATPASE; ROTATION; ATP; STEPS
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-8084 (URN)10.1529/biophysj.106.103044 (DOI)000246401800006 ()2-s2.0-34250334739 (Scopus ID)
Note
QC 20100820Available from: 2008-03-07 Created: 2008-03-07 Last updated: 2010-08-20Bibliographically approved
4. Decay times in turnover statistics of single enzymes
Open this publication in new window or tab >>Decay times in turnover statistics of single enzymes
2008 (English)In: Physical review E, ISSN 1539-3755, Vol. 78, no 1, 010901-1-010901-4 p.Article in journal (Refereed) Published
Abstract [en]

The first passage times for enzymatic turnovers in nonequilibrium steady state display a statistical symmetry property related to nonequilibrium fluctuation theorems, which makes it possible to extract the chemical driving force from single molecule trajectories in nonequilibrium steady state. Below, we show that the number of decay constants needed to describe the first passage time distribution of this system is not equal to the number of states in the first passage problem, as one would generally expect. Instead, the structure of the kinetic mechanism makes half of the decay times vanish identically from the turnover time distribution. The terms that cancel out correspond to the eigenvalues of a certain submatrix of the master equation matrix for the first exit time problem. We discuss how these results make modeling and data analysis easier for such systems, and how the turnovers can be measured.

Keyword
Electron transitions; Data analysis; Decay constants; Decay times; Driving forces; Eigenvalues (of graphs); Exit time; First passage problem; First passage time distribution (FPT); First passage times (FPT); Kinetic mechanisms; Master equations; Non equilibrium fluctuations; Nonequilibrium steady state (NESS); Number of states; Single molecule (SM); Sub matrices; Symmetry properties; Turnover time
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-8085 (URN)10.1103/PhysRevE.78.010901 (DOI)000258178600005 ()2-s2.0-47249154762 (Scopus ID)
Note
QC 20100820. Uppdaterad från manuskript till artikel (20100820).Available from: 2008-03-07 Created: 2008-03-07 Last updated: 2010-08-20Bibliographically approved

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