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Modeling protein motors

Modeling protein motors

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Modeling protein motors

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  1. Modeling protein motors Jianhua Xing University of California, Berkeley Bacterial flagellar motor F1Fo ATPase

  2. Question 1: What are appropriate theoretical and simulation frameworks? A theoretical model should be • Simple • Not over-simplified • Useful

  3. Simple • Limited information • Insufficient mechanics treatment Mesoscopic models Chemical states of a rotor binding site: E: empty O: occupied • Computationally less demanding than atomic level simulations • Treats mechanics appropriately • Atomic level simulations • Provide atomic details • Limited by system size and simulation length • Require detailed structures Kinetic models

  4. + x _ I. General discussion 1. Molecular motors use chemical energy to perform mechanical work Occupied Potential Empty + Occupied state Empty state x Chemical transitions switch the system from one potential curve to another, and result in mechanical motion

  5. Dq DG rotor q Dq stator A generic molecular motor Free energy Angular position q Keller, Bustamante (2000), Biophys. J., 78: 541-556

  6. II. The Bacteria Flagellar motor 1. Summary of experimental studies H. Berg’s website

  7. Vibrio alginolyticus a). Structure of bacterial flagellar motor D. Thomas, N. Francis, and D. Derosier, unpublished EM image

  8. periplasm cytoplasm pmf = proton motive force ion = proton, sodium The “fuels”: trans-membrane ion motive force

  9. b) Mechano-chemical studies • The flagellar motor can • Generate torque 2700 ~ 4000 pN.nm • Rotate as fast as 1700 Hz • (1 Hz = 1 cycle/second) Under viscous load Under rotating electric field Fung, Berg (1995), Nature, 375: 809-812 Ryu, Berry, Berg (2000), Nature, 403:444-447 Chen, Berg (2000), Biophys. J. 78: 1036-1041 Gabel, Berg (2003), PNAS, 100:8748-8751 Sowa et al. (2005), Nature, 437: 916-919

  10. c) The Puzzle: ~ Linear decrease Torque ~ Constant Speed  pmf Fung, Berg (1995), Nature, 375: 809-812 Ryu, Berry, Berg (2000), Nature, 403:444-447 Chen, Berg (2000), Biophys. J. 78: 1036-1041 Gabel, Berg (2003), PNAS, 100:8748-8751

  11. 2. Our model a) We proposed the working mechanism based on available information Xing, Bai, Berry , Oster (2005), submitted

  12. b) We identified key ingredients from experiments The power stroke is driven by a conformational transformation in the stator that is triggered by the protons hopping onto and off the stator Elastic coupling Tight coupling The rotation of the motor is observed through a soft elastic linkage between the motor and the viscous load The ion channel through the stator is gated by the motion of the rotor Xing, Bai, Berry , Oster (2005), submitted

  13. Prob. density c) Mathematical modeling Motor Torque Brownian Torque Markovian chemical transitions Viscous Torque Load Torque + Langevin Fokker-Planck Potential based kinetic model Wang, Peskin, Elston (2003), J. Theor. Biol. 221:491-511 Xing, Wang, Oster (2005), Biophys. J. 89:1551-1563

  14. d) Our model can fit the data well Xing, Bai, Berry, Oster (2005), submitted

  15. 3. Physical explanation of the torque-speed relation a) Plateau: time scale separation & soft linkage Spring constant

  16. bead DG/Dq motor Crossover between the two time scales

  17. Elastic linkage allows multiple time-scales Conservative load Viscous load with spring Viscous load with rigid linkage Xing, Bai, Berry, Oster (2005), submitted

  18. Pushed away from transition region Free energy Angular position q Free energy Angular position q b) Sharp transition: positive feedback

  19. rotor Ryu, Berry, Berg (2000), Nature, 403:444-447 Low speed region: thermodynamic limit c) Prediction more stators  more power High speed region: Destructive interference Xing, Bai, Berry, Oster (2005), submitted

  20. more stators  more steps: depends on relative phases between stators Free energy Angular position q 2 stators 1 stator

  21. d) The same physics explains other puzzles Yasuda et al. (1998), Cell (93) 1117-1124 Mycoplasma causes diseases like pneumonia. Its sliding rate depends on temperature linearly. Miyata, Ryu, Berg (2002), J. Bacter., 1827-1131

  22. 4. Summary of flagellar motor • The observed flagellar motor dynamics is due to • Internal conformational change • Soft elastic linkage between motor and load • Tight coupling • Localized chemical transitions

  23. Dynamics Structure Mathematical modeling Question 2: How to construct a mesoscopic model? Fit data and suggest experiments

  24. III. ATP synthesis with the F1Fo ATPase 1. the F1Fo ATPase THE F1Fo ATPase THE F1 PART Fo model: F1 model: Xing, et al. (2004), Biophys. J. 87: 2148-2163 Xing, Liao, Oster (2005), PNAS, in press

  25. F1 Fo 2. The F1 part Various experimental studies serve as the model basis Single molecule measurements Biochemistry measurements Crystal structures Mutation studies

  26. Intrinsic elastic energy open close open Empty ADP + Pi ATP Free energy open closed Empty ~ 20 KBT ADP 200 300 0 100 Substrate binding energy b/g & b/e interactions Rotation angle [degree] Constructing the potentials: qualitative thinking Berzborn, Schlittler (2002), FEBS Lett. 26828, 1-8 Ma, et al. (2002), Structure 10, 921-931

  27. Fo torque: Empty open closed Constructing the potentials: qualitative thinking open close open Rotation without synthesis Correct sequence Free energy G ADP+Pi ATP ADP Empty 200 300 0 100 Rotation angle [degree] Xing, Liao, Oster (2005), PNAS, in press

  28. Empty ADP Right timing/tight coupling is ensured by specific b/g & b/e interactions Xing, Liao, Oster (2005), PNAS, in press

  29. Boyer’s binding change mechanism From announcement of 1997 Nobel Prize in chemistry ~ 20 KBT Require pmf ADP binding helps ATP release at another site Mg.ADP inhibition state Reveal dynamic features withoutany calculation! Free energy G Xing, Liao, Oster (2005), PNAS, in press

  30. The model can fit steady state ATP synthesis data The model reveals multiple reaction pathways Tomashek, JJ et al. (2004), J. Biol. Chem. 279: 4465-4470 Xing, Liao, Oster (2005), PNAS, in press

  31. 3. Summary of the model on ATP synthesis • Our model • integrates a large body of experimental observations • proposes a set of free energy potentials, which contains almost all dynamic information • makes many experimentally testable predictions

  32. IV. SUMMARY Theoretical/Computational/Systems biology: require intimate collaboration between experimentalists & theoretician I have used molecular motor studies to show that theoretical modeling can: • Integrate and transform information • Bridge structural and dynamical studies • Predict dynamical behaviors • Suggest new experiments

  33. V. ACKNOWLEDGMENT • Richard Berry (Oxford) • Fan Bai (Oxford) • Peter Dimroth (ETH, Switzerland) • Christoph v. Balmoos (ETH, Switzerland) • George Oster • Jung-Chi Liao • Oleg Igoshin • Andrew Spakowitz • Oleksii Sliusarenko • Jing Chen • Joshua Adelman • Hongyun Wang (UC Santa Cruz) • Sean Sun (JHU) Financial support: NIH

  34. δ a c11 Fo b γ ε F1 α3β3 δ The End