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Interaction of motor proteins with obstacles

Interaction of motor proteins with obstacles. Helicase unwinding of DNA. M. D. Betterton Department of Applied Mathematics University of Colorado at Boulder. joint work with Frank Jülicher MPIPKS, Dresden. http://www.mpipks-dresden.mpg.de/mpi-doc/julichergruppe/.

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Interaction of motor proteins with obstacles

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  1. Interaction of motor proteins with obstacles Helicase unwinding of DNA M. D. Betterton Department of Applied Mathematics University of Colorado at Boulder joint work with Frank Jülicher MPIPKS, Dresden

  2. http://www.mpipks-dresden.mpg.de/mpi-doc/julichergruppe/

  3. Not all motors move on an infinite periodic track

  4. The Polymerization Ratchet • Growth of a polymer near a wall wall F polymer given enough space, next monomer can bind Peskin, Odell, and Oster, Biophys J65, 316 (1993)

  5. The Polymerization Ratchet Dogterom and Yurke, Science278, 856 (1997) Mogilner and Oster, Eur Biophys J28, 235 (1999) Carlsson, Phys Rev E62, 7082 (2000) Kolomeisky and Fisher, Biophys J80, 149 (2001) and important applications to cell motility, …

  6. MCAK • Kinesin-related ATPase • Localizes to microtubule ends http://www.mpi-cbg.de/research/groups/howard/projects.html Hunter et al. Mol. Cell 11 445, (2003)

  7. MCAK • Accelerates MT depolymerization 100x • Appears to processively depolymerize • MCAK off rate 0.054 s-1 • Tubulin dimer off rate 1 s-1 http://www.mpi-cbg.de/research/groups/howard/projects.html Hunter et al. Mol. Cell 11 445, (2003)

  8. Nucleic-acid motorsRNA Polymerase http://fajerpc.magnet.fsu.edu/Education/2010/Lectures/26_DNA_Transcription.htm

  9. NA-based motorsRibosome http://ntri.tamuk.edu/cell/ribosomes.html

  10. NA-based motorsExonuclease http://www.stanford.edu/group/blocklab/Exo2.gif

  11. NA-based motorsHelicase

  12. Hopping rates: Position: n m Interacting Hopping Model 1D lattice Two fluctuating degrees of freedom

  13. Position: n m Hypothesize interaction potential

  14. Interaction changes rates Detailed balance

  15. n=m-1 Simplest interaction • Exclusion interaction • Steric inhibition • n=m forbidden

  16. n=m-1 Steric Inhibition

  17. Hard-wall Potential

  18. Questions • How does changing the interaction potential change the motion of the complex? • Is there an optimal potential for fastest motion?

  19. Helicase opens dsNA • Motor protein – fueled by ATP hydrolysis • Can open duplexes of DNA-DNA, DNA-RNA, or RNA-RNA +ATP +ATP (Assumes strands don’t re-anneal)

  20. Cellular Role of Helicases All cellular processes involving nucleic acids Replication Transcription Translation RNA processing DNA repair Important for Genome Stability

  21. helicase binds 3’ 5’ single strand double strand helicase translocates helicase moves junction displaces strand Bird et al. Nucl Acids Res26, 2686 (1998) Dillingham et al. Biochemistry39, 205 (2000) Dillingham et al. Biochemistry41, 643 (2002)

  22. Passive Doesn’t interact directly with duplex Waits for fluctuation to advance Inhibits closing Hard wall Active Interacts with duplex Destabilizes duplex Increases opening rate Mechanism Lohman and Bjornson, Ann Rev Biochem 65, 169 (1996) Singleton and Wigley, J. Bacteriol184, 1819 (2002)

  23. Mutation Studies support idea of an active mechanism • Mutate PcrA residues which touch duplex • Unwinding rates decrease 10–30x Soultanas et al. EMBO Journal19, 3799 (2000)

  24. k+ k- 5’ 3’ Helicase motion

  25. k+ k- 5’ 3’ Helicase motion If out of equilibrium can have k+>k- PcrA: k+-k- =80 bases/s Dillingham et al. Biochemistry41, 643 (2002)

  26. DNA ss-ds junction motion

  27. Junction at base m Junction at base m+1 Junction motion Closing lowers energy

  28. Effects neglected • Helicase binding/unbinding • DNA flexibility • Different biochemical states of helicase • DNA sequence variability • Effects of randomness on unzipping • Lubensky and Nelson Phys Rev E 2002 • Effects of randomness on motor protein motion • Kafri, Lubensky and Nelson cond-mat 2003

  29. Computing Unwinding Rate probability of finding helicase at n, junction at m, time t

  30. Simulation of Full Equations • Junction • Closing rate = 0.1/time step • Opening rate 0.1/7 • Helicase • Forward hop rate = Closing rate/100 • Backward hop rate = Forward rate/40 • Start with uniform junction position • Run for 25 closing times

  31. Helicase position n Thanks to Alex Barnett Junction position m

  32. Simulation of Full Equations • NA closes quickly compared to helicase hop • Speed up movie 500x

  33. Helicase position n Thanks to Alex Barnett Junction position m

  34. Separate dynamics Rates depend on j only

  35. Difference-variable equation DNA Helicase

  36. Increase j Decrease j Difference-variable equation

  37. Difference-variable dynamics equilibrate quickly compared to midpoint motion Boundary conditions: zero-current solution

  38. Forward rate at j Backward rate at j Prob at j Steady-State Unwinding Rate • Find current the average current in l • Unwinding velocity

  39. Hard-Wall Opening • Effective chemical potential of opening must be larger than the free energy change of DNA closing

  40. Numbers: upper bound • Assume Bp at junction is open 1/7 of the time When helicase tries to move forward, it succeeds with probability 1/7

  41. Varying step size • Hard-wall unwinding velocity drops rapidly with increasing step size

  42. Questions • How does changing the interaction potential change the unwinding rate? • Is there an optimal potential for fastest opening?

  43. The Step • Energetic Cost Uo for dsDNA and helicase to overlap by one base Relatively faster opening slower forward hop

  44. Increase opening Decrease closing Determining Rates • A degree of freedom remains

  45. One-Step Unwinding Rate • One-step active opening faster than passive

  46. Multi-step Staircase • Each step height Uo • For larger number of steps n, v increases more rapidly

  47. Multi-step Staircase For large n, maximum at Optimal potential cancels base pairing energy Opening neutral Helicase crystal structures suggeset n of 5-10

  48. Interaction potential 1 2 -1 0 Difference variable m-n Worse than Hard Opening: Negative Step Height Thanks to Seth Fraden Well depth of 2kT decreases velocity to 0.2 of hard-wall velocity

  49. Force-velocity curves • Soft opening, one step • Force changes base-pairing energy • Result strongly depends on step height

  50. Summary • Simple model for motor protein-obstacle interactions • Comparison of active and passive helicase unwinding • Predict changes if vary • k+/k- • Base-pair free energy • Speed decrease from active to passive • Model: factor of 7 (hard to soft) • Model: factor of 35 (soft to well) • Experiment: factor of 10-30

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