500 likes | 624 Views
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/.
E N D
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
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)
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, …
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)
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)
Nucleic-acid motorsRNA Polymerase http://fajerpc.magnet.fsu.edu/Education/2010/Lectures/26_DNA_Transcription.htm
NA-based motorsRibosome http://ntri.tamuk.edu/cell/ribosomes.html
NA-based motorsExonuclease http://www.stanford.edu/group/blocklab/Exo2.gif
Hopping rates: Position: n m Interacting Hopping Model 1D lattice Two fluctuating degrees of freedom
Position: n m Hypothesize interaction potential
Interaction changes rates Detailed balance
n=m-1 Simplest interaction • Exclusion interaction • Steric inhibition • n=m forbidden
n=m-1 Steric Inhibition
Questions • How does changing the interaction potential change the motion of the complex? • Is there an optimal potential for fastest motion?
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)
Cellular Role of Helicases All cellular processes involving nucleic acids Replication Transcription Translation RNA processing DNA repair Important for Genome Stability
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)
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)
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)
k+ k- 5’ 3’ Helicase motion
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)
Junction at base m Junction at base m+1 Junction motion Closing lowers energy
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
Computing Unwinding Rate probability of finding helicase at n, junction at m, time t
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
Helicase position n Thanks to Alex Barnett Junction position m
Simulation of Full Equations • NA closes quickly compared to helicase hop • Speed up movie 500x
Helicase position n Thanks to Alex Barnett Junction position m
Separate dynamics Rates depend on j only
Difference-variable equation DNA Helicase
Increase j Decrease j Difference-variable equation
Difference-variable dynamics equilibrate quickly compared to midpoint motion Boundary conditions: zero-current solution
Forward rate at j Backward rate at j Prob at j Steady-State Unwinding Rate • Find current the average current in l • Unwinding velocity
Hard-Wall Opening • Effective chemical potential of opening must be larger than the free energy change of DNA closing
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
Varying step size • Hard-wall unwinding velocity drops rapidly with increasing step size
Questions • How does changing the interaction potential change the unwinding rate? • Is there an optimal potential for fastest opening?
The Step • Energetic Cost Uo for dsDNA and helicase to overlap by one base Relatively faster opening slower forward hop
Increase opening Decrease closing Determining Rates • A degree of freedom remains
One-Step Unwinding Rate • One-step active opening faster than passive
Multi-step Staircase • Each step height Uo • For larger number of steps n, v increases more rapidly
Multi-step Staircase For large n, maximum at Optimal potential cancels base pairing energy Opening neutral Helicase crystal structures suggeset n of 5-10
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
Force-velocity curves • Soft opening, one step • Force changes base-pairing energy • Result strongly depends on step height
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