Interaction of motor proteins with obstacles

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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
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http//www.mpipks-dresden.mpg.de/mpi-doc/julicherg
ruppe/
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Not all motors move on an infinite periodic track
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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 J 65, 316
(1993)
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The Polymerization Ratchet
Dogterom and Yurke, Science 278, 856
(1997) Mogilner and Oster, Eur Biophys J 28, 235
(1999) Carlsson, Phys Rev E 62, 7082
(2000) Kolomeisky and Fisher, Biophys J 80, 149
(2001) and important applications to cell
motility,
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MCAK

• Kinesin-related ATPase
• Localizes to microtubule ends

http//www.mpi-cbg.de/research/groups/howard/proj
ects.html
Hunter et al. Mol. Cell 11 445, (2003)
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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/proj
ects.html
Hunter et al. Mol. Cell 11 445, (2003)
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Nucleic-acid motorsRNA Polymerase
http//fajerpc.magnet.fsu.edu/Education/2010/Lectu
res/26_DNA_Transcription.htm
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NA-based motorsRibosome
http//ntri.tamuk.edu/cell/ribosomes.html
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NA-based motorsExonuclease
http//www.stanford.edu/group/blocklab/Exo2.gif
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NA-based motorsHelicase
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Interacting Hopping Model
1D lattice Two fluctuating degrees of freedom
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Hypothesize interaction potential
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Interaction changes rates
Detailed balance
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Simplest interaction

• Exclusion interaction
• Steric inhibition
• nm forbidden

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Steric Inhibition
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Hard-wall Potential
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Questions

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

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Helicase opens dsNA

• Motor protein fueled by ATP hydrolysis
• Can open duplexes of DNA-DNA, DNA-RNA, or RNA-RNA

ATP
ATP
(Assumes strands dont re-anneal)
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Cellular Role of Helicases
All cellular processes involving nucleic acids

• Replication
• Transcription
• Translation
• RNA processing
• DNA repair

Important for Genome Stability
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Bird et al. Nucl Acids Res 26, 2686
(1998) Dillingham et al. Biochemistry 39, 205
(2000) Dillingham et al. Biochemistry 41, 643
(2002)
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Mechanism

• Passive
• Doesnt interact directly with duplex
• Waits for fluctuation to advance
• Inhibits closing
• Hard wall

• Active
• Interacts with duplex
• Destabilizes duplex
• Increases opening rate

Lohman and Bjornson, Ann Rev Biochem 65, 169
(1996) Singleton and Wigley, J. Bacteriol 184,
1819 (2002)
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Mutation Studies support idea of an active
mechanism

• Mutate PcrA residues which touch duplex
• Unwinding rates decrease 1030x

Soultanas et al. EMBO Journal 19, 3799 (2000)
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Helicase motion
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Helicase motion
If out of equilibrium can have kgtk- PcrA k-k-
80 bases/s
Dillingham et al. Biochemistry 41, 643 (2002)
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DNA ss-ds junction motion
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Junction motion
Closing lowers energy
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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

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

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Helicase position n
Thanks to Alex Barnett
Junction position m
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Simulation of Full Equations

• NA closes quickly compared to helicase hop
• Speed up movie 500x

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Helicase position n
Thanks to Alex Barnett
Junction position m
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Separate dynamics
Rates depend on j only
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Difference-variable equation
DNA Helicase
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Difference-variable equation
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Difference-variable dynamics equilibrate quickly
compared to midpoint motion
Boundary conditions zero-current solution
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Steady-State Unwinding Rate

• Find current the average current in l
• Unwinding velocity

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Hard-Wall Opening

• Effective chemical potential of opening must be
  larger than the free energy change of DNA closing

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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
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Varying step size

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

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Questions

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

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The Step

• Energetic Cost Uo for dsDNA and helicase to
  overlap by one base

Relatively faster opening slower forward hop
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Determining Rates

• A degree of freedom remains

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One-Step Unwinding Rate

• One-step active opening faster than passive

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Multi-step Staircase

• Each step height Uo
• For larger number of steps n, v increases more
  rapidly

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Multi-step Staircase
For large n, maximum at Optimal potential
cancels base pairing energy Opening
neutral Helicase crystal structures suggeset n
of 5-10
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Worse than Hard Opening Negative Step Height
Thanks to Seth Fraden
Well depth of 2kT decreases velocity to 0.2 of
hard-wall velocity
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Force-velocity curves

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

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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