Force and Velocity

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Force and Velocity Measured for Single
Molecules of RNA Polymerase
Michelle D. Wang, Mark J. Schnitzer, Hong Yin,
Robert Landick, Jeff Gelles, Steven M.
Block M. D. Wang and S. M. Block,
Department of Molecular Biology and Princeton
Materials Institute, Princeton University,
Princeton, NJ 08544, USA. M. J. Schnitzer,
Departments of Physics and Molecular Biology,
Princeton University, Princeton, NJ 08544,
USA. H. Yin and J. Gelles, Department of
Biochemistry, Brandeis University, Waltham, MA
02254, USA. R. Landick, Department of
Bacteriology, University of Wisconsin, Madison,
WI 53706, USA. Science 30 October 1998, Vol. 2,
pp. 902-907.
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Key Points Facts
The relationship between applied force F and
steady-state velocity V is a fundamental
characteristic of the enzyme mechanism itself.

• F-V relationships have been determined for three
  biological motors
• ensembles of myosin in contracting muscles,
• single molecules of kinesin moving along
  microtubules,
• and the rotary engine that spins bacterial
  flagella.

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The Actual Setup
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Alternative Setups
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Force Affects Translocation
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Open- and Closed-Loop Trapping Modes
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Transcription Stall Forces

• Transcription stalled at trap stifnesses of 0.25
  and 0.29 pN/nm
• This corresponds to a force of 30 to 35 pN
• Previously reported 14 pN (1995, ref. 2)
• 20 of beads were not stopped
• Irreversible stalls caused by prolonged exposure
  to laser light
• Stalls did not occur in a homogeneous fasion
• gt Stall force might be a function of nucleotide
  sequence
• New setup (not even optimized) improves the
  following
• Photodamage is minimized with the feedback loop
• Higher peak powers can be achieved (stronger
  traps)
• Dynamic response of the system improved
• Force can be recorded in ms
• RNAP can be stopped within seconds (5-40 fold
  faster)

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Transcription Stall Force
In the presence of saturating NTPs and 1 µM PPi,
the stall force was 25 pN. Raising the
pyrophosphate (PPi) concentration to 1 mM slowed
the mean elongation rate at low force by 2.3-fold
and yielded a stall force of 23 pN, which is not
significantly different. This change reduces the
estimated free energy for the RNAP condensation
reaction by mass action and the fraction of free
energy converted into mechanical work near stall
is estimated at 44 for 1 mM PPi (and 18 at 1 µM
PPi) which resembles kinesin that spends roughly
half its available free energy as mechanical work
near stall.
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Force and Velocity Measurements
1 bp 0.338 nm
Low-load gt no change
High-load gt Stall!
Once trap properties are calibrated and
adjustments are made for series compliance, it is
possible to convert measurements of bead
displacement and trap stiffness directly into
records of time-varying force and RNAP position
along the template, and thereby into RNA
transcript length
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Force-Velocity Relationships for RNAP
v, a dimensionless velocity (normalized to the
unloaded speed V0) and f, a dimensionless force
(normalized to the force at halfmaximal velocity
F1/2), before averaging.
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Comparisons with Theory

• Stalling is an elongation-incompetent state
• RNAP slides backwards (5-10 bps)
• Maintains register between DNA and RNA
• Resumes transcription after reduction of load
• RNAP moves bidirectionaly through a distance
  corresponding to 5-10 bps
• Similar for these models is
• Reaction schemes are tightly coupled
• One condensation reaction per bp
• Involve large-scale movement of the RNAP
  associated with stalling
• Large drop in velocity upon stall is incompatible
  with single bp load-stepping
• The rate limiting transition is not
  load-dependent over most of the force range
• The F-V curves are convex

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