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Grabbing the Cat by the Tail: Studies of DNA Packaging by Single 29 Bacteriophage
Particles Using Optical Tweezers
Acknowledgements
Sander TansDouglas SmithSteven B. SmithYann ChemlaAathi Karunakaran
University of California, Berkeley
Shelley Grimes
Dwight Anderson
University of Minnesota
Bacteriophages
Icosahedral bacteriophages have played an central role in the development of Molecular Biology
Simplest infectious organisms known
Capsid: an empty protein shell that contains the genetic material of the phage
Tail and associated protein filaments
Replicative cycle
Bacteriophage 29
Volume of the capsid:
V ~ 56 x 10-3 m3
Length of 29 DNA:
19, 285 bp ~ 6.5 m
DNA confinement
DNA is compacted about 6000x inside the phage head
DNA concentration: ~ 500 mg/ml
Opposing packaging: electrostatic repulsion, bending rigidity, entropy loss, dehydration.
DNA must be kept inside the bacteriophage head at significant pressures.
The packaging motor
• The head-tail connector (gp 10)
Mw = 36 KDaStoichiometry = dodecamerStructure recently solved
Other views of the connectorTop view with DNA model in channel
Side view: showing two monomers and DNA
CryoEM reconstruction of Capsid with connector crystal structure fit in
Ref. Guasch A et al, JMB (2002)
The packaging motor (Cont’d)
• The packaging RNA (pRNA)
174 bases (57KDa) , Stoichiometry = 6mer (5mer)(structure unknown)
The packaging motor (Cont’d)
• An ATPase (gp 16)
Mw = 39 Kda Stoichiometry = most likely 6/phage Structure unknown
The ATPase (gp16)
gp16 – DNA dependent ATPase
Optical Tweezers
BeamAxis
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Double Beam Force Measuring Laser Tweezers
ObjectivesCharacterize the Force vs. Velocity relation of a novel motor that may couple rotation to translation.
Determine the stall force of the motor
Does an internal pressure build up in the head? Ifso, how much?
Where in the motor cycle does DNA translocation occur?
What is the step size of the motor
Constant forcefeed-back
No feed-back
Experimental Setup
Packaging at Constant Force
Video by Yann Chemla and Aathi Karunakaran
QuickTime™ and aMotion JPEG A decompressor
are needed to see this picture.
• Initial packaging rates ~ 100 bp/sec. • Pauses are frequent. Ave. pause duration: 4 s ± 5 s. Neither the pause duration nor the intervals between pauses are Poisson distributed. Occur more often at higher fillings.
Constant force (5 pN) experiments
Effect of the extent of packaging on pausing frequency
Motor fluctuations
Observed rate variations are 5x larger than noise which is
~ 4 bp/s at 1 Hz bandwidth.
MotorFluctuations
Noise
Internal Pressure
• Rate decreases to zero as head fills up
• Up to 105 % of the 29 genome is packaged before stalling
• An internal pressure must be building up due to DNA confinement.
8 complexesaveraged &smoothed
A singlecomplex
External force = 5 pN
What is the internal pressureat the end of packaging?
Packaging without Force Feedback
Video by Yann Chemla and Aathi Karunakaran
QuickTime™ and aMotion JPEG A decompressor
are needed to see this picture.
Pipette & trap positions fixed
Trap & pipette positions fixed ->> Length Force
Motor stalls at high force.
A powerful motor
Average stall force = 55 pN
Max. forcemeas. > 70 pN
Force-velocity relationshipSingle complex traces:
- Stall force and initial speed vary
- Curve shapes are similar
Mean traces for 2 fillings:F vs. velocity curves: at 1/3 filling at 2/3 filling the curve is displaced to the left by ~ 14pN
External Force = 5 pN
1/3 filling
2/3 filling
Force additivity
The good overlap observed by shifting one curve relative to the other suggests that the internal and external forces acting on the motor add.
Ext. and Int. forces
must be acting at the
same point on motor.
Internal Force
No internal force in first half
Internal force ~50pN at completion
Pressure ~6 MPa or 60 kg/cm2
How is this pressure used? Phage infection
Work done by the motor
Work done to package all DNA: 7.5x10-17 J (2x104 kT or 8.2 x 104 pN nm)
Available energy per ATP : 120 pN nmMaximum work done per ATP : 37 pN nm(load = 55 pN; suppose step size=2 bp)
efficiency ~ 30%(lower bound)
Partitioning the work
Total work done by the motor = 8.2 x 104 pN nm(or ~ 20,000 kBTs)
Ebending= EI/2L = kBTP /2L = 2,180 pN nm (~ 530 kBTs)
Econfig. loss = 900 pN nm (~ 220 kBTs)
Therefore, the dominant factor in the work done by the motor appears to be the DNA
electrostatic self-repulsion and dehydration
Mechanochemistry of the motor:dependence of rate on [ATP]
5M ADP, 5M PiForce clamp: <F>~7pN
The motor obeys Michaelis-Menten kinetics
V=Vmax
[T]n
(KM)n+[T]n
1 ATP hydrolyzed/cycle, no cooperativity between ATPases
Hill coefficient n=1
F-v relationships for various [ATP]
V decreases monotonically vs. F, ATP two regimes F<40pN, F>40pN
less force dependence at low ATP
5mM ADP, 5mM Pi
M1 M2ATP
ATP
ADP
Pi
M3
ADP
Pi
Where is the translocation step?
1. Binding movement step: k1 and k-1 are F dependent Vmax force independent Vmax/KM force dependent KM force dependent
2. Reaction movement step: k2 is F dependent Vmax force dependent Vmax/KM force dependent KM force dependent
3. Release is the movement step: k3 is force dependent Vmax force dependent Vmax/KM force independent KM force dependent
(Keller and Bustamante, Biophys. J. 2000)
At high ATP, v = Vmax, binding very fast: v depends on k2, k3, independent of k±1
At low ATP, v = Vmax[T]/KM, binding is rate limiting: v depends on k1, k-1, k2 , independent of k3
binding
reaction
release
M1 +T <--> M2T --> M3D --> M1 + Dk1
k-1
k2 k3
kcat = k2 k3/ (k2 + k3) ~ Vmax
KM= (k2 + k-1) k3 / k1(k2 + k3)
Vmax/KM = (k2 +k-1)/(k1 + k2)
Force dependence of Vmax, KM
Vmax/KM ~ constant
Vmax decreases with force KM decreases with force
Translocation coincides with release
Our data is consistent with the translocationstep coinciding with the release of products of the catalysis
M1 M2ATP
ATP
ADP
Pi
M3
ADP
Pi
Movementstep
Step size
Measure distribution of times spent in a bin of size l (which can be >> xrms and d) “residence time ”
P(t,l/d) = e-t/, =d/vtl/d-1
l/d
1(l/d-1)!
l, v are known d?
Distribution of residence times is well-defined
For an enzyme that performs the steps in a purely randomfashion (i.e., its stepping follows Poisson’s statistics) and has one rate-limiting step, this distribution is:
If noise xrms >> step size d, we cannot measure d directly
<t>=l/v, <t2>-<t>2=dl/v2
Residence times
Measure residence time distributions P(t,l) vs. [ATP]
Fit to distributions to obtain step size d
Extrapolation to [ATP] 0 gives d~2bp
d = 2.15
Current questions
• What is the organization of the DNA inside the capsid
• Does the motor rotate during translocation?
• How does the DNA structure affect the activity of the motor?
- chargeless DNA- ssDNA
• What is the molecular mechanism of energy transduction?
“Once I met a man who grabbed acat by the tail and learnt 40% more about cats that the man who didn’t”
Mark Twain