1. Grabbing the Cat by the Tail: Studies of DNA Packaging by Single f29 Bacteriophage Particles Using Optical Tweezers
Many biological processes often involve directional movement and transport of chemical species across membranes against electrochemical potential gradients, along linear tracks, or into small compartments. These directional processes are carried out by tiny machine-like devices which operate as Molecular Motors, converting chemical energy into force and displacement. But they are unlike macroscopic engines in that, because of their dimensions, the many small parts that make up these motors must operate at energies only marginally higher than those of the thermal bath and, thus, are subjected to large fluctuations.

2. Acknowledgements Sander Tans Shelley Grimes Douglas Smith
Steven B. Smith
Yann Chemla
Aathi Karunakaran
University of California, Berkeley
Shelley Grimes
Dwight Anderson
University of Minnesota

3. 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

4. Replicative cycle
The question of how the dsDNA bacteriophages get their genomic DNA on the inside of the virus particle, surrounded by their protein capsid on the outside, has been on the minds of virologists probably since Salvador Luria and Thomas Anderson made the first electron micrographs of phage T2 and saw tadpole-shaped objects that they likened to spermatozoa (Luria and Anderson, 1942). Initially it seemed obvious that the DNA must first condense into a compact form, after which the capsid proteins would come together to form a shell around it. The problem was framed in its current form about 25 years ago when it was shown—astonishingly at the time—that during the latter stages of a phage infection, an empty protein shell is assembled first, and then the DNA is somehow transported across the shell into the interior (Luftig et al., 1971; Kaiser et al., 1975).

5. Bacteriophage f29 Volume of the capsid: V ~ 56 x 10-3 mm3
Length of f29 DNA:
19, 285 bp ~ 6.5 mm

6. DNA confinement DNA must be kept inside the bacteriophage head at
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.

7. The packaging motor • The head-tail connector (gp 10) Mw = 36 KDa
Stoichiometry = dodecamer
Structure recently solved

8. Other views of the connector
Top view with DNA model in channel
CryoEM reconstruction of Capsid
with connector crystal structure fit in
Side view: showing two monomers and DNA
Ref. Guasch A et al, JMB (2002)

9. The packaging motor (Cont’d)
• The packaging RNA (pRNA)
174 bases (57KDa) ,
Stoichiometry = 6mer (5mer)
(structure unknown)

10. The packaging motor (Cont’d)
• An ATPase (gp 16)
Mw = 39 Kda
Stoichiometry = most likely 6/phage
Structure unknown

11. gp16 – DNA dependent ATPase
The ATPase (gp16)
gp16 – DNA dependent ATPase

12. Optical Tweezers
Beam
Axis

13. Double Beam Force Measuring Laser Tweezers

14. Objectives Characterize 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? If
so, how much?
Where in the motor cycle does DNA translocation
occur?
What is the step size of the motor

15. Experimental Setup Control experiments confirm this interpretation:
Constant force
feed-back
No feed-back
Experimental Setup
Control experiments confirm this interpretation:
Proheads bound to antibody-coated microspheres, efficiently package biotinylated f29 DNA in bulk experiments
No movement is observed when the pro-heads are omitted and the DNA is attached to the beads held by the tweezers
Packaging can be reversibly stalled by adding an excess of non-hydrolizable ATP analog.

16. Packaging at Constant Force
Video by Yann Chemla and Aathi Karunakaran

17. Constant force (5 pN) experiments
Single complexes are attached between beads
Movement observed when ATP is added
Several microns packaged at constant force (~5pN)
Long DNA construct: 1.8x f29 genome
Packaging is extremely efficient. In over 95% of the measurements, movements of several micro-meters could be followed.
It takes about 5.5 min ± 0.8 min (s.d.) on average to package an amount of DNA equal to the f29 genome.
A single complex exhibits siginificant rate fluctuations
Plot pack. Rate vs amount of genome that has been packaged.
Single complex, several….
Start: rate is …
((variations: here e.g. pause))
• 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.

18. Effect of the extent of packaging on pausing frequency

19. Motor fluctuations
Motor
Fluctuations
Noise
Observed rate variations are 5x larger than noise which is
~ 4 bp/s at 1 Hz bandwidth.

20. Internal Pressure • Rate decreases to zero as head fills up
8 complexes
averaged &
smoothed
A single
complex
External force = 5 pN
• Rate decreases to zero as head fills up
• Up to 105 % of the f29 genome is packaged before stalling
• An internal pressure must be building up due to DNA
confinement.

21. What is the internal pressure at the end of packaging?

22. Packaging without Force Feedback
Video by Yann Chemla and Aathi Karunakaran

23. Pipette & trap positions fixed
Switch to different mode of measuring: Keep pos. fixed.
phage reels in DNA but bead is held back by trap, Increases tension in DNA & ((motor pulls bead out of trap center.))
See time trace F incr; L decr.
At some point, force on motor is too large > stalls
((Observe slipping behavior: motor loses grip, but recovers and continues pack.))
Use this data to find out how force affects the speed of the motor
Trap & pipette positions fixed ->> Length Force
Motor stalls at high force.

24. A powerful motor Average stall force = 55 pN Max. force
Histogram of Stall Force: 55pN.
Pretty high force for mol. motors.
One of largest reported for molecular motors.
Indication that its task requires such large forces. >> next slide
Max. force
meas. > 70 pN

25. Force-velocity relationship
Single 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
Plot Rate vs Force. For the external force to affect the rate of packaging, it must be that the actual translocation is the rate limiting step of the reaction under the conditions in which we carry out the experiment.
thin line example single complex
Thick black line is smoothed version;
colored lines are 2 other examples
StallF, Vel vary somewhat; shape similar
>> to find average behavior: normalize & average
2/3 case appears there is intern. Force. Of 14pN.
Know this value because needs less ext force to stall the motor it; it is helped by internal force.
Main assumption: int & ext force add to act on motor
1/3 case no internal force: on plateau; vel has not yet been reduced
Appears reasonable. Especially, when shift curve get good Overlap: indicates motor properties not changed ((, forces just add.))
1/3 filling
2/3 filling

26. 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.
Appears vel reduced by force, even for lowest forces
For expl. Diff than what has been reported for rnaPolymerase, the vel does not depend on force at low force
vel reduces faster near end >> second step.
Such curves are useful; create constraints on possible models.
Will not discuss these implications here

27. Internal Force No internal force in first half
Get Int. force vs. amount pack.
Use previous curves
There are some quite striking and non-trivial features in this plot.
First that the force builds only in the second half. ((In First half no build up.)) Shows that the process is highly nonlinear.
at completion, the internal force is quite high ~50pN (or …). Kind of pressure you find in oxygen bottle. Translates into considerable stress on capsid proteins,
What is the biological function of this? Internal pressure driving the injection
end: non equilibrium Indication that it is not trivial for DNA to find optimum configuration >> leads to higher pressure; can relax if enough time
No internal force in first half
Internal force ~50pN at completion
Pressure ~6 MPa or 60 kg/cm2

28. How is this pressure used? Phage infection

29. 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 nm
Maximum work done per ATP : 37 pN nm
(load = 55 pN; suppose step size=2 bp)
efficiency ~ 30%
(lower bound)

30. Partitioning the work Total work done by the motor = 8.2 x 104 pN nm
(or ~ 20,000 kBTs)
Ebending= EIq/2L = kBTP q/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

31. Mechanochemistry of the motor: dependence of rate on [ATP]
To get some insight into the kinetic mechanism of the motor and its mechanochemistry, we carried out a series of experiments to investigate the ATP dependence of the rate of packaging.
Force clamp: <F>~7pN
5mM ADP, 5mM Pi

32. The motor obeys Michaelis-Menten kinetics
[T]n
(KM)n+[T]n
Hill coefficient n=1
V=Vmax
1 ATP hydrolyzed/cycle, no cooperativity between ATPases

33. F-v relationships for various [ATP]
V decreases monotonically vs. F, ATP
two regimes F<40pN, F>40pN
5mM ADP, 5mM Pi
less force dependence at low ATP

34. Where is the translocation step?k1 k2 k3
M1 +T <--> M2T --> M3D --> M1 + D
k-1
kcat = k2 k3/ (k2 + k3) ~ Vmax
KM= (k2 + k-1) k3 / k1(k2 + k3)
Vmax/KM = (k2 +k-1)/(k1 + k2)
At low ATP, v = Vmax[T]/KM, binding is rate limiting: v depends on k1, k-1, k2 , independent of k3
At high ATP, v = Vmax, binding very fast: v depends on k2, k3, independent of k±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 M1 M2
ATP
ADP Pi M3
binding
reaction
release
(Keller and Bustamante, Biophys. J. 2000)

35. Force dependence of Vmax, KM
Vmax/KM ~ constant
Vmax decreases with force
KM decreases with force

36. Translocation coincides with release
Our data is consistent with the translocation
step coinciding with the release of products of
the catalysis M1 M2
ATP
ADP Pi M3
Movement
step

37. Step size
If noise Dxrms >> step size d, we cannot measure d directly
Measure distribution of times spent in a bin of size Dl (which can be >> Dxrms and d)  “residence time ”
Distribution of residence times is well-defined
For an enzyme that performs the steps in a purely random
fashion (i.e., its stepping follows Poisson’s statistics) and
has one rate-limiting step, this distribution is: 1
(Dl/d-1)!
tDl/d-1
tDl/d
P(t,Dl/d) = e-t/t, t=d/v
Dl, v are known  d?
<t>=Dl/v, <t2>-<t>2=dDl/v2

38. Residence times Measure residence time distributions P(t,Dl) vs. [ATP]
Fit to distributions to obtain step size d
d = 2.15
Extrapolation to [ATP]  0 gives d~2bp

39. 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?

40. “Once I met a man who grabbed a
cat by the tail and learnt 40% more
about cats that the man who didn’t”
Mark Twain