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

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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

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• 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

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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