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.

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

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 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).

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

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.

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

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)

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

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

Optical Tweezers Beam Axis

Double Beam Force Measuring Laser Tweezers

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

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.

Packaging at Constant Force Video by Yann Chemla and Aathi Karunakaran

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.

Effect of the extent of packaging on pausing frequency

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

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.

What is the internal pressure at the end of packaging?

Packaging without Force Feedback Video by Yann Chemla and Aathi Karunakaran

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.

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

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

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

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

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 nm Maximum 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= 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

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

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

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

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)

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 translocation step coinciding with the release of products of the catalysis M1 M2 ATP ADP Pi M3 Movement step

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

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

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 a cat by the tail and learnt 40% more about cats that the man who didn’t” Mark Twain