Kinetics of DNA Injection In Bacteriophage Paul D. Grayson Mandar M. Inamdar Rob Phillips Caltech Prashant K. Purohit UPenn William M. Gelbart UCLA Jané Kondev Brandeis University Paul D. Grayson Mandar M. Inamdar Rob Phillips Caltech Prashant K. Purohit UPenn William M. Gelbart UCLA Jané Kondev Brandeis University Bacteriophage λ Ross Inman, Wisconsin-Madison

Phage Life Cycle

What is The Question? Animal virus enter completely into the host cell. Bacteriophage inject only their genome into the cell. How do bacteriophage inject their genome? How fast is the injection? Is it all in the head? Whittaker lab, Cornell

Some Experimental Background Rate of ejection in T7, Molineux et al. DNA injection from λ into vesicle Roessner et al. Injection rate in λ, Novick and Baldeschwieler Time (seconds)Fluorescence Intensity Injection in λ, P. Grayson Ejection is driven by RNA Polymerase

What’s in the head? Head is packed with DNA. Osmotically shocked T2 Capsid. Φ29 schematic, Tao et al. Regularly arranged DNA in T7 capsid, Cerritelli et al.

It is really crowded in there! Virus Type HostDNA Length (kbp) Diameter (nm) Packing Density Phage Φ29B Phage T4B Phage λB HerpesH AdenovirusH MimivirusA B: Bacterium H: Human A: Amoeba

Tight Packing Imply High Forces? Capsid Modeling Bending Energy Interaction Energy

Tight Packing Imply High Forces? The high forces can be utilized to eject the phage DNA. Bustamante et al.

Kinetics of DNA Injection Two dominant injection mechanisms: –Push: Pressure-driven –Pull: Enzyme/Protein-driven Pressure due to tight DNA packing. Enzymes consume ATP, binding proteins may form a ratchet. DNA Proteins

Phage show variety of Ejection behavior

Internal Force Driven DNA ejection into vesicle Mean First Passage Time (MFPT) : Average time taken to travel a certain distance. Depends on the total free energy of the DNA: U(x) = U capsid (L-x) + U vesicle (x) Crowding from vesicle can mimic DNA injection in crowded in vivo environment. Bohm et al.

How fast is the DNA injected? Diffusion Constant: D ≡ length 2 /time

DNA ejection is helped by binding proteins Three time scales: Τ translocation : Time required for translocation Τ on, Τ off : On and Off times for binding proteins Τ off À Τ translocation À Τ on : Perfect Brownian Ratchet Τ translocation À Τ on, Τ off : Pulling Langmuir force ΔG/s plus ratchet.

Results Proteins The pushing internal force is dominant in early stages. The pulling DNA-protein interactions take over in later stages.

Conclusions The internal force is a dominant mechanism at least in early stages. The DNA ejection in a vesicle may mimic the in vivo situations, where the macromolecular crowding resists the DNA injection. The binding proteins speed-up the injection rate and helps internalization of the genome against osmotic pressure.

The Singular Case of T7 T7 is highly pressurized. The internal pressure plays no role at any time. What’s the utility of so much pressure? Speculation: Remove the protein core outside the capsid. Molineux et al. Pressure as function of length x of cylindrical core in the capsid

Bacteriophage T7 capsid can be approximated as a sphere of 30 nm diameter. It also has a central cylindrical core, 21 nm wide and 26 nm long, formed of proteins gp14, gp15 and gp16. The initial stage of the DNA injection mechanism in T7 happens as follows: How the cylindrical core comes out of the phage capsid is not known. But we show that the force acting on it from the compressed DNA in the capsid is very large. The central cylindrical core gets outside the phage capsid. It then forms an extended tail which burrows through the peptidoglycan and forms a pathway for DNA injection. Radius of capsid, R out = 30 nm Cylinder radius, R cyl = 10.5 nm DNA length, L = X 0.34 nm Length of cylinder left, x DNA injection in T7

Neglecting the bending energy the interaction energy of the DNA inside the capsid is given by, The force on the cylindrical core of the DNA is given by differentiating the energy with respect to the core length, x. The pressure on the cylindrical capsid is given by dividing the force with the area of the capsid. Fo = pN/nm 2, c = 0.3 nm are parameters, and depend on salt type and strength Force as function of length x of cylindrical core in the capsid Pressure as function of length x of cylindrical core in the capsid

Internal Force Driven DNA ejection into vesicle Mean First Passage Time (MFPT) : Average time taken to travel a certain distance. Depends on the total free energy of the DNA: U(x) = U capsid (L-x) + U vesicle (x) The MFPT is given by:

Ejection against Osmotic Pressure