1 CHAIN TRANSLOCATION IN A BIOLOGICAL CONTEXT INJECTING VIRAL GENOMES INTO HOST CELLS Roya Zandi Mandar Inamdar David Reguera Rob Phillips Joe Rudnick [CHUCK KNOBLER]

2 ANIMAL CELL ENTRY *Virus gets in by binding to receptor in cell membrane *Whole viral particle enters cell *Virus forms and exits via budding

3 *Cells are each surrounded by a rigid (cellulose) wall, which must be “broken” (e.g., by abrasion) in order for viral particles to enter *Consequently, a large number of viral particles enter the cell simultaneously, where they are disassembled and replicated *New virions leave cell through existing shared-wall channels Plasmodesmata (shared-wall channels)

4 BACTERIAL CELL INFECTION BY VIRUS * Virus binds to receptor and ejects genome *Viral particle stays outside cell! Only its genome enters *Virion leaves via lysis of cell

k B T 10 pN U -(dU/dx)=f x/L Bacteriophage Its dsDNA genome, nm long, is highly stressed in its capsid (30 nm radius), due to: Electrostatic Repulsion DNA is packed at crystalline density and is highly crowded Bending Energy Persistence length, 50 nm, implies DNA is strongly bent 30 nm Can calculate energy (U) of DNA as a function of length (L-x) inside

6 Internal Force, pN Percentage of genome ejected Osmotic Force: There is a an opposing force, resisting entry of the chain into the cell, equal to the work per unit length that must be done against the osmotic pressure (  ) in the cell f osmotic   This internal force drives the genome out along its length. But, it falls sharply as ejection proceeds, and…

7 EXPERIMENT: COUNTERBALANCE EJECTION FORCE BY ESTABLISHING AN EXTERNAL OSMOTIC PRESSURE f eject = f resist Capsid permeable to H 2 O and to ions, but not to PEG Measure DNA concentration by 260-nm absorption -- but must distinguish DNA ejected from that remaining in capsid

8 Experimental Design Phages (sedimenting material) Ejected/digested DNA + PEG v v Spin down phage by centrifugation PEG8000 Phages And nuclease (not shown explicitly) Ejected/digested DNA nucleotides Add receptor

9 Evilevitch, Lavelle, Raspaud, Knobler and Gelbart Proc. Nat. Acad. Sci. (USA) 100, 9292 (2003). UV absorbance of DNA ejected from phage as a function of PEG8000 concentration. PEG

10 Extent of Ejected DNA vs Osmotic Pressure in Solution

atms ONLY PART OF GENOME IS DELIVERED TO HOST CELL?! EFFECT OF GENOME LENGTH ON EJECTION FORCE P. Grayson M. Inamdar P. Purohit R. Phillips A. Evilevitch C. M. Knobler W. M. Gelbart

12 Stiff chain of length L is “threaded” into a solution of particles that can bind to it at sites separated by distance s; chain diffusion constant is D rod s L TRANSLOCATION (DIFFUSION) INVOLVING PARTICLE BINDING, AND…RATCHETING Binding particles interact with sites on chain via  LJ potential (  =s, in this case) mimic of bacterial cytoplasm viral capsid

13 SUPPPOSE BINDING PARTICLES STICK IRREVERSIBLY AT EACH ENTERING SITE… [G. Oster et al.]

14 BUT, OTHERWISE…

15 Rigid rod (with black monomers) of length L moves distance x into cell (radius R s ) containing N binding particles Brownian Molecular Dynamics (MBD) MORE GENERAL TREATMENT OF TRANSLOCATION…

16 f(k B T/s ) x(s) The filled squares show the force calculated directly in the MBD simulation, for 2R s =24, L=16, N=100,  /k B T=5, and D rod =D o /16; the open circles show the same for D rod 60 times smaller. Solid curve is computed from the full, coupled, equations for chain diffusion in the presence of binding particles; dashed curve is obtained from assumption of fast equilibration of particle binding.

17 Fast equilibration of particle binding

18 f(k B T/s ) x(s) Dashed curve is obtained from solution to the quasi-equilibrium equation for  (x,t); solid curve is computed by solving the full, coupled, diffusion equation for  (x,n,t). The filled squares show the force calculated directly in the MBD simulation, for 2R s =24, L=16, N=100,  /k B T=5, and D rod =D o /16; the open circles show the same for D rod 60 times smaller.

19 TRANSLOCATION, INCLUDING PUSHING AND PULLING FORCES

k B T 10 pN U -(dU/dx)=f x/L RECALL THAT DNA is packed at crystalline density and is highly crowded, hence involving a large energy of self-repulsion AND because its persistence length is larger than the capsid size, a significant bending energy is also involved ENERGY ‘COST” (U) IS RELIEVED AS EJECTED LENGTH (x) INCREASES

21 EFFECT OF RATCHET ON U(x) Langmuir 0.5 x (L 2 /D) 4 6 Internal force + Langmuir

22 EFFECT OF LANGMUIR FORCE ON U(x) -- ADD  /s TO f i ’s:

23 EFFECT OF OSMOTIC FORCE -- SUBTRACT f osmotic FROM f i ’s: driving force drops below 1pN when fraction ejected reaches 50%

24 BINDING/UNBINDING (ON/OFF) EQUILIBRIUM COMPETING TIME SCALES FOR TRANSLOCATION

25 diffusionratchetingpulling  off  on WHERE IS  diff =s 2 /D rod ON THE TIME SCALE OF BINDING/UNBINDING?

26 FUTURE WORK: GENOME EJECTION -- PHAGE Investigate effects on injection, of: internal osmotic pressure (all) DNA-binding proteins (e.g., T5) RNA polymerase (e.g., T7) Build mimics of the bacterial cell, i.e., reconstituted vesicles -- either lipid bilayers or A-B-A block copolymers Complement with single-cell, in vivo, studies, monitoring -- in real time -- the entry of the viral genome into bacterial cytoplasm [P. Grayson, R. Phillips]

27 L. T. Fang, C. M. Knobler, W. M. Gelbart + DNA-binding proteins…