CHAIN TRANSLOCATION
IN A BIOLOGICAL CONTEXT
INJECTING VIRAL GENOMES
INTO HOST CELLS
Roya Zandi
Mandar Inamdar
David Reguera
Rob Phillips
Joe Rudnick
[CHUCK KNOBLER]
1
ANIMAL CELL ENTRY
*Virus gets in by binding to
receptor in cell membrane
*Whole viral particle
enters cell
*Virus forms and exits via
budding
2
Plasmodesmata
(shared-wall channels)
*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 3
BACTERIAL CELL INFECTION BY VIRUS
* Virus binds to receptor and ejects genome
*Viral particle stays outside cell! Only its genome enters
4
*Virion leaves via lysis of cell
Bacteriophage l
Its dsDNA genome, 17000 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
104 kBT
0
U
0
-(dU/dx)=f
10 pN
0.5
x/L
1.0
0
0
0.5 x/L 1.0
5
This internal force drives the genome out along its length. But, it falls
sharply as ejection proceeds, and…
Internal Force, pN
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 (P) in the cell
50
20
Osmotic Force:
fosmotic a P
0
0
30
60
Percentage of genome ejected
6
EXPERIMENT: COUNTERBALANCE
EJECTION FORCE BY ESTABLISHING
AN EXTERNAL OSMOTIC PRESSURE
feject = fresist
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Capsid permeable to H2O
and to ions, but not to PEG
Measure DNA concentration by 260-nm absorption
-- but must distinguish DNA ejected from that
7
remaining in capsid
Experimental Design
PEG8000
Phages
And nuclease (not
shown explicitly)
Ejected/digested
DNA nucleotides
Add receptor
v
Spin down phage by
centrifugation
Ejected/digested DNA
+ PEG
v
Phages
(sedimenting
material)
8
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
9
Extent of Ejected DNA vs Osmotic Pressure in Solution
10
EFFECT OF GENOME LENGTH ON EJECTION FORCE
A. Evilevitch
C. M. Knobler
W. M. Gelbart
P. Grayson
M. Inamdar
P. Purohit
R. Phillips
3-4 atms
ONLY PART OF GENOME IS DELIVERED TO HOST CELL?!
11
TRANSLOCATION (DIFFUSION) INVOLVING PARTICLE BINDING,
AND…RATCHETING
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 Drod
s

viral capsid




Binding particles interact with
sites on chain via e-s LJ
potential
 (s=s, in this case)

L


mimic of bacterial cytoplasm
12
SUPPPOSE BINDING PARTICLES STICK
IRREVERSIBLY AT EACH ENTERING SITE…
L2
 diffusion 
Drod
2
L s
Ls
s
 ideal ratchet 

(  diffusion)
s Drod Drod
L
Can then introduce a " ratcheting velocity" , v :
L
L
Ls
 ratchet 


, and hence
v ratchet (Drod /k B T) f Drod
kB T
f ratchet 
s
[G. Oster et al.]
13
BUT, OTHERWISE…
Q : What is the force exerted by reversibly
binding ( e) particles (volume fraction  )?
A : (P.- G. de Gennes) The 1D Langmuir pressure!
kB T
f reversible  P1D Langmuir 
ln[1  ee / kB T ]
s
e
kB T
e kB T


 f ratchet
s
s
14
MORE GENERAL TREATMENT OF TRANSLOCATION…
Rigid rod (with black monomers) of
length L moves distance x into cell (radius
Rs) containing N binding particles
Brownian Molecular Dynamics (MBD)
15
f(kBT/s)
x(s)
The filled squares show the force calculated directly in the MBD
simulation, for 2Rs=24, L=16, N=100, e/kBT=5, and Drod=Do/16;
the open circles show the same for Drod 60 times smaller.
Solid curve is computed from the full, coupled, equations for chain
diffusion in the presence of binding particles; dashed curve is
16
obtained from assumption of fast equilibration of particle binding.
(6x /s)!
V
A(x,n) Langmuir  -ne - k B T log
- k B T(N - n)log
n!(6x /s - n)!
(N - n)v
(x,n,t) 
1 A(x,n)

 Drod (
 )
t
x
k B T x
x

1 A(x,n)

N
 Dn (
  ),
Dn  s Do
n
k B T n
n
V
Fast equilibration of particle binding
( x,t) 
f (x)

 Drod (
 )
t
x
kB T
x

A(x,n)  exp(-A(x,n) /k B T) 


f (x)   dn
x 
 dn exp(-A(x,n) /k B T) 


17
f(kBT/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 2Rs=24, L=16, N=100, e/kBT=5, and Drod=Do/16;
18
the open circles show the same for Drod 60 times smaller.
TRANSLOCATION, INCLUDING PUSHING AND PULLING FORCES
( x,t) 
dU /dx)
( x,t)
 Drod (
( x,t) 
)
t
x
kB T
x
1
t(x) 
Drod
x
U(x1 ) x
U(x 2 )
 dx1 exp(- k T )  dx 2 exp( k T )
B
B
0
x1
x 2 exp(- fx /kB T)  fx /k B T -1
t constant force (x; f ) 
Drod
( fx /k B T) 2
x /s
t(x) U(x)ratchet
dU
  t constant force (s; f i 
dx
i1
x is
)
x(t)
t(x)  x(t) 
 fraction ejected
Ltot
19
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
U(x)  Urepulsion(L - x)  Ubending(L - x)
104 kBT
U
-(dU/dx)=f
10 pN

0
0
0.5
x/L
1.0
0
0
0.5 x/L 1.0
20
EFFECT OF RATCHET ON U(x)
0.5 x 10-4
1
(L2/D)
4
6
Internal force + Langmuir
Langmuir
21
EFFECT OF LANGMUIR FORCE ON U(x) -- ADD e/s TO fi’s:
22
EFFECT OF OSMOTIC FORCE -- SUBTRACT fosmotic FROM fi’s:
driving force drops below 1pN
when fraction ejected reaches 50%
f ratchet  ( f osmotic:3 atm 1pN)  f Langmuir
( f
max
internal
)
23
BINDING/UNBINDING (ON/OFF) EQUILIBRIUM
on  off , G  e  kTln   0
[off ] - G 1 - e koff
K
e
 e 
( 1)
[on]

kon
COMPETING TIME SCALES FOR TRANSLOCATION

1
(average particle spacing) 2
1
(
)  off 

k on
Do
(N /V ) 2 / 3 Do
(
1
1
)  on   off   off
k off
K
Third time scale is  diff
s2

Drod
24

WHERE IS diff=s2/Drod ON THE TIME SCALE OF BINDING/UNBINDING?
diffusion
off
ratcheting on
pulling
diffusion :  diff   off   on
L2
 trans 
, F 0
Drod
ratcheting :  off   diff   on
Ls
kB T
 trans 
  ratchet, F 
Drod
s
pulling :  off   on   diff
Ls /Drod
kB T
G
kB T
G
 trans 
  ratchet, F 
ln(1 e ) 

G
ln(1 e )
s
s
s
25
FUTURE WORK: GENOME EJECTION -- PHAGE
Build mimics of the bacterial cell, i.e.,
reconstituted vesicles -- either lipid
bilayers or A-B-A block copolymers
Investigate effects on injection, of:
internal osmotic pressure (all)
DNA-binding proteins (e.g., T5)
RNA polymerase (e.g., T7)
Complement with single-cell, in vivo, studies, monitoring -- in real
time -- the entry of the viral genome into bacterial cytoplasm
[P. Grayson, R. Phillips]
26
L. T. Fang, C. M. Knobler, W. M. Gelbart
+ DNA-binding proteins…
27