chain translocation in a biological context
DESCRIPTION
CHAIN TRANSLOCATION IN A BIOLOGICAL CONTEXT INJECTING VIRAL GENOMES INTO HOST CELLS Roya Zandi Mandar Inamdar David Reguera Rob Phillips Joe Rudnick [CHUCK KNOBLER]. ANIMAL CELL ENTRY *Virus gets in by binding to receptor in cell membrane - PowerPoint PPT PresentationTRANSCRIPT
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
5
104 kBT 10 pN
01.00.5 0
0 0 0.5 1.0
U -(dU/dx)=f
x/L x/L
Bacteriophage 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
6
Inte
rnal
For
ce, p
N
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
0 30 60
50
20
0fosmotic
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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
feject = fresist
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 remaining in capsid
8
Experimental Design
Phages (sedimenting material)
Ejected/digested DNA + PEG
v
v
Spin down phage by centrifugation
PEG8000
PhagesAnd 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
020406080100
0 4 8 121620Osmotic pressure of the external solution, atm
Percent of DNA ejected from the phage capsids, %
11
3-4 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 Drod
€
↔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
€
τ diffusion =L2
Drod
τ ideal ratchet =L
s
s2
Drod
=Ls
Drod
(=s
Lτ diffusion )
Can then introduce a "ratcheting velocity", v :
τ ratchet =L
vratchet
=L
(Drod /kBT) f=
Ls
Drod
, and hence
fratchet =kBT
s
SUPPPOSE BINDING PARTICLES STICK IRREVERSIBLY AT EACH ENTERING SITE…
[G. Oster et al.]
14€
Q : What is the force exerted by reversibly
binding (ε) particles (volume fraction φ)?
A : (P. - G. de Gennes) The 1D Langmuir pressure!
freversible = Π1D Langmuir =kBT
sln[1+ φeε / kBT ]
ε >>kBT ⏐ → ⏐ ⏐ ε
s>>
kBT
s= f ratchet
BUT, OTHERWISE…
15
Rigid rod (with black monomers) of length L moves distance x into cell
(radius Rs) containing N binding particles
Brownian Molecular Dynamics (MBD)
MORE GENERAL TREATMENT OF TRANSLOCATION…
16
f(kBT/s)
x(s)
The filled squares show the force calculated directly in the MBD
simulation, for 2Rs=24, L=16, N=100, /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 obtained from assumption of fast equilibration of particle binding.
17
€
A(x,n)Langmuir
= −nε − kBT log(6x /s)!
n!(6x /s − n)!− kBT(N − n)log
V
(N − n)v
∂ρ(x,n, t)
∂t=
∂
∂xDrod (
1
kBT
∂A(x,n)
∂xρ +
∂ρ
∂x)
+∂
∂nDn (
1
kBT
∂A(x,n)
∂nρ +
∂ρ
∂n), Dn ≅ σ
N
VDo
∂ρ (x, t)
∂t=
∂
∂xDrod (
f (x)
kBTρ +
∂ρ
∂x)
f (x) = dn∂A(x,n)
∂x∫ exp(−A(x,n) /kBT)
dnexp(−A(x,n) /kBT)∫
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Fast equilibration of particle binding
€
⇒
18
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, /kBT=5, and Drod=Do/16;
the open circles show the same for Drod 60 times smaller.
19
€
∂(x, t)
∂t=
∂
∂xDrod (
dU /dx)
kBTρ (x, t) +
∂ρ (x, t)
∂x)
t(x) =1
Drod
dx10
x
∫ exp(−U(x1)
kBT) dx2 exp(
U(x2)
kBT)
x1
x
∫
tconstant force(x; f ) =x 2
Drod
exp(− fx /kBT) + fx /kBT −1
( fx /kBT)2
t(x)U(x)+ratchet = tconstant force(s; f i =dU
dxi=1
x / s
∑ x= is)
t(x)⇒ x(t)⇒x(t)
Ltot
≡ fraction ejected
TRANSLOCATION, INCLUDING PUSHING AND PULLING FORCES
20
104 kBT 10 pN
01.00.5 0
0 0 0.5 1.0
U -(dU/dx)=f
x/L x/L
RECALL THATDNA 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)
21
EFFECT OF RATCHET ON U(x)
Langmuir
0.5 x 10-4 1 (L2/D) 4 6Internal force + Langmuir
22
EFFECT OF LANGMUIR FORCE ON U(x) -- ADD /s TO fi’s:
23
EFFECT OF OSMOTIC FORCE -- SUBTRACT fosmotic FROM fi’s:
€
f ratchet < ( fosmotic:3 atm ≈1pN) < fLangmuir (<< f internalmax )
driving force drops below 1pN when fraction ejected reaches 50%
24
€
on ⇔ off , ΔG = ε + kT lnφ > 0
K =[off ]
[on]= e−βΔG =
1
φe−βε =
koff
kon
(<1)
BINDING/UNBINDING (ON/OFF) EQUILIBRIUM
COMPETING TIME SCALES FOR TRANSLOCATION
€
(1
kon
↔)τ off ≈(average particle spacing)2
Do
≈1
(N /V )2 / 3 Do
(1
koff
↔)τ on =1
Kτ off > τ off
Third time scale is τ diff ≡s2
Drod
25
diffusion ratcheting pulling
τoff τon
WHERE IS τdiff=s2/Drod ON THE TIME SCALE OF BINDING/UNBINDING?
€
diffusion : τ diff < τ off < τ on
τ trans =L2
Drod
, F = 0
ratcheting : τ off < τ diff < τ on
τ trans =Ls
Drod
≡ τ ratchet , F =kBT
s
pulling : τ off < τ on < τ diff
τ trans =Ls /Drod
ln(1+ φeβΔG )< τ ratchet , F =
kBT
sln(1+ φeβΔG ) ≈
ΔG
s>>
kBT
s
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…