vesicle self-reproduction: the onset of the cell cycle saša svetina ljubljana, slovenia
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Vesicle self-reproduction: the onset of the cell cycle Saša Svetina Ljubljana, Slovenia KITPC, Beijing May 10, 2012. Vesicle self-reproduction: the onset of the cell cycle Saša Svetina Ljubljana, Slovenia KITPC, Beijing May 10, 2012. - PowerPoint PPT PresentationTRANSCRIPT
Vesicle self-reproduction: the onset of the cell cycle
Saša SvetinaLjubljana, Slovenia
KITPC, Beijing May 10, 2012
Vesicle self-reproduction: the onset of the cell cycle
Saša SvetinaLjubljana, Slovenia
KITPC, Beijing May 10, 2012
Application of the shape equation in.the research on the origin of life
Some characteristics of vesicles that could be relevant for the life process
Vesicles:• compartmentalize the space • can grow by incorporation into the membrane of a new material and by the inflow of solution • may exhibit the phenomenon of self-reproduction• are, on the basis of the criterion for the self-reproduction, able to evolve • have the capacity to increase their complexity
Many cellular processes that involve membrane transformations arose from processes that occur also at the level of vesicle. During the evolution they were developed into deterministic machineries
A motto
(Svetina and Žekš, Anat. Rec. 2002)
An outline
Shapes of growing vesiclesVesicle properties that are essential for the process of vesicle self-reproduction The implications with regard to the cell cycle
Vesicles can grow and attain shapes at which they are apt to divide
Vesicles can be induced to grow by incorporating into their membranes new molecules and by transmembrane transport of the solution
Under some special circumstances such growth can lead to the formation of twin shapes, i.e. shapes composed of two spheres connected by a narrow neck
Experiments by Mojca Mally, Ljubljana
A vesicle growing at constant volume may exhibit a variety of budded shapes
spherical growth
sudden burst of buds
consecutive bud formation
invagination
evagination
(Peterlin et al., Phys Chem Lipids 2009)
There is a condition which determines whether a vesicle grows as a sphere or not
This condition can be derived by taking into consideration membrane bending energy
or ?
where C1 and C2 are principal curvatures, dA is the element of membrane area, kc membrane bending constant and C0 its spontaneous curvature,
and the transport of the material across the membrane
dACCCkW c
2
02121
Spontaneous curvature is the result of membrane asymmetry
W. Helfrich Z. Naturforschung c 1973
2674 citations up to 27.4.2012
A membrane with spontaneous curvature C0 would tend to make a spherical vesicle with the radius R0 = 2/C0
and thus attain zero bending energy (because for the sphere C1 = C2= 1/R0)
dACCCkW c
2
02121
The non-spherical shapes can be theoretically predicted by the
minimization of the reduced bending energy (w =W/8πkc)
dacccw2
02141
with c1 = RsC1, c2 = RsC2, c0 = RsC0 and Rs the radius of the sphere with the membrane area AShapes are thus characterized by the reduced spontaneous curvature c0 and the reduced volume v
34 3 /Rvolumevesicle
VVv
ss
The shape phase diagram of the spontaneous curvature model
Taken from Seifert et al., Phys. Rev. A 64 (1991)
c0 = RsC0
Vesicle bending energy in the vicinity of the sphere
Δwb (the reduced bending energy minus the reduced bending energy of the sphere) in dependence on v plotted for different values of c0 = C0Rs
The pressure due to the bending energy, Δpℓ, derived by Ou-Yang and Helfrich (1989) :
)6(203 s
s
c RCRkp
(Božič and Svetina, PRE 2009)
0)2(2 0023 sscss RCRCkRpR
The graphs show at which values of the pressure difference (Δp) and membrane
tension (σ) a vesicle is spherical Ou-Yang and Helfrich (1989) also presented generalized Laplace equation:
p
Sphere is stable as long as pp
)6(203 s
s
c RCRkp
ck
A prototype model for vesicle growth
pALdtAdV
p )(
It is assumed that membrane area (A) duplicates in time Td dT
t
02AtA
c0 = RsC0 is increasing in time because membrane area A is increasing in time and Rs = (A/4π)
Volume (V) changes are determined by the hydraulic permeability Lp
(Božič and Svetina, Eur Biophys J 2004)
Remember: Δp is increasing while Δpℓ is decreasing in
time:
Consequently, these two Δp-s eventually become equal.
pp
pd
s
LTRp2
2ln )6(2
03 ss
c RCRkp
Stability of the spherical shape of a growing vesicle
pALdtAdV
p )(
The volume is changing according to the time dependence of the area which means that Δp depends on the flux
The relevant part of the shape phase diagram of the spontaneous curvature
model
Taken from Seifert et al., Phys. Rev. A 64 (1991)
c0 = RsC0
In the c0 – v shape diagram a vesicle has to transform from v = 1, c0 = 2 into
v = 1/2 , c0 = 22
c0,cr
The trajectory from a sphere to the twin shape in the c0 – v shape phase diagram
Vesicle doubling cycle is divided into phases
Vesicle first grows as a sphere, and after it reaches the critical size (first arrow) its shape begins to change until it becomes a composion of two spheres connected by a narrow neck
Td membrane area doubling time Lp membrane hydraulic permeability kc membrane bending constant Co membrane spontaneous curvature time/Td
The criterion for vesicle self-reproduction
This criterion relates internal and external properties of the system and thus represents a condition for the selectivity.
pcpd CkLT 40
ℓp = 1.85pd
s
LTRp2
2ln
)6(203 s
s
c RCRkp
ℓp > ℓp,min = 1.85
When ℓp > 1.85, the two spheres of the final shape have different radii. The average doubling time is larger than at ℓp,min = 1.85
pcpd CkLT 40
ℓp ℓp,min
Vesicle division needs not be symmetric
85.1CkLT 40cpd
Variability of vesicle doubling time at the asymmetrical division
Variable is the phase of spherical growth because smaller daughter vesicle needs more time to reach the critical size than larger daughter vesicle.
Rs = √A/4π
ℓp =
ℓp,min ℓp
The addition of new components (e. g. a solute that can cross the membrane) increases the complexity of the system (Božič and Svetina, Eur Phys J 2007)
The concentration of solute (Φ) oscillates. During the first phase it decreases and during the second phase it increases. The opposite is valid for ΔP.
0VV
v
0AA
P
0
ℓp : reduced hydraulic permeabilityps : reduced solute permeabilityΦ0 : reduced outside solute concentration
The condition for vesicle self-reproduction in the case of added solute
The variability of the generation time is increased
The size of daughter vesicles after few generations attains a steady distribution with pronounced variability.
Basic facts about the cell cycle
The cell cycle is divided into phases. Its generation time is variable. The most variable is the G1 phase. The concentration of many cell cycle proteins is oscillating
Vesicle self-reproduction and the cell cycle have many common
featuresThe division of the cycle into phases
The start of the division phase by the commitment process
The variability of cycle generation times
The length of the growth phase is more variable
Both vesicle and cell constituents exhibit concentration oscillations(Svetina, chapter in Genesis 2012)