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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

Applicationoftheshapeequationin.theresearch on theoriginoflife


Some characteristicsofvesiclesthatcouldberelevantforthelifeprocess

Vesicles:

  • compartmentalizethe space

  • cangrowby incorporation into the membrane of a new material and by the inflow of solution

  • may exhibit the phenomenon ofself-reproduction

  • are, on the basis of the criterion for the self-reproduction, able to evolve

  • have the capacity to increase their complexity


A motto

Manycellularprocesses that involve membrane transformationsarosefromprocessesthatoccuralso at thelevelofvesicle.

Duringtheevolutiontheyweredevelopedintodeterministicmachineries

(Svetina and Žekš, Anat. Rec. 2002)



An outline

Shapesofgrowing vesicles

Vesiclepropertiesthat are essentialfortheprocess of vesicle self-reproduction

The implications with regard to thecell 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

(Peterlin et al., Phys Chem Lipids 2009)

spherical growth

sudden burst of buds

consecutive bud formation

invagination

evagination


There is a condition which determines whether a vesicle grows as a sphere or not

or

?

This condition can be derived by taking into consideration membrane bending energy

where C1andC2are principal curvatures, dAis the element of membrane area,kcmembrane bending constant andC0its spontaneous curvature,

andthe transport of the material across the membrane


Spontaneous curvature is the result of membrane asymmetry grows as a sphere or not

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 radiusR0= 2/C0

and thus attain zero bending energy (because for the sphere C1 = C2= 1/R0)


The non-spherical shapes can be theoretically predicted by the minimization of the reduced bending energy (w =W/8πkc)

withc1= RsC1, c2= RsC2, c0= RsC0and

Rstheradiusofthespherewiththe membrane areaA

Shapes are thuscharacterizedbythereducedspontaneouscurvaturec0andthereducedvolumev


The shape phase diagram of the spontaneous curvature model the minimization of the reduced bending energy (

c0= RsC0

Taken from Seifert et al., Phys. Rev. A 64 (1991)


Vesicle bending energy in the vicinity of the sphere the minimization of the reduced bending energy (

(Božič and Svetina, PRE 2009)

Δwb(the reduced bending energy minus the reduced bending energy of the sphere) in dependence on v plotted for different values ofc0 = C0Rs

The pressure due to the bending energy, Δpℓ, derived by Ou-Yang and Helfrich (1989) :


The graphs show at which values of the pressure difference ( the minimization of the reduced bending energy (Δp) and membrane tension (σ) a vesicle is spherical

Ou-Yang and Helfrich (1989)alsopresentedgeneralized Laplace equation:

Sphere is stable as long as


A prototype model for vesicle growth the minimization of the reduced bending energy (

It is assumedthat membrane area (A) duplicates in time Td

(Božič and Svetina, Eur Biophys J 2004)

c0= RsC0 is increasing in time because membrane area A is increasing in time andRs = (A/4π)

Volume (V) changes are determinedbythehydraulicpermeabilityLp


Stability of the spherical shape of a growing vesicle the minimization of the reduced bending energy (

Thevolume is changingaccording to the time dependenceoftheareawhichmeansthatΔpdepends on theflux

Remember:

Δp is increasingwhileΔpℓ is decreasing in time:

Consequently, thesetwoΔp-s eventuallybecomeequal.


The relevant part of the shape phase diagram of the spontaneous curvature model

c0= RsC0

Taken from Seifert et al., Phys. Rev. A 64 (1991)


The trajectory from a sphere to the twin shape in the spontaneous curvature modelc0 – v shape phase diagram

In the c0 – v shape diagram a vesiclehas to transform

fromv = 1, c0 = 2into

v = 1/2 , c0 = 22

c0,cr


Vesicle doubling cycle is divided into phases spontaneous curvature model

Vesicle first grows as a sphere, and after it reaches the critical size (first arrow) its shape begins to change until it becomesa composion of two spheres connected by a narrow neck


The criterion for vesicle self-reproduction spontaneous curvature model

ℓp = 1.85

This criterion relates internal and external properties of the system and thus represents a conditionforthe selectivity.


Vesicle division needs not be symmetric spontaneous curvature model

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

ℓp >ℓp,min = 1.85

ℓp,min

ℓp


Variability of vesicle doubling time at the asymmetrical division

Rs = √A/4π

Variable is thephaseofsphericalgrowthbecausesmallerdaughtervesicleneeds more time to reachthecriticalsizethanlargerdaughtervesicle.

ℓp,min

ℓp

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)

Theconcentrationofsolute (Φ) oscillates. Duringthefirstphase it decreasesandduringthesecondphase it increases. Theopposite is validforΔP.


The condition for vesicle self-reproduction in the case of added solute

ℓp : reduced hydraulic permeability

ps : reduced solute permeability

Φ0 : reduced outside solute concentration

The variability of the generation time is increased

Thesizeofdaughtervesiclesafterfewgenerationsattains a steadydistributionwithpronouncedvariability.


Basic facts about the cell cycle added solute

The cell cycle is divided intophases. Its generation time is variable. The most variable is the G1 phase. The concentration of many cell cycle proteins is oscillating


Vesicle self-reproduction added solute and the cell cycle have many common features

Thedivision of the cycle into phases

The start ofthedivision phase bythecommitment process

The variability of cycle generationtimes

The length of the growthphase is more variable

Both vesicleandcellconstituentsexhibitconcentrationoscillations

(Svetina, chapter in Genesis 2012)



Most of the presented analysis was done in collaboration with Bojan Božič

Thank you for your attention!


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