Vesicle self-reproduction: the onset of the cell cycle Saša Svetina Ljubljana, Slovenia

1. Vesicle self-reproduction: the onset of the cell cycle Saša Svetina Ljubljana, Slovenia KITPC, Beijing May 10, 2012

2. Vesicle self-reproduction: the onset of the cell cycle Saša Svetina Ljubljana, Slovenia KITPC, Beijing May 10, 2012 Applicationoftheshapeequationin.theresearch on theoriginoflife

3. 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

4. A motto Manycellularprocesses that involve membrane transformationsarosefromprocessesthatoccuralso at thelevelofvesicle. Duringtheevolutiontheyweredevelopedintodeterministicmachineries (Svetina and Žekš, Anat. Rec. 2002)

5. An example is budding in vesicles and cells Vesicles: Cells:

6. An outline Shapesofgrowing vesicles Vesiclepropertiesthat are essentialfortheprocess of vesicle self-reproduction The implications with regard to thecell cycle

7. 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

8. 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

9. 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

10. 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 radiusR0= 2/C0 and thus attain zero bending energy (because for the sphere C1 = C2= 1/R0)

11. 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

12. The shape phase diagram of the spontaneous curvature model c0= RsC0 Taken from Seifert et al., Phys. Rev. A 64 (1991)

13. Vesicle bending energy in the vicinity of the sphere (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) :

14. The graphs show at which values of the pressure difference (Δp) and membrane tension (σ) a vesicle is spherical Ou-Yang and Helfrich (1989)alsopresentedgeneralized Laplace equation: Sphere is stable as long as

15. A prototype model for vesicle growth 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

16. Stability of the spherical shape of a growing vesicle Thevolume is changingaccording to the time dependenceoftheareawhichmeansthatΔpdepends on theflux Remember: Δp is increasingwhileΔpℓ is decreasing in time: Consequently, thesetwoΔp-s eventuallybecomeequal.

17. 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)

18. The trajectory from a sphere to the twin shape in the c0 – 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

19. 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 becomesa composion of two spheres connected by a narrow neck

20. The criterion for vesicle self-reproduction ℓp = 1.85 This criterion relates internal and external properties of the system and thus represents a conditionforthe selectivity.

21. Vesicle division needs not be symmetric 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

22. Variability of vesicle doubling time at the asymmetrical division Rs = √A/4π Variable is thephaseofsphericalgrowthbecausesmallerdaughtervesicleneeds more time to reachthecriticalsizethanlargerdaughtervesicle. ℓp,min ℓp ℓp =

23. 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.

24. 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.

25. Basic facts about the cell cycle 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

26. Vesicle self-reproduction 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)

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

28. Most of the presented analysis was done in collaboration with Bojan Božič Thank you for your attention!