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 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 example is budding in vesicles and cells Vesicles: Cells:

An outline Shapes of growing vesicles Vesicle 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 C 1 and C 2 are principal curvatures, dA is the element of membrane area, k c membrane bending constant and C 0 its spontaneous curvature, and the transport of the material across the membrane

Spontaneous curvature is the result of membrane asymmetry W. Helfrich Z. Naturforschung c citations up to A membrane with spontaneous curvature C 0 would tend to make a spherical vesicle with the radius R 0 = 2/C 0 and thus attain zero bending energy (because for the sphere C 1 = C 2 = 1/R 0 )

The non-spherical shapes can be theoretically predicted by the minimization of the reduced bending energy (w =W/8πk c ) with c 1 = R s C 1, c 2 = R s C 2, c 0 = R s C 0 and R s the radius of the sphere with the membrane area A Shapes are thus characterized by the reduced spontaneous curvature c 0 and the reduced volume v

The shape phase diagram of the spontaneous curvature model Taken from Seifert et al., Phys. Rev. A 64 (1991) c 0 = R s C 0

Vesicle bending energy in the vicinity of the sphere Δw b (the reduced bending energy minus the reduced bending energy of the sphere) in dependence on v plotted for different values of c 0 = C 0 R s The pressure due to the bending energy, Δp ℓ, derived by Ou-Yang and Helfrich (1989) : (Božič and Svetina, PRE 2009)

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: Sphere is stable as long as

A prototype model for vesicle growth It is assumed that membrane area (A) duplicates in time T d c 0 = R s C 0 is increasing in time because membrane area A is increasing in time and R s =  (A/4π) Volume (V) changes are determined by the hydraulic permeability L p (Božič and Svetina, Eur Biophys J 2004)

Remember: Δp is increasing while Δp ℓ is decreasing in time: Consequently, these two Δp-s eventually become equal. Stability of the spherical shape of a growing vesicle 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) c 0 = R s C 0

In the c 0 – v shape diagram a vesicle has to transform from v = 1, c 0 = 2 into v = 1/  2, c 0 = 2  2 c 0,cr The trajectory from a sphere to the twin shape in the c 0 – 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

The criterion for vesicle self-reproduction This criterion relates internal and external properties of the system and thus represents a condition for the selectivity. ℓ p = 1.85

ℓ p > ℓ p,min = 1.85 When ℓ p > 1.85, the two spheres of the final shape have different radii. The average doubling time is larger than at ℓ p,min = 1.85 ℓpℓp ℓ p,min Vesicle division needs not be symmetric

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. R s = √A/4π ℓ p = ℓ p,min ℓpℓp

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.

ℓ p : reduced hydraulic permeability p s : reduced solute permeability Φ 0 : 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 features The 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)

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

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