A model of the growth of S. pombe combining both shell mechanics and
protein localization profiles.
E Couturier1, JF Abenza-Martinez2, RE Carazo-Salas2, J Dumais3
1
2
USACH Santiago
Gurdon Institute Cambridge
3
UAI Viña del Mar
Presenting author's e-mail address: [email protected]
S. pombe is a tip growing cell. Among other tip growing cells (pollen tubes, hyphae of fungi
…) S. pombe is the one whose genetic is the most advanced. Many proteins, which are involved
in cell wall synthesis, can be easily visualized by fluorescence. S. pombe offers a very promising
model to couple gene expression and mechanic of the cell wall.
The main result of the mechanic of tip growth is that the growth anisotropy equalled the
antisotropy of elastic deformations or, equivalently, tip growth tensor equalled the elastic
deformation tensor up to a scalar prefactor [1]. This prefactor would originate in the local
chemistry of the cell wall.
The localization profile of many proteins related to cell wall growth were tested as prefactors.
The protein CRIB, an activation factor of Cdc42, was shown to be the best prefactor (see on the
left side of the Figure A). Two different and independent growth models were realized to
properly check this assertion. The first model, the most widely employed for tip growth, uses
strain rates as way to implement growth [2]. The second model describes growth as a change in
the rest length of the growing wall. The former is derived from membrane axisymmetric shell
theory, whereas the latter includes both bending and transverse shear effects necessary to
describe the mechanic of the wall just after division [3]. This second model allowed us to
evaluate the effect on cell shape of turgor-driven swelling of the septum after cell division as
well as the effect on the cell shape of tip growth. The shape of the division scar was very
accurately reproduced. The material properties of both the septum and the cell wall were
evaluated using division and plasmolysis movies (see Figure B). We found a ratio of turgor
pressure over the Young modulus of 0.018± 0.0008 and a Poisson ratio of 0.033± 0.005 (N=24).
The behaviour of the septum after division was best described by a septum whose rest length is
1.25 times larger than the width of the turgid cell.
Once gathered these informations a recent experiment using a spheroplast was numericaly
reproduced. The experiment is the following [4]: The cell wall of a typical S. pombe cell is
depolymerized using chemicals. The cell becomes spherical. After a while the cell wall
repolymerized around the cell and a protrusion begins to grow whose diameter is close to the
typical cell diameter. It then divides. The daughter is then typical. The initial conditions of the
simulation were very simple and realistic: a sphere bearing no stress was swelled by turgor (see
Figure C) It was then grown using the CRIB profile and divided using the septum model. It
reproduces many quantitative features of the experiments such as the diameter of the daughter
cell, the size of the scar, the morphology of the old growing pole versus the new pole.
Figure: A. Typical S.pombe cell and distribution profile of CRIB observed by fluorescence. B. Two examples of
S.pombe cells at both turgid (Cell on the left of each image) and plasmolized state (Cell on the right of each image).
C. The time goes from left to right. An initial sphere (violet contour) which bears no stress is swelled in a
spheroplast (red contour). It is grown using the second model and the CRIB profile as prefactor. It is then divided.
The daughter cell septum straight and at rest in the cell is swelled once swelled divide. The old pole continues to
grow a while. Then the new pole grows. At each step the violet contour stands for the plasmolyzed state.
[1] Rojas ER, S Hotton, J Dumais, “Chemically-mediated mechanical expansion of the pollen tube cell wall,”
Biophysical Journal Vol. 101, pp. 1844–1853 (2011).
[2] Dumais J, SL Shaw, CR Steele, SR Long, PM Ray, “An anisotropic-viscoplastic model of plant cell
morphogenesis by tip growth,” Int J Dev Biol Vol. 50, pp. 209–222 (2006).
[3] Su FC, Taber LA, “Torsional boundary layer effects in shells of revolution undergoing large axisymmetric
deformation” Computational Mechanics Vol 10, pp 23-37. (1991).
[4] Kelly FD, Nurse P, “De Novo Growth Zone Formation from Fission Yeast Spheroplasts,” PLoS ONE (2011).