1. One-side membrane and inside cell adhesion
X.H. Zhou
Department of Mathematics and Physics, Fourth Military Medical University, Xi’an , P.R. China

2. 1. Starfish vesicle and one-side membrane
1.1 The difference between cell membrane and soap film
Soap film, which composed of two layers of phosphoprotein and a layer of water .
Cell membrane, which composed of two layers of phosphoprotein in water.

3. Total energy including the Lagrange parameters
For Closed shapes:
For open shapes:
cell membrane:
soap film:
soap film

4. cell membrane: soap film:
So the total energy for soap film is reduce to
(10-9次方的读法) 10 to the power of -9 (minus nine) draw [drɔ:] Newton per meter
When kc=0,kg=0, the cell membrane model reduces to soap film model

5. 1.2 Shape Equation: For soap bubble: Open vesicle:
Z. C. Ou-Yang and W. Helfrich, Phys. Rev. Lett. 59, 2486 (1987).
For soap bubble:
Open vesicle:
Capovilla, Guven, and Santiago, Phys. Rev. E 66, (2002);
Tu and Ou-Yang,
Phys. Rev. E 68, (2003).
For soap film:

6. 1.3 Numerical solutions obtained by using Surface Evolver
Initial shapes

7. Several stable shapes

8. Shape transformation
dumbbell

9. Division process
divide

10. Stable phase diagram
These results obtained by increasing the v with fixed C0. If a stable shape change into another shape at a point (v, C0), we find a stable boundary point.
X.H Zhou, et al,
Int. J. Mod. Phys. B, (2008)

11. One-side soap film X.H Zhou, et al,
Int. J. Mod. Phys. B, (2010)
Shape a is a photograph of a soap film on a wire, shape b is obtained by using Surface Evolver. We should note that they are one-side minimal surfaces. In this result, we choose fixed boundary which means that the boundary line tension coefficient g in the energy:
should be taken as the coupling energy between the membrane and boundary.

12. Other one-side soap films Question: are there one-side cell membranes?
For one-side surface, we don’t know H is positive or not, because the
normal vector n can not be defined. But we should note that H 2 is assured.
Thus we think that we can use Surface Evolver to minimize the energy: ∫H2ds to
find solutions for shape equations of open vesicle.

13. 2. Inside cell adhesion Ghoroghchian, et al, PNAS, 102 2922 (2005)
The outer cell adhesion, inner cell adhesion.
Ghoroghchian, et al, PNAS, (2005)

14. 2.1 The model ( planar case)
Energy functional

15. Lagrange equations
Boundary conditions

16. 2.2 Typical results ( P=0) a c b
From figure a to e, we choose different h, which the ratio of the length of inner shape and outer shape.
Question: what these shapes
look like? d e

17. 2.3 Egg shape There are 5 layers of membranes in each egg.
The inner shell membrane adherers on the egg white and the outer shell membrane adherers on the shell. In most cases, the inner shell membrane and outer shell membrane adherer together. But at the air cell, there is no adhesion.
We should note that the formation the shell membranes are before the formation of shell, because that we need calcium to deposit on the outer shell membrane to form shell.

18. We guess that the shape of the egg is relate to the adhesion of the inner and outer shell membranes. We are trying to find the relation.

19. Acknowledgements Recommendation
I only have a master degree and have 10 papers about biophysics. If any oversea professor is interested in my work and need a good worker and PHD student, please contact me. I am not the most clever boy, but I am sure l can be the most diligent boy.
Acknowledgements
Thanks to the organizers of this program and especially to professors Ou-Yang, Tu and Zhang.