Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation

Pages: 537 - 548, Volume 4, Issue 3, September 2005

doi:10.3934/cpaa.2005.4.537       Abstract        Full Text (1560.4K)

Qiang Du - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA, United States (email)
Chun Liu - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)
R. Ryham - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)
X. Wang - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: In this paper, we study the effects of the spontaneous curvature on the static deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Generalizing the phase field models developed in our previous works, we deduce a new energy formula involving the spontaneous curvature effects. Several axis-symmetric configurations are obtained through numerical simulations. Some analysis on the effects of the spontaneous curvature on the vesicle membrane shapes are also provided.

Keywords:  Phase field, elastic bending energy, cell embrane, spontaneous curvature, numerical simulation, solution branches.
Mathematics Subject Classification:  49Q10, 92B05, 74K15.

Received: November 2004;      Revised: April 2005;      Published: June 2005.