INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Int. J. Numer. Meth. Biomed. Engng. 2012; 28:346–368 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.2475 Axisymmetric multicomponent vesicles: A comparison of hydrodynamic and geometric models Jinsun Sohn 1, * ,† , Shuwang Li 2 , Xiaofan Li 2 and John S. Lowengrub 3 1 Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, USA 2 Department of Applied Mathematics, Illinois Institute of Technology, 10 W. 32nd St., Chicago, IL 60616, USA 3 Department of Mathematics, University of California, Irvine, Irvine, CA, USA SUMMARY Using a mathematical model, we investigate the role of hydrodynamic forces on three-dimensional axisym- metric multicomponent vesicles. The equations are derived using an energy variation approach that accounts for different surface phases, the excess energy associated with surface domain boundaries, bending energy and inextensibility. The equations are high-order (fourth order) nonlinear and nonlocal. To solve the equations numerically, we use a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. We also derive equations governing the dynamics of inextensible vesicles evolving in the absence of hydrodynamic forces and simulate numerically the evolution of this geometric model. We find that compared with the geometric model, hydrodynamic forces provide additional paths for relaxing inextensible vesicles. The presence of hydrodynamic forces may enable the dynamics to overcome local energy barriers and reach lower energy states than those accessible by geometric motion or energy minimization algorithms. Because of the intimate connection between morphology, surface phase distribu- tion and biological function, these results have important consequences in understanding the role vesicles play in biological processes. Copyright © 2012 John Wiley & Sons, Ltd. Received 10 August 2011; Revised 21 December 2011; Accepted 24 January 2012 KEY WORDS: multicomponent vesicle; line tension; bending stiffness; inextensibility; boundary integral method; small scale decomposition; stokes flow; geometric and hydrodynamic model 1. INTRODUCTION Biological membranes are well-known for their critical role in cell functions, and thus have been the subject of many studies. Recent experiments on giant unilamellar vesicles demonstrate that there exists a rich variety of behavior of multicomponent vesicles. Spinodal decomposition into distinct surface domains (e.g., liquid-ordered, liquid-disordered) known as rafts (or domains), raft coarsening, viscous fingering, vesicle budding, fission and fusion are all observed with concomi- tant changes in membrane morphology [1–11]. Membrane heterogeneity and the formation of rafts is thought to play an important role in many biological processes such as vesicle tracking [12] and signal transduction [13], adhesion [14, 15], protein targeting and regulation [16], bud- ding, endocytosis and exocytosis [17]. Rafts have also been implicated with diseases including Alzheimer’s and Parkinson’s diseases [18], as well as infection by bacteria and viruses [19, 20]. In addition, multicomponent vesicles have also been proposed as efficient vehicles for targeted drug delivery [21]. *Correspondence to: Jinsun Sohn, Department of Mathematics, Biomedical Engineering, Chemical Engineering and Material Science, University of California, Irvine, CA, USA. † E-mail: jinsunks@math.ucla.edu Copyright © 2012 John Wiley & Sons, Ltd.