LaCàN Seminar Series in Computational Science and Engineering
Dimitri Kaurin obtained his MS degree in theoretical physics at ENS Cachan and is now a Ph.D candidate at LaCáN research group, under the supervision of Prof. Marino Arroyo. His work focuses mainly on modelling soft adhesions mediated by mobile binders.
We re-examine a classical problem in soft-matter physics: the specific adhesion between deformable elastic objects, such as vesicles, mediated by mobile adhesion molecules. Physically and from a continuum perspective, the system can be understood as a membrane with bending rigidity, subject to a fixed tension by a loading device such as a micropipette, with mobile adhesion molecules. These molecules can diffuse and react by attaching with partners in a neighboring vesicle. The binding kinetics strongly depend on the distance to potential partners in the neighboring membrane. The unbinding kinetics depend on the force experienced by the binders. Moreover, bonds can exhibit different force dependent rates such as catch bonds or slip bonds (1). Such problems are well studied at equilibrium but the dynamics have been barely explored. Following seminal work (2), which identifies possible scenarios governing the dynamics of binding or unbinding, the system is treated as a biphasic problem with a sharp interface delimitating the bound and unbound regions of the vesicle. The force and distance dependent binding/unbinding kinetics are captured by coupling this large-scale model with a smaller-scale model relying on scale separation. We have formalize the problem in the framework of Onsager’s variational principle (3), providing a systematic procedure to generate the governing coupled equations of the problem that capture the interplay between diffusion, reaction and mechanics and we examine this problem with numerical calculations. The emphasis here is made on the binding-unbinding dynamics, the influence of their conformation and the corresponding force-dependence of the unbinding rate of adhesion molecules.
 S. Rakshit, Y. Zhang, K. Manibog, O. Shafraz, and S. Sivasankar, “Ideal, catch, and slip bonds in cadherin adhesion,” Proceedings of the National Academy of Sciences, vol. 109, no. 46, pp. 18815–18820, 2012.
 P.-G. de Gennes, P.-H. Puech, and F. Brochard-Wyart, “Adhesion Induced by Mobile Stickers: A List of Scenar- ios,” Langmuir, vol. 19, pp. 7112–7119, aug 2003.
 M. Doi, “Onsagers variational principle in soft matter,” Journal of Physics: Condensed Matter, vol. 23, no. 28, p. 284118, 2011.