ABSTRACT
One of the important problems which can be treated in a nonlinear thermodynamics perspective is the relation between structure and function of membranes (biological membranes or reconstituted lipid membranes). In this paper, we will address the process of bioadhesion (adhesion of two cells/vesicles or adhesion of a cell/vesicle to a substratum). The structure of the membrane affects the ability of the membrane to deform and to be fixed to some other cell or to some substratum. This structure is highly heterogeneous, composed usually of a fluid lipidic bilayer where proteins are inserted. The possibility of the appearance of organized behavior
(dissipative structures) in such systems has recently received attention. Indeed, in the thin aqueous layer (100-1000 A) between the cells or between cell and substratum, long-range molecular forces due to van der Waals attraction usually compete with the presence of repulsive forces of different origins (electrical, hydration or steric) and lead to the formation of a new stable stationary state (spatially periodic pattern). These patterns are observed in cell/cell or cell/solid support interactions (periodic contacts of the order of 1 jum), or also in lipid vesicles of different composition adhering to a solid. The appearance of those patterns can be explained by an interfacial instability theory. Based on the asymptotic procedure of reduction of the full set of governing (Navier-Stokes) equations and boundary conditions, the dynamics of the aqueous layer is well described by a set of nonlinear evolution equations (NEE). Specific interactions (present for instance in bioadhesion by lock-and-key molecules) can also be included in the dynamical formalism by considering a chemical reaction between receptors (on the membrane) and sites (on a solid substratum). The method proposed here is composed of three different steps: a linear stability analysis to identify thresholds for constraints, a bifurcation calculus to predict the onset of new patterns near critical points, and numerical simulations to describe the full nonlinear dynamics. At each step, comparison with experimental data confirms the validity of the nonlinear thermodynamics approach to analyze the appearance and the dynamics of bioadhesion in a number of different situations.
