Modeling multicomponent reactive membranes

Using analytical calculations and computer simulations, we study binary AB and ternary ABC membranes that respond to an external stimulus by interconverting A and B components. The C component is assumed to be nonreactive and is incompatible with both A and B. We also assume that A and B have different spontaneous curvatures. The dynamics of the ternary system is described in terms of three order parameters: two specify the local composition and a third characterizes the local height of the membrane. Our description of the two-component membrane is based on a recent model proposed by Reigada [Phys. Rev. E. 72, 051921 (2005)]; we extend the latter approach by explicitly including the effects of the membrane's surface tension on the phase behavior of the system. By performing a linear stability analysis, we determine the behavior of the reactive AB membrane for a given bending elasticity and surface tension at different values of the reaction rate coefficients. We also numerically integrate the governing dynamic equations, and the results of these simulations are in agreement with the analytical predictions. For the two-component membranes, we calculate two critical values of the reaction rate coefficients, which define the behavior of the system, and plot the phase diagrams in terms of different parameters. We illustrate that the surface tension of the membrane strongly affects these critical values of the reaction rate coefficients and therefore the location of the phase boundaries. We also pinpoint the regions on the phase diagram where the late-time behavior is affected by the initial fluctuations, i.e., where such a reactive system has some "memory" of its prior state. In the case of the three-component system, we show that the presence of the nonreactive C component strongly affects the composition and topology of the membrane, as well as critically altering the propagation of the traveling waves within the system.