A multiscale and multidisciplinary approach to curvature modulated sorting in biological membranes

Connecting different theoretical approaches, curvature modulated sorting in lipid bilayers fixed on non-planar surfaces is investigated. First, we present a continuous model of lateral membrane dynamics, described by a nonlinear PDE of 4th order. We then prove the existence and uniqueness of solutions of the presented model and simulate membrane dynamics using a finite element approach. Adopting a truly multiscale approach, we use dissipative particle dynamics (DPD) to parameterize the continuous model, i.e. to derive a corresponding macroscopic model. Our model predicts that curvature modulated sorting can occur if lipids or proteins differ in at least one of their macroscopic elastic moduli: gradients in each modulus, the spontaneous curvature, the bending rigidity or the Gaussian rigidity create characteristical curvature dependent patterns. The structure and dynamics of these membrane patterns is investigated qualitatively and quantitatively. Simulations show that relevant time scales decrease exponentially with the difference in each of the elastic moduli. Furthermore, our results suggest that the Gaussian rigidity plays an equivalent role in lateral sorting as the other two moduli, which are well known to influence lateral sorting. In addition, we find that the use of upscaled models compared with common linear approximations can trap the system in different local minimum patterns. That emphasizes the importance of realistic dynamics and parameters in mathematical modeling of biological membranes.