In-Plane Membrane Ordering and Topological Defects

Intrinsic properties of biological membrane constituents dominantly influence the shape of biological membranes and consequently their functionality. This impact is in particular pronounced if anin-plane membrane order is present. In such cases topological defects (TDs) inevitable appear if membranes' topology is different from the toroidal one. TDs give rise to spatial non homogeneities which might trigger various functional responses in membranes, such as membrane fission, tabulation and vesiculation. In the paper we describe minimal continuum-type models which consider in-plane ordering within membranes focusing on TDs. We consider cases with nematic-type orientational (quadrupolar) ordering. We first present the Deviatoric Curvature (DC) model and the Minimal Extrinsic Curvature (MEC) model, respectively. The DC model demonstrates that the deviatoric curvature plays similar role as an external ordering field. Using the MEC model we show that membrane structures possess TDs which obey classical topological theorems. Finally, we present the Landau-type modelling which is particularly adequate in studies focusing on impacts of TDs