Simple differences in the protein-membrane attachment mechanism have functional consequences for surface mechanics.

This paper describes two methods for propagating coupled membrane and embedded particle dynamics with ensembles that are valid to second order in the deformation of the membrane. Proteins and functional lipids associate with cellular membranes, and their attachments influence membrane physical and dynamical properties. Therefore, it is necessary to accurately model the coupled dynamics of the membrane and any associated material of interest. We have developed two methods for coupling membrane and particle dynamics that differ in the binding mechanism of the particle to the surface. The "on-surface" mechanism should be used for particles that slide along the membrane; this description leads to an effective reduction in the membrane surface tension. The "in-surface" mechanism treats the particles as tightly bound to the lipidic binding sites; the method avoids double counting lateral entropy of implicitly modeled lipids. We emphasize the differences between these two mechanisms, when it is appropriate to use them, and how the methods differ from previously used dynamic methods.