Fluctuation-Induced Forces Between Inclusions in a Fluid Membrane Under Tension

Abstract

We develop an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each object's shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.

Lipid Domain Co-localization Induced by Membrane Undulations

“…Thus, membrane undulations also promote co-localization of the softer Ld domains, in agreement with experimental observations (31,32). Such a symmetry is absent when the domains are far apart (17).…”

“…A case in point is the development of membrane undulations at finite temperature, which in turn gives rise to algebraically decaying, fluctuation-induced interactions between membrane inclusions that are more rigid or softer than the background phase (15)(16)(17)(18)(19). Importantly for the present problem, it is well-known that the Lo domains are more rigid than the Ld ones, with a bending rigidity of k Lo $ 2 À 3 k Ld (20,21).…”

“…For completeness, we will discuss separately the cases of non-overlapping and partially overlapping domains; the intermediate-range case, where domain separation is rz2R, will not be discussed, as it is not amenable to explicit analytic treatment. (17). In the presence of a substrate, on the other hand, domain interactions become exponentially small beyond a characteristic domain separation, r à ¼ max½ðs=a 2 Þ 1=2 ; ðk 0 =a 2 Þ 1=4 .…”

Effective field theory approach to fluctuation-induced forces between colloids at an interface

“…This is one of the limits considered in Ref. [19]. These authors restrict to two scatterings, analogously to truncating the cumulant expansion after the second, which is justified by the weakness of the perturbations.…”

“…In fact, usage of scattering approaches for electromagnetic Casimir interactions has a long history and has led to recent developments [15][16][17][18] in the field, concerning analytical results. Very recently, thermal Casimir interactions between biological membrane inclusions were studied in a similar spirit [19].…”