Determination of Line Tension in Lipid Monolayers by Fourier Analysis of Capillary Waves

Abstract

In the past decade, intense interest has focused on the phase separation and lateral organization of two-dimensional lipid systems. In this manuscript, we describe a method for extracting the interfacial line tension between coexisting monolayer phases through direct observations of thermal fluctuations using fluorescence microscopy and digital image processing. We demonstrate that the interfacial line tension calculated from the capillary wave spectrum is in good agreement with previous measurements employed using other experimental techniques. A distinct advantage of this method is that line tensions can be extracted directly from acquired images. In addition, small line tensions are measured, enabling characterization of phase separated membranes near critical points. Future applications of this method are briefly discussed.

Relating domain size distribution to line tension and molecular dipole density in model cytoplasmic myelin lipid monolayers

“…1.4 pC∕m, which corresponds to 0.85-0.45 D∕nm 2 ; this is consistent with the size distribution growing more polydisperse and shifting to larger mean domain sizes with increasing surface pressure. This trend of decreasing line tension and dipole density difference with surface pressure is consistent with previous measurements for binary dimyristoylphophatidylcholine (DMPC)-cholesterol (CHOL) monolayers, particularly when a miscibility transition is approached (5,(16)(17)(18). However, while the measured dipole density difference for the control CYT monolayers is in the same range as the simple DMPC-CHOL mixtures (18,35), the line tensions we find are about two orders of magnitude less than for the binary mixtures, which range from (100-1,000 fN).…”

“…The size and lifetime of rafts depends on the energy costs of forming phase-separated lipid domains, and hence on the line tension, λ, and dipole density difference, Δm. To date, λ and Δm have been measured for a limited number of monolayer compositions by analyzing the relaxation of deformed, individual domains (16) and by analysis of the fluctuations of the domain boundaries of individual large domains (14,17,18). Here we present a unique way of measuring λ and Δm from the entire distribution of domain sizes in lipid monolayers assuming this distribution is at equilibrium (or at least metastable equilibrium).…”

Dynamics of thermally driven capillary waves for two-dimensional droplets

“…70 It would therefore be interesting to study the dynamics of thermally driven capillary waves in these lipid systems. 33,69 However, it remains to be seen if the continuum approaches are still valid 19,20 for domains of smaller dimensions, as well as in dynamical measurements. A rough estimate using Ӎ 0.5 pN, surface viscosity of =5 ϫ 10 −7 Ns/ m, 72 and Eq.…”

“…With advancements in experimental techniques such as fluorescence microscopy and imaging, researchers also started to study thermally driven capillary waves in biological systems, such as phase separated biopolymer solutions, 31 and quasi-two-dimensional systems such as lipid bilayer membranes and monolayers at the airwater interface. [32][33][34] In this paper, we use the linearized Navier-Stokes equation for an incompressible fluid to obtain a quantitative description of the interfacial roughness of a binary droplet system. Using linear response, we derive the dispersion relation.…”

Cell-Sized Liposomes and Droplets: Real-World Modeling of Living Cells

“…We found that the discs showed a marked difference in membrane edge fluctuation between isomers; fluctuation of the trans -membrane edge was greater than that of the cis -membrane edge. The relationship between the Fourier coefficients and wave number and line tension is given by $false\langle a_k^{2}false\rangle +false\langle b_k^{2}false\rangle =\frac{2k_{B}T}{\pi r_0\gamma }\frac{1}{k^2-1}$ , where a k and b k are the Fourier coefficients, k B is the Boltzmann constant and T is the absolute temperature [47]. The analysis of the membrane edge fluctuation revealed that the line tension of trans -membranes ( γ trans = 5.0 ± 2.2 × 10 −2 pN) was smaller than that of cis -membranes ( γ cis = 1.5 ± 0.4 × 10 −1 pN).…”