Advanced Flicker Spectroscopy of Fluid Membranes
Hans-Günther Döbereiner,Gerhard Gompper,Christopher K. Haluska,D. M. Kroll,Peter G. Petrov,Karin A. Riske +5 more
TL;DR: This work presents a new method, advanced flicker spectroscopy of giant nonspherical vesicles, which makes it possible to simultaneously measure both parameters for the first time, and makes it Possible to easily characterize membrane curvature as a function of environmental conditions.
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Abstract: The bending elasticity of a fluid membrane is characterized by its modulus and spontaneous curvature. We present a new method, advanced flicker spectroscopy of giant nonspherical vesicles, which makes it possible to simultaneously measure both parameters for the first time. Our analysis is based on the generation of a large set of reference data from Monte Carlo simulations of randomly triangulated surfaces. As an example of the potential of the procedure, we monitor thermal trajectories of vesicle shapes and discuss the elastic response of zwitterionic membranes to transmembrane pH gradients. Our technique makes it possible to easily characterize membrane curvature as a function of environmental conditions.
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Figures
![FIG. 4. Normalized histograms [ R p a da 1] of the elliptical shape fluctuations of a prolate SOPC vesicle (RA 5:2 m) with varying external pH of 7.7 (open circles), 8.1 (open squares), and 8.5 (open triangles) at constant internal pH 7.7. Gaussian fits are shown. With increasing pH gradient the vesicle develops a more elongated shape (larger a2) with decreasing fluctuations.](/figures/fig-4-normalized-histograms-r-p-a-da-1-of-the-elliptical-1ky54jcg.png)
FIG. 4. Normalized histograms [ R p a da 1] of the elliptical shape fluctuations of a prolate SOPC vesicle (RA 5:2 m) with varying external pH of 7.7 (open circles), 8.1 (open squares), and 8.5 (open triangles) at constant internal pH 7.7. Gaussian fits are shown. With increasing pH gradient the vesicle develops a more elongated shape (larger a2) with decreasing fluctuations. 
FIG. 3. Thermal trajectory of a prolate vesicle in c0; v parameter space with a radius RA 4:8 m and g 0:21. The experimental points correspond to temperatures T 25:0 C, 29:4 C, 34:2 C, and 38:8 C. The crossing points of a linear fit to the trajectory with the upper (budding) and lower spinodal (prolate-oblate transition) are indicated. For the bending modulus we find 35 5 kBT. 
FIG. 2. Simulated mean-square amplitude h a22i of shape fluctuations as a function of the effective spontaneous curvature c0. Note the peak at the prolate-to-oblate transition. Three different values of the reduced volume are shown, as indicated. The other parameters are =kBT 25, 0:90, and g 0:37. 
FIG. 5. Spontaneous curvature c0 as a function of external pH for g 0:8. Note that the reduced volume and bending modulus, which are given in brackets, v; , remain constant. v, c0, and are obtained simultaneously via comparison of the data shown in Fig. 4 to Monte Carlo simulations. 
FIG. 1. Experimental and theoretical vesicle shapes. (A) Phase contrast micrograph (v 0:828). The scale bar corresponds to 5 m, (B) simulation snapshot. The parameters in the simulations are v 0:825, =kBT 25, 0:90, c0
![FIG. 4. Normalized histograms [ R p a da 1] of the elliptical shape fluctuations of a prolate SOPC vesicle (RA 5:2 m) with varying external pH of 7.7 (open circles), 8.1 (open squares), and 8.5 (open triangles) at constant internal pH 7.7. Gaussian fits are shown. With increasing pH gradient the vesicle develops a more elongated shape (larger a2) with decreasing fluctuations.](/figures/fig-4-normalized-histograms-r-p-a-da-1-of-the-elliptical-1ky54jcg.webp)
Citations
Thermodynamics of membrane elasticity--a molecular level approach to one- and two-component fluid amphiphilic membranes, part II: applications.
TL;DR: It is found that the bending modulus of mean curvature becomes negative for two-component membranes approaching the limit of phase separation at constant chemical potentials.
5
Surface tension and Laplace pressure in triangulated surface models for membranes without fixed boundary
TL;DR: In this paper, a Monte Carlo (MC) study is performed to evaluate the surface tension of spherical membranes that may be regarded as the models of the lipid layers, and the authors use the canonical surface model defined on the self-avoiding triangulated lattices.
5
•Posted Content
Surface tension and Laplace pressure in triangulated surface models for membranes without fixed boundary
TL;DR: In this paper, a Monte Carlo (MC) study is performed to evaluate the surface tension of spherical membranes that may be regarded as the models of the lipid layers, and the authors find reasonable consistency between surface tension and frame tension in the region of sufficiently large bending rigidity or sufficiently large $A/N$.
4
Dependence of the surface tension on the shape of surface boundary
TL;DR: In this paper, the surface tension of membranes is calculated by means of the Monte Carlo simulation technique on two types of cylinders made of rubans of size L 1 and L 2, where the rubans are the same for the projected area and different in the ratio L 1 / L 2.
2
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TL;DR: In this article, the authors describe the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations, and the preferred shapes arise from a competition between curvature energy which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect.
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Evan Evans,W. Rawicz +1 more
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