Quasi-spherical vesicle

Henriksen, J.R., and Ipsen, J.H. (2002) Thermal undulations of quasi-spherical vesicles stabilized by gravity. European Physical Journal E, 9 (4), 365-374. 

Equilibrium dynamics of vesicles comprises the dynamical fluctuations around locally stable mean shapes. Quantitatively, such fluctuations have been studied for quasi-spherical vesicles [29,61] and for prolate shapes in the vicinity of the budding transition [33]. A nontrivial example of dynamical equilibrium fluctuations has been observed at the prolate-oblate transition [62]. As the activation energy between the two locally stable shapes is just a few k T, occasionally thermal fluctuations are large enough to drive the vesicle into the other minimum. This system thus constitutes one of the few examples showing a thermally induced macroscopic bistability. 

The generalized K-S model is designed to capture the vesicle flow behavior for non-spherical shapes sufficiently far from a sphere. For quasi-spherical vesicles, a derivation of the equations of motion by a systematic expansion in the undulation amplitudes gives quantitatively more reliable results. An expansion to third order results in a phase diagram [200, 201], which agrees very well with Fig. 28. 

Schneider, M.B., Jenkins, J.T., and Webb. W.W. (1984) Thermal fluctuations of large quasi-spherical bimolecular phospholipid-vesicles. Journal of Physics, 45 (9), 1457-1472. 

The form of the stochastic equations (105) and (106) is motivated by the following considerations. The first term in (105), dF/da, is the thermodynamic force due to bending energy and volume constraints it is calculated from the free energy F a). The second term of (105) is the deformation force due to the shear flow. Since the hydrodynamic forces elongate the vesicle for 0 < 0 < r/2 but push to reduce the elongation for - r/2 < 0 < 0, the flow forces should be proportional to sin(20) to leading order. The amplitude A is assumed to be independent of the asphericity a. C,a and A can be estimated [205] from the results of a perturbation theory [199] in the quasi-spherical limit. Equation (106) is adapted from KeUer-Skalak theory. While B is a constant in KeUer-Skalak theory, it is now a function of the (time-dependent) asphericity a in (106). 

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