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Vesicles are globular structures. For example, in solution micelles can be assembled from some chain amphiphiles that have the head groups all pointing to solution and the hydrocarbon tails inside. In hydrophobic environment such as oil, inverted micelles can be formed: The head groups prefer to stay inside whereas the tails prefer to be exposed to the medium. We propose here a very simple vesicle model. We do not attempt to model the medium-head group and -tail interactions explicitly. We use a united-atom simplification to model the chain amphiphiles, which means that an "atom" in a chain should be viewed as a group of atoms instead of just a single atom. The interactions of the head group with solvent water molecules are not explicitly modeled. In order to mimic these complicated hydrolation interactions that actually causes the formation of the structure, the head groups are restrained by harmonical potentials between them (an approach similar to van der Plog and Berendsen's pioneering work). The emphasis is on the inter-amphiphilic interactions and its role on stablizing the globular structure, i.e. the architectual mechanics for the micelle structure. Perhaps the most interesting feature of our idealized model is a striking dynamical behavior that such a structure exhibits when no stochastic factors are introduced to the dynamics. (Note: This is, of course, unrealistic because micelles always collide with solvent atoms randomly, however, the dynamical behavior of a system in the absence of thermal noise, which is sometimes called intrinsic vibrational modes by theoreticians, is believed to be more important than stochastic perturbations in determining the thermodynamical activities of a structure.)
In the above model, the kinetic energy and velocity distribution at different times will be shown on the fly when you run the model as it is. Since the structure is axisymmetric and the velocities of all the atoms were set to zero at the beginning, the time evolution of this distribution is axisymmetric. One can observe that sometimes the velocities of atoms at the same radial distance to the center all become tangential, while velocity vectors at different circles point to opposite tangential directions, suggesting the existence of a collective twisting mode. On the other hand, the cases that all the velocity vectors are normal to the surface correspond to the axial stretching mode (one of the breathing modes). You can toggle the force distribution on, too. As is the velocity vector distribution, the force distribution is axisymmetric. You will observe that sometimes there is a contraction tendency of the radial distance between the two outermost layers of the vesicles, sometimes the forces want to whirl the vesicles around -- the resultant forces acting on the two outermost layers become tangential.
As usual, you can change the van der Waals parameters of the atoms to see what happens. You will find that chains consisting of much smaller atoms cannot form a globular structure of the present size, whereas stronger repulsions caused by increasing the van der Waals radii of the chain atoms result in an enlargement of the innermost circle. This is because the inter-chain repulsive forces want to disintegrate the vesicles, but the inter-chain attractive forces want to put them together, so the result of the compromise between attractions and repulsions is an increment of micelle size, as a response to the increasing of chain atom sizes. If the repulsions become great enough, such that the medium-head group and -tail interactions cannot compete with them, the micelle will be disrupted. Theoretically, one can study the relationship of stability of micelles with temperature (the thermal expansion or the susceptibility to thermal effects), the van der Waals radii (or equivalently, the number of monomers), and the length of the chains (one can conjecture that if the chains are too long, spherical micelles cannot form, though they might form nonspherical micelles). Interestingly, when solvent molecules are explicitly present, the head groups will form with water molecules a thin hydration layer, in which some of them may penetrate a little bit into the hydrophobic tail region. We can imagine that it is this hydration layer that cements the architecture of micelles from the outside. P. van der Plog and H. J. C. Berendsen, Molecular dynamics simulation of a bilayer membrane, Journal of Chemical Physics Vol. 76, P. 3271, 1982
Lipid molecules have polar head groups with zero net charges. In a non-polar solvent, the head groups will seek to stay together so as to minimize the electrostatic potential energy, forming spheres.
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