Lipid bilayers and interfaces

In biological systems lipid bilayers are subject to many different interactions with other entities. These can range from proteins that are attached to the hydrophilic region of the bilayer or transmembrane proteins that interact with the hydrophobic region of the lipid bilayer. Interaction between two membranes is also very common. To gain more insight into the thermodynamic, structural and mechanical consequences we experimentally and theoretically investigated the interactions of a lipid bilayer with various types of interfaces. More specifically, we have analysed the transmembrane protein-lipid interaction by a computational self-consistent field method and have studied the adhesion of vesicles onto gold experimentally. Some aspects of the latter problem were also analysed theoretically.   There exists a computationally inexpensive, yet qualitatively accurate and realistic method to molecularly model the bilayer membrane in the presence of surfaces, namely the self-consistent field theory. This approach makes use of a large number of approximations. Important ones are: the discretisation of space by using a lattice, the non-self-avoidance of chains implying freely jointed chains and the replacement of binary interactions by an external potential leading to the (local) mean field ansatz.  When a transmembrane hydrophobic inclusion is present in the lipid membrane the bilayer around it is disturbed. The structural perturbation of the lipid bilayer around these inclusions have an exponentially decaying wave-like appearance. There are many factors that influence this. The most important ones are the shape of the inclusion, the hydrophobic length of the inclusion, the local interaction between the inclusion and the bilayer, the hydrophobic bilayer thickness and the mechanical characteristics of the lipid bilayer. At distances larger than the bilayer thickness the wavelength and the decaylength of this exponentially decaying wave are exclusively determined by the  mechanical and structural properties of the bilayer. This means that the wavelength and the decaylength can be described by the thickness, the bending modulus and the area compression-expansion modulus of the bilayer. The amplitude and the offset of the perturbation are on the other hand set by the properties of the inclusion. Indeed, the hydrophobic length mismatch, i.e., the difference between the hydrophobic length of the inclusion and the hydrophobic thickness of the lipid bilayer, and the contact interaction between the inclusion and the lipid bilayer are the key variables.   The free energy of insertion is mainly determined by the contact interaction energy between the inclusion and the lipid bilayer and it shows a parabolic dependence on the hydrophobic length mismatch. The free energy of insertion is minimal at a hydrophobic length mismatch where the bilayer perturbations are minimal. We argued that there is a subtle interplay between the entropy loss of the lipid tails adjacent to the surface and the contact interaction between the inclusion and the lipid tails.   Important for the  biological performance, we found that overlap of the perturbed regions of the bilayer around two or more inclusions can cause attractive or repulsive interaction between such inclusions depending on the distance between them. This non-monotonic interaction force with the distance between inclusions, is directely linked to the non-monotonic structural perturbations mentioned already. This lipid mediated free energy of interaction between the inclusions can be divided into three different regimes each with their own length scale. These are the short-range segmental, the intermediate-range conformational and the long-range elastic contributions. The short-range contribution is only present when one or two lipids are in between the inclusions. This interaction depends strongly on the Flory-Huggins interaction between the inclusion and the lipid tails. The intermediate-range contribution is present at separations on the length scale of approximately the bilayer thickness. This interaction shows an exponentially decaying dependence on the separation between these inclusions and is a consequence of the confinement of the lipid tails in between these inclusions. The long-range contribution is determined by the elastic properties of the bilayer and has an exponentially decaying wave-like appearance, with a wavelength that is the same as the perturbation wave length of the bilayer.   Our SCF analysis complements available simulations on the one hand and mesoscopic models on the other. Moreover, they may help to analyse experiments and explain observations in biomembranes.    In the second part of this thesis we examined the adhesion of negatively charged DOPG vesicles and zwitterionic DOPC vesicles to a gold surface using quartz crystal microbalance and surface plasmon resonance techniques. Gold has a hydrophilic surface where lipid vesicles adsorb intact. When the vesicle radius was above approximately $40$ nm the DOPC vesicles completely cover the surface, whereas below this radius the surface coverage decreases with decreasing vesicles size. When spherical vesicles adsorb onto a surface they deform. The shape deformation of the adsorbed vesicles increases with increasing vesicles size. The diminished deformation for the smaller vesicles results in a relatively small interaction area between the vesicles and the gold surface resulting in less lipid-surface interactions. Self-consistent field model calculations on a single vesicle are in line with these experimental results. The calculations showed that the relative deformation of the vesicles has a linear dependence on the vesicles radius. They furthermore showed that below a certain minimal vesicle radius the deformation is completely absent resulting in a lipid-surface interaction energy that vanishes.    Self-consistent field calculations further indicate that the lipid-surface interaction can be divided into three different regimes. In the weak interaction regime the adhesion of the vesicles is not accompanied by drastic changes in the bilayer structure and the vesicle is deformed elastically. In this case the adhesion of the vesicles is energetically favourable over the adhesion of an equally sized bilayer patch. The adhesion of lipid vesicles to the gold surface can most likely be categorised in this regime. In the second intermediate interaction regime the adsorbed vesicles are energetically unfavourable compared to equally sized bilayer patches. The deformation of these vesicles remain in the elastic regime and therefore they do not transform into an adsorbed lipid bilayer patch. In the strong interaction regime the adsorption of the vesicles is strongly energetically unfavourable compared to equally sized bilayer patches and this interaction is so strong that local molecular rearrangements take place to increase the bilayer curvature. This results in adsorbed vesicles that are very susceptible to fusion and/or rupture. An interesting prediction is that the adsorption energy of a vesicle does not depend on the bilayer rigidity. This means that the adsorption energy is a constant, and fixed by the interaction energy between the lipid molecules and the surface. At the same time the deformations of the vesicles increase with diminishing rigidity, which means that although the interaction is the same, the vesicles with different rigidity can be present in different interaction regimes.    As already mentioned, lipid vesicles adsorb intact onto a gold surface. However, on many other surfaces lipid vesicles transform after adsorption into a supported lipid bilayer. We studied the importance of electrostatic interactions for the adhesion strength of DOPC and DOPG vesicles to a gold surface. This was done by varying the pH, the ionic strength and an externally applied electrostatic potential. Varying the pH of the solution has an effect on the protonation of the oxide groups present at the gold surface. As a consequence the surface charge ranges from a positive charge below pH$=5$ to negative charge above pH$=5$. In the case of negatively charged DOPG vesicles, we showed that there is a relation between the adsorbed amount and the pH. The adsorbed amount was larger at low pH compared to high pH and remained approximately constant in the pH range $6-10$. There is still some adsorption in this pH range, from which it can be concluded that besides the electrostatic interaction also other interactions, such as the van der Waals or other chemical interactions, play a role.   The ionic strength has a rather strong influence on the adhesion of DOPG vesicles, while the adsorbed amount of DOPC vesicles remains approximately constant. Both experiments and self-consistent field modelling showed that the adsorbed amount decreases with decreasing ionic strength. This relation can be attributed to the fact that the headgroup density of the DOPG vesicle decreases with decreasing ionic strength, which results in less favourable non-electrostatic lipid-surface interactions.   The externally applied potential had no effect on the adsorption DOPG vesicles. This can be attributed to the fact that externally applied potential can only be varied over a limited range, because otherwise redox reactions reaction at the gold surface start to play a role. This means that the surface potential range is too small to influence the interaction energy of the DOPG and the DOPC bilayer. With self-consistent field modelling it was shown that if redox reaction did not occur and the externally applied potential could be varied over a larger range, the interaction energy between the lipid bilayer and the gold surface could be divided into four different regimes. These regimes vary from weakly attractive to strongly attractive.   It can be concluded that the adhesion of DOPG vesicles onto gold is parly determined by electrostatic interactions. Because the vesicles are weakly bound to the gold surface, the electrostatic interaction can influence the adsorption of intact vesicles. However they are never strong enough to induce transition of the adsorbed vesicles to a flat supported bilayer. In the case of DOPC vesicles the electrostatic interactions have a negligible effect   The organisation of proteins in lipid membranes is identified as one of the central issues in molecular biology. We have tried to unravel the role of the lipid matrix in the protein insertion problem. Our results may be important, for example in the case of transmembrane proteins with multiple transmembrane $\\alpha$-helices, because the short-range lipid-mediated interactions of these transmembrane helices can directly influence the quaternary structure of these proteins. Besides generic issues discussed in the present thesis there are numerous molecular specific aspects. These problems will undoubtelly attract many scientific activities in the years to come. Lipid vesicles at surfaces attracted a lot of attention in the last ten years. Vesicles adhesion is used frequently to generate supported lipid bilayers. Such interfacial layers gives the opportunity to study the properties and interactions of these lipid bilayers and use these layers in biotechnological applications. We tried to unravel some details of the interactions of lipid layers with a gold surface. Our results may be used to understand why in some cases supported bilayers are formed while in other vesicles stay intact at the surface. Understanding this will give us the opportunity to control the fusion of lipid vesicles on a surface. Fusion of vesicles in a plane is also an issue in biological processes such as the formation of the cell plate in plant cell division.