Recepción de Mercaderías

Concomitantly the overlap of a solid sphere with radiusRa is given by:

ξsphere ≈ εex 2εex+εp 3 2 λr Ra 2 1−λr/_Ra+e− 2Ra λr (1 +λr/_Ra) . (3.5)

Notably, the quantity Vpξsphere grows with R3a for Ra λr and is proportional to

Ra for Ra λr. This is in contradicts the relation published in reference [37],

where the overlap is found to be proportional to Raexp(−2Ra/λr).1 Moreover, it

is interesting to note that the curvature (e.g. described by the dependency on Ra)

was not taken into account by the authors of reference [43], which is reflected by the straight trend line in Figure B.2 (cf. appendix B), i.e., when going to smaller particle radii.

Using this geometric factor, the maximum frequency shift for a particle is easily estimated using the relation

∆νmax=1/2ξ δε (Vp/Vs) ν0. (3.6)

Most of the data that are presented in this thesis were taken with a resonator with major radius Rmajor= 32.72µm and minor radius Rminor = 3.85µm. We obtain the

mode intensity distribution from Comsol simulations and find that the evanescent intensity distribution of the TM00 mode can be parametrized by a Gaussian with full width half maximum of σF W HM = 1.44µm in latitudinal direction and by an

exponential decay ∼ exp (·/λr) with λr = 84 nm in radial direction. Then typical

values ofξfor a solid spheres in water with radii ofRa= 25 nm andRa = 50 nm and

a refractive index ofnSOPC= 1.46 are ξsphere = 0.24 andξsphere = 0.18, respectively.

For a vesicle with the same properties and a wall thickness of 4 nm values ofξvesicle =

0.30 and ξvesicle = 0.21 are found. We note that the evanescent field of a frequency

split mode exhibits an intensity modulation along the azimuthal direction which is modeled by the factorE(r)¯

2 split ∝2 cos 2_(y·M mode/Ra)× E(r)¯ 2

non−split. The factor

×2 accounts for a peak evanescent intensity that is twice as large compared to the one of the non-split mode. Likewise the maximum signal and thus the sensitivity of a split mode is two times larger. However differences in the frequency shift distribution arise from a changed intensity profile, which will be discussed in section 3.3.

3.2. Properties of lipid bilayers and lipid vesicles

In this section, a short overview on the properties of lipid bilayers and lipid vesicles is given, to motivate both, the lipid membrane functionalization method and the use of small unilamellar lipid vesicles as test bodies for the sensor. We provide examples of biological processes and applications that disclose the abundance ofthings going on on the length and time scale that is now accessible with our sensor.

The term lipid describes a vast class of biomolecules that is best characterized by a symptomatic insolubility in water. At the root of this macroscopic behavior lies

1_{The authors introduce the decay lengthLwhich is approximately equal toλ}

46 3. Measuring the adsorption of single lipid vesicles

a common hydrocarbon chain that repels polar solvents. A particular important category of lipids are phospholipids that consist of a polar head group, such as choline, and two fatty acid tails.

Phospholipids are ubiquitous in nature and represent an integral component of biomembranes. When suspended in water, due to their amphiphilic nature, they spontaneously arrange in stable bilayer sheaths, with the polar heads pointing to- wards the outside [114]. These lipid bilayers can form spheroidal superstructures that were first reported by Alec Bangham in 1964 [115] and that were later termed liposomes by Gerald Weissman [116], which are – by definition – artificially created vesicles that consist of one or more lipid bilayers [117]. The more general expres- sion “lipid vesicle” therefore includes liposomes and both term are used equivalently here. Liposomes exist in different forms and sizes and they are accordingly referred to as, e.g., small unilamellar vesicles (SUV) with a size inferior to 1µm and a shell consisting of a single lipid bilayer. Other frequently used terms comprise large mul- tilamellar vesicles (LMV) on the lower µm scale and giant uni- or multilamellar vesicles (GUV and GMV) with diameters up to 200µm.

Lipid bilayers form the plasma membrane of a cell, together with embed- ded membrane proteins and glycolipids. The cell membrane constitutes the barrier that separates the cell from its environment and it is supported by the cytosceleton. As such it is responsible for the regulation of cell transport, which can roughly be divided into three pathways. (i) Small molecules, i.e. gas molecules in solution, can diffuse through the cell wall. (ii) Secondly, membrane channels actively con- trols the passage of specific ions and small molecules. The state of the channel (open or closed) can hereby depend on a variety of parameters, i.e. the transmem- brane electric potential or the presence of messenger molecules. (iii) Lastly, proteins, hormones, and other mid-size molecules are transported via vesicle exo- and endocy- tosis. Both are complex processes that involve a considerable number of membrane proteins and that are of particular interest here, because they fall well within the sensitivity range of our sensor.

Exocytosis describes a secretion process where molecules, such as neurotransmitters (that are engulfed in innercellular liposomes) are released from the cell to the ex- tra cellular environment. Briefly the vesicle is transported to its engagement site (trafficking), e.g. along the axon towards the synaptic gap. There it loosely binds (tethering) until a messenger initiates the docking process, followed by vesicle fusion with the cell membrane, where the cargo is released [118]. The process involves a variety of membrane proteins and is subject to ongoing research [119]. For example different pathways of vesicle fusion have been observed [120], including a process where the liposome fully merges with the membrane to be recycled elsewhere [121], as opposed to an incomplete release, where a fusion pore opens and closes again after partial release of the cargo (kiss-and-run). The reverse process, endocyto- sis, involves the formation of a vesicle from the cell membrane, the uptake of the target, and finally a cleaving process that detaches the newly created transporter from its host. As an example, the former can be initiated by the polymerization of clathrin, which attaches to and curves the membrane to form a negative of the vesicle [122, 123]. However other mechanism of vesicle formation and retrieval have

3.2 Properties of lipid bilayers and lipid vesicles 47

been reported and many details of the processes remain to be solved [120].

Next to their physiological role, the potential of liposomes as model membrane systems was recognized right from their discovery [117, 114]. In many cases bi- ological systems are enormously complex, and researchers turn towards artificial, reduced systems with a limited number of constituents [124]. For example GUVs can be aspired with a micropipette [125], a technique that allows to control and measure membrane tension at the same time and, e.g., study phase transitions of a lipid bilayer. Furthermore, starting from a single GUV, the interaction and func- tioning of isolated molecules can be observed without interfering signals from other physiological processes that one would encounterin vivo. Such a biomimetic system was, for example, established by A. Roux et al. to study the polymerization and hydration dynamics of dynamin and its role in vesicle fission [126, 127]. Small unil- amellar vesicles were recently used to study the interaction of a single virus with a lipid membrane [128].

Intherapeutic applicationsliposomes are used as carrier vessels for drug delivery. Hereby the pharmaceutic agent is enclosed in a unilamellar or multilamellar vesicle before application [129]. Liposomal drug delivery holds several advantages compared to the direct injection of the free drug [130]. First of all the agent is protected against degradation and a circulation time of up to two days has been reported, holding the potential of gradual drug release and avoiding high initial concentrations. Moreover, the lipid material of the vesicle is a priori bio-compatible and does not run the risk of triggering an immunoreaction. Lipoplexes and liposomes for non-viral gene delivery have been extensively studied [131]. Finally, when specific targeting can be achieved [132] using specially designed receptors, the total amount of the drug can be drastically reduced, avoiding side effects and leading to a diminishment of the overall stress on the immunosystem.

For the totality of these reasons, there is plentiful scientific and medical interest in lipid vesicle as drug carriers. In the following we will show that we are able to observe single lipid vesicles with a time resolution in the µs-regime, which is sufficient to resolve the adsorption and spreading dynamics of distinct vesicles. Such sensitivity opens up a broad range of applications and experiments that belong to the class of processes described above.

3.2.1. Preparation of lipid vesicles

A variety of different methods to prepare lipid vesicles has been reported, for exam- ple fast immersion of lipid emulsion in ethanol or sonication of large multilamellar vesicles that are formed by simple hydration of a lipid film. Giant unilamellar vesi- cles with diameters exceeding 100µm are efficiently prepared using electroformation on platinum electrodes [133, 134] or on ITO (indium tin oxide) coated coverslips [91]. Here we focus on the extrusion method, where the lipid is hydrated, and the emulsion is forced through a polycarbonate membrane, whose pore diameter deter- mines the final size of the vesicles. In particular we use the Avanti Mini-Extruder,

48 3. Measuring the adsorption of single lipid vesicles

Placing polycarbonate Polycarbonate membrane _{installed between syringes}

a b

Placing polycarbonate

membrane on spacer installed between syringes

Avanti mini extruder

c

N b f t di l

Number of extruding cycles

100 nm

d

Figure 3.2.: Extrusion of lipid vesicles using the Avanti Mini-Extruder. (a) A lipid emulsion is forced through a polycarbonate membrane with pore size∼100 nm. The picture on the left shows a teflon support with an O-ring. The polycarbonate membrane is placed on the O-ring (right picture) and clamped with a second teflon support. The membrane is wetted during installation, and care is taken to avoid air bubbles. (b) The assembly is mounted and strained in a stainless steel housing. Two gastight syringes (1 ml, Hamilton) are inserted to the channels on either side. The emulsion is then inserted on one side and pushed through the membrane into the

second syringe. For a 100 nm pore size and a 1 mg/ml SOPC emulsion, an initial

force of ∼ 50N is required to sustain a flow of ∼ 10µl/s. (c) With each extruding cycle, the originally dull emulsion clears up. In the photo series, the imprint on the backside of the syringe becomes more and more visible. Typically 11−15 cycles are performed. (d) A cryo electron micrograph of extruded lipid vesicles from reference [137]. The bilayer structure of the lipid membrane manifests in the contrast of the vesicle walls.

shown in Figure 3.2 (b), which allows us to produce lipid vesicles of determinis- tic size, with a relatively narrow size size distribution [114, 135, 136]. Moreover, the process does not require expensive equipment and can readily be adopted in a physics laboratory. In the following paragraph we will give a detailed description of the vesicle preparation process that addresses anyone who aims at repeating the process.

Protocol: Lipid vesicle preparation

The phospholipid 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholinein (SOPC, Avanti Polar Lipids) is dissolved in chloroform to yield a concentration of 20 mg/ml and is stored at −20◦C. Glass vials with a volume of four milliliter and matching lids with PTFE fittings are cleaned using a mixture of 65 parts of chloroform, 25 parts of methanol, and 1 part water. The ingredients of the cleaning solution are mixed and filled into the vials and lids. After ∼ 4 min the solution is disposed and the cleaning cycle is repeated one or two more times. Stirring, shaking, or wiping is not necessary.