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# Membrane Scattering

Membrane scattering is one of the premier methods of categorizing membranes and membrane components, such as proteins. In order to understand the scattering techniques and their respective usefulness, you must understand the membranes you are studying at a basic level to see if your experimental data agrees with theoretical practice.

## Membrane Structure and Organization

The Phospholipid bilayer is comprised of lipid molecules composed of a polar head group and a fatty acid tail. The lipid molecules arrange themselves into a bilayer where the heads face outwards towards the water and the tails are inside the membrane away from water.

Figure 1 Phospholipid bilayer space-filling model

#### Components

Natural bilayers are usually composed of phospholipids, which have a hydrophilic head and two hydrophobic tails each.

The first region on either side of the bilayer is the hydrophilic head group. [6]The most common lipid head group: Phosphatidylcholine is pictured below in Figure 2

The fatty acid tails come in all shapes and sizes and are categorized by the types of bonding present. Unsaturated fatty acids have double bonds that form kinks in the chain, while saturated fatty acids do not. All of the categories are shown below in Figure 3.

Figure 2: Phosphatidylcholine                                Figure 3: Fatty acid chain categories

#### Formation of Membranes

When phospholipids are exposed to water, they mostly arrange themselves into a two-layered sheet (a bilayer) with all of their tails pointing toward the center of the sheet. They can also form other structures; such as micelles- which are single-layered- or small spherical bilayers called liposomes. Lipid tails can have kinks that cause the tail region to be wider than the head group that can cause an inverted micelle. When the head is wider than the tail region a typical micelle is formed.

Figure 4: By Mariana Ruiz Villarreal ,LadyofHats (Own work) [Public domain], via Wikimedia Commons​

### Surface Characteristics

While lipid tails primarily modulate bilayer phase behavior, it is the head group that determines the bilayer surface chemistry. Most natural bilayers are composed primarily of phospholipids, although sphingolipids such as sphingomyelin and sterols such as cholesterol are also important components.

Figure 5: Lipid bilayer with surface characteristics

#### Phase Structures

Just like the heads, the tails of lipids can also affect membrane properties, for instance by determining the phase of the bilayer. The bilayer can adopt a solid gel phase state at lower temperatures but undergo phase transition to a fluid state at higher temperatures, and the chemical properties of the lipids' tails influence at which temperature this happens.

Figure 6: Differing packing methods in the different phases of lipid bilayers along with the layer structure.

#### Curvature

A biological membrane is commonly described as a two-dimensional surface, which spans a three-dimensional space. It is not sufficient to determine the membrane curling that is seen in a single cross-section of the object, because in general there are two curvatures that characterize the shape each point in space. The radii of these two circular fragments, R1 and R2, are called the principal radii of curvature, and their inverse values are referred to as the two principal curvatures.[2]

Figure 8

$c1 = 1/R1$

$c2 = 1/R2$

The principal curvatures C1 and C2 can vary arbitrarily and thereby give origin to different geometrical shapes, such as cylinder, plane, sphere and saddle.

Figure 9: This graphic describes how some lipids do not self assemble into bilayers and depending on their curvatures form other structures and surfaces.

## Scattering Characterization Techniques

Despite being only a few nanometers thick, the bilayer is composed of several distinct chemical regions across its cross-section. These regions and their interactions with the surrounding water have been characterized over the past several decades with x-ray reflectometry,[4] neutron scattering[5] and nuclear magnetic resonance techniques.

#### Neutron Scattering

Neutron diffraction (elastic scattering) is used for determining structures; Inelastic neutron scattering is used for the study of atomic vibrations and other excitations

Since neutrons are electrically neutral, they penetrate matter more deeply than electrically charged particles of comparable kinetic energy; therefore they are valuable probes of bulk properties. Neutrons interact with atomic nuclei and magnetic fields from unpaired electrons. The neutrons cause pronounced interference and energy transfer effects in scattering experiments. Unlike an x-ray photon with a similar wavelength, which interacts with the electron cloud surrounding the nucleus, neutrons primarily interact with the nucleus itself.

#### Small-angle neutron scattering (SANS)

SANS is an experimental technique that uses elastic neutron scattering at small scattering angles to investigate the structure of various substances at a mesoscopic scale of about 1 - 100 nm.

Small angle neutron scattering is in many respects very similar to small-angle X-ray scattering (SAXS); both techniques are jointly referred to as small-angle scattering (SAS). Advantages of SANS over SAXS are its sensitivity to light elements, the possibility of isotope labeling, and the strong scattering by magnetic moments.

### X-Ray Scattering

X-ray reflectivity sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR, is a surface-sensitive analytical technique used to characterize surfaces, thin films, and multilayers.[1][2][3][4] It is related to the complementary techniques of neutron reflectometry and ellipsometry.

Figure 10:

The basic idea behind the technique is to reflect a beam of x-rays from a flat surface and to then measure the intensity of x-rays reflected in the specular direction (reflected angle equal to incident angle). If the interface is not perfectly sharp and smooth then the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the interface normal to the surface.

#### Small-angle X-Ray Scattering (SAXS)

Figure 11: X-ray scattering experimental setup

##### Point-collimation instruments

This SAXS instrument uses pinholes that shape the X-ray beam to a small circular or elliptical spot that illuminates the sample. Thus the scattering is centro-symmetrically distributed around the primary X-ray beam and the scattering pattern in the detection plane consists of circles around the primary beam.

Since the size of the illuminated sample volume is so small, the scattered intensity is small and therefore the measurement time is on the order of hours.

Measurement times can be reduced greatly if focusing optics like bent mirrors or bent monochromator crystals or collimating and monochromating optics like multilayers are used. Point-collimation allows the orientation of non-isotropic systems (fibressheared liquids) to be determined.

##### Line-collimation instruments

This type of SAXS confines the beam only in one dimension so that the beam profile is a long but narrow line. The illuminated sample volume is much larger compared to point-collimation and the scattered intensity at the same flux density is proportionally larger. Thus measuring times with line-collimation SAXS instruments are much shorter compared to point-collimation and are in the range of minutes.

A disadvantage is that the recorded pattern is essentially an integrated superposition (a self-convolution) of many pinhole adjacent pinhole patterns. The resulting 'smearing' can be easily removed using model-free algorithms or deconvolution methods based on Fourier transformation, but only if the system is isotropic.

Line collimation is of great benefit for any isotropic nanostructured materials, e.g. proteins, surfactants, particle dispersion and emulsions.

### Interferometric Scattering Microscopy (iSCAT)

Supported lipid bilayers (SLB) are frequently used to study processes associated with or mediated by lipid membranes. The mechanism by which SLBs form is a matter of debate, largely due to the experimental difficulty associated with observing the adsorption and rupture of individual vesicles.

Interferometric scattering microscopy (iSCAT) is used to directly visualize membrane formation from nanoscopic vesicles in real time. Using this technique a number of previously proposed phenomena such as vesicle adsorption, rupture, movement, and a wave-like bilayer spreading can be observed. iSCAT provides a unique combination of sensitivity, speed, and label-free imaging capability.

Figure 12

Direct Observation and Control of Supported Lipid Bilayer Formation with Interferometric Scattering Microscopy. Joanna Andrecka Katelyn M. Spillane Jaime Ortega-Arroyo , and Philipp Kukura *. Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.

ACS Nano20137 (12), pp 10662–10670
DOI: 10.1021/nn403367c
Publication Date (Web): November 19, 2013

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