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Liquid Crystals: A Model For Cell Membranes Case Essay Supervisor: Dr. Angus Bain

Abstract TCSPC techniques are used to measure the vertically and horizontally polarised fluorescence from an Oxazine 4 sample in solution with 5CB. The fluorescence anisotropy R(t) is then used to infer structural and dynamical parameters of the sample as a function of temperature, such as: the lifetime of the excited (fluorescent) state, rotational diffusion timescales of individual molecules and of locally ordered domains, the cone angle, and ground state order parameters. A virtual temperature for the nematic to isotropic transition is found from Landau-de Gennes theory to be T*=(12±2)°C, below the actual TNI≈33°C. Analogies between these results and cell membranes are discussed, with suggestions as to how these techniques may be exported to a biological system.

Contents 1. 2. 3. 4. 5. 6. 7. 8.

Introduction The Cell Membrane Liquid Crystal Structure Preliminary Results With Oxazine4 Probing the Structure of 5CB Conclusions References Appendices

page 1 page 2 page 3 page 4 page 8 page 19 page 20 page 21

1. Introduction The liquid crystal environment provides an excellent physical model with which to understand more about the more complex biological system of a cell membrane. The phases studied in this investigation show many analogies with a phospholipid bilayer. In the same way that the phosphate heads and fatty acid tails in a membrane tend to show orientational order whilst retaining a fluid structure, the molecules in the nematic phase of a liquid crystal are aligned to a nematic director. The locally ordered domains in the isotropic phase are also closely analogous to domains found in cell membranes, known as lipid rafts17. Fluorescence techniques such as FRET18 can yield information about the size and order of these domains. This investigation uses a liquid crystal structure doped with a fluorophore: this mirrors more closely the biological system, in which a structured membrane is

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interspersed with other molecules such as proteins and cholesterol. By considering the polarisation of fluorescence from these molecules, the microscopic order, structure and dynamics of the environment can be probed. Recent work using a cholesterol analogue as a fluorophore illustrates how these techniques can be exported to a biological environment successfully.

2. The Cell Membrane 2.1 Structure The cell membrane is a thin layer of molecules which surrounds the entire cytoplasm of the cell. In plants, fungi and some bacteria this is located in between the cell wall and cytoplasm, whereas in animals it forms the outermost boundary of the cell. The overall structure is complex and contains a huge range of component proteins and other molecules depending on the cell, but the basic ‘skeleton’ of the membrane is conserved. The phospholipid molecule is the main building block: a polar phosphate head with a long chain of hydrophobic fatty acids. The lowest energy state (at standard physiological temperatures) is a bilayer, oriented such that the hydrophobic tails point inwards, enclosed by the hydrophilic phosphate heads.

Figure 2.1.1: The phospholipid bilayer (http://www.health.bcu.ac.uk/physiology/phospholipid02.gif) A variety of other molecules perform specialised roles, such as protein pumps and ion channels. Despite the fact that the orientations of the phospholipids forming the membrane are well defined, the overall structure is fluid, with proteins able to move among the phospholipids1. This shows many similarities with the nematic phase of liquid

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crystals (see Section 3). Additional molecules such as cholesterol alter the fluidic properties and diffusion rates of phospholipids within the bilayer2. 2.2 Function The cell membrane has the vital function of separating the intracellular environment from the extracellular, both physically and electrochemically. The combination of polar and hydrophobic layers makes it impermeable to water-soluble compounds and ions. This allows electrochemical gradients to be established by differences in concentrations on either side of the membrane. Protein pumps, or ion channels that are only permeable to certain species help to control these concentrations. As well as these transporter proteins that span the membrane, some may extrude only on the extracellular surface, and some may be only present on the inside of the cell. Other such functions of these include providing binding domains for certain ligands, for example neurotransmitter binding on the post-synaptic membrane of a dendrite.

3. Liquid Crystal Structure The particular liquid crystal used in this study is 4-n-pentyl-4’-cyanobiphenyl (5CB). What follows is a brief overview of the liquid crystalline behaviour which will be of relevance. The term liquid crystal arises since these substances share some properties conventionally associated with liquids, and some only found in crystalline solids. This intermediate liquid crystal phase of matter in fact consists of several sub-phases, which can be characterised both by correlations in the orientations of molecules and in the positions of the molecules. In thermotropic liquid crystals such as 5CB, transitions between these phases are driven by temperature changes. 3.1 Nematic phase Just above room temperature our sample is in the nematic phase. 5CB molecules exhibit strong orientational order, a property also found in crystalline solids with a lattice structure. There is a strong correlation between orientations over a long range (relative to the molecule size). The nematic director ( nˆ ) is the direction in which the molecules tend to point. Molecules can however either be rotated through 180 degrees with respect to each other: 5CB is centrosymmetric and uniaxial4 and so pointing in the direction of the vector nˆ is energetically equivalent to the vector - nˆ . The distribution of orientations is € of spherical harmonics (see Appendix i). most easily described in the basis €

€

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Figure 3.1.1: Cartoon of molecular arrangement in the nematic phase of liquid crystals. The nematic director points directly upwards [http://matdl.org/]

On the other hand, there is no long-range correlation between the positions of the molecules. In this respect it behaves like an isotropic liquid, showing no positional order. One effect of this orientational order is that the sample is birefringent to electromagnetic radiation. Waves polarised in the axis of the nematic director will experience a different refractive index to those polarised perpendicular to it. In terms of this experiment, the sample will have a different reflectivity to vertically polarised radiation than to horizontally polarised radiation6. 3.2 Isotropic phase Above the transition temperature TNI, the liquid crystal begins to move into the isotropic phase. The range of inter-molecular interactions is greatly reduced, and the sample no longer shows any global orientational order. However, short-range interactions still persist, over a length scale ξ(T) which continues to decrease with increasing temperature5. Over this short range, domains form in the sample, in which the molecular orientation is locally correlated; on the global scale there is no preferred orientation. The size of these domains will be proportional to the correlation length ξ(T), and therefore will also decrease with increasing temperature. This will affect the relaxation dynamics, as investigated in Section 5.

4. Preliminary Results With Oxazine 4 For a comprehensive record of the experiments and techniques, please see the accompanying lab. book.

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4.1 Structure of Oxazine 4 The fluorescent dye used to probe the arrangement of liquid crystal molecules later in the experiment is Oxazine 4. It consists of an approximately rod-like molecular structure, much longer in one dimension than in the two others. Being a member of the Xanthene class of fluorophores, it has the following general molecular arrangement:

Figure 4.1.1: General structure of Xanthenes [http://media-1.web.britannica.com]

In the case of Oxazine 4, X is Nitrogen and Y is Oxygen. In solution it appears blue or purple in colour, as will be confirmed by the absorption spectra in Section 4.2. Given its relatively large molecular structure, it has a complex energy level structure consisting of many rotational and vibrational levels. The energetics of fluorophores is discussed more fully in Appendix ii. Oxazine 4 molecules can make a transition from a singlet electronic ground state (S0) to an excited state (S1) by the absorption of a photon. The dipole moment for this transition is known to lie along the long axis of the molecule3. The direction of this dipole moment is therefore a good indicator of the orientation of the Oxazine 4 molecule itself. Information about these orientations is used in Section 5 to infer the distribution of molecular orientations in an ordered environment such as a liquid crystal solution. 4.2 Absorption Spectra Solutions of Oxazine 4 in ethylene-glycol (EG) were prepared in three different concentrations: 1.1 x 10-3 M, 1.1 x 10-4 M and 1.1 x 10-5 M. This provides an isotropic, unordered environment to test the properties of the fluorophore before its behaviour in a liquid crystal solution is investigated. These solutions were placed into thin cells, constructed to have a width of around 100µm in the direction of the optical path. This is achieved by attaching glass slides between strips of mylar of approximately this thickness. This helps to minimise the reabsorption of fluorescence photons by other Oxazine molecules further along the beam path, which would alter the measured spectrum. A spectrometer is used to measure the transmitted intensity of light across a range of wavelengths when light from a broadband Xenon lamp is passed through these thin cells. This is compared with the intensities measured when the same source is passed through a thin cell containing only EG, and the difference gives a measurement of the absorption spectrum of Oxazine 4:

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Figure 4.2.1: Absorption of Ox4 in EG (1.1 mM) 1.2 1 Optical Density /a.u.

0.8 0.6 0.4 0.2 0 380

480

580

-0.2

680

780

880

Wavelength /nm

Figure 4.2.2: Absorption of Ox4 in EG (0.1 mM) 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 -0.01

380

480

580

680

780

880

-0.02

Clearly the more concentrated solution gives a much more defined spectrum, showing a peak of absorption at around 620nm. Significant errors are present in the spectrum from the weaker solution, especially around the very high and very low wavelengths. This is likely to be because the background levels of ultraviolet and infrared radiation in the lab will be very low. The output of the Xenon light source in these regimes is also very low, and therefore the error from subtracting two very small readings

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in obtaining the optical density will be greatly magnified. The lower concentration of 1.1 x 10-5 M was too weak to be of use. This is compared with the absorption spectrum for a (rubbed) cell containing Oxazine 4 in 5CB, concentration (2.5±0.5) x 10-4 M:

Figure 4.2.3: Combined absorbance of Ox4 in 5CB (0.25 mM) compared with individual absorbances of Ox4 and 5CB 0.6

Optical Density /a.u.

0.5 0.4 0.3 0.2 0.1 0 -0.1

350

450

550

650

750

850

Wavelength /nm Ox4 and 5CB (Ref: pure EG cell)

Pure 5CB

"Ox4"

The combined spectrum of Oxazine 4 and 5CB was taken using a cell filled with pure EG as a reference spectrum (since this has no significant absorbance of its own). Figure 4.2.3 shows that this combined absorbance can be explained by a direct addition of the absorption of low wavelength UV light by the 5CB, and the more structured absorption spectrum of the dye. Although 5CB still absorbs a little in the visible range, this is low compared with Oxazine 4 absorption and does not vary rapidly with wavelength, so should not corrupt the later results. Another source of error is present in these results: Oxazine 4 molecules that have become excited by absorbing light may then relax by emitting a fluorescence photon. Some of these photons may enter the spectroscope and appear as extra ‘transmitted’ light, thus making the sample appear less optically dense at that wavelength. Given that the emission spectrum overlaps with the absorption spectrum (see Section 4.3), it is difficult to disentangle this effect from the true absorption. However, this effect is likely to be small: fluorescence is emitted isotropically, so the actual proportion of excited molecules which will emit observable fluorescence is: Pobserved

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d2 = ΦF 2 r

{4.2.4}

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Where d is the radius of the spectroscope aperture, r is the distance from sample to spectroscope, and ΦF is the fluorescence quantum yield ΦF. Given that this ratio is