Thermal properties of lipid bilayers

3.3.1 The lipid bilayers phases

Bilayers can be found in several phases depending on the temperature and the lipid types forming the bilayer. The structure of the bilayer depends on the lipid: the dipole in its head and the length and unsaturation degree of its chains.

The main phases are the gel phase and the liquid phase. The main difference between those phases is the area per lipid and the thickness of the bilayer.

The gel is thicker than the liquid but the area per lipid is larger in the liquid phase. In addition to those main organisations other phases are accessible to the bilayer are [60,169]:

• a crystalline phase where the lipids are ordered in the three directions. It is the Lc phase reported on Figure3.3.

• a gel phase, where the lipids are often tilted by about 30^◦, this corresponds to the Lβ and Lβ’ phases illustrated in Figure 3.3.

• a ripple phase made of a linear combination of gel and liquid phases. It is represented as the Pβ’ phase in Figure 3.3.

• a liquid phase. The lipids are disorganised and there is no periodicity. It is the Lα phase depicted in Figure3.3.

When the bilayer phase is ordered, in common cases, it takes the form of a two dimensional hexagonal structure. At lower temperatures, a cubic phase structure also exists. Those structures have been investigated using X-ray or neutron scattering [170,181,182].

Figure 3.3: Lipid bilayers exist in different phases, crystalline (Lc), gel (Lβ’), ripple (Pβ’) or fluid (Lα) depending on the temperature. The higher the temperature, the less organised is the bilayer [60].

3.3.2 Thermal behaviour

A phase transition is the result of the reorganisation of the ensemble of the lipids and a phase transition temperature corresponding to the gel/liquid phase transition can be defined for lipid bilayer made of only one type of lipid. This phase transition is a first order phase transitions, as a consequence, the heat

capacity of the bilayer diverges at the transition temperature as illustrated on Figure 3.4 [169]. This Figure also shows that the per lipid volume in the membrane depends on the temperature. The increase of the volume is due to an increase of the lipid-lipid distance as the bilayer thickness is larger in the gel phase.

0 10 20 30 40 50 60

Temperature (°C) 1100

1150 1200 1250

Volume (Å3 .lipid-1 )

Subgel

Gel

Ripple

Fluid

Heat capacity

Figure 3.4: The volume of a DPPC lipid bilayer increases with temperature and at each phase transition, the heat capacity is maximum and the volume changes rapidly [169].

The transition temperature varies with the type of lipid constituent the mem-brane. The more saturated are these lipids, the higher the transition temper-ature. This mechanism is explained by the double bonds in the carbon chain in unsaturated lipids. This bond induces angle differences in the carbon chain preventing perfect stacking of the lipids and leading to more space between lipids as illustrated in Figure 3.5. As a result, the membrane is more flexible and "fragile" [136].

However, the melting temperature cannot be deduced from the unsaturation degree of the lipids because among lipids with the same unsaturation degree, the transition temperature varies. An example of the temperature values is provided in Table3.1. The transition temperature depends on many parameters [146] such as the position of the double bonds in the chains, the lipid size, the polar head, etc ...

Figure 3.5: Unsaturated lipids have rigid angles due to their double bond(s), which prevents the perfect stacking of the lipids and disturbs the order of the bilayer.

Lipid common name # of -CH₂-:# of CH=CH (position) Melting temperature (^◦C)

DMPC 14:0, 14:0 23

DPPC 16:0, 16:0 41

DOPC 18:1 (9), 18:1 (9) -20

DLPC 18:2 (9:12), 18:(9,12) -53

POPC 16:0, 18:1 (9) -2

DMPS 14:0, 14:0 35

DMPE 14:0, 14:0 50

DMPA 14:0, 14:0 50

Table 3.1: Melting temperature of different lipids from [146]. Those data show the effect of the double bond(s) in the lipid tails on the melting temperature. While there is no general law, there is a correlation between the number of double bonds and the melting temperature.

3.3.3 Heat conduction

The most un-addressed properties of lipid bilayers are their heat conduction properties. In most cases when modelling the heat conduction, the bilayer is neglected which is reasonable but with nanosystems being developed to act close to the bilayer and at short scale, this approximation can be questioned.

Plus, when nanoparticles are injected into a living body, they often enter in the cell by being encapsulated into vesicles. Thus, if those particles heats up, the thermal conductance of the membrane is a part of the model. There is a Non-Equilibrium Molecular Dynamics simulation on a DPPC lipid bilayer in gel phase computing the in-plane and cross plane thermal conductivity [119]. The cross-plane thermal conductivity of the bilayer is found to be 0.25 W.m⁻¹.K⁻¹ and 0.10 W.m⁻¹.K⁻¹, in the in-plane direction. This difference is explained by the structure of the bilayer and the type of forces between the atoms. In the plane of the bilayer, the lipid are relatively far apart and interact through van der Waals and dipole-dipole interactions while in the cross direction, the atoms are covalently bonded except at the interface between the two monolayers. This layer-layer resistance is the main thermal resistance in the cross-plane direction.

As a result, lipid bilayers conduct heat less than water and are a thermal barrier in the cell environment.