Lipid bilayer systems
3.4 Response to electric field
Lipid bilayers are electric isolator as due to their structure, they are not per-meable to ions. Their capacitance can be defined and measured experimentally and is commonly known to be of the order of 0.01 F.m2 [14,168,15,115,137].
However, electrical fields are known to impact the lipid bilayer structure is the case of the electroporation, where a voltage induces the formation of holes in the membrane.
3.4.1 Electroporation
The electroporation consists in applying an electric on the lipid bilayer to in-crease its permeability. The application of a transmembrane voltage of at least 0.5 to 1 V on the membrane allows large molecules such as DNA to pass through the bilayer. Electroporation is commonly used to increase the permeability of cell membranes and introduce new coding DNA in a bacteria for instance [120].
Large molecule passing through the membrane indicates that this phenomenon is related to the creation of holes of nanometer scale in the bilayer. The mech-anism proposed in many studies and numerical simulations [152,151,161,162]
is a local reorganisation of the lipids. Some lipids would gradually flip by an angle up to 90◦ forming a hole in the bilayer but the lipids still face the water with their hydrophilic head as indicated in Figure3.6.
Figure 3.6: Organisation of the lipids in an electroporated bilayer. This structure is created when the transmembrane voltage is higher than a threshold of 0.5 to 1 V.
3.4.2 Nerve pulse propagation and axon models
The measurement of the effects of electric fields on lipid bilayers is motivated by the study of the nerve pulse propagation. A nerve is composed of a bundle of axons. An axon is a projection of a cell called neurone and is responsible of the transmission of information. Signals are carried by the neurones through the propagation of an action potential along the axon. This potential was measured by Cole and Curtis in 1939 on a squid axon [26]. It consists in a transient potential difference propagating along the axon. This measured potential is represented in Figure 3.7.
This potential propagation was later described by Hodgkin and Huxley [64]
who considered the role of the ion channels in the propagation of this action potential. Considering that potassium and sodium channels are distributed on the membrane along the axon, they open after the voltage pulse and thus influence the potential in their environment and other channels in their vicinity.
To quantify this process, the electrical model of the axon membrane that is depicted on Figure 3.8, has been taken from [60], have been introduced. Ion channels are modelled as resistances (R) or conductances (g), the lipid bilayer is a conductance and a leakage of ionsILthrough it is considered. This scheme is repeated along an axon of radiusaand resistanceRi. The equation describing the nerve pulse is established as follows:
a 2Ri.∂2U
∂x2 =Cm∂U
∂t +gK(U−EK) +gN a(U −EN a), (3.1) where Cm is the conductance of the lipid bilayer,EK and EN a are the poten-tial difference created by the different concentration of potassium and sodium respectively. Those quantities and their arrangement are represented in Figure 3.8.
This model is satisfying to describe the potential measurements carried out on axons but later experiments revealed [142, 163] that heat was released then absorbed from the axon when the action potential propagates. Experimental results from [142] are reproduced in Figure 3.9.
The transmembrane voltage is at most 100 mV and is thus smaller than the
0 1 2 3 4 5 6 7 8 9 10 Time (ms)
0 50 100
Potential (mV)
Figure 3.7: Transmembrane voltage measured during the action potential propagation [26]
Figure 3.8: Electrical model of an axon as introduced in the Hodgkin and Huxley model for action potential propagation from [60].
0 40 80 120 160 200 Time (ms)
Heat flux
Figure 3.9: Heat released and absorbed during the action potential propagation from experimental data [142]. This reversible behaviour is similar to what is observed in phase transitions.
500 mV required for electroporation but this voltage might still change the structure of the bilayer. The release of heat followed by an absorption hints that this effect takes root in a reversible behaviour. It is thus plausible that this phenomenon, which cannot be explained by the Hodgkin-Huxley model, is due to a voltage-induced phase transition of the lipid bilayer, the voltage being here the action potential. This problem has been addressed by theoretical and experimental studies [159, 9] revealing that the electric field induces a change of the lipid bilayer structure or phase. The difference of energy between the gel and the liquid phase is∆H ≈30 kJ.mol−1 [60] which can induce a heating of about 1◦C of the bilayer.
3.5 Conclusion
In this chapter, the structural aspects of lipid bilayers have been presented and the common forms of those membranes in water have been introduced: small, large and giant unilamellar or multilayer vesicles. The thermal relaxation of lipid bilayers is mostly un-addressed. One numerical calculation studied the heat conduction in a gel DPPC lipid bilayer and has revealed that its cross-plane thermal conductivity is 0.25 W.m−1.K−1 and thus the membrane constitutes a thermal barrier in water. The most studied heat relaxation property in bilayer is the phase transition. The bilayer’s phase depends on the temperature and the main phase transition occurs between the gel and the liquid at a temperature that depends on the lipid types that has been tabulated for pure lipid bilayers.
However, the temperature is not the only way to affect the structure of a bilayer and it is known that electric fields increase their permeability by opening holes.
This mechanism requires a transmembrane voltage of at least 0.5 V. In nature, the action potential, a transmembrane voltage of about 0.1 V is suspected to induce a reversible change of the bilayer structure due to a heat release followed by a cooling observed during the propagation of the action potential.
As a result, the structure of the bilayer could be controlled by the application of electric fields and the hypothesis of a voltage-induced phase transition of the lipid bilayer is investigated in the following chapters.