Modeling Bilayer Systems as Electrical Networks

Bilayers are synthetically made cell membranes that are used to study cell membrane properties or make functional devices that use the properties of the cell membrane components. Lipids and proteins are two of the main components of a cell membrane. Lipids are amphiphilic molecules that can self assemble into organized structures in the presences of water and this self assembly property can be used to form bilayers. Because of the amphiphilic nature of the lipids, a bilayer is impermeable to ion flow. Proteins are the active structures of a cell membrane that opens pores through the membrane for ions and other molecules to pass. Proteins are made from amino acids and have varying properties that depend on its configuration. Some proteins are activated by reactions (chemical, thermal, etc) or gradients induced across the bilayer. One way of testing bilayers to find bilayer properties is to induce a potential gradient across a membrane that induces ion flow and this flow can be measured as an electrical current. But, these pores may be voltage gated or activated by some other stimuli and therefore cannot be modeled as a linear conductor. Usually the conductance of the protein is a nonlinear function of the input that activates the protein. A small system that consists of a single bilayer and protein with few changing components can be easily modeled, but as systems become larger with multiple bilayers, multiple variables, and multiple proteins, the models will become more complex. This paper looks at how to model a system of multiple bilayers and the peptide alamethicin. An analytical expression for this peptide is used to match experimental data and a short study on the sensitivity of the variables is performed.