Modeling Bilayer Systems as Electrical Networks

Two of the main components of cell membranes are lipids and proteins. Lipids are the passive structure of the membrane that acts as a barrier between the inner and outer portions of the cell. Proteins are the active structure of the membrane that allows signaling, energy conversion, and open channels between the inner and outer portions of the cell. Artificially made membranes, called bilayers, can be made from natural or artificial membrane components at the interface of aqueous volumes. Some bilayer properties are measured by inducing an artificial potential gradient across the bilayer to induce ion flow. This ion flow is measured by measuring the resulting current output of the device that induced the potential gradient. The lipids of the membrane act electrically as a small conductor and capacitor in parallel where the measured capacitance is related to the area of the bilayer. Some proteins act electrically as an additional conductor in parallel to the lipids with varying conductance properties depending on the specific protein. Some proteins are pores that allow ions to flow freely through the membrane and others are gated and allow ions to flow at different levels depending on the size and polarity of the potential gradient. A large system with multiple aqueous volumes and multiple bilayers made of just passive membrane components can be modeled as an electrical network of resistors and capacitors. The addition of proteins to this network increases the complexity of the system model because the proteins usually do not act as a linear conductance and numerical methods are used to approximate what is happening in the system. This paper shows how a system of multiple aqueous volumes and multiple bilayers can be modeled as a system of first order odes, numerically solved, and then compared to the published results of a similar system.