Thermodynamically equivalent silicon models of voltage-dependent ion channels

We model ion channels in silicon by exploiting similarities between the thermodynamic principles that govern ion channels and those that govern transistors. Using just eight transistors, we replicate--for the first time in silicon--the sigmoidal voltage dependence of activation (or inactivation) and the bell-shaped voltage-dependence of its time constant. We derive equations describing the dynamics of our silicon analog and explore its flexibility by varying various parameters. In addition, we validate the design by implementing a channel with a single activation variable. The design's compactness allows tens of thousands of copies to be built on a single chip, facilitating the study of biologically realistic models of neural computation at the network level in silicon.