A circuit theory of protein structure

Abstract

Protein secondary and tertiary structure is modeled as a linear passive analog lumped electrical circuit. Modeling is based on the structural similarity between helix, sheet, turn/loop, and helix pair in proteins and inductor, capacitor, resistor, and transformer in electrical circuits; it includes methods from circuit analysis and synthesis. A protein circuit is a one-port with a restrictive circuit topology (for example, the circuit for a secondary structure cannot be a Foster II ladder or a Wheatstone-like bridge). It has a rational positive real impedance function whose pole-zero distribution serves as a compact descriptor of secondary and tertiary structure, which is reminiscent of the Ramachandran plot. Standard circuit analysis methods such as node/loop equations and pole-zero maps may be used to study differences at the secondary and tertiary levels within and across proteins. Pairs of interacting proteins can be modeled as two-ports and studied via transfer functions. Similarly circuit synthesis methods can be used to construct protein circuits whose real counterparts may or may not exist. An analysis example shows how a protein circuit is constructed for thioredoxin and its pole-zero map obtained. A synthesis example shows how an electrical circuit with a single Brune section is obtained from a specified set of poles and zeros and then mapped to an artificial protein with a helix pair (corresponding to the transformer in the Brune section). Possible applications to folding, drug design, and visualization are indicated.