RLC(M) circuit models of protein structure: analysis, visualization, shape synthesis, and pattern matching

Protein structure at the secondary and tertiary levels is modeled using RLCM circuits via the mapping turnrarrR, helixrarrL, sheet or salt/disulphide bridgerarrC, and helix pairrarrM. Standard network analysis methods may be applied to the resulting RLC(M) circuit, whose circuit topology is restricted because of the linear nature of the protein's primary sequence (for example, a secondary circuit can be a Foster I but not Foster II ladder). The impedance function Z(s), a rational positive real function of the complex frequency s, can be used to study differences in structure at both levels within and across proteins. This is illustrated with a set of sample proteins. In particular, the phase plot appears to have signature-like properties. Conversely, network synthesis methods at the secondary (and sometimes tertiary) level augmented by modifications at the tertiary level lead to artificial protein structures which may or may not exist, but when a circuit can represent a protein it may be used to construct an approximate tertiary shape. The circuit may also be used as a schematic diagram, for tracking changes during folding, and in searching for patterns among proteins.