SITE-SPECIFIC THERMODYNAMICS OF ISING NETWORKS - A THEOREM FOR LINEARLY CONNECTED SUBSYSTEMS

An Ising network consists of a set of N units existing in two possible states, 0 and 1. If two units Contact each other in the network, there is a nearest neighbor interaction that depends only on the states of the units. If an Ising network can be split into two independent subsystems by deleting the contact between two units, then these units specify each other's site-specific properties and the state of either unit uniquely specifies the state of the other. This theorem holds regardless of (a) the dimensional embedding of the network as a whole, (b) the precise interaction geometry among the units within either subsystem, and (c) the intrinsic energy for the 0 --> 1 switching of any given unit. Either subsystem in the network can be considered as a probe for the state of the unit in the other subsystem to which the probe is connected. Application of the theorem to the analysis of the site-specific properties of the biologically relevant case of a linear network, or heteropolymer, yields a rather counterintuitive result. Knowledge of the state of the end unit in the network, as a function of the change in the thermodynamic driving force for the 0 --> 1 transition, is sufficient to completely resolve the energetics of the network. (C) 1994 John Wiley and Sons, Inc.