State-dependent interactions between binary elements. (A) Each binary element can transition between its two possible configurations (0 and 1) according to intrinsic rate constants γ and δ, which are defined by the height of a single transition state energy barrier (G_‡) in relation to the free energy of each of the elements configurations G₀ and G₁ as defined in Eqs. 1 and 2. (B) An illustration of a pair of binary elements i and j, where each element is represented by a pair of circles for its two possible configurations and its intrinsic transition rates between configurations are shown as arrows. Broken lines indicate the four possible state-dependent interactions for the two elements, each of which is labeled with its three state-dependent interaction energies as described in the Materials and methods. (C) Kinetic scheme represented by the pair of binary elements in B, where each state of the system is shown as a circle labeled with the configurations of each of the elements, and the possible transitions between states reflecting a change in configuration of either of the elements are shown as arrows. Transition arrows are labeled with their rate constants, including all of the possible interaction factors as defined in Eqs. 3–6.