Figure 2. Functional tunability of network motifs to attain static output objectives.

A: Predefined steady-state objective: [x₀₀ x₀₁] = [0 1], [x₀₂ x₀₃] = [4.5 5.5], [x₀₄ x₀₅] = [9 10]; [y₀₀ y₀₁] = [0 1], [y₀₂ y₀₃] = [4.5 5.5], [y₀₄ y₀₅] = [9 10]; obj₁₁, obj₁₂, and obj₁₃: X^* is low and Y^* is low, intermediate, or high; obj₂₁, obj₂₂, and obj₂₃: X^* is intermediate and Y^* is low, intermediate, or high; obj₃₁, obj₃₂, and obj₃₃: X^* is high and Y^* is low, intermediate, or high. PSO implementation: steady-state levels of motif output responses were arbitrarily set to the following values: [X^* Y^*] = [1.5 1.5] (xy_{1.5_1.5}); [X^* Y^*] = [1.5 8.5] (xy_{1.5_8.5}); [X^* Y^*] = [8.5 1.5] (xy_{8.5_1.5}); and [X^* Y^*] = [8.5 8.5] (xy_{8.5_8.5}). Model parameters of all motifs were initialized to identical values as follows: 1) PSO was pre-implemented to identify model parameters that generated such static outputs for the linear motif; 2) these parameters were used for the core structure of all other network motifs; 3) the kinetic constants of the additional reactions were set to zero. B: Motif tunability to static output objectives obtained through random sampling of model parameters. C: Motif tunability to static output objectives obtained through PSO sampling of model parameters necessary for ODE implementation. Particle positions were initialized to the point xy_{1.5_1.5}. CV was defined as the ratio between the standard deviation and the mean computed across the 100 parameter sets identified by using PSO. Given the 12 motif topologies, 9 objective areas, and 100 sets of identified parameter, PSO was implemented 10,800 times.