Combinatorics of feedback in cellular uptake and metabolism of small molecules

Krishna et al. 10.1073/pnas.0706231105.

Supporting Information

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SI Figure 4
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SI Figure 4

Fig. 4. Behavior of all eight entangled feedback loop motifs. This figure extends Fig. 2 of the main text, to show the behavior of i-motifs also. Plots show the steady state values of s(middle column) and influx (sT = gEs+ s, right column) as a function of s. In all plots, the black curve shows the behavior for standard parameter values. The red curve shows the behavior when only the transport loop is active, i.e., E = 1. The blue curve is produced by keeping T = 1, i.e., only the metabolism loop is active. The plots were made in the same way as Fig. 2 of the main text.

SI Figure 5

Fig. 5. Behavior of eight entangled feedback loop motifs for varying K_E/K_T ratios. The plots show steady state s and influx values as a function of s, just as in Fig. 4, for: black, K_E = K_T = 1; magenta, K_E = 2, K_T = 1; red, K_E = 10, K_T = 1; cyan, K_E = 1, K_T = 2; blue, K_E = 1, K_T = 10.

SI Figure 6

Fig. 6. Behavior of eight entangled feedback loop motifs with self-regulation of R. Parameters are chosen so these motifs match the non-self-regulated motifs when all of the R molecules are in the active state. The plots show steady state s and influx values as a function of s, just as in Fig. 4, for: black, no self-regulation; red, self-activation; blue, self-inhibition.

SI Figure 7

Fig. 7. Linear stability analysis of the steady states. For each motif, at each s, we compute the Jacobian at the corresponding steady state, and determine its eigenvalues. The plot shows the maximum real part of the three eigenvalues obtained from each Jacobian. All four motifs are shown: blue (socialist and fashion), magenta (consumer), red (collector).

SI Figure 8

Fig. 8. Response to large perturbations in external small molecule concentration. For each motif, we make 2-fold jumps in s(both up and down) at time 0, and plot the trajectory of s. At times less than zero, the system is at a steady state with s = 1 (blue), 10 (magenta), and 100 (red).