Schematic Illustration of Our Modeling Methodology and of the Probability of Closure

<div><p>In this four-node network example, node A is the input (as ABA is the input of the ABA signal transduction network), and node D is the output (corresponding to the node “Closure” in the ABA signal transduction network). The nodes' states are indicated by the shading of their symbols: open symbols represent the off (0) state and filled symbols signify the on (1) state. To indicate the connection between this example and ABA-induced closure, we associate D = off (0) with a picture of an open stomate, and D = on (1) with a picture of a closed stomate. The Boolean transfer functions of this network are A* = 1, B* = A, C* = A, D* = B and C (i.e., node A is on commencing immediately after the initial condition, the next states of nodes B and C are determined by A, and D is on only when both B and C are on).</p> <p>(A) The first column represents the networks' initial states; the input and output are not on, but some of the components in the network are randomly activated (e.g., middle row, node B). The input node A turns on right after initialization, signifying the initiation of the ABA signal. The next three columns in (A) represent the network's intermediary states during a sequential update of the nodes B, C, and D, where the updated node is given as a gray label above the gray arrow corresponding to the state transition. This sequence of three transitions represents a round of updates from timestep 1 (second column) to timestep 2 (last column). Out of a total of 2² × 3! = 24 possible different normal responses, two sketches of normal responses are shown in the top two rows. The bottom row illustrates a case in which one node (shown as a square) is disrupted (knocked out) and cannot be regulated or regulate downstream nodes (indicated as dashed edges).</p> <p>(B) The probability of closure indicates the fraction of simulations where the output D = 1 is reached in each timestep; thus, in this illustration the probability of closure for the normal response (circles) increases from 0% at time step 1 to 100% at timestep 2. The knockout mutant's probability of closure (squares) is 0% at both time steps.</p>