Transition diagrams for Markov-chain model (MCM).

<p>(a) A 2-state MCM, redrawn from the original <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#pone-0032376-g002" target="_blank">Figure 2</a> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#pone.0032376-Ko2" target="_blank">[21]</a>. <i>p₁</i> and <i>p₂</i> are probabilities of transitions between a state of active transcription (ON), where TFs bind to a promoter and form a stable transcription initiation complex, and a state of no transcription (OFF). (b) 3-state MCM. To account for both activator-bound and repressor-bound states, two 2-state MCMs are combined, where unbound state (i.e., neither activator nor repressor bound) represents a state of basal-level transcription. <i>P_A1</i>, <i>P_A2</i>, <i>P_R1</i> and <i>P_R2</i> are transition probabilities between the states.</p

Model prediction matches more closely to the experimental observation.

<p>(a) Simulated dose-response relationship between [dox] and promoter activity (normalized gene induction levels). (b) Hill functions showing estimated switching probabilities (<i>P_A1, P_A2, P_R1,</i> and <i>P_R2</i>) against [dox]. Values of P_A1+P_R1 against [dox] are also shown. To show the relationship between (a) and (b), these graphs are aligned by the [dox]. (c) Comparisons between model predictions and experimental observations.</p

A strategy of parameter estimation for a 3-state MCM.

<p>All the parameters for the 3-state MCM were estimated from the published data only on the dose-response experiments of activator only and repressor only <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#pone.0032376-Rossi1" target="_blank">[20]</a>. In the case of activator only, parameters in <i>P_Act</i> (Eq. <b>3</b> or Eq. <b>10</b>) were estimated by using the observed dose-response curve (<i>OBS_Act</i>: a Hill function of [dox]) represented by the equation (Eq. <b>4</b> or Eq. <b>11</b>) in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#s4" target="_blank">Materials and Methods</a> section. The repressor only case (<i>OBS_Rep</i>, <i>P</i>_Rep) was handled in the same manner.</p

Stochastic simulation using a 3-state MCM yields all-or-none responses.

<p>In a cell population, steady-state distributions of gene induction were stochastically simulated by the 3-state MCM using the estimated parameters described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#pone-0032376-g002" target="_blank">Figure 2</a>. Red, black, and green lines present the peaks of transcription levels in the “repressor-bound,” “unbound,” and “activator-bound” states, respectively. A gray vertical bar indicates the increasing concentrations of [dox], which correspond to the experimental conditions reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032376#pone.0032376-Rossi1" target="_blank">[20]</a>.</p