Stability of the steady states.

<p>(a) The plot shows the positions of the four steady states of the parasite’s life cycle in the space spanned by the three principal components. The black trajectories around each stage are the result of simulations conducted using the model (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146947#pone.0146947.e026" target="_blank">Eq (8)</a>) without external cues. A slightly perturbed steady state was used as the initial condition. The system fluctuates around the corresponding steady state. (b) Temporal behavior of the overlap between the state of the system at time <i>t</i> and the amastigote steady state (blue), the epimastigote steady state (red), the metacyclic tryp. steady state (green), or the trypomastigote steady state (yellow). (c) 2D projection of the pseudo-potential landscape with the four basins of attraction corresponding to each of the parasite’s stages. The circular black arrows represent the system’s fluctuation around the steady states, just as seen in Fig 3a.</p

Schema of the network inferring method.

<p>(a) The microarray data corresponding to the parasite’s four steady states are normalised. (b) The total of 8,904 gene-expression levels of each stage is reduced to 339 clusters representing the variables of our systems. (c) An ensemble of 300 training sets including fluctuations around the steady states is constructed from the steady states. Using singular value decomposition (SVD), the minimal <i>L</i>₂-norm solution for each <i>D</i>_<i>ss</i> is determined. (d) A sparse connectivity matrix, <b>W_ss</b>, is derived from the probability distribution <i>P</i>_<i>ij</i>(<i>w</i>) by using a pruning method based on a location test. (e) A new training set is constructed from the transitions between the amastigote (A), epimastigote (E), metacyclic tryp. (M) and trypomastigote (T) stages. Intermediate states (small circles) between the stages are assumed to exist. It is also considered that an unknown external cue (black arrow) is responsible for the transitions. (f) By means of using SVD, the <i>L</i>₂-norm solution, <math><msub><mi>W</mi><msub><mi>L</mi><mn>2</mn></msub></msub></math>, is determined. This solution is in turn used to find another solution, <b>W_t</b>, which includes information concerning the steady states. This procedure is used to infer the weighted links between genes, <i>w</i>_{<i>i</i>,<i>j</i>}, and to answer two questions: which genes are affected by the external cues, and how they are regulated (up or down) by the environment.</p

The life cycle of <i>T. cruzi</i>.

<p>(a) Sketch illustrating the life cycle of the parasite. (b) Plots illustrating the transcriptional snapshots of the parasite’s four stages. After a dimensional reduction analysis of the microarray dataset, we have found that the four steady states can be represented by 339 variables. Each of these variables (cells in the 19 × 18 array) corresponds to the intra-cluster average of the log-transformed relative expression level of the genes that belong to the corresponding cluster. Since gene assignment to the clusters is the same for all states, the arrays can be directly compared with one another.</p

Representation of transitions between the steady states caused by external cues.

<p>(a) The plot shows the trajectories of the system from an initial to a final steady state under the influence of an external cue in the space spanned by the three principal components. A slightly perturbed steady state was used as the initial condition. Since amastigote-to-trypomastigote and trypomastigote-to-amastigote transitions overlap, only the first one is shown. Each trajectory has 10 intermediate states represented by small circles. (b), (c), (d) and (e) 2D projections of the pseudo-potential landscapes corresponding to the phenotypic transitions mentioned above.</p

Life cycle module.

<p>(a) Architecture of the seven-node subnetwork linked to the parasite’s life cycle. The action of environmental cue <i>μ</i> = 4 is shown as an example. (b) Boolean dynamics of the life cycle module. The basin of attraction of the seven-node module under the action of environmental cue <i>μ</i> = 4 is shown. This external signal leads the network to the trypomastigote state. Here, the nodes represent the module states and the edges represent the transitions. The module states are characterised by the sign of the clusters, which in turn are arranged in box according to their cluster IDs. Under the action of this perturbation, the final state is always the trypomastigote stage (white box). Some states reach this final state by going through different intermediate steps, while others (represented by the biggest circle) reach it in only one step.</p

Synchronization for interacting clock neurons: Actogram and histograms.

<p>A: Double plot actogram (for 7 days under LD condition followed by 7 days under DD condition) of averaged corresponding to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033912#pone-0033912-g009" target="_blank">Fig. 9</a> for , (other parameter values are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033912#pone-0033912-t001" target="_blank">Table 1</a>). The 7 days under LD condition are indicated by the white-black bars. B1, B2: Histograms of phase shift. C1, C2: period obtained by fitting Eq. (2) to the time course of concentration at each clock neuron. B1, C1 correspond to LD condition, and B2, C2 to DD condition.</p

GRN representation of the steady states of <i>T. cruzi</i>.

<p>The network edges represent the regulatory links between the gene clusters, while the nodes represent the clusters themselves. The labels inside the nodes correspond to the cluster IDs. Additional information about the clusters can be found in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146947#pone.0146947.s013" target="_blank">S5</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146947#pone.0146947.s015" target="_blank">S7</a> Tables. The regulatory links indicate either the activation (arrows) or the repression (lines ending in circles) of the clusters. A seven-node subnetwork that controls the dynamics of the parasite’s life cycle is highlighted.</p

Synchronization degree and period for noninteracting clock neurons.

<p> (top), period (bottom), in the -space, obtained by averaging over a set of 50 noninteracting pacemakers in the last 5 days. Plots on the left correspond to LD condition, plots on the right correspond to DD condition ().</p

Synchronization degree and period for interacting clock neurons with

<p><b> and </b><b>. </b> (top) and period (bottom) in the -space, obtained by averaging over the cell population in the last 5 days, when the transport into the nucleus, , is replaced by , and the transport from the nucleus, , is replaced by . Panels on the left correspond to LD condition, and panels on the right correspond to DD condition ().</p

Synchronization degree and period for interacting clock neurons with

<p><b>. </b> (top) and period (bottom) in the -space, obtained by averaging over the cell population in the last 5 days, when the transport into the nucleus, , is replaced by . Panels on the left correspond to LD condition, and panels on the right correspond to DD condition ().</p