Parameter correlations.

<p>This figure shows correlation matrices for parameter values derived from linear analysis (A), and bootstrapping (B), for <i>Kr</i> (green frame), <i>kni</i> (red frame), and <i>gt</i> (blue frame). Parameter notation: (production rate), (decay rate), (diffusion rate), and (production delay; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi.1003281.e004" target="_blank">equation 1</a>). Colors indicate sign and strength of correlations. Matrices in (A) are calculated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi.1003281.e131" target="_blank">equation 6</a> (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#s4" target="_blank">Materials and Methods</a>). Matrices in (B) are derived from the singular value decomposition of bootstrap distributions.</p

The systems biology modeling cycle.

<p>This cycle illustrates the interplay of experiment and modeling in modern systems biology (adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi.1003281-Kitano1" target="_blank">[26]</a>). Expression data are acquired and quantified. A model is formulated based on a regulatory hypothesis intended to explain the observed expression patterns. The model is solved and fit to data (reverse engineering). Model output and parameter values are then analysed to yield predictions and interpretations of the biological data. If necessary, the process is repeated—acquiring new data and improving the model—until a satisfactory explanation of the observed phenomena is achieved. Model fits are shown on the left. The panel describing the model depicts the processes of protein production, diffusion, and decay within and between nuclei (energids; lower panel). The upper panel shows the mitotic schedule (M: mitosis, red; otherwise: interphase, blue background), with those time points indicated for which we have data. See text for details.</p

Comparison of residual scores and parameter estimates obtained from pLSA and eSS optimisation approaches.

<p>Comparison of residual scores and parameter estimates obtained from pLSA and eSS optimisation approaches.</p

Comparison of model output and measured protein concentrations.

<p>(A) Spatial profiles of <i>Kr</i> (green), <i>kni</i> (red), and <i>gt</i> (blue) for early (T1), mid (T4), and late (T8) time classes during C14A. X-axes represent A–P position (in %), Y-axis show relative concentrations (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi-1003281-g002" target="_blank">Figure 2A</a>). (B) Temporal dynamics of peak concentrations for the central <i>Kr</i> domain (left), the abdominal <i>kni</i> domain (centre), and the posterior <i>gt</i> domain (right). X-axes represent time, Y-axes show relative concentrations (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi-1003281-g002" target="_blank">Figure 2C</a>). In all panels, model output is shown as a dashed black line; measured protein concentrations are shown as dark colored lines (mean) and lightly shaded background (standard deviations).</p

Confidence intervals for parameter estimates.

<p>This figure shows 95% confidence intervals for parameters (production rate), (decay rate), (diffusion rate), and (production delay; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#pcbi.1003281.e004" target="_blank">equation 1</a>) for <i>Kr</i> (green), <i>kni</i> (red), and <i>gt</i> (blue). are independent, dependent intervals obtained from linear analysis (connected solid lines), are intervals obtained from bootstrapping (dashed lines). Dots (on solid lines) represent eSS parameter estimates, diamonds (on dashed lines) those from SA. Striped grey background indicates parameter values that lie outside the search space limits used for optimisation. Note that only a subregion of the search space is shown in each panel (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003281#s4" target="_blank">Materials and Methods</a> for values of search space limits).</p

Comparison of gap gene mRNA and protein expression patterns.

<p>(A) Time series showing integrated one-dimensional expression patterns of gap gene mRNA (left column) and protein (right column) along the A–P axis in cleavage cycle C14A (time classes T1–T8). <i>Kr</i> is shown in green, <i>kni</i> in red, and <i>gt</i> in blue. X-axes represent A–P position in %, where 0% corresponds to the anterior pole of the embryo. Y-axes represent mRNA and protein concentrations in relative units. Grey background indicates the region displayed in (B). (B) Space-time plots indicating domain boundary positions of the central <i>Kr</i> domain (top), the abdominal <i>kni</i> domain (middle), and the anterior and posterior domains of <i>gt</i> (bottom). Solid patterns indicate mRNA patterns, dashed lines protein. Time flows downwards. (C) Temporal dynamics of peak expression for the central <i>Kr</i> domain (top), the abdominal <i>kni</i> domain (middle), and the posterior <i>gt</i> domain (bottom). Solid lines indicate mRNA, dashed lines protein. Relative concentrations (as in (A)) are plotted against time.</p