A genetic network for the biological clock from [7].

<p>Molecular species (<i>i.e.</i>, reactants or products) in the network are represented by boxes. The <i>white-collar-1</i> (<i>wc-1</i>), <i>white-collar-2</i> (<i>wc-2</i>), <i>frequency</i> (<i>frq</i>), <i>and clock controlled gene</i> (<i>ccg</i>) gene symbols can be superscripted 0, 1, r0, r1, indicating, respectively, a transcriptionally inactive (0) or active (1) gene or a translationally inactive (r0) or active (r1) mRNA. Associated protein species are denoted by capitals. A phot (in yellow) denotes a photon species. Reactions in the network are represented by circles. Arrows entering circles identify reactants; arrows leaving circles identify products; and bi-directional arrows identify catalysts. The labels on each reaction, such as S₄, also serve to denote the rate coefficients for each reaction. Reactions labeled with an S, L, or D denote transcription, translation, or degradation reactions, respectively. Reactions without products, such as D₈, are decay reactions. Reactions, such as A and P, have cooperative kinetics: (A) n WCC+<i>frq</i>⁰→<i>frq</i>¹ and (P) WCC+m FRQ→WC-2+m FRQ. The n and m are Hill coefficients or cooperativities. Only one reaction, the “A” reaction, has a back reaction, , <i>frq</i>¹→n WCC+<i>frq</i>⁰, included, with non-zero rate. The rate constants specify the right hand side of the kinetics model in equation (1) through the Law of Mass Action in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#s2" target="_blank">Materials and Methods</a>.</p

A 90% knock-down of the <i>wc-1</i> gene is the MINE experiment.

<p>The decadic log of the MINE criterion det(E) is displayed as a function of percent remaining activity of the three clock genes <i>wc-1</i>, <i>wc-2</i>, and <i>frq</i>. The matrix E is the correlation matrix of the predictions, emphasizing independence of predicted data points f(.,u_i). The predictions are for the mRNA levels of <i>wc-1</i>, <i>wc-2</i>, and <i>frq</i> over time.</p

MINE calculation to determine when to start sampling (t_L) and how often (t_S).

<p>The MINE surface is plotted as function of the lag t_L in hrs and spacing t_S in hrs; higher values on the MINE surface suggest the preferred design points (t_L, t_S). Color contours of the log of the MINE criterion det(E) are overlayed as a function of the lag (t_L) and spacing (t_S) to show points on the surface of similar MINE values. The MINE surface suggests to start sampling immediately (small t_L) and to make the spacing (t_S) between observations as large as possible. The maximum permissible spacing (t_s) between observations is 5 hrs, as determined by two constraints. One, there is the cost constraint of 13 microaray chips per cycle, and two, beyond a 50 hr experiment in cycle 1 stable oscillations in liquid culture are not guaranteed.</p

Transcriptional profiles of individual genes with upstream LRE elements in the dark (cycle 1) in the functional categories of: (A) regulation (MIPS functional classification categories 1.02.04, 11.02.03, and 16, [37]); (B) putative phosphatases/kinases (functional classification category 14.07.03); (C) signal transduction (categories 30.01, 32.01, 32.05, 34.11); (D) Development and growth (categories 40.01, 40.02, 41.01, 43.01).

<p>The mean mRNA level of each gene was subtracted from the 13 individual mRNA levels measured on each gene in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone-0003105-g006" target="_blank">Fig. 6</a>. Data are from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone-0003105-g006" target="_blank">Fig. 6</a>.</p

Computing Life Paradigm.

<p>The “perturb” and “observe” steps represent the experimentation phase; the “fit”, “predict” and “evaluate” steps are the main components of the genetic network ensemble simulation phase; and the “select” step is the MINE design phase which closes the Computing Life workflow cycle.</p

RT-PCR results for cycles 1–3 validate results of oligonucleotide arrays for <i>wc-1</i>, <i>wc-2</i>, and <i>frq</i> mRNA levels in cycles 1–3 of the Computing Life paradigm.

<p>The scale on the left is for fold expression change for oligonucleotide array measurements, and the scale on the right is fold expression change for RT-PCR results. rRNA was used as a standard in the RT-PCR experiments. Time on the x-axis is in hrs. Grey bars indicate lights off, and a white bar, lights on.</p

The clock of <i>N. crassa</i> is remarkably adaptive in its entrainment to varied artificial days.

<p>Replicate race tubes are inoculated at one end and subject to a 6 hr, 18 hr, and 48 hr artificial day over 7 ordinary days. The clock is manifested by the appearance of orange bands (<i>i.e.</i>, asexual production of spores) as the culture grows to the other end of the tube. In each artificial day the race tubes experienced (A) 3 hrs light and 3 hrs dark, (B) 9 hrs light and 9 hrs dark, or (C) 24 hrs light and 24 hrs dark. It can be seen that the number of conidial bands tracked the number of artificial days experienced. Race tubes were prepared as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Dharmananda1" target="_blank">[30]</a> and in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#s2" target="_blank">Materials and Methods</a> and were inoculated using the <i>bd</i> mutation (FGSC 1858).</p

Transcriptional profile of approximately 2436 putative genes with LREs upstream at 0, 4, 8, …, 48 hrs (values staggered on x-axis) after shift from light to dark (L/D) after background subtraction, normalization within arrays relative to the grand median of each chip, logging, and clustering with average linkage using Euclidean distance between mRNA profiles of different genes [38].

<p>The bright green is −3, and the bright red is +3 is expression level on a decadic log scale. Data arose from 13 chips probed with a biotin labeled aRNA. Over 43 known clock-associated genes are overlayed in the right margin of this microarray experiment including varied known <i>ccg</i> genes. Genes in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone-0003105-g002" target="_blank">Fig. 2</a> are represented at least 5 times on each chip (explaining why <i>frq</i> appears 5 times in the margin). The 2436 putative genes with LREs upstream were selected by fitting A₀+A sin (ωt+φ) by nonlinear least squares <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Ueda1" target="_blank">[44]</a> to the profile of each of the 11,000 genes, and those with a significant regression sum of squares contribution with respect to the amplitude A in F_1,9>5.12 (α = 0.05) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Bloomfield1" target="_blank">[94]</a> and with a period between 16 hrs and 30 hrs are displayed (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone-0003105-g001" target="_blank">Fig. 1</a> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Aronson1" target="_blank">[5]</a> for <i>frq</i>^r mRNA peak separation of 16 hrs and 30 hrs). This work <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Aronson1" target="_blank">[5]</a> establishes a standard for what is considered acceptable variation in the estimated period of the oscillator. See text for a reexamination of this standard. The smallest significant F_1,9 ( = 5.12) observed among circadian genes with upstream LREs had an estimated amplitude of 497 and 3.98 fold variation in mRNA levels over time in contrast to the amplitude of <i>frq</i> mRNA, 974+/−79. The smallest significant amplitude (63 with an F_1,9 = 8.29) estimated among circadian genes with LREs upstream had 1.44 fold variation in mRNA levels over time. A gray bar at the bottom indicates lights off.</p

Rate coefficients in the genetic network model (Fig. 4) of the biological clock (n = m = 4) based on data from cycles 1–3 predicting the clock's observed oscillations, light response, and <i>wc-1</i> perturbation (Fig. 17).

<p>Ensemble mean and ensemble standard deviation σ(X): = [2>−²]^1/2 for rate coefficients (<i>X</i>) in the <i>n</i> = <i>m</i> = <i>4</i> biological clock model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone-0003105-g004" target="_blank">Fig. 4</a>. For a <i>k</i>^th order reaction (with <i>k</i> = <i>1</i>,<i>2</i>, or <i>5</i>), the rate coefficient is given in units of 1/(hour×cu<i>^k−1</i>) where “cu” represents the arbitrary, but common model unit of concentration for all species, except for the <i>photon</i> species where 1 cu(photons) = 0.20 µmole(photons)/(s·m²), see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#s2" target="_blank">Materials and Methods</a>. The estimated value of 1/〈<i>D</i>₆〉≈5 hrs is consistent with the FRQ protein life-time of ≈4–7 hrs, estimated from the FRQ-decay data of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0003105#pone.0003105-Cheng2" target="_blank">[96]</a>.</p

The bright green is −3, and the bright red is 3 is expression level on a decadic log scale

Data arose from 16 chips probed with a biotin labeled aRNA. Over 43 known clock-associated genes are overlayed in the right margin of this microarray experiment including varied known genes. Genes in are represented at least 5 times on each chip (explaining duplicate entries of , for example). The 1725 genes with upstream LREs were selected by a t-test comparing the mean of the first seven time points in the dark with the mean of time points 24.333, 24.6667, 25, 26, 28, and 32 hrs in the light with those havin