PMC

The biological clock of N. crassa and its model entrain to an artificial day of 12-, 18-, and 36-h duration. (A) Six hours of light followed by 6 h of night and repeating. (B) Nine hours of light followed by 9 h of night and repeating. (C) Eighteen hours of light followed by 18 h of night and repeating. Dots indicate data points (), and shaded regions are the predictions of the model ensemble supplemented with one new reaction, C₃, to allow a light response: WC-1 + WC-2 + photon → WCC. The solid line is the mean of the ensemble predictions. The model ensemble here was initialized from an earlier accumulation run using published data (see Methods).

Comparison of experiments. A model ensemble for the genetic network in , with cooperativities n = m = 4, predicts various profiling data on the biological clock of N. crassa in the dark. In each image, predictions of the model ensemble for the decadic log (lg) of concentration (in model concentration units, cu; see Methods) are shown with ±2 ensemble SDs (shaded areas) about the ensemble mean (continuous lines). The points are the experimental log data. (A) Levels of conidiation for a bd mutant, hypothesized to be a measure of a CCG protein, over a 7-day interval. (B) Levels of wc-1^r = wc-1^r0 + wc-1^r1 and frq^r RNA over time t. (C) Levels of FRQ and WC-1 protein over time t.

A genetic network for the biological clock. Molecular species in the network are represented by boxes. The white-collar-1 (wc-1), white-collar-2 (wc-2), frequency (frq), and clock controlled gene (ccg) gene symbols can be superscripted 0, 1, r0, and r1, indicating, respectively, a transcriptionally inactive (0) or active () gene or a translationally inactive (r0) or active (r1) mRNA. Associated protein species are denoted by uppercase letters. Reactions in the network are represented by circles. Arrows entering circles identify reactants, arrows leaving circles identify products, and bidirectional arrows identify catalysts. The labels on each reaction, such as S4_, also denote the rate coefficients for each reaction. Reactions without products, such as D8, are decay reactions. Reactions A and P have cooperative kinetics: (A) n WCC + frq⁰ → frq¹ and (P) WCC + m FRQ → WC-2 + m FRQ. n and m are Hill coefficients or cooperativities. Only for the A reaction, a back reaction, (Ā) frq¹ → n WCC + frq⁰, is included, with nonzero rate coefficient Ā.

Comparison of model fits. Some model ensembles, using modified or simplified versions of the model in , outperform the original model in terms of χ² values. A histogram of values of χ² = −2 lnQ + const (see Methods) is shown for varying model ensembles. (A) The number of molecules of WCC (n) or FRQ (m) working together cooperatively (i.e., the Hill coefficients) in reactions A and P are varied with n = m. Also, the histogram of χ² values for a model ensemble without posttranscriptional regulation of wc-1 by FRQ is reported. Some models with less cooperativity in the action of WCC or FRQ (e.g., n = m = 3, dark-blue curve) or without posttranscriptional regulation (light-blue curve) have smaller χ² values on average than the n = m = 4 model. We have explored in detail models with n ≠ m (for n, m = 2,…, 4) with additional Monte Carlo runs as in ; it was unnecessary to consider n = 1 and m = 1,…,4 or m = 1 and n = 1,…,4 because these cases do not satisfy the condition nm > 4 necessary for oscillations (see SI Text). The best model ensemble (histogram most shifted to the left) to date remained n = m = 3. (B) The deactivation reaction (P) is varied, allowing five different deactivation mechanisms (including the one in , in black) to be compared for their goodness of fit. Each deactivation reaction is defined in B Inset.