Maximally Informative Next Experiment (MINE)
The objective of the MINE approach is to develop a quantitative criterion (or criteria) for the amount of additional information that can be gained about the genetic network from the “next” experiment to be performed; and then to maximize this “measure of additional information”, denoted by V(U), with respect to the choice of the design or “control” parameters of the next experiment, denoted by the control vector U. Control vector U comprises all those parameters which are known to, and are to some extent controllable by, the experimenter and which completely characterize measurements to be performed and the external conditions and perturbations applied to the biological system during the experiment. Two critical inputs for the MINE calculation are the underlying network kinetic rate equation model of the genetic network and any available “prior” or “old” experimental data. In a recently developed ensemble simulation approach 
, these two inputs are combined both to constrain the unknown kinetics model parameters and to predict the likely information content V(U) for the next experiment, given U. Technical details and underlying conceptual ideas of the MINE approach are described in the Materials and Methods
. Here we have used one of the MINE criteria in the Materials and Methods
det(E(U)), Eq. (16), to guide the design of new experiments on the biology of the clock. This criterion is the determinant of the ensemble correlation matrix E(U) between predictions
. The predictions here are of the log concentrations of wc-1
, and frq
mRNAs over time in the next experiment.
When the predictions of two models in the fitted ensemble (the collection of all models consistent with available data) are highly correlated, the models will be difficult to distinguish by the next experiment U; when the predictions of two models in the ensemble are less correlated, they will be more easily distinguished in the next experiment U. A higher value of the MINE criterion V(U) recommends the experiment U for which predictions between any two randomly selected models in the fitted ensemble are more uncorrelated and hence more distinguishable. Each MINE calculation is done within the constraint of a fixed budget (i.e., 13 microarray chips per experimental cycle or equivalently, 13 time points to be sampled). The budget and hence the number of time points determine the dimension of the correlation matrix E(U).
Two possible hypotheses have been developed for the clock mechanism in and , from 
. An older and slightly more realistic genetic network 
in was used to guide the MINEing because the simpler genetic network in was developed while the MINE experiments were underway. The older network 
allows a light and dark form of WCC 
. At the conclusion of the Computing Life enactment, these two different networks are tested against each other.
Cycle 1 - Which genes are circadian?
The first series of microarray experiments were designed to determine how many genes are under clock-control. If such genes were outputs of the clock mechanism in , then they should be able to maintain an endogenous rhythm of ~22 hrs (hrs) in the dark. The first experiment involves growing the organism in the dark for 48 hrs to observe the endogenous rhythm. The initial MINE design question concerns how often should we sample and when should we start sampling. The spacing between observations is denoted by tS
, and the delay till the first observation by tL
. The maximum in spacing (tS
) is limited by the time over which circadian rhythms are maintained in liquid culture and the cost constraint of 13 microarray chips (see Materials and Methods
). A MINE calculation using published data 
results in , based on the genetic network in .
The “best” experiment, with maximum det(E(U)) – in the upper back corner of – is to start sampling immediately and to use the maximum spacing of 4 hrs between observations. This was the microarray experiment, performed (see Materials and Methods
) with the results shown in . These experimental results would suggest that as many as 43% of the genes could be clock-controlled. A more detailed statistical analysis below reduces this percentage to 25%. There are 2436 (22%) circadian genes with light response elements
(LREs) upstream 
out of 11,000 genes, which is still considerably higher than 2–10% of circadian genes reported for Drosophila 
and Arabidopsis 
, and 10% higher than that reported in 
. Our percentage, however, is not out of line with estimates of 36% based on in vivo
enhancer traps in Arabidopsis 
In addition to the 11,000 N. crassa
genes on each chip (including 43 genes used as positive controls), the chips carried 633 negative control oligonucleotide sequences including those derived from plant, bacterial, phage, and N. crassa rDNA
sequences. The empirical false positive and false negative rates are reported in for each microarray experiment. For the first microarray experiment (cycle 1), the empirical false positive rate is 18% with the nominal significance level of the periodicity test used. Of these 4721 circadian genes, 2436 of them have a LRE upstream 
. With a multiple test correction suggested for microarray analysis by Storey 
and implemented as in Benjamini and Hochberg 
, the number of circadian genes with upstream LREs drops to 1460. In this multiple test correction the ranked list of genes sorted by their P-values is simply trimmed from the high end near the nominal significance level (of P-values) to control the False Discovery Rate (FDR) as described in 
. The target FDR is set to the nominal significance levels in . If we subtract the 18% of false positives, then 43−18
25% of the genome would appear to be under clock-control. The estimated percentage of circadian genes (25% corrected for false positives) is close to the uncorrected percentage of circadian genes with LRE(s) upstream (22%). Requiring the presence of an upstream LRE appears to be a good filter for circadian genes.
Table 1 Observed fraction of false positives and false negatives among 633 negative controls on each microarray chip (see Materials and Methods) and among 43 distinct genes as positive controls using reported clock-associated genes .
Circadian oscillations are seen in along rows by the alternating pattern of red (high expression) and green (low expression) for different genes, albeit with different phases. There also appear to be two clusters of known clock-associated genes with similar transcriptional profiles at the top and half way up with different phases. The distribution of periods of oscillation is found in with a mean of 24.92+/−0.09 hrs, implying the oscillations are circadian as predicted. This compares well with the average period between conidiating bands of 21.64+/−0.05 hrs obtained from 135 race tube assays (see Materials and Methods
A. Blue bars show the frequency (count/2436) of 2436 genes in by their period of oscillation in hrs.
The phase of the clock-controlled genes
is also interesting in . Dusk (L/D transition) is taken as the zero time. The phase
of 100% corresponds to being 360 degrees out of phase with genes at midnight. There are morning and evening genes in . The frq
mRNA has a phase of 48%+/−16% as a typical morning gene, and the wc-1
mRNA has a phase of 69+/−12% as a typical dawn gene, being a blue-light receptor 
. RNA metabolism genes tend to be dawn genes as well with a mean of 62+/−5% (), while regulators tend to be dusk genes with a mean of 28+/−9%. Cell cycle genes among clock-controlled genes
(in red in ) tend to be morning genes with a mean of 47+/−8%, as is the cell cycle checkpoint kinase prd-4 
. This is consistent with light triggering conidiation in . The phase of genes may provide some clues as to how the clock allows the organism to adapt to its environment (see Discussion
A naïve expectation might be that while the phase would vary between different ccg
s, as in , the gene periods in would be expected to be the same. Several possible causes for this variation in period of clock-controlled genes
in present themselves. There is noise in mRNA profiling measurements on which the period estimates are based; there is also intrinsic noise in mRNA levels from cell to cell 
; and we are observing the system over a short time interval covering only 2 periods of oscillation. As illustrated in 
, it can take longer than 2 periods before the limit cycle is established and, during the transient prior to that, neither period nor phase of oscillation are well-defined. The finite observation time also limits the accuracy of the measured period by way of an uncertainty principle 
: the shorter the observation time, the greater the uncertainty in frequency and period.
Cycle 1 microarray results were validated by RT-PCR (see next section) on twelve genes including wc-1
, and frq
relative to an rRNA standard with excellent quantitative agreement (). The surprise was seeing oscillations in the wc-2
mRNA with a period of 22.17 hrs+/−1.66 hrs, which have not been reported before (see validation in the next section). The presence of a LRE upstream of the wc-2
gene would suggest adding additional feedback loops to wc-1
in and to make them autoregulatory. Evidence for an autoregulatory loop for wc-1
has recently been provided 
. Oscillations in wc-1
mRNA are weak if plotted on the same scale as frq
mRNA levels, as expected 
. The periods for frq
, and wc-2
mRNA oscillations of 21.40+/−1.69 hrs, 23.5+/−2.47, and 22.17+/−1.66, respectively, in agree well with the period of banding in race tubes above, namely 21.64+/−0.05 hrs 
RT-PCR results for cycles 1–3 validate results of oligonucleotide arrays for wc-1, wc-2, and frq mRNA levels in cycles 1–3 of the Computing Life paradigm.
Cycle 2 - Which genes are light-responsive?
Each of these 2436 circadian genes from cycle 1 could be under the control of: (1) WCC; (2) a different oscillator 
; or (3) multiple oscillators 
; or be false positives. The chance of the latter is only 18% (see ). As shown in , an important element to the clock is light-entrainment. As the organism is grown under different “artificial days”, that is, different periods of alternating light exposure, the organism speeds up or slows down its biological clock.
If these genes were under WCC-control, then they should also be light-responsive according to the genetic network hypotheses in and . This poses the question of what artificial day period should be used for the experiment. A MINE calculation results in using published results 
plus the data in (cycle 1), i.e.
, the MINE calculations are cumulative with respect to data already obtained.
MINE calculation to determine what artificial day to use in cycle 2.
The MINE results, shown in , suggest a long artificial day with a half-period of daylight of between 19 and 24 hrs. A second cycle of microarray experiments was therefore performed in which the light was turned back on after 24 hrs in a 48 hour observation period (see Materials and Methods
). Results are shown in . Among these 3374 light-responsive genes (or 31% of N. crassa
genes), 1725 (or 16% of the genes) responded to light in and possessed LREs upstream. With the Benjamini and Hochberg 
multiple-test correction, 1026 out of these 1725 genes with upstream LREs remain significant. In a similar experiment Lewis et al. 
report detecting 22 light-responsive genes induced out of 1343 distinct genes arrayed as cDNAs, or 3%, and Ma et al. 
report 34% of the unique genes in Arabidopis thaliana
induced or repressed. Among the 31% of light-responsive genes detected here, up to 17% could be false positives, leaving 14%
31%−17% as light-inducible. Among the 31% of light-responsive genes, 56% were induced (as opposed to repressed). The percentage of 0.56×14%
8% is still higher than the 3% of Lewis et al. 
(and less than the 31% of A. thaliana
). The estimated percentage of light-responsive genes (14% corrected for false positives) is close to the uncorrected percentage of light-responsive genes with LRE(s) upstream (16%). Requiring an upstream LRE also appears to be a good filter for light-responsive genes.
Figure 10 Transcriptional profile of approximately 1725 genes with LREs upstream at 0, 4, 8, …, 24, 24.3333, 24.6667, 25, 26, 28, …, 48 hrs (values staggered on x-axis) after shift from light to dark (L/D) followed by D/L transition 24 hrs later, (more ...)
A total of 768 genes were both circadian and light-responsive (), and the chance that any one of these 768 genes is a false positive would be (0.18)×(0.17)
0.03 (), since the experiments were done independently. These 768 genes then remain candidates for ccg
s in or . The response by genes to light falls into two clusters, one cluster being turned off (in the top part of ) and one cluster being turned on (in the bottom part of ). The positive response of some genes to light appears largely transient with a burst of expression after the Dark-to-Light (D/L) transition while other genes appear to have a sustained response after the D/L transition. Most of the known clock-associated genes fall within the bottom cluster of light-responsive genes with LREs upstream, as expected.
Figure 11 Classification of 4380 N. crassa genes with upstream LREs in a Venn Diagram by their response in each of the three microarray experiments: (1) cycle 1 (assay for circadian rhythm); (2) cycle 2 (assay for light response); and (3) cycle 3 (assay for response (more ...)
As a control, these results from cycle 2 were compared with a near replicate of this experiment reported in 
, using a different microarray technology and only a sample of the genes in N. crassa
. With a power of 53% () in our experiments, we would expect to see around 53% concordance with the experiments reported in 
. In fact, we saw 64%+/−20% of the genes reported as light-responding in 
in our cycle 2 experiments with good agreement to the 53% expectation.
Cycle 3 - Which genes are under WCC-control?
Another prediction of the genetic networks in or is that if WCC were dialed down (i.e.
, the mRNA level of wc-1
is reduced by use of a QA-inducible promoter as described in Materials and Methods
), then a gene under its direct or indirect control should experience a sudden change in its mRNA level. To test this with a gene knock-down experiment, it is necessary to ascertain first what gene should be perturbed to yield maximum information about the genetic network in . A MINE calculation was done using published results 
plus the data in (cycle 1) and the data in (cycle 2) as described in Materials and Methods
The MINE calculation in , suggests that the most informative knock-down is to reduce wc-1
to 10% of its original transcriptional activity. As detailed in Methods and Materials
, the knock-down was engineered with a mutation in the native wc-1
and with a quinic acid inducible copy of wc-1+
introduced at another locus, producing a knock-down to 30% of its original activity; the results are shown in . A total of 4655 WCC-responsive genes were found to respond, but only 2323 of these genes had a LRE upstream as reported in . With the Benjamini and Hochberg 
multiple-test correction, 1445 out of these 2323 genes with upstream LREs remain significant. The estimated percentage of WCC-responsive genes (20% corrected for false positives) is close to the uncorrected percentage of WCC-responsive genes with LRE(s) upstream (21%). Requiring an upstream LRE remains a good filter for WCC-responsive genes.
A 90% knock-down of the wc-1 gene is the MINE experiment.
Figure 13 Transcriptional profile of approximately 2323 genes with upstream LREs at 0, 0.1667, 0.3333, 0.5000, 0.6667, 0.8333, 1, 2, 4, 8 hrs (time points appear on x-axis) after shift simultaneously from light to dark (L/D) and from quinic acid (0.3%) (more ...)
Most of the frq gene mRNAs were dialed down, as expected. The frq gene belongs to a cluster of genes being turned off in the top part of . Both wc-1 and wc-2 responded differently than frq and belong to the second larger cluster of genes being turned on (at least transiently) in the bottom part of . They have a fast transient response about 20–40 m after the QA/GAL (L/D) transition and then a drop off (see ).
Also of interest are the 440 genes that are both circadian and light-responsive, but not under WCC control in . These 440 light-responsive and circadian genes which are not apparently under WCC-control, could be responding indirectly to genes under the control of WCC. They could also be false-negatives under the WCC-responsive assay (); they could be responding through a yet to be identified oscillator 
; or they could be responding through multiple oscillators 
. The chance that any one of them is a false positive is 0.03
(0.18)×(0.17). The genes cpc-1
, NCU05429, and ccg-16
(WO6H02), have been previously identified as candidates for being under the control of another oscillator 
. All three were found to be circadian here (confirming the results in 
), and cpc-1
were found to be light-responsive as well. All of them were found not to be WCC-responsive here, although in the case of ccg-16
this appears to be a false negative 
Lewis et al. 
conducted a related experiment that over-expressed wc-1
. Only 18% of the induced genes corresponded to ones that we detected. A similar result was seen with overexpression of CLOCK in Drosophila 
. There could be a variety of explanations, but it is not unexpected in a signaling system that over-expression leads to a different outcome than a knock-down, particularly when there are other coupled interacting pathways to those in or . See, for example, the platelet-derived growth factor β receptor (PDGFRβ) signaling system 
or the sonic Hedgehog (shh
) signaling system in neurogenesis 
, where high and low levels of shh
have different neurogenetic outcomes. The response of the clock to wc-1
over-expression is apparently not the same as lowering wc-1
expression. An additional MINE calculation analogous to (results not shown) also suggested that that an over-expression experiment would not be as informative as a knock-down.
The Computing Life paradigm has led us to the discovery of 328 clock-controlled genes
supported by all three series of microarray experiments and having an upstream LRE. Among these 328 genes, the chance of a false positive is (0.18)×(0.17)×(0.22)
0.0067 (), the three microarray experiments having been done independently. A total of 104 of these 328 genes survive the multiple test correction in all three cycles 
. These genes satisfy the three predictions of the genetic network and constitute clock-controlled genes
(). Of these 328 clock-controlled genes
, 314 of them are distinct on the arrays (some genes are represented multiple times; see Materials and Methods
Direct test of the auto-feedback loops activating wc-1 and wc-2
All three cycles of microarray experiments support the presence of auto-feedback loops for WCC activating wc-1
. In cycle 1 there was evidence that wc-1
mRNAs were circadian in . In cycle 2 there was a fast light-response by wc-1
(of less than an hour) in . In cycle 3 both wc-1
were WCC-responsive in and have upstream LRE elements. An experiment with a short 6 hr artificial day is predicted by a MINE calculation in to be highly informative about the genetic network in . A prediction of the genetic network in is that the auto-feedback loops added should permit entrainment to a short artificial day of 6 hrs duration (as in ) independent of FRQ. To test this hypothesis, a strain (93-4) with a frq
mutation was subjected to a short artificial day as seen in . As can be seen, the rapid conidiation pattern with frq
in is indistinguishable from a bd
mutant in . To rule out that the conidiation response to a short artificial day is under the control of an independent light-response pathway, a mutant in bd
(87-84-6) was generated by a cross, bd his-3
(FGSC 3914). As can be seen (), the wc-1
mutation almost entirely removed banding under the artificial day of 6 hrs. To confirm this finding, the bd
(87-84-6) strain was transformed with a plasmid containing a QA-inducible wc-1+
as described (
and Materials and Methods
) and was found to band weakly when wc-1+
was induced and not to band when wc-1+
was not induced (results not shown). This establishes that banding under a short artificial day is under the direct clock control of wc-1
. In a similar entrainment experiment a double mutant wc-2KO
from the cross wc-2KO
(FGSC 11124, 65)×bd
(FGSC 1858) was subjected to a 6 hr artificial day. As can be seen in , wc-2
also nearly removed all banding. As a final confirmation of these experiments, the frq
gene was over-expressed on .001 M QA as well as turned off on glucose in a strain with a QA-inducible copy of the frq
gene (see Materials and Methods
), and these two conditions had no effect on the rapid banding (results not shown). These results serve to confirm that the rapid light response to a 6 hr day is due to the auto-feedback loops to wc-1
) and not due to the FRQ oscillator.
Light entrainment response under short artificial day by frq and wc-1 mutations provides evidence for autofeedback loops on wc-1 and wc-2 in .
The clock mechanism of three genes wc-1, wc-2, and frq is pleiotropic in its effects on metabolism
These 314 clock-controlled genes identified are involved in a broad range of biological functions: DNA metabolism, replication, repair, cell cycle, RNA metabolism, transport, carbon and energy metabolism, isoprenoid biosynthesis (including carotenoids), development, and signaling (). Periods and phases of all 295 (314–19; see below about 19) ccgs are similar in distribution to all circadian genes () with upstream LREs.
The clock of N. crassa has 295 distinct clock-controlled genes of diverse function as outputs.
The connection of the clock to development has been reported (ccg-2
, and con-6
). A recent connection to RNA metabolism has been through the frequency RNA helicase
) gene, whose product FRH co-immunopreciptates with FRQ 
. The microarray experiments here identified frh
and 16 additional genes in RNA metabolism under clock control (). In addition to frh
, 4 additional genes with products homologous to ATP-dependent RNA helicases in S. cerevisiae
, namely ROK1
, and RRP3
, are among the 295 clock-controlled genes
. At least three of these RNA helicases are involved in ribosomal RNA processing. While ribosome transcription is not under clock control (the ribosomal RNAs are not circadian in Cycle 1), almost all of the ccg
s in RNA metabolism are involved in ribosome processing and assembly, i.e.
ribosome biogenesis. These include SEN2
, and PAB1
homologs in S. cerevisiae
. The yeast PAB1
is a poly-A binding protein, and LHP1
is another distinct RNA-binding protein involved in the maturation of tRNAs and snRNAs. LHP1
has been implicated not only in the biogenesis of noncoding RNAs, but a recent ChIP/chip experiment in S. cerevisiae
has demonstrated that it targets a number of mRNAs 
. The RNase P (POP4
) binds to the RPR1
RNA, which is also a target of Lhp1p, and the PAB1
mRNA is also apparently a target of Lhp1p in yeast as well 
. Inada and Guthrie 
also report enrichment of the gene encoding the snoRNA U3 among targets of Lhp1p. The product of UTP5
is part of the processome containing the U3 snoRNA and involved in ribosome biogenesis. The clock's regulation of the ribosome appears to occur through its biogenesis rather than its transcription. This is a novel mechanism by which the clock can regulate clock-controlled genes
Connections of the clock to DNA metabolism are recently reported in humans 
. A human clock CLK2 protein physically associates with S-phase checkpoint components ATR, ATRIP, claspin, and the checkpoint kinase, Chk1. Also human CLK2-depleted cells accumulate DNA damage, engage in radio-insensitive DNA synthesis, and fail to recruit proteins, such as RAD51
, functioning in human recombination pathways. Here several putative checkpoint-associated proteins (e.g.
, NCU00560 and NCU04326) as well as 8 genes involved directly in purine/pyrimidine metabolism (NCU0 7590, 8359, 4323, 6262, 3194, 5542, and 4195) and repair (uvs-6/NCU00901
) appear to be clock-controlled genes
. The uvs-6
gene is a homolog of RAD50
in S. cerevisiae
involved in double-stranded break repair. As predicted from the results on humans 
, the RAD51
/NCU02741) was circadian and light-responsive in N. crassa
in cycles 1 and 2, but not WCC-responsive (cycle 3).
The clock connection to the cell cycle has been only recently reported in Neurospora through prd-4
, a homolog of Chk2 in yeast, a second checkpoint kinase 
. In addition to prd-4
, we have identified 2 other putative cell cycle checkpoint genes as clock-controlled genes
(NCU00560 and NCU04326), homologs of CDC4
in S. cerevisiae
. Up to 16% of rhythmic genes (cycle 1) may be involved in the cell cycle in some mouse tissues in contrast to the 3% in identified by more stringent criteria (i.e.
, positive in cycles 1–3) in N. crassa 
In that carbon metabolism showed up as significant and may have arisen due to the use of the QA-inducible switch in the last series of microarray experiments, one additional control was performed with wild type (OR74A – see Materials and Methods
) in which many QA-inducible genes were identified with microarrays by a shift from 1.5% sucrose to 0.3% QA over a 0 to 8 hr window 
. Of the 314 distinct clock-controlled genes
identified, only 19 of them were QA-inducible (with most of them being unclassified in function). Only 2 of the QA-inducible clock-controlled genes
were involved in carbon metabolism. Subtracting the 19 QA-inducible ccg
s from the 314 distinct ccg
s, 295 clock-controlled genes
Approximately one-half of these 295 clock-controlled genes
are of unknown function. The most prevalent known function among these genes are phosphatases and kinases. They make up almost half 
of the 23 genes with products involved in protein synthesis (), processing, and degradation, and at least three of the genes under DNA metabolism are known kinases/phosphatases as well (CK1, HHP1 homolog, and PP1). This plethora of phosphatases and kinases may reflect the role they play in modifying/linking the functions of wc-1
, and frq
as regulators of (to) other pathways, as well as in the coupling of the clock to varied signaling pathways and the cell cycle. For example, the phosphatases PP1 and PP2a, dephosphorylate FRQ in vitro
, thereby altering oscillator behavior 
, and the kinases CK1a and CKII mediate the phosphorylation of WCC 
. After that, DNA metabolism, RNA metabolism, and carbon/energy metabolism represent equally important outputs of the clock. The clock outputs are representative of the frequency of these functions in the proteome 
with two exceptions: a deficit of transport and unclassified genes that are ccg
Figure 16 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, ); (B) putative phosphatases/kinases (more ...)
While only one ccg
in has a product classified as a transcriptional activator (PRO1
homolog) involved in fruiting body development (kal-1
, NCU07392, 
), four other ccg
genes were classified as regulators. Their individual cyclical transcriptional profiles are given in . One of these putative regulators is an inferred ornithine decarboxylase antizyme involved in sulfur and nitrogen regulation (NCU07155) 
. This connection has also been reported in Arabidopsis 
. The remaining putative regulators identified under clock control in or were NCU00045, NCU01640 (rpn-4
), and NCU06108.
Earlier work has suggested a link between signal transduction pathways for conidiation and the clock 
. From microarray analysis here the clock is tied into a number of other signal transduction pathways as well, including stress (ccg-9/NCU09559
), oxidative stress (NCU05169), light (vivid/NCU03967
), mating (ccg-4/NCU02500
), and osmo-sensing (os-1
). The last output to the clock has only been reported recently (). For example, cut-1
involved in osmo-sensing has been reported to be under WCC control 
. Jones et al. 
have reported a role of rrg-1
in osmo-sensing reminiscent of the os
mutants. The genes rrg-1
have an upstream LRE and were found to be circadian in cycle 1, but not light-responsive or WCC-responsive 
Identifying an ensemble of genetic networks for the biological clock of N. crassa
The culmination of Computing Life is the identification of an ensemble of genetic networks describing how the clock functions from 3 cycles of microarray experiments initiated from published data 
. Results are summarized in . For 69%
(100×18/26) of the rate constants in common with 
, standard errors were reduced by the addition of data from cycles 1–3. Measured lifetimes of the wc-1
mRNA and FRQ protein remain concordant with estimated values in with an order of magnitude increase in the amount of data (see ). The long lifetime of the wc-1
mRNA provided a critical test of the genetic networks 
, and the long lifetime of the wc-1
mRNA of 7.4 hrs
continues to be supported by microarray data here. Transcription rates of frq
, A and
, as well as the deactivation rate of WCC, P, were previously identified as critical parameters for maintaining oscillations through the negative feedback loop in 
. These constants are now more sharply defined in . Eleven of the 26 parameters identified in of 
are not significantly different from those in , although a majority of the rate constants are estimated more precisely. Precision of cycles 1–3 are assessed further in the next section and .
The quality of fit of the model usually improves in successive cycles through the Computing Life paradigm. Several measures of fit are reported.
The behavior of the ensemble is displayed in . In cycle 1 the predicted oscillations of frq
mRNAs are displayed with microarray measurements. The predicted oscillations in wc-1
mRNAs are much reduced relative to the frq
mRNAs. In cycle 2 in the first 24 hrs the measurements and predictions track those in cycle 1; the correlation over all 87808
12544×7 microarray features between cycles 1 and 2 for the first 7 time points is 0.82. When the light is turned back on at 24 hrs into the cycle 2 experiment, the coordinated response of the ensemble and microarray data (particularly the frq
mRNA) to light can be seen as the clock resets 
. In cycle 3, the slow decline in the wc-1
mRNAs is seen corresponding to a lifetime of 7.4 hrs
. An alternative ensemble in from Yu et al. 
was tested and performed about the same as the genetic networks in ; the distribution of chi-squared statistics 
for the ensemble fitted to is largely overlapping with the distribution of chi-squared statistics for the networks in (results not shown). By Occam's Razor the simpler network with fewer parameters in is then preferred. The series of model-guided experiments now has identified and selected an ensemble of genetic networks describing the clock mechanism in .
An ensemble of genetic networks predicts the mRNA levels of wc-1, wc-2, and frq for cycles 1–3.
Comparison of the precision and power of microarray experiments in cycles 1–3 with other microarray experiments
A standardized way of assessing progress in the Computing Life paradigm as well for comparing the power of different microarray experiments here with others in the literature and in the future would be useful. Progress here is measured by the error per observation σ2 or error variance.
In linear and nonlinear models a standard approach to estimating the precision of an experiment is to estimate the error variance σ2 
, as it appears in the likelihood for the genetic network 
. Townsend 
illustrates by simulation and data analysis that such a common variance component can be extracted from each of a variety of microarray experiments and used to compare different experiments. Under the multivariate Gaussian assumption leading to the likelihood in 
, a simple estimator for the error per observation σ2
can be constructed for successive cycles of the Computing Life paradigm:
where n is the number of observations, χ2min
is the minimum chi-squared statistic over the ensemble 
, and σ02
is a preliminary estimate of the error per observation in the multivariate Gaussian likelihood 
. This preliminary estimate of σ02
was allowed to vary across observations. In the preliminary data drawn from the literature 
is 0.02 for the genetic network in 
and used on the RHS of expression above. Preliminary estimates of σ02
, and 36σ02
for published data 
, microarray data in cycles 1–3, and for conidial banding data from , respectively, were used in calculating χ2min
. These weightings were selected to give equal weight per time to different experiments in the ensemble fitting process.
In , the progress in reducing the error variance in successive cycles through the Computing Life paradigm is reported. The fourth cycle began with a switch to the genetic network in . In cycle 4 all experiments in different cycles were allowed to have their own initial conditions for initial species concentrations. An additional 842 data points of conidial banding data were collected under the regimen of a 48 hr artificial day (cycle 2). A downward trend in the estimated error variance across cycles is evident.
The final estimate of σ2
is 0.03, slightly larger than our initial guess based on published data from Northerns, Westerns, and race tubes 
. The advantage of having this estimated error variance is that it can be readily compared with other families of models, such as simpler linear models, used in microarray analysis 
as well as to other experiments by other laboratories. The estimated error variance also allows diagnosis of whether or not further experiments will refine the model ensemble. Based on the downward trend in the estimated error variance further cycles would be predicted to be profitable.
In each cycle of the Computing Life paradigm we constructed a test statistic (F or t) for a response on a gene by gene basis and calculated the same for all genes with LRE elements. Imagine extracting a ranked list of these significant statistics in a particular cycle. Townsend 
has shown that the median value of this significant test statistic in this list is a good proxy for power from simulations. This statistic is called the gene expression level 50 (GEL50
). With each GEL50
statistic, there can be an associated fold-change in expression level that can often be substituted for the original statistic for ease of interpretation. The advantage of this GEL50
statistic is that it allows easy comparison across experiments reported in the literature and in the future. The GEL50
is reported for cycles 1–3 in . These values are in the range of at least 5 other microarray studies