Cell culture was scaled up to systematically follow the growth and development of as many as a hundred Dictyostelium clonal populations at a time (Figure 1a). We designed a robotic system (Figure 1b; see Materials and methods) to capture both early and later events in the morphogenetic cycle. Figure 1c summarizes a typical experiment with our wild-type strain, AX4. Cell-cell signaling mediated by extracellular cAMP was visualized by detecting optical density fluctuations that reflect cell shape change in response to passing cAMP waves 181920. By 3 hours after the cells begin to develop, a few fragments of weak optical-density waves have begun to emerge from the background (Figure 1c, 3 hours; see also Additional data file 1 for a movie), a characteristic feature of self-organization in excitable systems 21. During the next few hours, cells show little directed movement and the cell density is spatially uniform (Figure 1c, 5 hours). The images were enhanced by subtracting consecutive frames (Figure 1c, 3 hours and 5 hours; right panels compared to the left; Additional data file 2). Optical density waves quickly develop spiral cores, which become organizing centers for cell territories by 6.5 hours, when territories of different sizes with aggregating streams of cells are readily apparent (Figure 1c, 6.5 hours; see Additional data file 1). By 15 hours these territories have become rounded masses of cells, the majority of which by 18 hours have reached the motile slug stage, each slug containing from a few thousand to around 10⁵ cells (Figure 1c, 18 hours; Additional data file 3). By around 40 hours the slugs have migrated and culminated to form fruiting bodies (Figure 1c, 40 hours).

The entire video clip from the first stage of our analysis can be summarized by wavelet analysis, where wave frequency and power spectrum are plotted as a function of time (see Materials and methods) 16. The wavelet power spectrum (Figure 1d; z-axis in pseudocolor) represents the strength of the signal oscillating at the specified periodicity (s) (Figure 1d; y-axis) as the system develops in time (Figure 1d; x-axis). A typical analysis with wild-type cells is illustrated in Figure 1d. At t = 150 minutes, long-period (15 min) features have begun to emerge. The wave period evolves slowly and smoothly to t = 275 minutes, levels off for 50 minutes, then abruptly switches off as cells migrate to form well defined territories. At approximately t = 400 minutes a second long-period feature emerges, corresponding to the cell streaming pattern seen in Figure 1c at 6.5 hours. These results are in good agreement with observations on wild-type cells grown under conventional culture conditions 16, and provide us with a quantitative summary of the first 12 hours of development.

We have sampled 1,800 insertional mutants, hereafter referred to as the 'unbiased set' from an ongoing large-scale mutagenesis project 22, and 400 or so containing many previously isolated mutants (see Materials and methods). In addition to the quantitative features just described for the early developmental stages, qualitative features such as cell morphology during axenic growth, slug motion/morphology and fruiting body structure (Table 1) were obtained from the movies and observation of the samples by microscopy. From these features, a phenotype matrix p_ij was obtained (see Materials and methods). The matrix is a digital representation of whether or not strains exhibited aberrant behavior at each stage of development.

In Figure 2a, the mutants have been categorized on the basis of the phenotype matrix and using a hierarchical clustering method 23. Our first result is that 83% of the total number of mutant clones (1870 of 2257) cannot be distinguished from wild type (blue-green in Figure 2a), possibly because the insertion is in an intergenic region, or the mutated gene exists redundantly, or it is nonessential for growth and development under the present conditions. The second noticeable feature of these data is the number of strains clustered at the bottom of Figure 2a (139 clones appearing with two or more yellow boxes) and sparsely distributed elsewhere. Many of these exhibited slow vegetative growth and the low cell-density effect associated with it despite multiple attempts to grow them. This phenotype may be largely due to a systematic bias carried over from the parent, as most of them are from the same transformant set. After removing these clones from the dataset, we estimate that 1 to 2% are defective in genes that, while permitting vegetative growth on bacteria, interfere with normal growth in axenic medium. For several mutants in this category, we were able to confirm the observed behavior independently by disrupting the gene by homologous recombination (data not shown). The third feature of this dataset is the remaining strains with developmental phenotypes, representing 4% of the clones in the unbiased mutant set (76 strains out of 1,799) and 32% in the previously characterized mutant set.

Strains that exhibited almost no development, or aberrant behavior throughout all developmental stages, are clustered at the top of Figure 2a (expanded in Figure 2b; N = 30). This cluster includes a group of 'developmentally null' mutants in which genes such as mkpA, piaA, yakA and dagA are disrupted. Other groups include DG1105, DG1037, DG1122 from an earlier screen (W. Loomis, unpublished work), as well as another group that includes the protein kinase A pathway genes rdeA and regA (described in detail below). These mutants not only show early developmental defects, they also continue to exhibit aberrant behavior until mound formation, and are either stalled or show further aberrant behavior during slug migration and culmination. The above mutant clusters are followed by a cluster consisted of mutants with similarly severe phenotype plus growth-stage defects (Figure 2c).

Another major mutant cluster contains clones showing defective behavior at the slug and culmination stage, but wild-type behavior during aggregation (Figure 2d). Particularly noticeable are five mutants disrupted in tagB/C, mutations in tipA, tipB, tipC, and tipD, and multiple occurrence of mutants with insertions in the yelA gene and the dhkA gene. At the bottom of Figure 2d there are strains that show aberrant behavior in the early stage of development, but nevertheless form mounds, then again exhibit deficient slug and fruiting-body structure. A large number of mutants defective in early signaling are also defective later in development (Figure 2d) even though they appear to stream normally to aggregation centers. This suggests either that the gene products are used at two or more different times during development - for example, cAMP metabolism 24 - or that wave phenotype dictates later aspects of morphogenesis in a way we do not yet fully understand. Finally, some strains exhibited aberrant behavior during the early signaling to aggregation stages, but no striking phenotypes during later stages (see Additional data file 4). These strains may be contrasted with those exhibiting defects only at the slug stage (see Additional data file 4) or the culmination stage (Figure 2e), such as those disrupted in the cellulose synthase gene dcsA (Figure 2e).

We noticed that independent clones disrupted in the same gene co-cluster, providing strong validation of our profiling approach. In general, the developmental stages observed for most of the published mutants examined here agree with the literature. Mutants previously characterized as aggregation minus fail to aggregate, and stalk-defective mutants fail to make stalks. A caveat of the present coarse-grained representation is that similarities in the more detailed phenotypes are not reflected in clustering. We should note that detailed phenotypes, such as the break up of aggregation territories seen in chemotaxis-defective mutants of erkA 25, mekA 26 and phdA, 27 and long stalks in dhkA 28 also agree well with known mutant phenotypes.

However, not all of the phenotypes were consistent with the literature. This includes V31742 from the new unbiased mutant set carrying an insertion in dstA, a gene encoding the STATa transcription factor, which under our assay conditions was defective only from the slug stage on, whereas a delay earlier in development has been reported 29. There were also some that exhibited phenotypes undocumented in the literature. For the two most conspicuous clones (disrupted in splA and lvsB), we showed that the phenotype could not be recapitulated by an independent knockout. In these cases, a secondary mutation introduced by the REMI vector is the likely cause of the observed defects. While it is possible that some of the differences between independent isolates are due to subtle differences in cell density and the growth condition at the outset of each experiment, we note that phenotyping was repeated two or more times, and thus it is likely that the clustering reflects either differences traceable back to mutant gene structure or the highly plastic nature of the mutant phenotype (for example, tipC, modA, yelA).

Several wavelet parameters serve to characterize the wild-type phenotype of early cAMP signaling. The peak of the averaged wavelet power spectrum was traced, and the time of the cessation of signaling t_end was determined. The resulting one-dimensional data can be clustered, yielding a group of samples that failed to exhibit normal oscillation patterns (Figure 3a, and see the next section). We have done this by first placing sample runs into four groups using K-mean clustering of the wavelet transform (see Figure 3a), then removing possible pleiotropic effects during the growth phase by cross-verification with the phenotype cluster. A similar analysis using hierarchical clustering yields a continuous profile without apparent structure or organization. The first two clusters in Figure 3a contain samples with slight differences in the onset that is within that observed in the wild type. The third cluster in Figure 3a, with delayed wave-onset time, contains mostly low-density samples, whereas samples in the last cluster failed to establish waves. There is a faint secondary peak above the first peak in the wavelet portrait that signifies a deviation from the symmetric sinusoidal form of oscillation. Although these secondary peaks may be important to characterize mutants with altered forms of oscillation, such as stmF 30, we have confined our analysis here to the main frequency.

On the basis of the samples that fell into the top three clusters in Figure 3a, we sought to obtain the distribution of the cAMP wave phenotype in order to gain insights into the underlying self-organizing mechanism. At t = t_end, the main frequency 1/s = 1/s* and the peak wavelet power spectrum was extracted. Figure 3b records the distribution of maximum frequency 1/s* of the optical density oscillations. The maximum frequency is narrowly distributed, with an average of 0.24/min (standard deviation (SD) ± 0.03). This is equivalent to cells reaching approximately a 4.2-min period oscillation, in agreement with previous studies 183132. Compared with the tight distribution of signal frequencies, the wavelet power spectrum follows a log-normal distribution, with mean 0.197 (SD ± 0.132) (Figure 3c). Cessation of oscillations t_end is well fitted by a Gaussian distribution (Figure 3e). A tight frequency distribution and a broad (log-normal) amplitude distribution have also been reported recently in the p53 system 33 and may be a widespread feature of nonlinear oscillations in cells.

The number of spiral wave cores, which is a good measure of the number of cell territories that will later form, also follows a Gaussian distribution (Figure 3d). This distribution is most plausibly explained by the fact that core formation is intrinsically stochastic in nature 1634. It is also likely that the observed distribution depends on sample to sample variability in cell density which may correlate with the oscillation frequency (see below), although the number of aggregation centers is known to be relatively insensitive to cell density above 400 cells/mm² 35, and our experiments were carried out at around 7,000 cells/mm². To exclude such complications, the data in Figure 3b-i were obtained from selected samples exhibiting spiral wave propagation where the growing cells had reached confluence and showed no growth defects (N = 1,639; top three clusters in Figure 3a). We noticed that the number of aggregates exceeds the number of spiral cores because streams tend to break up just before aggregation completes. The extent of late stream break up was highly variable from sample to sample, even for the same strain, and therefore this phenotype was not considered as a robust trait for further annotation.

Spiral wave formation is a complex phenomenon that depends on the developmental trajectories of the cells; that is, how the mode of signaling 36, sensitivity to the signal 16 and kinetics of signaling 32 develop in time. We investigated this aspect by displaying the related data as scatter plots (Figure 3f-i). We note the following. First, when the system develops quickly, there is a weak tendency for the oscillation frequency to be smaller (Figure 3f). Second, there appears to be a weak positive correlation between the amplitude and t_end (Figure 3g) and a negative correlation between the amplitude and the frequency at t_end (Figure 3h). Heterogeneity in the signaling response has been reported at the single cell level 3738. Because our analysis is based on data from groups of cells, wavelet amplitude mainly reflects the coherence among the cells of the periodic cytoskeletal rearrangement upon cAMP stimulation. The data, therefore, suggest that the cells are participating in periodic signaling more heterogeneously when the system takes a shorter time to reach the streaming stage, and/or when it reaches a high-frequency oscillation state. We see that in high-frequency samples, more spiral cores are observed (Figure 3i). From the slope, there is roughly a fivefold increase in maximal number of spiral cores as the frequency increases from 0.17/min to 0.25/min. This is difficult to explain simply by scaling of the territory pattern with wavelength alone, because one can only expect an increase of approximately 1.5-fold. Rather, the data suggest a causal relationship between the formation of spiral cores and heterogeneity in cell excitability.

As described above, early-stage mutants that failed to exhibit the typical developmental time course in optical-density oscillations can be systematically picked up by the clustering of the wavelet transform (Figure 3a, the bottom cluster). The mutants detected in this way display a range of severity in signaling defects. For example, V10233 (Figure 4a) is disrupted in the piaA gene, which encodes a TOR (target of rapamycin) complex protein that is required for the cAMP pulse-induced activation of adenylyl cyclase 39. Neither optical-density waves nor signs of aggregation are visible, as expected from the known null phenotype of piaA mutants. V10285 (DG1105; dictyBase ID: DDB0220018) shows local pulsatile waves, and development at this stage is prolonged (Figure 4b). V10199 (DG1037; dictyBase ID: DDB0191301) shows slow oscillations of extended duration (Figure 4c), and development appears to be arrested during early aggregation. Owing to the long period of the optical-density oscillations, the wavelength of the spirals is extended, and therefore only a few spiral wave territories appear. Finally, V10682 is able to develop after growth and starvation on bacterial plates, but on non-nutrient agar, development is delayed from early aggregation on (Figure 4d). Optical-density wave onset is late, and wave periodicity remains long and never reaches the characteristic 5-min oscillation. The gene disrupted in this strain (dictyBase ID: DDB0218077) encodes a protein homologous to the conserved clc6/7 type chloride channel family protein 40.

In contrast to the mutants described above, all of which are strongly defective in early signaling, two strains (V10258 and V30230) that exhibit notably altered wave and aggregation phenotype (Figure 5b, c) are found together in the clustered array (Figure 2b). In these mutants, waves propagate for very short distances before annihilating when they crash into each other. Compared with wild-type behavior (Figure 5a), periodic signaling begins early in both strains, and the signaling duration is abbreviated to 1 hour (Figure 5, magenta bar in right panels). Cells aggregate precociously, forming small mounds with very little evidence of streaming toward a spiral center. Furthermore, the aggregation process is completed in 3 hours. These features are clearly seen in the wavelet analysis (Figure 5, right panels). We note the striking similarity of the wavelet portrait for these two strains.

Strain V30230 and V10258 carry an insertion in the regA and rdeA genes, respectively. The regA gene encodes an intracellular cAMP phosphodiesterase with a response regulator domain at the amino terminus 4142, and the rdeA gene encodes the only known histidine phosphotransfer domain protein in Dictyostelium discoideum. A biochemical study has shown directly that a receiver domain of RdeA relays phosphate groups to the amino-terminal response regulator domain of RegA and that phosphodiesterase activity of RegA is stimulated by phosphorylation of the amino-terminal receiver domain 42. We have recently shown that PKA pathway mutants show similar crowded-wave phenotypes due to the emergence of abnormally large numbers of spiral cores, and thus this independent isolation of insertions in rdeA and regA is an important confirmation of a recent model of pattern formation that incorporates coupling of external cAMP oscillations to internal cAMP levels 16. Other genotyped mutants related to this pathway were those with insertions in dhkA, dhkC, dhkJ and acrA. Mutants in dhkC (V10588) show early slow waves reminiscent of other previously studied PKA pathway mutants pkaR^- 16 or dhkK (D1125N) 43 (data not shown). In contrast, dhkA and acrA show mutant phenotypes only at later stages consistent with their specific roles during slug to culmination stage. A mutant in dhkJ was found in the wild-type cluster.

The slug is a multicellular structure consisting of anterior prestalk cells and posterior prespore cells that migrates towards favorable environments for culmination. Studies suggest that propagating waves of cAMP not only direct cell aggregation during the early stage of development, but may also coordinate cell migration in the slug stage 1744. Slug migration velocity is typically of the order of several hundred micrometers per minute; therefore its characterization is difficult without time-lapse imaging.

Our dynamical profiling approach reveals mutants with coordination defects. A mutant V10633 of a putative GATA activator (dictyBase ID: DDB0220467) forms chubby slugs that are mostly developmentally arrested at this stage (Figure 6b, right panel). Migration is almost absent, as is evident from the slug trajectories (Figure 6b right panel). Some slugs do culminate to form fruiting bodies with small spore heads. The video records allow one to discriminate mutants with such behavior from those that proceed to the slug stage but show deficient migration. In V30524 (Figure 6c), the slugs move with less path persistence compared to wild type (Figure 6a). V30524 carries an insertion in an open reading frame (dictyBase ID: DDB0187422) that encodes an arginine-N-methyltransferase, a conserved PRMT5 family protein involved in post-translational modification of proteins involved in RNA processing, DNA repair, and transcriptional regulation 45.

Note that we did not base our phenotypic scoring on the ability of slugs to sense light or thermal gradients, and therefore we have probably missed genes implicated in these processes for example, gefL 46 (Additional data file 5). Another phototaxis mutant that was nevertheless scored (Figure 2d, abpC) may be more severely impaired in morphogenesis because of other defects 47.

Clones of random insertional mutants generated by restriction-enzyme-mediated insertion (REMI) 60 and wild-type D. discoideum cells were grown on fresh lawns of Klebsiella aerogenes on SM agar for 3 to 4 days. The cells were picked from a feeding-front of a plaque into 2 ml growth medium (PS medium 1 l; 10 g Special Peptone (Oxoid, Basingstoke, UK), 7 g Yeast Extract (Oxoid), 15 g d-glucose, 0.12 g Na₂HPO₄·7H₂O, 1.4 g KH₂PO₄, 40 μg vitamin B12, 80 μg folic acid) supplemented with 1 × Antibiotic-Antimycotic (Gibco; Invitrogen, Carlsbad, CA). Typically, 30 clones were cultured in parallel using five six-well plates (Costar 3506; Corning, Lowell, MA). After incubation at 22°C for one day, bacteria and other debris were removed by gentle shaking followed by aspiration of the medium. Fresh PS medium was then added and the cell density was readjusted if necessary. The cells were allowed to attach to the bottom of the plate and incubated at 22°C for another 24 h. Cell density in the initial inoculation was typically 2 × 10⁶ cells/well. Under these conditions, wild-type AX4 cells attach robustly to the plate surface and appear non-polarized. They grow and divide about three times at a doubling time of approximately 12 h before reaching confluency at 7 × 10⁶ cells/well.

Growth medium was then removed and the cells were resuspended in 1 ml DB (10 mM KH₂PO₄/Na₂HPO₄, 2 mM MgSO₄, 0.2 mM CaCl₂; pH 6.5) and transferred to a 1% agar (Gibco Bactoagar) surface prepared in six-well plates where they were allowed to settle for 15 min to form a monolayer. Supernatant was removed and the plates were allowed to dry for 15 min in a sterile hood.

The life cycle of 2,257 mutagenized clones was analyzed. Clones were of two major types. To test the generality of our approach, we analyzed a collection of mutants generated by restriction-enzyme-mediated insertional (REMI) mutagenesis, many of which have been published. These strains came from the Loomis and Shaulsky laboratories. They are numbered V00262 to V10300. To test our methods to discover new mutants with developmental phenotypes by unbiased random REMI mutagenesis, we analyzed a subset of an extensive collection developed at Baylor. This is the V10301-V11139 and V30000-V31999 series. Whenever the phenotype deviated from wild type, the time-lapse experiment was repeated, with the result that 882 clones were examined more than once. Of these, 357 were repeated two or more times. REMI mutagenesis provides a convenient and relatively unbiased way to conduct genome-wide forward genetic screens, allowing the investigator to rapidly identify the insertion site by plasmid rescue and inverse PCR. The insertion sites for the entire set were determined at Baylor University 22. Those with suspected aberrant phenotypes were resequenced at Princeton University on a strain-by-strain basis (see below).

Genomic DNA was prepared by a salting-out method 61 from cells shaken overnight in phosphate buffer (20 mM KH₂PO₄/Na₂HPO₄ pH 6.5). Approximately 1 μg of DNA was cut with the six-cutter restriction enzymes EcoRI, ClaI, BglII or SpeI (New England Biolabs, Ipswich, MA). Digested DNA was electrophoresed in 1% TAE agarose gels and used for Southern blot analysis. Plasmid pBSRΔ Bgl was cut with BamHI and HindIII and the resulting 1.4-kb fragment containing the Blasticidin resistance cassette 62 was P³²-labeled and used as a probe. Digests that yielded a specific band of 6 to 12 kbp were chosen for plasmid rescue. DNA (6 μg) was cut and then circularized using T4 DNA ligase (New England Biolabs). The ligation reaction was purified and used to transform electro-competent SURE cells (Stratagene, La Jolla, CA). Clones were selected on LB ampicillin plates and three clones were typically picked for plasmid DNA preparation and sequencing. Sequencing reactions were performed from both ends of the inserted vector pBSR1 63 using T7 and SP6 primers.

For inverse PCR, approximately 100 ng of DNA was first digested with RsaI, which recognizes sites close to both ends of the inserted vector pBSR1. The digest was heat inactivated, purified using silica columns (PCR purification kit; Qiagen, Valencia, CA) and circularized with T4 DNA ligase. Using the circularized DNA as a template, two PCR reactions were performed to amplify flanking DNA from the ends of the inserted vector. The primers for the T7 end were (T7) 5'-TAATACGACTCACTATAGGG-3' and (InvT7R2) 5'-CTGCACTACCAATCGCAATGG-3'. For the SP6 side, they were (InvSp6L) 5'- GCCGCGTTCTAACGACAATA-3' and (InvSp6R) 5'-TCATACACATACGATTTAGGTGACA-3'. Positive PCR reactions were purified using silica columns (PCR purification kit; Qiagen) and sequenced using T7 or SP6 primers. For some PCR samples, sequencing reactions were performed after cloning the PCR product into TOPO pCR2.1 vector (Invitrogen). The sequence was parsed and BLAST-searched against the Dictyostelium chromosome sequence using EMBOSS 64 with a script written in Perl 65 and then manually inspected to identify insertion positions.

We were able to identify the insertion sites of the vector for approximately 80% of the 300 clones that were examined more than once. For the other 20%, Southern analysis revealed that there were no appropriate six-cutters available for plasmid excision, and/or where inverse PCR failed. Of the 344 different clones genotyped in Princeton, the two ends of the inserted vector were found at separate loci in 42 cases. Such anomalous insertion events have also been reported following REMI mutagenesis in Saccharomyces cerevisae 66. For those mutants described in detail, gene disruption was repeated by homologous recombination using the isolated plasmid obtained by the methods described above. Wild-type AX4 was electroporated with the linearized plasmid following a standard protocol 67. Positive clones were selected in PS medium supplemented with 10 μg/ml Blasticidin S (MP Biomedicals, Solon, OH) and recombination was verified by PCR.

An imaging robot was constructed using industrial automation assemblies. It is a gantry system, with two x-y instrument platforms ganged together, one positioned above the sample holding area, the other below, each driven by digital servo drives (Gemini GV; Parker Automation, Cleveland, OH) (Figure 1b). The drives are operated through a programmable two-axis servo controller (6K2; Parker Automation). The servo tuning and axis-control programs were written using Motion Planner software (Parker Automation). The upper gantry platform houses a 1/3-inch format CCD camera (LCL-903HS; Watec, Orangeburg, NY) with a macro lens. The dark-field illumination optics consisting of a fiber-optics light guide and lenses, is mounted on the lower platform. Although this is a belt-driven system, feedback loops in the controllers allowed positioning over the 2 m × 2 m sample platform with a reproducibility of around 100 μm rms (root mean square). Time interval fluctuation measured at a single well for both the first and second time intervals was typically 0.1 sec (standard deviation). The robot was housed in a light-tight room at a constant temperature of 22°C. Six-well plates were placed on a stage that can hold up to 100 accurately aligned in the x-y plane. Images from a 16.8 mm × 12.6 mm area from each well were captured and transferred to a computer, where they were digitized and stored in 640 by 480 pixel 8-bit grayscale TIFF format using a frame grabbing board (LG-3; Scion Corporation, Frederick, MD). Image files were written to a high capacity hard-disk system (Xserve RAID; Apple Computer).

Image acquisition, frame stacking and frame subtraction were accomplished using Java-based plug-in applications written for ImageJ 68. These files were encoded in MPEG-4 format using ImageJ and Quicktime Pro (Apple Computer) for easy viewing over the Internet using a streaming server. Subtracted movie files were encoded at 12 frames/sec. The first and second half of the original movies were encoded at 48 and 36 frames/sec, respectively. Movie files, wavelet data and annotation data were stored on a MySQL server. Data acquisition, data management and statistical analyses using the MySQL database were performed with web-based queries written in PHP and the R statistical package 69. Raw data can be found on our website 70.

Wavelet analysis was performed as described 16 with some modification. Briefly, from the original TIFF movie files, time-series ρ (x, y; t) of average pixel intensity from 3 × 3 pixel areas at coordinate (x, y) were sampled from a mesh of 20 pixel intervals (M = 2,048 sites). From the time-series, normalized wavelet power spectra averaged over space were obtained by

| W ( s , t ) | 2 ¯ = 1 M ∑ x , y 1 σ xy  2 | ∑ n ' = 0 N − 1 ρ ( x , y ; t ) ψ { ( n ' − n ) Δ t / s } | 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegyvzYrwyUfgarqqtubsr4rNCHbGeaGqiA8vkIkVAFgIELiFeLkFeLk=iY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqVepeea0=as0db9vqpepesP0xe9Fve9Fve9GapdbaqaaeGacaGaaiaabeqaamqadiabaaGcbaWaa0aaaeaacqGG8baFcqWGxbWvcqGGOaakcqWGZbWCcqGGSaalcqWG0baDcqGGPaqkcqGG8baFdaahaaWcbeqaaiabikdaYaaaaaGccqGH9aqpdaWcaaqaaiabigdaXaqaaiabd2eanbaadaaeqbqaamaalaaabaGaeGymaedabaacciGae83Wdm3aa0baaSqaaiabbIha4jabbMha5bqaaiabbccaGiabbkdaYaaaaaaabaGaemiEaGNaeiilaWIaemyEaKhabeqdcqGHris5aOWaaqWaaeaadaaeWbqaaiab=f8aYjabcIcaOiabdIha4jabcYcaSiabdMha5jabcUda7iabdsha0jabcMcaPiab=H8a5jabcUha7jabcIcaOiabd6gaUjabcEcaNiabgkHiTiabd6gaUjabcMcaPiabfs5aejabdsha0jabc+caViabdohaZjabc2ha9bWcbaGaemOBa4Maei4jaCIaeyypa0JaeGimaadabaGaemOta4KaeyOeI0IaeGymaedaniabggHiLdaakiaawEa7caGLiWoadaahaaWcbeqaaiabikdaYaaaaaa@8028@

where Δt is the time interval of the time series ρ(x, y; t) with variance σ_xy², and ψ is the Morlet wavelet:

ψ(η) = π^-1/4 exp[iω₀η-η² /2]

where ω₀ = 6. These procedures were automated and integrated with image acquisition. Feature extraction from the wavelet analysis was performed using a script written in Perl that traces the peak of the wavelet power spectrum as a function of time. A running average with a time interval of 6.7 min was used to remove short time-scale fluctuations. The resulting trace data were clustered using a K-means algorithm with the Euclidean distance as a similarity metric.

For each developmental stage - growth, early wave, aggregation, mound, slug and fruiting body - deviation from reproducibly robust wild-type behavior at each stage was noted (Table 1). This information was ranked into four different categories p_ij = -1, -1/2, 0 or 1, where i ∈ 16 stands for ordered developmental stage (for example, i = 1 is the growth stage) and j represents the sample number. Category p_ij = 1 is thus the value for a given wild-type phenotype, and p_ij < 1 signifies the severity of the mutant phenotype. p_ij = -1 corresponds to a null phenotype, meaning that a developmental stage-specific behavior and morphology was completely absent, either because of developmental arrest at that particular stage, or at a preceding stage. p_ij = -1/2 is assigned when a clear deviation from wild-type behavior could be identified (for example, slow oscillations, short stalk, and so on). A phenotypic score of p_ij = 0 was assigned when the phenotype could not be distinguished from phenotypic fluctuations exhibited from experiment to experiment with wild-type cells. Many clones (V10546-V10646, V10676-V10696, V30001-V30896, V31301-V31596) systematically showed late slug behavior characterized by loss of cells from the slug posterior and early culmination. These were assigned p_ij = 0 and treated as wild type for clustering purpose. Multiple sample runs were averaged by taking the maximum

q s j = max ⁡ i = 1 N s p i j MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGXbWaaSbaaSqaaiaadohacaWGQbaabeaakiabg2da9maaxadabaGaciyBaiaacggacaGG4baaleaacaWGPbGaeyypa0JaaGymaaqaaiaad6eacaWGZbaaaOGaamiCamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@41F4@

for strain s with N_s repeated runs. Although this filtering approach loses some information relative to simple mean averaging, it supplies a more rigorous justification for the claim that a given strain is defective in some aspect of development. Hierarchical clustering was performed by Cluster 3.0 71 using Pearson correlation as a similarity metric. The mean of all pairwise distances were used during clustering. The resulting trees were visualized by Java TreeView 72.