Gene expression waves Cell cycle independent collective dynamics in cultured cells Masa Tsuchyia 1 , Sum T. Wong 2 , Zhen X. Yeo 3 , Alfredo Colosimo 4 , Maria C. Palumbo 4 , Lorenzo Farina 5 , Marco Crescenzi 6 , Alessia Mazzola 6 , Rodolfo Negri 7 , Michele M. Bianchi 7 , Kumar Selvarajoo 1 , Masaru Tomita 1 and Alessandro Giuliani 6 1 Institute for Advanced Biosciences, Keio University, Yamagata, Japan 2 Bioinformatics Institute, Singapore 3 Genome Institute of Singapore, Singapore 4 Physiology and Pharmacology Department, University of Rome ‘La Sapienza’, Italy 5 Department of Computer and Systems Science, University of Rome ‘La Sapienza’, Italy 6 Istituto Superiore di Sanita’, Environment and Health Department, Rome, Italy 7 Department of Cell and Developmental Biology University of Rome ‘La Sapienza’, Italy Much of the success in molecular genetics has been accomplished by setting aside the concerns about the possible existence of a collective organized behaviour of cultured cells. Cell cultures were considered as ergo- dic ensembles of independent units (cells) randomly scattered in different phases of their biological cycle. This allowed us to refer any result to a sort of ‘average cell’ and then base the interpretation of the data com- ing from millions of cells present in a culture on molecular level considerations [1,2]. The presence of a coordinated behaviour of cells in the plate requires complementing these average cell explanations with another level of analysis, relative to the ‘culture-as-a- whole’. The observation of synchronization of cultured yeast cells in terms of transcriptional activity led to the notation that collective modes of whole population of cells indeed influence transcriptional machinery. This synchronization, having a characteristic frequency much faster than (and recognized as a multiple of) the cell cycle, was ascribed in yeast to metabolic cycles in which the entire culture alternates between reductive and oxidative phases [2,3]. Klevecz et al. [2] made the prediction of the widespread presence of these collec- tive modes not only in yeast, but also in mammalian cultured cells. The same prediction is at the basis of two other recent studies [4,5] describing a sort of ‘tem- poral architecture of eukaryotic growth’ consisting of genome wide oscillations in transcription acting as a Keywords cell–cell communication; metabolic cycle; microarray; ribogenesis cycle; systems biology Correspondence A. Giuliani, Istituto Superiore di Sanita’, Environment and Health Department, Viale Regina Elena 299, 00161, Rome, Italy Fax: +39 0649 902999 Tel: +39 0649 902579 E-mail: alessandro.giuliani@iss.it (Received 1 March 2007, revised 28 March 2007, accepted 3 April 2007) doi:10.1111/j.1742-4658.2007.05822.x The ergodic hypothesis, which assumes the independence of each cell of the ensemble from all the others, is a necessary prerequisite to attach single cell based explanations to the grand averages taken from population data. This was the prevailing view about the interpretation of cellular biology experi- ments that typically are performed on colonies of billions of cells. By ana- lysing gene expression data of different cells going from yeast to mammalian cell cultures, we demonstrate that cell cultures display a sort of ‘ecology-in-a-plate’ giving rise to a rich dynamics of gene expression that are independent from reproductive cycles, hence contradicting simple ergo- dic assumptions The aspecific character of the observed coordinated gene expression activity inhibits any simple mechanistic hypothesis and high- lights the need to consider population effects in the interpretation of data coming from cell cultures. Abbreviation PCA, principal component analysis. 2878 FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS sort of metronome; this interpretation was further clar- ified by Tu and McKnight [6]. Beside the mechanistic bases of such oscillatory behavior, a still neglected point in our opinion is that such oscillations imply some sort of coordination among cells, and an exploration of the origins of such coordinated behaviour could be of importance. Bacteria are able to communicate with each other through the accumulation of specific signalling mole- cules that enable each bacterium to sense the number of surrounding bacteria (cell density): this mechan- ism, called quorum sensing, is responsible for huge structures called biofilms, which often cover the sur- face of ponds and lakes and can be considered as rudimental forms of multicellular organization [7,8]. Recent evidence suggests that yeast too exhibits quorum sensing and that this type of regulation is based on signals carried by aromatic alcohols [9]. As in bacteria, quorum sensing in yeast seems to be linked to the onset of spatial organization of colon- ies that, in the presence of a shortage of nutrients, optimize the use of resources. The quorum sensing phenomenon demonstrates the ability of populations of unicellular organisms to behave as a coordinated whole, thus, at least in principle, giving a biological plausibility to a between-cells coordinated genome expression activity. When we consider mammalian cells, at the level of tissues and organs, cell ensembles need to be coordi- nated, thus escaping from the ergodic assumption cor- respondent to the complete independence among the individuals inside a population and the consequent equivalence between temporal and population statis- tics so that a behaviour observed at the colony level can be immediately referred to a single cell. The non- ergodicity at tissue level (e.g. the synchronization of nodal cells in heart) is necessary for a coherent beha- viour corresponding to the physiological activity of the tissue to be put into operation. This coordination can be achieved in a number of ways (e.g. hormonal, nervous and neuroendocrine signalling). However, no similar observation was made in the case of cultured cells other than the observation of crossed nutrition linked to the need for a critical mass of cells to start a viable colony [10]. We investigate, in plate conditions, whether organ- ized behaviour can be considered as a universal cellular property, in terms of synchronized gene expression. Using temporal microarray data, we demonstrate: (a) asynchronous (in terms of reproductive cycle) cultures display the same gene expression modes as synchron- ous yeast cultures; (b) the presence of cell cycle inde- pendent transcription modes in mammalian cultured cells; and (c) the involvement of the entire transcrip- tome in the observed dynamics without any preference for specific classes of genes (e.g. those involved in metabolic cycles). Our result points to the presence of a highly ordered, coordinated, genome wide mRNA abundance dynamics of cultured cells, indicating the fallacy of the ergodic hypothesis for cell populations in culture and the need to consider population level phenomena when interpreting gene expression studies. Results Synchronous and asynchronous ribogenesis related gene expression data of yeast possess ordered dynamics The SMALL data set was analysed for the mutual correlation of the 17 genes’ (14 ribogenesis + 3 trans- cription factors) expression values between the syn- chronous (synchronization method: pheromone alpha) and asynchronous series made of 18 time points in the range 0–120 min at 7 min intervals. All the expression time series were strongly correlated between the asyn- chronous and synchronous modes with a Pearson r in the range 0.88 (FHL1 gene) to 0.99 (RPP2A gene) and an average correlation of 0.93. The almost total consistency between the synchron- ous and asynchronous time course of gene expression implies that the oscillations of the above genes are not pure noise but follow a still unknown ordered dyna- mics. Thus, we analysed the matrix with the different time points relative to the asynchronous condition as statistical units and the different gene expressions as variables by means of principal component analysis (PCA) in order to find the signature of a nonrandom temporal structure. We discovered the presence of the by far most important first mode (PC1) explaining 59% of total gene variability. The existence of a ‘ribo- genesis cycle’ had been proposed previously [3–5] so we initially concentrated on the ribogenesis gene set. To give more strength to our result, we shift our focus from a set of 14 genes (SMALL) to the entire ribogene- sis-related set of genes consisting of 275 ORFs (WHOLE) and repeated the above analysis. As in the SMALL set, we found a striking correlation between asynchronous ⁄ synchronous time courses for the 275 WHOLE gene set (average Pearson correlation 0.90; SD ¼ 0.07). This points to a basically cell cycle independent correlation structure of the entire ribogenesis gene set. This set (WHOLE), when submitted to PCA as for the asynchronous condition, generated a first M. Tsuchyia et al. Collective behaviour of cultured cells FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS 2879 mode explaining the 54% of total variability, showing an effective dimensionality of the system very similar to the set of 14 genes despite the different number of genes. The time courses of the first mode of the whole set of 275 ribogenesis genes (pc1whole) and of the subset of 14 genes (pc1small) are compared in Fig. 1(A), which shows the scores of the first principal compo- nents for both data sets. As is evident from the figure, not only pc1whole and pc1small have the same relative importance in the organization of the variability of the two sets (54% and 59%, respectively), but also they have an almost coincident time course, pointing to the same dynamical process. Synchronous and asynchronous randomly selected gene expression data of yeast possess ordered dynamics To answer the question of whether the process is ribo- some-specific, we performed the same analysis on 275 randomly selected genes from the entire yeast genome repository. The results obtained were absolutely coin- cident with the results obtained in the two previous analyses, with a synchronous ⁄ asynchronous average Pearson correlation of 0.89 (SD ¼ 013) obtained for the the random extracted genes set that is not signifi- cantly different from ribosome set whereas the first mode of the random set (pc1rand) explained the 52% of total gene variability. Spearman correlation gave identical results. It is worth considering the list of the few genes that did not display a significant correlation between the asynchronous and synchronous modes (Table 1). It is also worth noting how the majority of the genes that escape from the strict synchronous ⁄ asynchronous correlation out of the set of 275 genes are strictly cor- related with the pheromone alpha specific mechanism of action (Table 1, indicated by an asterisk). More- over, MFA1 is both the gene less correlated between synchronous and asynchronous modes and the one most directly involved in the pharmacological effect of pheromone alpha. This provides indirect but very strong proof for both the ‘pharmacological synchroni- zation’ independence of the observed genome wide oscillations and the fact that specific pharmacological effects are superimp superimposed on genome wide oscillations interrupting the spontaneous oscillation of the affected transcripts. The time course of the random gene selection first mode (pc1rand) is completely coincident (Pearson r ¼ 0.95) with that of the ribogenesis mode (Fig. 1B). Random gene selection first mode is more similar to the whole ribogenesis selection than the small ribo- genesis set, and a partial correlation exploiting the mutual interrelation among pc1whole, pc1small and pc1rand excluded the ribogenesis cycle as the driving force of the observed pattern, showing that the pc1small–pc1whole correlation is driven by their mutual correlation with pc1rand, thus indicating an aspecific (from the point of view of the biological role of the involved genes) character of the extracted mode. In order to obtain an idea of the amount of vari- ation at the single gene level explained by the above described mode, we calculated a scale independent index of the range of variation of each of the 7160 ORFs in the yeast data set for the asynchronous condition. For the ith ORF, this index, which we Fig. 1. (A) First mode dynamics of the SMALL and WHOLE data sets. The two data sets refer to 14 and 275 ribogenesis related genes, respectively. (B) First mode dynamics of 275 randomly extracted (RAND) and 275 ribogenesis related (WHOLE) genes. Collective behaviour of cultured cells M. Tsuchyia et al. 2880 FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS denominated as normrange (normalized range), was equal to: NormrangeðiÞ¼ðMAX À minÞÁmin À1 ð1Þ where MAX and min are the maximal and minimal transcription values scored in the 18 time points, respectively. Normrange scored a median value of 5.41 (i.e. an almost five-fold variation in transcription, which is well above the threshold usually set for identifying the genes whose activity is modified by a given treatment) and a very positively skewed distribution (skewness ¼ 12.51), resulting in a mean value of 96. This mean value (and the extremely high standard deviation of 585) is reminiscent of many genes having an on ⁄ off regulation during the time course studied. Globally, these statistics reveal a very coherent oscillation that is not simply interpretable in terms of random noise. When considering the dual space (GENOME data set) having the 7160 ORFs as statistical units and the 18 time points as variables, we obtain a complement- ary view of the same phenomenon. In this case, we shift from the actual transcription values (used in the previous analyses) to their normalized counterparts (each ORF subtracted of the mean and divided by its standard deviation), so as to avoid the presence of a trivial size component capturing the quasi-totality of the variance. The dual character of this space with respect to the previous analyses implies the projection of the time points on the loading space instead of the score space [13,14]. Figure 2 illustrates the first mode of the whole ribo- genesis set (scores) and of the entire genome (loa- dings), respectively. Notwithstanding the relevant differences (change of reference space from genes to samples, 7160 ORFs versus 275 ribogenesis genes, normalized versus abso- lute data) between the two analyses, the first mode (pc1genome) of GENOME space is very strictly corre- lated (r ¼ –0.75, note that the sign of the component is arbitrary) with the first mode of the WHOLE set as depicted in Fig. 2(C) reporting the correlation between the scores (WHOLE) and the loadings (GENOME data set) of the time points in the two analyses. Genome wide oscillatory behaviour observed with no specific link to a physiological role in yeast In order to confirm the above results with an inde- pendent experiment, we applied PCA to the data (asynchronous data set) relative to the elutriation experiment. The analysed data set had the 14 time samples as rows, each separated by 30 min, and the 275 ribogenesis related genes (RIBO) and 275 random extracted genes (RAND) as columns. For both data sets, we extracted the first three components (pcribo1– pcribo3 and pcrand1–pcrand3), respectively. The first component explained 54.5% and 55.4% of the total variance in RIBO and RAND sets, respectively, con- firming the alpha-factor results with respect to the relative importance of the first mode in the explanation of genome wide expression variability. The second and third components too had the same eigenvalue distribution in both RIBO and RAND data sets (pcribo2 ¼ 12.8, pcribo3 ¼ 9.3; pcrand2 ¼ 12.08, pcrand3 ¼ 8.7%). Moreover, the between-component Table 1. Genes with the lowest synchronous ⁄ asynchronous correlation. The table reports all genes from the 275 random set which escape from strict sync ⁄ async correlation. The majority are directly linked with the pheromone alpha specific mechanism of action (as indicated by an asterisk). Gene ontology Synchronous ⁄ asynchronous correlation Biological role MFA1 0.083 Mating pherormonepheromone alpha factor* CIS3 0.106 Cell wall construction of buds* SWE1 0.315 G 2 ⁄ M transition, cyclin dependent* CHS1 0.353 Cytokinesis, activated by pherormonepheromone alpha* TSL1 0.395 Bud emergence, sporulation* HXT2 0.46 Glucose transporter, regulated by starvation PHD1 0.491 Pseudohyphal growth* IME4 0.492 Sporulation, starvation dependent* CIT2 0.545 Tricarboxylic acid cycle AQY1 0.548 Spore maturation* PNC1 0.56 Replicative life span regulator* AFR1 0.571 Alpha factor pherormonepheromone regulator* PCL1 0.571 Cyclin dependent kinase M. Tsuchyia et al. Collective behaviour of cultured cells FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS 2881 scores Pearson correlation scored a near to unity value (pcrand1–pcribo1 ¼ 0.98, pcrand2–pcribo2 ¼ 0.96, pcrand3–pcribo3 ¼ 0.91), indicating a strict concor- dance in the temporal modes coming from the two sets. Figure 3 reports the first three modes of the RAND data set. It is worth noting the pcrand1 scales with an elutriation cell cycle that is considerably slower (due to the ethanol with respect to the glucose carbon source) than the alpha-factor experiment. Conse- quently, instead of the approximately 20 min periodic- ity observed for alpha-factor experiment, we have a 2-h periodicity for the first component of the elutria- tion set. This finding is in accordance with the hypo- thesis of a coupling between the duration of the metabolic and reproductive cycles [1–6], even if in this case we demonstrated the general character of the genome wide oscillation with no specific link to any physiological role of the interested genes. Human fibroblasts cell cycle independent ordered dynamics Having demonstrated the presence of relevant collec- tive modes of gene expression in yeast, we looked for evidence of the same phenomenon in other cellular systems. We analysed the data by Cho et al. [11] relative to the cell cycle of human fibroblasts (SALK data set). In this case, we have no asynchronous experiment and the cells were synchronized by means of double thymi- dine block. Nevertheless, we know in advance the cells display an 18 h cycle; thus, any mode displaying a sen- sible different characteristic frequency can be safely interpreted as demonstrating cell cycle independent collective dynamics. In this case too, we adopted a completely unsupervised approach by calculating the PCA over the matrix having the expression values rel- ative to 7077 ORF (base 2 logarithm of the ratio Fig. 3. The first three modes (pc1rand1–pc1rand3) of the gene expression dynamics for the elutriation data set. Fig. 2. (A) First mode of WHOLE data set (the same as in Fig. 1B). (B) First mode dynamics of the GENOME data set; due to the change of reference frame, here the loadings are reported. (C) The correlation between the WHOLE and GENOME data sets. Collective behaviour of cultured cells M. Tsuchyia et al. 2882 FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS between the actual expression value at each time point and the average value over the entire time span) as rows (statistical units) and 13 time points sampled at 2 h intervals from t 0 to t 24 as columns (variables). We performed three separate PCAs for the entire data set (whole) and for two independent random extractions of 275 ORFs (small1, small2). Figure 4 reports the first mode of the three analyses, showing a remarkable homogeneity across different data sets and an approxi- mate period of 8 h, which is completely distinct from the cell cycle periodicity. The between modes Pearson correlation coefficients near to unity indicates the non-noisy character of the extracted modes, pointing to the highly coordinated gene expression behaviour of these cells. HeLa cells display whole genome cell cycle independent ordered dynamics The last data set we analysed was taken from the study by Whitfield et al. [12] dealing with HeLa cell cycle. The authors were aware of the presence of spu- rious ‘modes’ in the data when analysed with singular value decomposition (practically correspondent to PCA), which they attributed to experimental artefacts. Similarly, when we analysed the data, we discovered that such modes and their wild nonstationarity led us to interpret them along the same line as Whitfield et al. [12]. However, when we studied the data with the usual whole genome ⁄ small random selection strategy, we discovered the presence of the same modes in both the whole genome and small random selection situations. These modes had a different relative weight in terms of the percent of variance explained but, nevertheless, were very repetitive across the two conditions, thus pointing to a coordinated response of the cell culture shaping its gene expression dynamics. Figure 5 reports the data relative to one of the experiments by Whitfield et al. [12]. Each panel of the figure compares a mode of the entire genome expres- sion dynamics with a corresponding mode relative to a small 275 genes extraction. Overall, there is a marked invariance of the dynamics across the whole genome and the random selection (global canonical correlation between the whole and small sets ¼ 0.95). Discussion To date, the presence of massive gene expression syn- chronization was shown to be due to presence of meta- bolic cycles [1,3,4]. We show that the most relevant oscillations of transcriptional activities are due to func- tionally aspecific modes, involving the whole transcrip- tome rather than being confined to specific classes of genes involved in metabolic cycles. Our result suggests the presence of robust and nonrandom modes in asyn- chronous yeast cultures, basically independent of the biological function of genes. We also demonstrate aspecific mRNA abundance waves for mammalian cell cultures. We still are unable to comment on the mecha- nistic causes of these waves, or the way they could also be linked to changes of mRNA degradation rates instead of changes in transcription activity. What is crucial in our opinion is that these results point to a nonergodic behavior of cell cultures and to a sort of ‘ecology-in-a-plate’ that could change our perspective with respect to interpreting microarray data. What could be the advantage to cells of maintaining self-sustained gene expression cycles? A possible answer comes from the the Prisoner’s dilemma scheme [15], a classical game theory paradigm explaining ‘altruistic’ behavior where the long-term advantage for the colony is selected over the small-term advantage for the individual. The mutual collaboration between neighbouring cells ends up being a selective advantage for the population as a whole, which may contribute to the establishment of cyclic behaviour of alternate Fig. 4. The first mode for the entire genome data set and two ran- dom extractions of genes relative to the SALK data set. It is worth noting that the main mode explains a much lower percentage of variation with respect to yeast analyses (approximately 17–19% compared to 50–60%), but nevertheless maintains a very strong invariance between different choices of genes. M. Tsuchyia et al. Collective behaviour of cultured cells FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS 2883 ‘production’ and ‘stealing’ phases relative to some extracellular protein needed by the colony as a whole. An intriguing candidate is the lectin-like protein involved in flocculation, a cell wall protein that binds to mannose chains on the surface of other cells to provide the physical substrate for colony formation (flocculation, a crucial step in quorum sensing). Other explanations are based on observed gene waves in yeast, which alternate between oxidative and reductive phases, optimizing the protection of DNA synthesis with respect to reactive oxygen species [4,6]. Our data, however, seem to suggest a relative inde- pendence of the transcription waves from the repro- ductive cycle as well as specific biological processes, and we prefer not to go too deep into the possible molecular mechanisms or functional consequences of having a ‘basic rhythm’ sustaining the transcription dynamics. Fig. 5. The pairwise comparison of modes extracted from the whole data set (HeLa cell cycle experiment number 3) and a small random selection from the same set. There is the possibility to recognize the same modes in the two sets even if they have a relative different importance in the two situations (the numbering of the modes is related to their ranking in terms of explained variance). Collective behaviour of cultured cells M. Tsuchyia et al. 2884 FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS Some basic features of the observed dynamics worthy of further comment First, the metabolic origin of these oscillations is plaus- ible, as well as their indirect link with the reproductive cycle in so far as any reproductive activity necessarily calls for the preliminary fulfillment of some energetic requirements. Second, there is a widespread presence throughout extremely different cell types, from yeast to human fibroblasts. Besides that, within each cell type, the involvement of the whole genome, and not of function- ally specialized subsets of genes, is demonstrated. Once again, such a generalized and aspecific character of gene expression waves could in principle be reconciled with some very basic anabolic and ⁄ or catabolic activity. Third, the tendency of any cell population to behave as a whole, namely to synchronize some fundamental functions independently from the reproductive behav- ior, requires looking for some form of communication between cells in the culture that probably is linked to reaching a critical density. The threshold population density above which such a collective behavior starts to emerge depends on a num- ber of largely unknown internal (cell type) and external (environmental) conditions. In this respect, any predic- tion based upon the artificial reproductive synchroniza- tion usually induced by chemicals appears useless. Fourth, the nature and role of the signals synchron- izing the activity of cultured cells still largely remains unknown. The literature in this field, for obvious prac- tical reasons, mainly deals with artificially induced rather than naturally occurring synchronization. It is difficult, however, to overemphasize the role of the lat- ter type of phenomena for understanding the higher hierarchies of cellular organization, from tissue to the organ level. All in all, our nonergodic hypotheses challenge the consideration of a cell culture as an ‘average cell’, as well as the automatic assignment to the molecular ⁄ single cell level of any kind of observation made on cultured cells. The demonstration of a rich and repeat- able dynamics in cell cultures uncovers the existence of a sort of ‘ecology-in-a-plate’, making another level of explanation worthy of special attention: the level of the colony as a whole. It seems fair to predict that many findings will accumulate along this avenue of research. Although coordinated cellular activity is obvious in tissues and organs, no similar finding exists in the case of cultured cells other than the observation of crossed nutrition linked to the need for a critical mass of cells to start a viable colony [10]. We investigate, in plate conditions, whether organ- ized behaviour can be considered as a universal cellular property, in terms of synchronized gene expression, Using temporal microarray data, we demonstrate: (a) asynchronous (in terms of reproductive cycle) cultures display the same gene expression modes as synchronous yeast cultures; (b) the presence of cell cycle independent transcription modes in mammalian cultured cells; and (c) the involvement of the entire transcriptome in the observed dynamics without any preference for spe- cific classes of genes (e.g. those involved in metabolic cycles). Our result points to the presence of a highly ordered, coordinated, genome wide mRNA abundance dynamics of cultured cells, indicating the fallacy of the ergodic hypothesis for cell populations in culture and the need to consider population level phenomena when interpreting gene expression studies. Experimental procedures The data sets The first data set we analysed was the yeast cell cycle data set from the pheromone alpha synchronization factor experiment [16], relative to both synchronous and asynchro- nous cell cultures. The analysed time series consisted of 18 time points sampled at 7 min intervals. This data set was studied under different forms: (a) statistical units ¼ 18 sub- sequent times, variables ¼ 14 ribogenesis related genes + 3 transcription factors known to be responsible of the regula- tion of the ribosome genes (SMALL); (b) statistical units ¼ 18 subsequent times, variables ¼ 275 ORFs consti- tuting the entire set of ribogenesis genes (WHOLE); (c) statistical units ¼ 18 subsequent times, variables ¼ 275 ORFs sampled at random (RAND) and (d) statistical units ¼ 6378 genes for which we have the full data, variables ¼ 18 time subsequent time points (GENOME). Analysis relative to (b) and (c) structures were repeated with data from elutriation experiment using the asynchro- nous cultures data and considering both a random collec- tion of genes and the 275 ribogenesis genes. The existence of relevant and stable collective modes sha- ping the dynamics of yeast gene expression in asynchronous cultures prompted us to look for gene expression waves in other biological systems. Due to the lack of such data in an asynchronous situation comparable to the yeast data, we analysed data sets from two different reproductive cycle synchronized systems, namely human fibroblasts [12] and HeLa cells [13]. The emergence of collective modes endowed with charac- teristic times that were completely different from the cell cycle in both these two systems was demonstrated in the space having time points as variables and both the entire M. Tsuchyia et al. Collective behaviour of cultured cells FEBS Journal 274 (2007) 2878–2886 ª 2007 The Authors Journal compilation ª 2007 FEBS 2885 set of genes and small random extractions from the whole set as rows. Statistical methods The discovery of collective modes in transcriptome data sets was performed by means of PCA [17,18]. The analysed data sets were studied on both row and column spaces by alter- nating analyses having the expression entities of different ORFs as variables (and consequently different time points as statistical units) and analyses having time points as vari- ables (and consequently different ORFs as statistical units). The use of PCA allowed us to detect highly anharmonic and nonstationary modes without being limited to station- ary oscillations. In the case of time samples as variables, different normal- ization methods were applied in order to eliminate the pres- ence of overwhelming ‘size’ components linked to the trivial existence of huge differences in the level of transcription of different ORFs. We used the classical z-score (zero mean, unit standard deviation) normalization for yeast data whereas human fibroblast and HeLa data were expressed in terms of the reported logarithm ratio. The gene-by-gene correlation between synchronous and asynchronous data was assessed by means of both Pearson and Spearman cor- relation coefficients. Acknowledgements The authors acknowledge the continuous exchange of ideas with their colleagues on these themes, especially Dr Margherita Bignami and Dr Romualdo Benigni. This work is supported by ‘Differing Fields Collabor- ation Grant’, JST CREST and the Ministry of Educa- tion, Culture, Sports, Science and Technology of Japan (MEXT). 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In this case too, we adopted a completely unsupervised approach by calculating the PCA over the matrix having the expression. ‘stealing’ phases relative to some extracellular protein needed by the colony as a whole. An intriguing candidate is the lectin-like protein involved in flocculation, a cell wall protein that binds to