Physica A 388 (2009) 17381746

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Physica A

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Local and global responses in complex gene regulation networksMasa Tsuchiya a,1, Kumar Selvarajoo a,1, Vincent Piras a, Masaru Tomita a,Alessandro Giuliani b,a Institute for Advanced Biosciences, Keio University, 14-1 Baba-cho, Tsuruoka, Yamagata 997-0035, Japanb Istituto Superiore di Sanita, Environment and Health Department, Viale Regina Elena 299, 00161, Rome, Italy

a r t i c l e i n f o

Article history:Received 15 July 2008Received in revised form 13 October 2008Available online 24 December 2008

PACS:87.17-d82.39-k84.35+1

Keywords:Biological statistical mechanicsSystems biologyCell culturesNetworks

a b s t r a c t

An exacerbated sensitivity to apparently minor stimuli and a general resilience of theentire system stay together side-by-side in biological systems. This apparent paradox canbe explained by the consideration of biological systems as very strongly interconnectednetwork systems. Some nodes of these networks, thanks to their peculiar location in thenetwork architecture, are responsible for the sensitivity aspects, while the large degree ofinterconnection is at the basis of the resilience properties of the system.One relevant feature of the high degree of connectivity of gene regulation networks is

the emergence of collective ordered phenomena influencing the entire genome and notonly a specific portion of transcripts. The great majority of existing gene regulationmodelsgive the impression of purely local hard-wired mechanisms disregarding the emergenceof global ordered behavior encompassing thousands of genes while the general, genomewide, aspects are less known.Here we address, on a data analysis perspective, the discrimination between local

and global scale regulations, this goal was achieved by means of the examinationof two biological systems: innate immune response in macrophages and oscillatinggrowth dynamics in yeast. Our aim was to reconcile the hard-wired local view of generegulationwith a global continuous and scalable one borrowed fromstatistical physics. Thisreconciliation is based on the network paradigm in which the local hard-wired activitiescorrespond to the activation of specific crucial nodes in the regulation network, while thescalable continuous responses can be equated to the collective oscillations of the networkafter a perturbation.

2008 Elsevier B.V. All rights reserved.

1. Introduction

Biological phenomena, at every scale of definition from protein folding [1,2] to the structure of ecological systems [3,4]passing through gene expression regulation [5] and physiology [6], display two seemingly alternative functioning modes.The first mode can be called hard-wired, for the possibility to be efficiently described by the node-arrow representationprevalent in modern biology and the second mode (statistical mechanics-like) in which collective phenomena are moreimportant than the specific elements involved. This second (collective) mode, despite successful applications in differentfields of cell biology [7,8] still appears under adopted by scientific community.In our opinion the integration of the two views in the analysis of biological data is of utmost importance, especially when

dealing with high throughput data where the extremely high number of dimensions asks for both a specific (the genesmostly involved) and an integrated (the response of the system at large) view.

Corresponding author. Tel.: +39 0649902579.E-mail address: alessandro.giuliani@iss.it (A. Giuliani).

1 Equal first authors.

0378-4371/$ see front matter 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.physa.2008.12.030

M. Tsuchiya et al. / Physica A 388 (2009) 17381746 1739

The hard-wired (local)mode implies the existence of crucial elementswhosemodification (alteration) ends up inmassiveresponses of the whole system. The now widely accepted metaphor of the cell regulation as a network, gives a rationale forthis behavior in terms of the removal (or the perturbation) of relatively few highly interconnected elements or hubs, thatin the realm of the so-called small-world network architecture can lead to system failure [9]. This gives an explanation forthe hard-wired specific mode of functioning and consequently to the response of the system to specific attacks given tocrucial hub elements [10].The collective mode, on the contrary, is largely independent of the specific microscopic elements involved and displays

co-ordinated motions and fluxes whose behaviour is largely invariant and independent of the nature of the elementsinvolved. The network metaphor allows us to rationalize this second behavioural mode in terms of the multiplicity ofalternative pathways in the network giving rise to equivalent collective behaviour of the system at large. The existenceof such generalized and largely invariant motions is at the basis of the error tolerance displayed by biological systems [10,11]. All in all the network paradigm allows us to rationalize the two apparently opposite features of biological systems ofbeing very sensitive to attacks on specific elements and of being very tolerant to errors.The recent decline in the ability to discover new drugs which sharply contrasts with the perceived increase in biological

knowledge is, in our opinion, linked to the almost complete exploitation of crucial nodes whose pharmacological activation(or inhibition) is more prone to give rise to a massive (hard-wired) response [12]. This interpretation is supported by therecent statistics on drug discovery by Overington et al. [13] indicating the greatmajority of recently developed drugs involvereceptor functions discovered decades ago. Therefore, for a potentially more effective drug development, an increasedattention to the understanding of bio-statistical mechanics (collective mode) should also be considered [14].In order to go into depth into the nature and character of these two modes of biological response and to demonstrate how

these modes are the extremes of the same spectrum of network based regulation, we investigate two biological examplesand show the co-existence of hard-wired and collective modes in the same system. We show how very simple statisticalapproaches can handle this kind of phenomena so allowing us to shed light into the nature of scalable behaviour in cellbiology.We hope that, even if simply phenomenological, the herewith presented hypotheses could open an interesting fieldof interaction between biologists and physicists.

2. Material and methods

2.1. Innate immune gene expression data

We analyzed published microarray data obtained from time-series experiments (0, 1, and 4 h) performed on peritonealmacrophages from wildtype, Myeloid Differentiation factor 88 (MyD88) knock out (KO), TIR-domain-containing adapter-inducing interferon (TRIF) KO, and MyD88/TRIF double knock out (DKO) mice treated with 100 ng/ml of LPS (SalmonellaMinnesota Re595, Sigma) [15]. Affymetrix mouse expression array A430 microarray chips were used for gene expressiondetection. The microarray datasets obtained from these experiments contain expression levels for 22690 Affymetrix probeset IDs. To specifically investigate cellular processes for LPS response we also reprocessed our experimental data using Ro-bust Multichip Average for further background adjustment and to reduce false positives [16].

2.2. Yeast gene expression data

Temporal gene expression activity is also measured by Affymetrix standard platform applied to yeast (Saccharomycescerevisiae) cells grown in different conditions. The aim was to analyze the differential gene expression during cellreproductive cycle. A set of 7160 ORFs was studied along 18 time points in two parallel cultures A and B. Culture A wasallowed to grow freely with the cells scattered in all the phases of their reproductive cycle. Culture B on the contrary wassynchronized by a drug (pheromone alpha) that synchronizes the cell population in the same phase of the reproductivecycle to make the cells to duplicate at the same time. The pharmacologically induced synchronization lasts for two or threereproductive cycles, then the cells loose their mutual correlation and the culture desynchronizes. Synchronous condition isattained when the cells are put in phase as for their cell division cycle by the use of a pharmacological treatment withpheromone-alpha and the asynchronous condition is when the cells are randomly scattered in all the phases of theirduplication cycle [17]. The presence of large and repeatable rhythms in gene expression was highlighted using an SVDapproach [17].

3. Results and discussion

3.1. Analysis of gene expression in innate immune response

The first example we present has to do with the phenomenon of innate immunity, mainly mediated by the Toll-likereceptor (TLR) activation and the consequent spreading of the response to different cell functionalities giving rise to theimmune defense at the level of the whole organism. The TLRs play a critical role in mammalian first line of defense againstinvading pathogens by recognizing a variety of pathogen-associatedmolecular patterns (PAMPs) such as lipopolysaccharides

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Fig. 1. A simplified schematic of the TLR4 signaling pathway. The TLR4 activates theMyD88 (green arrows) and TRIF-dependant (orange arrows) pathwaysafter LPS recognition, resulting in the activation of key transcription factors AP-1, NF-B and IRF-3 to regulate expression of pro-inflammatory cytokinesand interferons. The Knock out of both MyD88 and TRIF genes (DKO) completely inhibits this mechanism of action. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

(LPS). The activation of TLRs in immune cells results in the induction of proinflammatory cytokines which togetherwith antigen presenting capacity recruit nave T-cells and activate acquired immunity [18]. The malfunctioning of theseprocesses leads to proinflammatory diseases such as autoimmune diseases, atherosclerosis, asthma etc [19]. Among the 13known mammalian TLRs, the TLR4 is the most studied. The activation of TLR4, by LPS, triggers the Myeloid Differentiationfactor 88 (MyD88)-dependent pathway and the TIR-domain-containing adapter-inducing interferon- (TRIF)-dependentpathways [20]. The main role of the MyD88-dependent pathway is to initiate the induction of proinflammatory cytokinesand the TRIF-dependant pathway, on the other hand, induces Type I Interferons (IFNs) and chemokines [19] (Fig. 1).Here we analysed the whole genome expression of Affymetrix standard platform encompassing 22690 different ORFs

after LPS stimulation and refer to 12 experimental conditions (4 genotypes at 3 time points); Wildtype, MyD88 KO, TRIFKO, and MyD88/TRIF DKO at 0 (t0), 1 (t1) and 4 h (t4) [15]. The basic metrics adopted for the genotype comparisons was thePearson correlation coefficient on the entire genome expression vector as well as to different extractions of specific genesubsets (random and immune-related). Unlike the use of DNA microarrays to identify specific genes, we treated genes asanonymous members of a single ensemble containing N genes and calculated the samples similarity in terms of Pearsoncorrelation. This ensemble property of the population of genes is a robust measure [21] that is not biased by noise at thelevel of individual genemeasurement.Moreover, with different choices ofN extractions (entire transcriptome, only cytokinegenes, random extraction of genes) allows for a straightforward proof of different hypotheses on the data.Givenwe are dealingwith samples of the same cell-type, genome-wide correlations are extremely high (Pearson r around

0.98) indicating a strong common order parameter influencing the expression level of the entire genome, correspondent tothe cell-type characterization [22]. These results are coincident with the results obtained by Chang et al. on erythroid celllineages [23] using the same metrics (Table 1 and Fig. 2). The presence of such an invariant order spanning more thantwenty-thousand elements (genes, ORFs) and around four orders of magnitude of expression levels is a signature of generalorder parameters organizing the entire cell regulation network. This striking organization (Fig. 2) is, in our opinion, a factof nature that, for its dimensions and invariance, asks for a deep thinking in analogy of what happened for other collectivephenomena in magnetism, laser coherence, super-fluid helium, hydrodynamic instabilities, etc.Next, we investigated the variation of correlation in time for different expression vectors in the four analyzed genotypes

(Fig. 3). In (A) the correlations are studied as for the entire genome (22690 ORFs). It is worth noting that, even if the

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Table 1Pearson correlation coefficients between all conditions (genotypes and and time points).

Wildtype Wildtype Wildtype MyD88KO MyD88KO MyD88KO TRIF KO TRIF KO TRIF KO DKO DKO DKO0 h 1 h 4 h 0 h 1 h 4 h 0 h 1 h 4 h 0 h 1 h 4 h

Wildtype0 h

1.000 0.996 0.990 0.995 0.996 0.995 0.997 0.996 0.994 0.992 0.993 0.994

Wildtype1 h

1.000 0.992 0.994 0.995 0.995 0.995 0.997 0.995 0.988 0.989 0.992

Wildtype4 h

1.000 0.985 0.987 0.993 0.989 0.989 0.996 0.979 0.982 0.983

MyD88 KO0 h

1.000 0.997 0.995 0.997 0.995 0.992 0.993 0.993 0.995

MyD88 KO1 h

1.000 0.997 0.997 0.997 0.993 0.992 0.993 0.994

MyD88 KO4 h

1.000 0.996 0.995 0.996 0.989 0.990 0.991

TRIF KO0 h

1.000 0.998 0.996 0.992 0.994 0.994

TRIF KO1 h

1.000 0.996 0.990 0.991 0.992

TRIF KO4 h

1.000 0.987 0.988 0.989

DKO0 h

1.000 0.997 0.996

DKO1 h

1.000 0.997

DKO4 h

1.000

Fig. 2. Relationship between global gene expressions in several conditions and time points. The correlation coefficients between the gene expressionlevels of two different samples is near to unity pointing to a coordinated behavior involving more than twenty thousand genes and spanning four order ofmagnitude of expression levels.

correlations remain very high and near to unity, nevertheless there is a consistent and repeatable change in all the fourgenotypes with the correlation steadily decreasing with time (1 h is more correlated with 0 h than 4 h). These progressiveresponses which are identical in all the four genotypes rule out the effect of chance and remained almost exactly the samewhen the correlation was computed over random extractions of genes. As expected, the wild-type condition displays amore marked general displacement in time than all KO conditions, signature of a more marked immune response [15]. Thesame kind of behavior is obtained with random extraction of genes; Fig. 3B reports the average profiles of 30 extractions

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Fig. 3. Auto-correlations analysis for (A) whole genome, (B) random ORFs extractions and (C) 10 cytokines genes (tnf, il1b, il12, il6, il8, ccl3, ccl4, socs3,socs1 and cxc10) after LPS stimulation. x-axis represents time (in hours), and y-axis represents the correlation coefficient with t0. Available in color fromPhysica A website.

of 100 genes picked up randomly. This is another proof of the non-noisy character of the observation, even for so smalldisplacements from unitary correlations, and points to the fact that the observed collective expression response is scalablesince a reduced space (random extractions) reproduces the behavior of the entire genome.This scalable response is also present in DKO samples. This is remarkable, since DKOmice do not have any phenotypically

relevant immune response when submitted to LPS. The scalable, genome-wide response is thus something different fromthe specific hard wired cytokine related response generalizing immune response to the whole organism level. Neverthelessthis transcriptome-wide, scalable and aspecific response is in some way correlated to the specific response given it roughlyfollows the order of magnitude of the specific response with the consequent ordering (in decreasing level of activation) ofsamples from wildtype to single KOs and DKO.Weused the samemetrics (Pearson r) to focus the hard-wired cytokinemediated response; Fig. 3C reports the correlation

of the different genotype samples with the correspondent 0 h vector computed over a selection of 10 TLR4-related pro-inflammatory cytokine genes (tnf, il1b, il12, il6, il8, ccl3, ccl4, socs3, socs1 and cxcl10). The differences with the collectiveaspecific mode are striking: between 0 and 1 h the displacement (response) is already very evident, r drops to 0.81 whilein the global mode the minimal correlation with the initial state is greater than 0.99 (Fig. 3A). Moreover, at odds with thewhole genome and random extractions, the different genotypes show clearly distinct patterns: the absence of both MyD88and TRIF totally abolishes the hard-wired response, so the line correspondent to DKO becomes parallel to the time axis.To investigate the transition from specific (hard-wired) to collective behavior, we performed two statistical experiments;

(i) we evaluated the average standard deviation of temporal correlation coefficients of randomly chosen ORFs (in stepsof 10 up to 300) from wildtype whole genome and found the order parameters (collective behavior) occurs at around 70ORFs, since beyond 70 ORFs, the standard deviation of temporal correlation coefficients did not alter noticeably (Fig. 4).Similar observations were also made for all KO conditions, (ii) we removed highly expressed ORFs from wildtype wholegenome and interestingly found removal of similar number of ORFs (70) resulted in the shift of the response curve fromsteep to gentle gradient indicating the transition from dominant (hard-wired, specific) to weak (collective) response (Fig. 5)[Tsuchiya et al., submitted]. Therefore,we can safely affirm that culturedmacrophages submitted to LPS stimulation produceboth hard-wired specific immune response and non-specific general response where the transition occurs at around70 ORFs.This finding could be very useful when considering the effect of drug intervention, the distinction between specific and

collective response can help us target molecules that results in desired specific response, and at the same time does notaffect the entire non-specific response which could lead to detrimental side-effects. Recently, there has been a growinginterest in the development of so-called weak binding aspecific drugs or network drugs [24] which instead of presenting

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Fig. 4. Average standard deviation of auto-correlation of randomly chosen ORFs (in steps of 10 up to 300) from wildtype whole genome, (A) 1 h and(B) 4 h after LPS stimulation. Average standard deviations was calculated from 30 standard deviations in correlations computed for 30 groups of n ORFs,10 < n < 300. The order parameters (collective behavior) occurs at around 70 ORFs. Available in color from Physica A website.

Fig. 5. Auto-correlations profiles of all conditions after removing highest expressed ORFs between 0 and 1 h. (A)Wildtype, (B) MyD88 KO, (C) TRIF KO and(D) DKO conditions. Bend in correlations appears after removal of 70most up-regulated ORFs in any condition, except DKO. Available in color from PhysicaA website.

a specific target molecule, rather exert their action on many different molecular targets in terms of general modulation,thus acting as biological general response modifiers. This general collective response could have a crucial importance inthe differentiation pathways of different cell lineages as suggested by Chang et al. [23].

3.2. Analysis of gene dynamics in yeast

The second example has to do with the onset of largely non-specific whole genome expression waves probably linkedtometabolic cycles. This example shows a completely reversed situationwith respect of the first one. In the innate immunity,the small number of proinflammatory genes representing hard-wired mode were responsible for the dominant biologicalphenomenon (effective onset of immune response at the whole organism scale) while the majority of genes exhibitedweaker collective behavior of still unknown biological significance. In gene expression waves, rather, the collective modeconstitutes the dominant biological phenomenon as the general effect size is much wider than the intensity of the hard-wired pharmacological effect.

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Table 2The table reports the only genes (out of 7160) for which a strict correlation between synchronous and asynchronous conditions does not hold.

Gene Sync/async correlation Biological role

MFA1 0.083 Mating pheromone alpha factoraCIS3 0.106 Cell wall construction of budsaSWE1 0.315 G2/M transition, cyclin dependentaCHS1 0.353 CytokinesisaTSL1 0.395 SporulationaHXT2 0.460 Glucose transportPHD1 0.491 Pseudohyphal growthaIME4 0.492 SporulationaCIT2 0.542 TCA cycleAQY1 0.548 Spore maturationaPNC1 0.563 Replicative life span regulatoraAFR1 0.571 Pheromone alpha regulatoraPCL1 0.571 Cyclin dependent kinasea

a These genes are directly linked to the pharmacological action of pheromone alpha, the agent used to synchronize cells.

In cell biology, cultures of cells are considered as ensembles of independent units randomly scattered in different phasesof their biological cycle, according to the ergodic hypothesis as considered in statistical physics. The acceptance of ergodichypothesis allows to considermeasurements taken on disheswhere huge populations (in the order of billions of cells) live toa single average cell and consequently to derive node-arrow static networks at themolecular level describingwhat happensinside this cell. However, at the level of single-cell,wild stochastic behaviorswith totally unpredictable bursts of bothmRNAand proteins expressions are observed [25]. Therefore, the onset of a coordinated behaviour [17,2628] of cells in a plate,demonstrates the occurrence of collective emergent properties and requires complementing average cell explanations withanother level of analysis, relative to the culture-as-a-whole. Globally, this situation resembles what physiologists knowsince decades in well connected systems like the brain (neurons) where highly correlated and reliable emergent behaviouris supported by single-cell randomness [2931]. A very convincing example of this kind of coordinated behaviour is theonset of metabolic cycles in cultured yeasts where very stable and reliable cycles of 2040 min characteristic period areobserved relative to both metabolic (oxygen consumption) and genetic (gene expression) parameters [27].We analyze yeast gene expression data in two cultures; asynchronous (A) and synchronous (B) populations [17], the

analyzed experiments refer to reproductive cell cycles and the synchronicity is intended in terms of DNA content in theculture obtained by means of pheromone alpha. Despite the fact cells in culture A randomly duplicate while cells in cultureB duplicate in a synchronous way, the level of expression of the analysed 7160 genes is strongly correlated along the 18time points between the two cases scoring an average Pearson correlation equal to 0.93, suggestive of the same generaltemporal architecture of gene expression in the two A and B cultures. This temporal architecture is not directly linked to cellcycle [17] at the global population level as we discover by the strong invariance between asynchronous (A) and synchronous(B) populations. Therefore, yeast whole genome expressions have dominant collective behavior basically independent ofpharmacological stimulus.Table 2 reports the few genes for which we did not observe a strict correlation between asynchronous (A) and

synchronous (B) cultures. The majority are known to be directly linked with the pheromone alpha (the pharmacologicalintervention used to synchronize cells) specific mechanism of action as specified by the asterisk. This is the image in lightof the specific, local, pharmacological action of the pheromone alpha that in this case affects only a very minor portion ofthe entire genome machinery while majority of genes follows almost exactly the same dynamics in both populations. Thisdynamics is depicted in Fig. 6 where the first component (pc1) coming from the SVD analysis of the matrix having as rowsthe time points and as columns different choices of genes in the A population is reported (this choice was dictated by thecomplete equivalence of A and B populations). Three gene subsets were chosen to run separate analyses in order to checkfor the scalability character of the process:

(1) SMALL= 17 genes linked to ribosome production (ribogenesis)(2) WHOLE= 275 ribogenesis related genes(3) RAND= 275 randomly chosen genes.As it is evident from the figure, the first component not only explains almost the same amount of variance in all the three

data sets, but has a practically coincident temporal profile with an anharmonic cycle of around twenty minutes. The samecycle was then confirmed to be present in the entire data set made of 7160 genes [17].The invariant character of the observed cycles that remains the same (independent of the considered gene sets taken into

consideration) and presents a strong scalability (independent of size of gene sets), demonstrates how the yeast populationself organizes following a sort of ecology-in-a-plate giving rise to a strong and reliable macroscopic order. Although suchcollective motions have been previously addressed to find metabolic correlations [27], the specific role of these expressionwaves is still elusive. In a recent review, Klevecz and colleagues [28] also clarified the distinction between these collectivemotions and duplication cycles of cells. The demonstration of coordinated gene expression activity spanning the entire yeastcolony asks for a complete re-thinking of the implicit ergodic hypothesis in cell biology [17,26].

M. Tsuchiya et al. / Physica A 388 (2009) 17381746 1745

Fig. 6. In panel (A) the first mode dynamics of the SMALL and WHOLE data set are reported. Panel (B) is relative to the RAND and WHOLE data sets. Thepresence of a clear and repeatable dynamics of gene expression at the level of the entire colony explaining more than half of the total gene expressionvariability and independent of the analyzed genes implies an elevated degree of synchrony among different cells and a clear departure from ergodicity.

4. Conclusions

Here we report the presence of two basic modes-of-action of biological systems focusing on the gene expressionregulation and attempted to put into a unitary frame both the extreme sensitivity of biological systems to the variationof very crucial variables (hard-wired responses) and their general robustness and resiliency (collective aspecific responses).In innate immunity, we observed hard-wired or specific mode playing dominant biological role, whereas the generalizedcollective or non-specific modewas confined to aminor role. Yeast gene expressionwaves displayed a completely reversedsituation inwhich by far themost important rolewas played by collective, scale-invariant, non-specificmodeswith the localpharmacological action exerting only a very minor action in terms of affected genes.Networkmetaphor in which the hard-wired response corresponds to the directed attack to specific crucial nodes and the

collectivemodes to slowly fluctuating activity of the network as awhole [10] allows us to reconcile the two perspectives intoa common frame. This corresponds to the spectrum going from portions of the network that can be easily isolated, as is thecase of hard-wired TLR4 pathway and whose functioning can be expressed in terms of node-arrow schemata, to the generalfunctioning of the network as a whole where a huge number of diverse processes work concertedly making necessary toacquire a statistical mechanics-like perspective.While preparing this manuscript, Chang et al. group [23] demonstrated thatthe departure from ergodicity of cell populations by means of the consequent phenotypic heterogeneity is at the base of thecommitment of different cell subpopulations to enter in separate differentiation trajectories. The different commitment ofcell sub-populations can be in turn appreciated in terms of the same transcriptome-wide metrics we used in our work.It is worth noting the distances between different cell lineages in terms of the Pearson metrics D (where D = 1 R withR = Pearson correlation) is of the same order of magnitude of the apparently minor effects we observed in the case ofinnate immunity (Chang et al. observed D values ranging from 0.009 to 0.012 in the first phases of differentiation) [23].The demonstration that within a clonal population of multipotent progenitor cells, spontaneous non-genetic populationheterogeneity primes the cells for different lineage choices and that, in turn, the progression along the differentiationpathways happens in terms of a genome-wide transcriptome displacement asks for a complementation of the classicalgene-specific approach to cellular biology with a much wider statistical-mechanics like perspective.What is important to stress is the need to complement the already accepted and exploited hard-wired specific biology

with the other portion of the spectrum made by collective motions and macroscopic order supported by microscopicstochasticity. This is crucial even for the design of future therapeutics where drugs are developed not solely for targetinghard-wire response that is possibly effective for acute diseases, but for chronic and degenerative diseases which mightrequire the consideration of collective responses.

Acknowledgments

Thisworkwas supported by Japan Science and Technology Agency/Core Research for Evolutional Science and Technology(JST CREST), Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), Research fund by YamagataPrefecture and Tsuruoka City, Japan.

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Local and global responses in complex gene regulation networksIntroductionMaterial and methodsInnate immune gene expression dataYeast gene expression data

Results and discussionAnalysis of gene expression in innate immune responseAnalysis of gene dynamics in yeast

ConclusionsAcknowledgmentsReferences