Universality and flexibility in gene expression frombacteria to humanHiroki R. Ueda*†‡§, Satoko Hayashi‡, Shinichi Matsuyama¶, Tetsuya Yomo¶储**††‡‡, Seiichi Hashimoto‡, Steve A. Kay§§,
John B. Hogenesch§¶¶, and Masamitsu Iino†*Laboratory for Systems Biology, Center for Developmental Biology, RIKEN, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan;†Department of Pharmacology, Graduate School of Medicine, University of Tokyo, 7-3-1 Bunkyo-ku, Tokyo 113-0033, Japan; ‡Molecular Medicine
Laboratories, Institute for Drug Discovery Research, Yamanouchi Pharmaceutical Co., Ltd., 21 Miyukigaoka, Tsukuba, Ibaraki 305-8585, Japan; ¶Symbiotic
Engineering, Department of Bioinformatic Engineering, Graduate School of Information Science and Technology, and ††Department of Biotechnology,
Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan; 储Department of Pure and Applied Sciences, University ofTokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan; **Precursory Research for Embryonic Science and Technology, Japan Science and Technology
Corporation, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan; ¶¶The Genomics Institute of the Novartis Research Foundation, San Diego, CA 92121;§§Department of Cell Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, CA 92037; and ‡‡Graduate School of Frontier
Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
Edited by Michael S. Waterman, University of Southern California, Los Angeles, CA, and approved January 9, 2004 (received for review September 28, 2003)

systems biology 兩 DNA microarray 兩 gene expression dynamics 兩transcription 兩 transcriptional organizationThe past decade has seen a growing number of model organisms with available draft or complete genome sequences
including Escherichia coli, Saccharomyces cerevisiae, Arabidopsis
thaliana, Drosophila melanogaster, Mus musculus, and Homosapiens. The availability of these resources and the developmentof tools such as DNA arrays that allow for high-throughput
experimental biology have been driving a paradigm shift in thelife sciences, from the molecular ‘‘one-gene-at-a-time’’ level to a
network or systems level (1–5).
Genome-wide experimental biology approaches offer theopportunity to work more efficiently (6), and also to explore foruniversal governing principles underlying the physiology. Several
recent microarray studies have investigated the large-scale organization of gene expression, revealing complex networks that
capitulate physiological processes such as the cell cycle, responses to environmental change, circadian rhythms, and developmental and tissue-specific gene regulation (6–10). However,universal features of gene expression dynamics that produce suchcomplex and dynamic cellular organizations have largely gone
unexplored. To comprehensively and quantitatively elucidate
these underlying gene expression dynamics, we analyzed genome-wide gene expression data collected from experimental
studies in E. coli, S. cerevisiae, A. thaliana, D. melanogaster, M.
musculus, and H. sapiens samples by using high-density oligowww.pnas.org兾cgi兾doi兾10.1073兾pnas.0306244101

nucleotide arrays. Here we show that the gene expression
dynamics follows the same and surprisingly simple principle from
E. coli to H. sapiens, where gene expression changes are proportional to their initial expression levels. Furthermore, we showthat this ‘‘proportional dynamics’’ or ‘‘rich-travel-more’’ mechanism can regenerate the observed complex and dynamic organization of the transcriptome.
Materials and Methods
E. coli. Cells of E. coli strain YMC21 lacking glutamine synthetasegene was collected under normal or symbiotic conditions as
described (11). Total RNA was isolated by using MasterPure
RNA purification kit (Epicentre Technologies, Madison, WI).
S. cerevisiae. Cells of S. cerevisiae strain FY1679 were grown inyeast extract兾peptone兾dextrose medium with aeration at 20 ⫾0.5°C to maintain an optical density of 0.5 at 600 nm (OD600) byusing a continuous culturing system. The culture was adapted to
12-h light兾12-h dark cycles (LD) for 2 days before samples wereobtained under LD conditions every 4 h starting at Zeitgeber
time (ZT) 0 over 2 days. Total RNA was isolated from 10-ml
cultures by using the hot phenol method.
A. thaliana. Wild-type Arabidopsis seeds of the Col-1 ecotype
were sown on Murashige and Skoog (MS) agar plates containing
3% sucrose. Seeds were stratified at 4°C for 2 days and thenplaced in growth chambers held at 22°C. Plants were grown in
LD cycles for 7 days and then released into constant light (60␮Einsteins䡠m⫺2䡠s⫺1). Starting at subjective dawn on day 9 [circadian time (CT) 0], plants were harvested every 4 h over 2 days.
Total RNA was prepared from the staged tissue samples by using
the Qiagen RNeasy Plant Mini kit (Valencia, CA).
D. melanogaster. white1118 flies were reared to LD and collectedunder LD or constant darkness conditions every 4 h starting at
ZT1 or CT1 over 2 days. Total RNA was prepared from 100
heads of 1-week-old adult males and females by using the Fast
RNA kit (BIO 101, Carlsbad, CA).
M. musculus Time Course Sampling. BALB兾c mice (male), pur-chased 5 weeks postpartum, were adapted to LD cycles for 2
weeks before samples were obtained under LD or constantThis paper was submitted directly (Track II) to the PNAS office.
Abbreviations: ZT, zeitgeber time; CT, circadian time; LD, 12-h light兾12-h dark; SCN,
suprachiasmatic nucleus.
§To

whom correspondence may be addressed. E-mail: uedah-tky@umin.ac.jp or
hogenesch@gnf.org.

© 2004 by The National Academy of Sciences of the USA

PNAS 兩 March 16, 2004 兩 vol. 101 兩 no. 11 兩 3765–3769

BIOCHEMISTRY

Highly parallel experimental biology is offering opportunities to
not just accomplish work more easily, but to explore for underlying
governing principles. Recent analysis of the large-scale organization of gene expression has revealed its complex and dynamic
nature. However, the underlying dynamics that generate complex
gene expression and cellular organization are not yet understood.
To comprehensively and quantitatively elucidate these underlying
gene expression dynamics, we have analyzed genome-wide gene
expression in many experimental conditions in Escherichia coli,
Saccharomyces cerevisiae, Arabidopsis thaliana, Drosophila melanogaster, Mus musculus, and Homo sapiens. Here we demonstratethat the gene expression dynamics follows the same and surprisingly simple principle from E. coli to human, where gene expression
changes are proportional to their expression levels, and show that
this ‘‘proportional’’ dynamics or ‘‘rich-travel-more’’ mechanism canregenerate the observed complex and dynamic organization of thetranscriptome. These findings provide a universal principle in theregulation of gene expression, show how complex and dynamic
organization can emerge from simple underlying dynamics, anddemonstrate the flexibility of transcription across a wide range of
expression levels.

darkness conditions every 4 h starting at ZT0 or CT0 over 2 days.
Slices (0.5 mm thick) of mouse brain were generated by using
Mouse Brain Matrix (Neuroscience) under LD or constantdarkness condition, and then the suprachiasmatic nuclei (SCNs)
were punched out bilaterally from the frozen slices under astereomicroscope with a microdissecting needle (gauge, 0.5mm). Livers were dissected and frozen in liquid nitrogen. Total
RNA was prepared from 50 pooled pairs of SCNs and fourpooled livers at each time point by using by TRIzol reagent(GIBCO兾BRL).
M. musculus and H. sapiens Tissue Sampling. Forty-seven humantissue samples and cell lines were obtained from commercial
sources and previously published research collaborations, and 45
mouse tissue samples were derived from dissections. Detailed
sample descriptions can be obtained on the web site (http:兾兾
expression.gnf.org) (6).

Microarray Experiments. We examined genome-wide RNA expression of E. coli, S. cerevisiae, A. thaliana, D. melanogaster, M.
musculus, and H. sapiens by using Affymetrix high-density
oligonucleotide probe arrays (GeneChip) representing ⬇4,200
E. coli, ⬇6,400 S. cerevisiae, ⬇8,200 A. thaliana, ⬇13,500 D.
melanogaster, ⬇10,000 M. musculus, and ⬇12,000 H. sapiens
genes, respectively (7, 8). We extracted total RNA from theorganisms, prepared biotinylated cRNA, hybridized samples to
GeneChip arrays, and obtained hybridization signals as described (6, 8–10).
cDNA synthesis and cRNA labeling reactions were performed
as described in the Affymetrix technical manual (Affymetrix,
Santa Clara, CA). We used Affymetrix high-density oligonucleotide arrays: E. coli Genome Array for E. coli, Yeast Genome
S98 Array for S. cerevisiae, Arabidopsis Genome Array for A.
thaliana, Drosophila Genome Array for D. melanogaster, Murine
Genome Array U74A for M. musculus (Murine Genome Array
U74A), and Human Genome Array U95A for H. sapiens. To
facilitate comparisons between samples, the obtained data werescaled globally such that the average of signal intensity for probe
sets of each GeneChip array is 1兾30. We defined this scaled
signal intensity values as an ‘‘expression level’’ of a gene and used
it in all subsequent analyses.
ANOVA. Statistical analysis (one-way ANOVA, P ⬍ 0.01) was

performed on gene expression data above from E. coli to human.
Expected false positives derived from the multiple testing are⬇1% of the tested genes.

Calculation of the Absolute Expression Change. We calculated theabsolute expression change 兩⌬k兩 ⬅ 兩k2 ⫺ k1兩 for individual genes
from an expression level (k1) to another expression level (k2),along two different conditions of E. coli, along the different ZT
and兾or CT in S. cerevisiae, A. thaliana, heads of D. melanogaster,liver and SCN of M. musculus, or along 45 M. musculus tissues
and 47 H. sapiens tissues. We calculated the absolute expression
change in all distinct pairs of different conditions.
Results and Discussion
To investigate systems-level features of RNA expression, we
analyzed the distribution of gene expression levels from our data
sets obtained from E. coli to H. sapiens. Fig. 1 shows that the
distribution of gene expression levels exhibits a power-law
distribution in which the probability that a gene has amount ofexpression, k, decays as a power law, P(k) ⬀ k⫺r. Furthermore,this genome-wide transcriptional organization is conserved from
E. coli to H. sapiens with the exponent r of the distribution ofgene expression levels close to 2 (1.69–2.09). This power-law
distribution is not artifactual because the hybridization signal
intensity of each probe on the arrays is linear along the cRNA
3766 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0306244101

Fig. 1. Evolutional conservation of transcriptional organization. The distributions of gene expression levels in E. coli (A), S. cerevisiae (B), A. thaliana (C),D. melanogaster (D), M. musculus (E), and H. sapiens (F) exhibit a power-law
distribution in which the probability that a gene has an expression level k,decays as a power law, P(k) ⬀ k⫺r. A straight line in each panel represents theestimated power-law distribution. The estimated value of exponent r is indicated in the lower left corner of each panel.

concentration (Fig. 5, which is published as supporting information on the PNAS web site) and as an analysis of serial analysis
of gene expression (SAGE) data (12–15) revealed a similar
power-law distribution and exponent from S. cerevisiae to H.
sapiens (Fig. 6, which is published as supporting information on
the PNAS web site). These results are also consistent with aprevious report on power-law distribution of gene expression
levels (16, 17). Collectively, these results indicate that network
regulation of genome-wide transcriptional organization is conserved between prokaryotes and eukaryotes.
To confirm these results and examine whether this quantitative property of transcription extends to temporal and spatial
gene regulation, we analyzed RNA expression from diverse
datasets at different ZT and兾or CT or tissues in S. cerevisiae, A.
thaliana, D. melanogaster, M. musculus, and H. sapiens. Fig. 7A,
which is published as supporting information on the PNAS web
site, shows that the distribution of gene expression levels exhibits
a power-law distribution P(k) ⬀ k⫺r with an exponent r close to
2 (Fig. 7 C–J). Importantly, statistical analysis (ANOVA) revealed that 3% of genes in S. cerevisiae, 16% of genes in A.
thaliana, 17% of genes in heads of D. melanogaster, and 8% ofgenes in liver and 8% of genes in SCN of M. musculus are
dynamically expressed along different ZT and兾or CT (P ⬍ 0.01).
Ueda et al.

BIOCHEMISTRY

Fig. 2. Characteristics in gene expression dynamics. (A–H) Transition probability T(k2, k1), where a gene with a certain expression level k1 changes its expression
level to k2, calculated from expression data in E. coli (A), S. cerevisiae (B), A. thaliana (C), heads of D. melanogaster (D), liver and suprachiasmatic nucleus of M.
musculus (E and F), 45 tissues of M. musculus (G), and 47 tissues of H. sapiens (H). Colors from red to yellow to green represent transition probability of descending
values. Gray indicates the value of zero (the lack of the transition data). (I–P) Proportionality in gene expression dynamics. The absolute expression level change(兩⌬k兩 ⬅ 兩k2 ⫺ k1兩) is plotted along the before-transition expression level k1 in E. coli (I), S. cerevisiae (J), A. thaliana (K), heads of D. melanogaster (L), liver andsuprachiasmatic nucleus of M. musculus (M and N), 45 tissues of M. musculus (O), and 47 tissues of H. sapiens (P) expression data. The estimated values for
exponent s from a log–log plot of absolute expression change against the before-transition expression level (i.e., 兩⌬k兩 ⬀ k1s) are indicated in the lower right cornerof each panel.

Mammalian tissue specific gene expression displays an evenmore dynamic pattern of expression; statistical analysis(ANOVA) revealed that 95% and 88% of genes are differentiallyexpressed in 47 H. sapiens and 45 M. musculus tissues, respectively (P ⬍ 0.01). Therefore, we analyzed the RNA expression in
47 tissues of H. sapiens and 45 tissues of M. musculus. Despite
differential expression of the vast majority of genes in these data
sets, Fig. 8A, which is published as supporting information on the
PNAS web site, shows that the distribution of gene expression
levels exhibits a power-law distribution P(k) ⬀ k⫺r with an
exponent r close to 2 (see also Fig. 8 B and C). Therefore, both
temporal and spatial gene expression regulation follows a powerlaw distribution despite the differential dynamic expression of a
substantial fraction of genes.
To investigate the type of dynamics that generates this evolutionary and spatio-temporally conserved power-law transcripUeda et al.

tional organization, we analyzed the systems-level features in
expression changes of individual genes. We calculated the transition probability T(k2, k1) of expression change by counting theincidence of expression changes for individual genes from an
expression level (k1) to another expression level (k2), along two
different conditions of E. coli (Fig. 2A), or for variouis conditions
in S. cerevisiae (Fig. 2B), A. thaliana (Fig. 2C), heads of D.
melanogaster (Fig. 2D), liver and SCN of M. musculus (Fig. 2 E
and F), or along 45 M. musculus tissues (Fig. 2G) and 47 H.
sapiens tissues (Fig. 2H). This analysis revealed that the transition probabilities are not random, but rather are highly dependent on the before-transition expression level (k1). For example,
transition from the higher expression levels spread more widely,whereas transition from the lower expression levels is confinedto the lower expression levels (Fig. 2 A–H). To exclude thepossibility that the narrower expression changes from lower
PNAS 兩 March 16, 2004 兩 vol. 101 兩 no. 11 兩 3767

Fig. 4. Theoretical model of proportional gene expression dynamics. (A)Transition probability matrix representing the theoretical model of proportional gene expression dynamics. The model transition probability T(k2, k1)
represents the probability of expression change from a certain expression
level k1 to other expression level k2 during unit time interval. Colors from red
to yellow to green represent transition probabilities of descending values. (B)The stationary distribution of gene expression calculated by using the modeled transition probability matrix from arbitrary initial distribution of gene
expression levels. The stationary distributions of model proportional exhibit a
power-law distribution in which the probability that a gene has an expression
level k, decays as a power law. The straight line represents the estimatedpower-law distribution P(k) ⬀ k⫺2.

Fig. 3. Proportional gene expression dynamics can regenerate the observed
transcriptional organization. Shown are the stationary distributions of gene
expression levels calculated by using transition probability matrices in Fig. 2
A–H from arbitrary initial distribution of gene expression levels. The stationary
distributions of E. coli (A), S. cerevisiae (B), A. thaliana (C), heads of D.
melanogaster (D), liver and suprachiasmatic nucleus of M. musculus (E and F),
45 tissues of M. musculus (G), and 47 tissues of H. sapiens (H) exhibit a
power-law decay in which the probability that a gene has an expression levelk, is P(k) ⬀ k⫺r. The straight line in each panel represents the estimatedpower-law distribution. The estimated value of exponent r is indicated in thelower left corner of each panel.

expression levels are caused by limit of detection for genes of low
intensity or ‘‘dead probe sets,’’ we applied the same analyses toprobe sets that pass a statistical criteria (ANOVA, P ⬍ 0.01), andwe obtained the similar results (data not shown).
To extract the quantitative characteristics of these gene expression dynamics, we analyzed relationships between the before-transition expression level (k1) and the absolute expression
change 兩⌬k兩 ⬅ 兩k2 ⫺ k1兩. Fig. 2 I–P shows that the absolute
expression change is proportional to the before-transition expression level from E. coli to H. sapiens. Stated differently,
although the absolute change from higher expression levels islarger, it is proportional to the initial before transition value. To
confirm this proportionality, we measured an exponent s from
log–log plot of absolute expression change (兩⌬k兩) against the
before-transition expression level k1 (i.e., 兩⌬k兩 ⬀ ks1) and found it
3768 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0306244101

to be close to 1 (Fig. 2 I–P). We also note that the absolute
expression change becomes asymptotically a small but nonzero
value with lower expression levels (Fig. 9, which is published as
supporting information on the PNAS web site). These results
suggest that the proportional gene expression dynamics underlie
genetic networks from E. coli to H. sapiens.
We then tested whether this proportional gene expression
dynamics can generate the observed power-law transcriptionalorganization. We calculated the stationary distribution of gene
expression levels by using transition probability matrices of E.
coli to H. sapiens (Fig. 2 A–H) from arbitrary initial distributionsof gene expression levels. We found that the simulated distribution of gene expression levels exhibits the power-law distribution P(k) ⬀ k⫺r, regardless of the initial distribution, with an
exponent r close to 2 (Fig. 3). These results suggest that gene
expression dynamics are conserved from E. coli to H. sapiens andthat this universal gene expression dynamic can regenerate theobserved power-law organization of gene expression levels.
To explore the relationship between proportional gene expression dynamics and power-law transcriptional organization,
we modeled these gene expression dynamics. We hypothesized
proportionality in gene expression dynamics; where the standard
deviation of gene expression change, 具兩dk兩典, increases in proportional to the before-transition gene expression level k. We next
hypothesized that the average of gene expression changes 具dk典 iszero, indicating that the expression level of each gene may
increase or decrease and it has no systematic tendency (seeSupporting Text, which is published as supporting information on
the PNAS web site). From these assumptions, we can derive thestationary distribution of gene expression levels and find that itexhibits the power-law distribution with an exponent ⫺2, i.e.,P(k) ⬀ k⫺2 (see Supporting Text and Fig. 10, which is publishedas supporting information on the PNAS web site, for details).
To validate this model, we implemented the model withparameters estimated from S. cerevisiae expression analysis (a ⫽0.25, b ⫽ 0.0006, s ⫽ 1 for 具兩dk兩典 ⫽ a(k ⫹ b)s, see Supporting Text).
Fig. 4A shows the transition probability matrix representing themodel gene expression dynamics (see Supporting Text and Fig.
11, which is published as supporting information on the PNAS
web site). The modeled transition probability matrix highly
resembles the transition probability matrix calculated from S.
Ueda et al.

cerevisiae expression data (Figs. 4A and 2B). Moreover, wedemonstrated that the stationary distribution generated by themodel transition probability matrix from any initial distributions
exhibits the power-law distribution P(k) ⬀ k⫺r with an exponentr close to 2 (Figs. 4B and 3B). For comparison, we also
implemented the model with other parameter values such as s ⫽0.5 or s ⫽ 2 and found much less agreement with observed
distributions, indicating the importance of proportional dynamics in generating observed power-law distributions (Fig. 12,
which is published as supporting information on the PNAS website). Based on these results, we concluded that gene expression
dynamics from E. coli to H. sapiens are governed by the same
proportional dynamics, where the expression level of each geneis dynamically changed in proportion to its initial expression
level, and that this proportionality in gene expression dynamics
has a critical role in generating the power-law organization ofgene expression levels.
Collectively, these results indicate that gene expression dynamics follows the same and surprisingly simple principles frombacteria to humans in which gene expression changes are proportional to their initial expression levels. Importantly, this
proportionality assures the same level of flexibility of expression
for highly expressed genes as well as for lower expressed genes.
This flexibility is vital for transcriptional regulation because both
highly expressed genes such as structural genes as well as morerare mRNAs such as G protein-coupled receptors have to change
their expression levels to adapt an environmental or developmental change.
Power-law distributions arise in the expression levels withproportional dynamics where highly expressed genes change
their expression levels more dynamically than less expressed
genes. This ‘‘rich-travel-more’’ mechanism generates power-law
distributions in the fixed networks with constant number ofcomponents and resembles the ‘‘rich-get-richer’’ mechanism(e.g., preferential attachment) that can generate the power-law
distributions in growing networks such as the World Wide Web,in which highly connected nodes have a higher chance than lessconnected nodes to linking to new nodes. Interestingly, we haveanalyzed the evolution of metabolic networks with similar
number of constituents, and found that the proportional dynam-

We thank Hideo Iwasaki and Takao Kondo for a continuous culturingsystem and Sumio Sugano and Yutaka Suzuki for stimulating discussion.
We also thank Koichi Shiozuka, Stancey L. Harmer, Akira Matsumoto,Teiichi Tanimura, Miho Kawamura, Wenbin Chen, Hisanori Wakamatsu, Akihito Adachi, Yasufumi Shigeyoshi, Andrew I. Su, Michael P.
Cooke, Keith A. Ching, Yaron Hakak, John R. Walker, Tim Wiltshire,and Anthony P. Orth for yeast, Arabidopsis, fly, mouse, and humangenome-scale expression measurement. We thank Tomoko Kojima,
Toshie Katakura, and Hiromi Urata for technical assistance. This study
was performed as a part of a research and development project of theIndustrial Science and Technology Program supported by New Energy
and Industrial Technology Development Organization (NEDO). This
work was also supported in part by Grants-in-Aid 11CE2006, 15207020,
12002003, and 15013235 and The 21st Century Center of Excellence
Program of the Ministry of Education, Culture, Sports, Science, andTechnology, Japan, and by a grant from Takeda Science Foundation.

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BIOCHEMISTRY

ics also underlies the evolution of metabolic networks with afixed or similar number of components (H.R.U., J.B.H., andM.I., unpublished data).
Recently, several studies have investigated the genome-wide
network structure of the metabolome (18–20), transcriptome(21–24), and proteome (25), and have revealed the universalityof the scale-free, modular, and hierarchical topology of biological networks (26–30). Moreover, several recent microarraystudies (4, 5) have identified the specific dynamics of specialized
systems including the cell cycle, environmental responses, circadian rhythms, development, and tissue-specific gene regulation. This present study illustrates generic gene expression
dynamics underlying regulation of transcription, complementing
previous work on generic genome-wide network structure or on
specific dynamics of specialized systems. A next challenge is,thus, the understanding of the systems-level features in the
network structure that generates this proportional dynamic, as
well as the investigation of the generality of proportional dynamics in other physiological processes, such as the regulation of
metabolic processes. The development of predictive models that
accurately represent biological processes in conjunction withhighly parallel experimental data should accelerate the understanding of additional underlying principles governing the complex and dynamic systems of life.