Gene Regulation at theSingle-Cell Level

Nitzan Rosenfeld,1* Jonathan W. Young,3 Uri Alon,1

Peter S. Swain,2* Michael B. Elowitz3.

The quantitative relation between transcription factor concentrations and therate of protein production from downstream genes is central to the functionof genetic networks. Here we show that this relation, which we call the generegulation function (GRF), fluctuates dynamically in individual living cells,thereby limiting the accuracy with which transcriptional genetic circuits cantransfer signals. Using fluorescent reporter genes and fusion proteins, wecharacterized the bacteriophage lambda promoter PR in Escherichia coli. Anovel technique based on binomial errors in protein partitioning enabledcalibration of in vivo biochemical parameters in molecular units. We foundthat protein production rates fluctuate over a time scale of about one cellcycle, while intrinsic noise decays rapidly. Thus, biochemical parameters,noise, and slowly varying cellular states together determine the effectivesingle-cell GRF. These results can form a basis for quantitative modeling ofnatural gene circuits and for design of synthetic ones.

The operation of transcriptional genetic cir-

cuits (1–5) is based on the control of pro-

moters by transcription factors. The GRF is

the relation between the concentration of

active transcription factors in a cell and the

rate at which their downstream gene products

are produced (expressed) through transcrip-

tion and translation. The GRF is typically

represented as a continuous graph, with the

active transcription factor concentration on

the x axis and the rate of production of its

target gene on the y axis (Fig. 1A). The shape

of this function, e.g., the characteristic level of

repressor that induces a given response, and

the sharpness, or nonlinearity, of this response

(1) determine key features of cellular behavior

such as lysogeny switching (2), developmen-

tal cell-fate decisions (6), and oscillation (7).

Its properties are also crucial for the design

of synthetic genetic networks (7–11). Cur-

rent models estimate GRFs from in vitro

data (12, 13). However, biochemical parame-

ters are generally unknown in vivo and could

depend on the environment (12) or cell history

(14, 15). Moreover, gene regulation may vary

from cell to cell or over time. Three funda-

mental aspects of the GRF specify the behav-

ior of transcriptional circuits at the single-cell

level: its mean shape (averaged over many

cells), the typical deviation from this mean,

and the time scale over which such fluctua-

tions persist. Although fast fluctuations should

average out quickly, slow ones may introduce

errors in the operation of genetic circuits and

may pose a fundamental limit on their ac-

curacy. In order to address all three aspects, it

is necessary to observe gene regulation in in-

dividual cells over time.

Therefore, we built Bl-cascade[ strains of

Escherichia coli, containing the l repressor

and a downstream gene, such that both the

amount of the repressor protein and the rate

of expression of its target gene could be

monitored simultaneously in individual cells

(Fig. 1B). These strains incorporate a yellow

fluorescent repressor fusion protein (cI-yfp)

and a chromosomally integrated target pro-

moter (PR) controlling cyan fluorescent pro-

tein (cfp). In order to systematically vary

repressor concentration over its functional

range (in logarithmic steps), we devised a

Bregulator dilution[ method. Repressor pro-

duction is switched off in a growing cell, so

that its concentration subsequently decreases

by dilution as the cell divides and grows into

a microcolony (Fig. 1C). We used fluores-

cence time-lapse microscopy (Fig. 1D; fig.

S1 and movies S1 and S2) and computational

image analysis to reconstruct the lineage tree

(family tree) of descent and sibling relations

among the cells in each microcolony (fig.

1Departments of Molecular Cell Biology and Physicsof Complex Systems, Weizmann Institute of Science,Rehovot, 76100, Israel. 2Centre for Non-linear Dy-namics, Department of Physiology, McGill University,3655 Promenade Sir William Osler, Montreal, Quebec,Canada, H3G 1Y6. 3Division of Biology and Depart-ment of Applied Physics, Caltech, Pasadena, CA 91125,USA.

*These authors contributed equally to this work.To whom correspondence should be addressed.E-mail: melowitz@caltech.edu

Fig. 1. Measuring agene regulation func-tion (GRF) in individualE. coli cell lineages. (A)The GRF is the depen-dence of the produc-tion rate of a targetpromoter ( y axis) onthe concentration ofone (or more) tran-scription factors (x ax-is). (B) In the l-cascadestrains (16) of E. coli,CI-YFP is expressedfrom a tetracyclinepromoter in a TetRþbackground and canbe induced by anhydro-tetracycline (aTc). CI-YFP represses produc-tion of CFP from the PRpromoter. (C) The reg-ulator dilution experi-ment (schematic): Cells are transiently induced to express CI-YFP and thenobserved in time-lapse microscopy as repressor dilutes out during cell growth(red line). When CI-YFP levels decrease sufficiently, expression of the cfp targetgene begins (green line). (D) Snapshots of a typical regulator dilution

experiment using the OR2*–l-cascade strain (see fig. S3) (16). CI-YFP proteinis shown in red and CFP is shown in green. Times, in minutes, are indicated onsnapshots. (Insets) Selected cell lineage (outlined in white). Greater timeresolution is provided in fig. S1.

B C

D

A

Repressor Concentration

Pro

duct

ion

Rat

e

Ptet-cIYFP PR-CFP

aTc

Pc-TetR

Time (cell cycles)

CI-YFPCFP

llec rep P

FY lat o

T) ela cs gol(

llec

rep

P

FC l

ato

T) e

l acs

rae

n il(

-2 -1 0 1 2 3 4 5 6 7 8

102

103

104

aTc

0.2

0.4

0.6

0.8

1

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25 MARCH 2005 VOL 307 SCIENCE www.sciencemag.org1962

S2). For each cell lineage, we quantified over

time the level of repressor (x axis of the

GRF) and the total amount of CFP protein

(Fig. 2A). From the change in CFP over time,

we calculated its rate of production (y axis of

the GRF) (16).

Regulator dilution also provides a natural

in vivo calibration of individual protein fluo-

rescence. Using the lineage tree and fluores-

cence data, we analyzed sister cell pairs just

after division (Fig. 2B). The partitioning of

CI-YFP fluorescence to daughter cells obeyed

a binomial distribution, consistent with an

equal probability of having each fluorescent

protein molecule go to either daughter (16).

Consequently, the root-mean-square error in

CI-YFP partitioning between daughters

increases as the square root of their total CI-

YFP fluorescence. Using a one-parameter fit,

we estimated the fluorescence signal of

individual CI-YFP molecules (Fig. 2B and

supporting online material). Thus, despite

cellular autofluorescence that prohibits detec-

tion of individual CI-YFP molecules, obser-

vation of partitioning errors still permits

calibration in terms of apparent numbers of

molecules per cell.

The mean GRFs obtained by these tech-

niques are shown in Fig. 3A for the PR

pro-

moter and a point mutant variant (fig. S3).

These are the mean functions, obtained by

averaging individual data points (Fig. 3B) in

bins of similar repressor concentration, indi-

cating the average protein production rate at a

given repressor concentration. Their coopera-

tive nature would have been Bsmeared out[ by

population averages (6, 17, 18).

These mean GRF data provide in vivo

values of the biochemical parameters under-

lying transcriptional regulation. Hill func-

tions of the form f(R) 0 b/E1 þ (R/kd)n^ are

often used to represent unknown regulation

functions (1, 6–10). Here, kd

is the con-

centration of repressor yielding half-maximal

expression, n indicates the degree of effective

cooperativity in repression, and b is the maxi-

mal production rate. Hill functions indeed fit

the data well (Fig. 3A and Table 1). The mea-

sured in vivo kd

is comparable to previous

estimates (2, 12, 13, 19) (see supporting online

text). The significant cooperativity observed

(n 9 1) may result from dimerization of repres-

sor molecules and cooperative interactions

between repressors bound at neighboring sites

(2, 12, 13, 19, 20). A point mutation in the

OR2 operator, O

R2* (20) (fig. S3), significant-

ly reduced n and increased kd

(Fig. 3A and

Table 1). Note that with similar methods it is

even possible to measure effective coopera-

tivity (n) for native repressors without fluores-

cent protein fusions (16).

We next addressed deviations from the

mean GRF. At a given repressor concentra-

tion, the standard deviation of production

rates is È55% of the mean GRF value. Such

variation may arise from microenvironmen-

tal differences (21), cell cycle–dependent

changes in gene copy number, and various

sources of noise in gene expression and other

cellular processes (22). We compared micro-

colonies in which induction occurs at differ-

ent cell densities (16). The results suggested

that the measured GRF is robust to possible

differences among the growth environments

in our experiments (fig. S6). We analyzed

the effect of gene copy number, which varies

twofold over the cell cycle as DNA repli-

cates. The CFP production rate correlated

strongly with cell-cycle phase; cells about to

divide produced on average twice as much

protein per unit of time as newly divided

cells (16). Thus, gene dosage is not com-

pensated. Nevertheless, after normalizing pro-

duction rates to the average cell-cycle phase

(16), substantial variation still remains in the

production rates, and their standard devia-

tion is È40% of the mean GRF (Fig. 3). The

deviations from the mean GRF show a log-

normal distribution (see supporting online text

and fig. S5).

These remaining fluctuations may arise

from processes intrinsic or extrinsic to gene

expression. Intrinsic noise results from sto-

chasticity in the biochemical reactions at an

individual gene and would cause identical

copies of a gene to express at different levels.

It can be measured by comparing expression

of two identically regulated fluorescent pro-

teins (22). Extrinsic noise is the additional

variation originating from fluctuations in

cellular components such as metabolites,

ribosomes, and polymerases and has a global

effect (22, 23). Extrinsic noise is often the

dominant source of variation in E. coli and

Saccharomyces cerevisiae (22, 24).

To test whether fluctuations were of intrin-

sic or extrinsic origin, we used a Bsymmetric

branch[ strain (16) that produced CFP and

YFP from an identical pair of PR

promoters

(Fig. 4D, movie S3). The difference between

CFP and YFP production rates in these cells

indicates È20% intrinsic noise in protein

production Eaveraged over 8- to 9-min in-

tervals (16)^, suggesting that the extrinsic

component of noise is dominant and con-

tributes a variation in protein production

rates of È35%.

Our measurements provide more detailed

analysis of extrinsic noise in two ways. First,

in previous work (22), extrinsic noise included

fluctuations in upstream cellular components,

including both gene-specific and global fac-

tors. Here, we quantify the extrinsic noise at

known repressor concentration, and so extrin-

sic noise encompasses fluctuations in global

cellular components such as polymerases or

Fig. 2. Data and calibration.(A) Fluorescence intensitiesof individual cells are plottedover time for the experimentof Fig. 1D. Red indicates CI-YFP, which is plotted on a log-arithmic y axis to highlight itsexponential dilution: As CI-YFPis not produced, each divisionevent causes a reduction ofabout twofold in total CI-YFPfluorescence. Green indicatesCFP, which is plotted on alinear y axis to emphasize itsincreasing slope, showing thatCFP production rate increasesas the CI-YFP levels decrease.A selected cell lineage is high-lighted (also outlined in Fig.1D). (B) Analysis of binomial errors in protein partitioning to find vy, theapparent fluorescence intensity of one independently segregating fluores-cent particle (16). Cells containing Ntot copies of a fluorescent particle(total fluorescence Ytot 0 vy I Ntot) undergo division (inset). If eachparticle segregates independently, N1 and N2, the number of copiesreceived by the two daughter cells, are distributed binomially, and satisfy

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN1j N2

2

� �2D Er

0ffiffiffiffiffiffiffiffiNtot

p=2. A single-parameter fit thus determines the value of

vy. Here we plot kN1 – N2k=2 (in numbers of apparent molecule dimers) versusNtot 0 N1 þ N2. Blue dots show the scatter of individual division events. Crosses(red) show the root-mean-square (RMS) error in protein partitioning and itsstandard error. The expected binomial standard deviation is shown in black.

R E P O R T S

www.sciencemag.org SCIENCE VOL 307 25 MARCH 2005 1963

ribosomes but not in the concentration of the

repressor, CI. Second, dynamic observations

permit us to measure extrinsic noise in the

rate of protein expression rather than in the

amount of accumulated protein. The present

breakdown should be more useful for model-

ing and design of genetic networks.

In cells, fast and slow fluctuations can

affect the operation of genetic networks in dif-

ferent ways. Previous experiments (22, 24–26)

used static Bsnapshots[ to quantify noise at

steady state and were thus unable to access

the temporal dynamics of gene expression.

However, a similar steady-state distribution

of expression levels can be reached by

fluctuations on very different time scales

(Fig. 4). Fluctuations can be characterized by

their autocorrelation time, tcorr

(16). The

magnitude of tcorr

compared with the cell-

cycle period is crucial: Fluctuations longer

than the cell cycle accumulate to produce

significant effects, whereas more rapid fluc-

tuations may Baverage out[ as cellular

circuits operate (27, 28). In these data, three

types of dynamics are observed (Fig. 4, A to

C): Fast fluctuations, periodic cell-cycle

oscillations due to DNA replication, and

aperiodic fluctuations with a time scale of

about one cell cycle.

We found that the trajectories of single-

cell lineages departed substantially from the

mean GRF over relatively long periods (Fig.

3B), with tcorr

0 40 T 10 min (Fig. 4E). This

value is close to the cell cycle period, tcc

045 T 10 min, indicating that, overall,

fluctuations typically persist for one cell

cycle. Therefore, if a cell produces CFP at a

faster rate than the mean GRF, this over-

expression will likely continue for roughly

one cell cycle, and CFP levels will accumu-

late to higher concentrations than the mean

GRF would predict.

Fig. 3. The GRF and itsfluctuations. (A) The meanregulation function of thewild-type l-phage PR pro-moter (blue squares) and itsOR2-mutated variant (OR2*,orange circles) are plottedwith their respective standarddeviations (dashed/dottedlines). Hill function approxi-mations (using parametersfrom Table 1) are shown(solid lines). (B) Variation inthe OR2* GRF. Individualpoints indicate the instanta-neous production rate of CFP,as a function of the amountof CI-YFP in the same cell, forall cells in a microcolony ofthe OR2*–l-cascade strain. The time courses of selected lineages in thismicrocolony are drawn on top of the data, showing slow fluctuationsaround the mean GRF. CI-YFP concentration decreases with time, and

consecutive data points along a trajectory are at 9-min intervals. Typicalmeasurement errors (black crosses) are shown for a few points. Data arecompensated for cell cycle–related effects (16).

101 102

apparent cI-YFP concentration [nM]

102

PF

Cetar no itcu dorp

llec selucelom tnerapp a[

-1ni

m -1

]

101 102

apparent cI-YFP concentration [nM]

102

PF

Cetar noitcudorp

llec selucelom tnerappa[

-1ni

m -1

]

wt mean GRFstandard dev.fit to HillOR2* mean GRFstandard dev.fit to Hill

A B

production ratesmean GRFselected lineageselected lineagemeasurement errors

Table 1. In vivo values of effective biochemicalparameters. Molecular units are estimated usingbinomial errors in protein partitioning (16) (Fig.2B), which may have systematic errors up to afactor È2. Concentrations are calculated fromapparent molecule numbers divided by cell vol-umes estimated from cell images (16), with anaverage volume of 1.5 T 0.5 mm3 (for which 1 nM 00.9 molecule/cell).

Parameter PR PR (OR2*)

n (degree ofcooperativityin repression)

2.4 T 0.3 1.7 T 0.3

kd [concentration ofrepressor yieldinghalf-maximalexpression (nM)]

55 T 10 120 T 25

b [unrepressed productionrate (molecules Icellj1 I minj1)]

220 T 15 255 T 40

E

DA

B

C

1

1.5

2

0 1 2 3 4 5 6 7

1

1.5

2

time [cell cycles]

1

1.5

2

lacitehtopyhetar noitcudorp

lacitehtopyhetar noitcudorp

lacitehtopyhetar noitcudo rp

Ptet-cIYFPY66F PR-CFP

PR-YFPaTc

Pc-TetR

0 20 40 60 80 100 120 140 1600

0.2

0.4

0.6

0.8

auto

corr

elat

ion

of p

rodu

ctio

n ra

tes

time [min]

total noise

2-t/40min

intrinsic noise

2-t/9min

Fig. 4. Fluctuations in gene regulation. (Left) Three types of variability observed here. (A) Fastfluctuations in CFP production, similar to those produced by intrinsic noise. (B) Periodic, cell cycle–dependent oscillations in CFP production, which can result from DNA replication. (C) Slowaperiodic fluctuations, such as extrinsic fluctuations in gene expression. (D) Intrinsic and extrinsicnoise can be discriminated using a symmetric-branch strain (16) of E. coli, containing identical,chromosomally integrated l-phage PR promoters controlling cfp and yfp genes. The strain alsoexpresses nonfluorescent CI-YFP from a Tet-regulated promoter. (E) The autocorrelation functionof the relative production rates in the l-cascade strains (blue squares) shows that the time scalefor fluctuations in protein production is tcorr È 40 min (blue). The difference between productionrates of YFP and CFP in the symmetric branch strain has a correlation time of tintrinsic G 10 min(red). The data and correlations presented are corrected for cell cycle–related effects (16).

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25 MARCH 2005 VOL 307 SCIENCE www.sciencemag.org1964

In contrast, the autocorrelation of the

intrinsic noise (16) decays rapidly: tintrinsic

G10 min ¡ t

corr(Fig. 4E). Thus, the observed

slow fluctuations do not result from intrinsic

noise; they represent noise extrinsic to CFP

expression (see supporting online text). The

concentration of a stable cellular factor would

be expected to fluctuate with a time scale of

the cell cycle period (7, 10). For instance,

even though intrinsic fluctuations in produc-

tion rates are fast, the difference between the

total amounts of YFP and CFP in the

symmetric branch experiments has an auto-

correlation time of ttotal

0 45 T 5 min (16). A

similar time scale may well apply to other

stable cellular components such as ribosomes,

metabolic apparatus, and sigma factors. As

such components affect their own expression

as well as that of our test genes, extrinsic

noise may be self-perpetuating.

These data indicate that the single-cell

GRF cannot be represented by a single-valued

function. Slow extrinsic fluctuations give the

cell and the genetic circuits it comprises a

memory, or individuality (29), lasting roughly

one cell cycle. These fluctuations are sub-

stantial in amplitude and slow in time scale.

They present difficulty for modeling genetic

circuits and, potentially, for the cell itself: In

order to accurately process an intracellular

signal, a cell would have to average its

response for well over a cell cycle—a long

time in many biological situations. This

problem is not due to intrinsic noise in the

output, noise that fluctuates rapidly, but rather

to the aggregate effect of fluctuations in other

cellular components. There is thus a funda-

mental tradeoff between accuracy and speed

in purely transcriptional responses. Accurate

cellular responses on faster time scales are

likely to require feedback from their output

(1, 4, 6, 10, 30). These data provide an

integrated, quantitative characterization of a

genetic element at the single-cell level: its

biochemical parameters, together with the

amplitude and time scale of its fluctuations.

Such systems-level specifications are neces-

sary both for modeling natural genetic circuits

and for building synthetic ones. The methods

introduced here can be generalized to more

complex genetic networks, as well as to

eukaryotic organisms (18).

References and Notes1. M. A. Savageau, Biochemical Systems Analysis (Addison-

Wesley, Reading, MA, 1976).2. M. Ptashne, A Genetic Switch: Phage Lambda and

Higher Organisms (Cell Press and Blackwell Science,Cambridge, MA, ed. 2, 1992).

3. H. H. McAdams, L. Shapiro, Science 269, 650 (1995).4. E. H. Davidson et al., Science 295, 1669 (2002).5. S. S. Shen-Orr, R. Milo, S. Mangan, U. Alon, Nature

Genet. 31, 64 (2002).6. J. E. Ferrell Jr., E. M. Machleder, Science 280, 895

(1998).7. M. B. Elowitz, S. Leibler, Nature 403, 335 (2000).8. T. S. Gardner, C. R. Cantor, J. J. Collins, Nature 403,

339 (2000).

9. A. Becskei, B. Seraphin, L. Serrano, EMBO J. 20, 2528(2001).

10. N. Rosenfeld, M. B. Elowitz, U. Alon, J. Mol. Biol. 323,785 (2002).

11. F. J. Isaacs, J. Hasty, C. R. Cantor, J. J. Collins, Proc.Natl. Acad. Sci. U.S.A. 100, 7714 (2003).

12. K. S. Koblan, G. K. Ackers, Biochemistry 31, 57 (1992).13. P. J. Darling, J. M. Holt, G. K. Ackers, J. Mol. Biol. 302,

625 (2000).14. R. J. Ellis, Trends Biochem. Sci. 26, 597 (2001).15. M. Mirasoli, J. Feliciano, E. Michelini, S. Daunert, A.

Roda, Anal. Chem. 74, 5948 (2002).16. Materials and methods are available as supporting

material on Science Online.17. P. Cluzel, M. Surette, S. Leibler, Science 287, 1652

(2000).18. G. Lahav et al., Nature Genet. 36, 147 (2004).19. I. B. Dodd et al., Genes Dev. 18, 344 (2004).20. B. J. Meyer, R. Maurer, M. Ptashne, J. Mol. Biol. 139,

163 (1980).21. J. A. Shapiro, Annu. Rev. Microbiol. 52, 81 (1998).22. M. B. Elowitz, A. J. Levine, E. D. Siggia, P. S. Swain,

Science 297, 1183 (2002).23. P. S. Swain, M. B. Elowitz, E. D. Siggia, Proc. Natl.

Acad. Sci. U.S.A. 99, 12795 (2002).24. J. M. Raser, E. K. O’Shea, Science 304, 1811 (2004).25. E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman,

A. van Oudenaarden, Nature Genet. 31, 69 (2002).26. W. J. Blake, M. Kærn, C. R. Cantor, J. J. Collins, Nature

422, 633 (2003).

27. H. H. McAdams, A. Arkin, Proc. Natl. Acad. Sci.U.S.A. 94, 814 (1997).

28. J. Paulsson, Nature 427, 415 (2004).29. J. L. Spudich, D. E. Koshland Jr., Nature 262, 467 (1976).30. P. S. Swain, J. Mol. Bio. 344, 965 (2004).31. We thank Z. Ben-Haim, R. Clifford, S. Itzkovitz, Z.

Kam, R. Kishony, A. J. Levine, A. Mayo, R. Milo, R.Phillips, M. Ptashne, J. Shapiro, B. Shraiman, E. Siggia,and M. G. Surette for helpful discussions. M.B.E. issupported by a CASI award from the BurroughsWellcome Fund, the Searle Scholars Program, andthe Seaver Institute. U.A. and M.B.E. are supportedby the Human Frontiers Science Program. P.S.S.acknowledges support from a Tier II Canada Re-search Chair and the Natural Sciences and Engi-neering Research Council of Canada. N.R. dedicatesthis work to the memory of his father, Yasha (Yaakov)Rosenfeld.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/307/5717/1962/DC1Materials and MethodsSOM TextFigs. S1 to S6References and NotesMovies S1 to S3

29 October 2004; accepted 4 February 200510.1126/science.1106914

Noise Propagation inGene Networks

Juan M. Pedraza and Alexander van Oudenaarden*

Accurately predicting noise propagation in gene networks is crucial forunderstanding signal fidelity in natural networks and designing noise-tolerantgene circuits. To quantify how noise propagates through gene networks, wemeasured expression correlations between genes in single cells. We found thatnoise in a gene was determined by its intrinsic fluctuations, transmitted noisefrom upstream genes, and global noise affecting all genes. A model wasdeveloped that explains the complex behavior exhibited by the correlations andreveals the dominant noise sources. The model successfully predicts thecorrelations as the network is systematically perturbed. This approach providesa step toward understanding and manipulating noise propagation in morecomplex gene networks.

The genetic program of a living cell is de-

termined by a complex web of gene networks.

The proper execution of this program relies on

faithful signal propagation from one gene to

the next. This process may be hindered by

stochastic fluctuations arising from gene ex-

pression, because some of the components in

these circuits are present at low numbers, which

makes fluctuations in concentrations un-

avoidable (1). Additionally, reaction rates can

fluctuate because of stochastic variation in the

global pool of housekeeping genes or because

of fluctuations in environmental conditions that

affect all genes. For example, fluctuations in

the number of available polymerases or in any

factor that alters the cell growth rate will

change the reaction rates for all genes. Recent

experimental studies (2–5) have made sub-

stantial progress identifying the factors that

determine the fluctuations in the expression of

a single gene. However, how expression fluc-

tuations propagate from one gene to the next

is largely unknown. To address this issue, we

designed a gene network (Fig. 1A) in which

the interactions between adjacent genes could

be externally controlled and quantified at the

single-cell level.

This synthetic network (6) consisted of

four genes, of which three were monitored in

single Escherichia coli cells by cyan, yellow,

and red fluorescent proteins (CFP, YFP, and

RFP). The first gene, lacI, is constitutively

transcribed and codes for the lactose repres-

sor, which down-regulates the transcription of

the second gene, tetR, that is bicistronically

transcribed with cfp. The gene product of

tetR, the tetracycline repressor, in turn down-

regulates the transcription of the third gene,

reported by YFP. The fourth gene, rfp, is under

Department of Physics, Massachusetts Institute ofTechnology, Cambridge, MA 02139, USA.

*To whom correspondence should be addressed:E-mail: avano@mit.edu

R E P O R T S

www.sciencemag.org SCIENCE VOL 307 25 MARCH 2005 1965

- 1 -

Supporting Online Material: Materials and Methods Strain construction: The CI-YFP fusion protein (Fig. 1B) was constructed by PCR, and contained the entire coding sequence of the wild-type cI gene fused directly to the coding sequence of the yfp gene (from pDH5 plasmid, University of Washington Yeast Resource Center). The cI-yfp gene was expressed from the tightly regulated PLtetO-1 promoter on the pZS21 plasmid (1), which is stable and difficult to cure. Integration of CFP with the PR promoter was performed as previously described (2). Since the cfp gene is chromosomally integrated, and the repressor concentration is independently measured, the results are not affected by possible variations in plasmid copy number or plasmid loss after the end of induction of cI-yfp expression. Full induction of cI-yfp expression by anhydrotetracycline (aTc) was sufficient to repress CFP production in the λ-cascade strain to undetectable levels. When not induced, the cI-yfp plasmid had no effect on CFP expression. Thus, the strain allows exploration of the full dynamic range of CFP regulation.

The OR2*-λ-cascade strain (Fig. S3) was constructed by site-directed mutagenesis of the PR promoter (Stratagene QuikChange Kit) with the following primers: 5’-GGATAAATATCTAACACCGTGCTTGTTGACTATTTTACCTCTGG and 5’-CCAGAGGTAAAATAGTCAACAAGCACGGTGTTAGATAT-TTATCC. This created a mutation which was previously designated as ‘VN’ (3). The underlined portion of the primers represents OR2 and the bold nucleotide is the site of the point mutation that changes a G to a T. The ‘symmetric branch’ strain (Fig. 4D) was strain MRR containing plasmid pZS21-cIYFP-Y66F. MRR contains CFP and YFP at separate, but equivalent, loci, approximately equidistant from the origin of replication, each under wild-type PR promoters (2). Plasmid pZS21-cIYFP-Y66F was identical to pZS21-cIYFP, except that site-directed mutagenesis was used to introduce a single point mutation converting the tyrosine at YFP position 66 (in the YFP chromophore) to phenyalanine, thereby eliminating repressor fluorescence. Experimental procedure and image acquisition: Cultures were grown overnight in LB + 15 µg/mL kanamycin at 37°C from single colonies, and diluted 1:100 in MSC media (M9 minimal medium + 0.6% succinate + 0.01% casamino acids + 0.15 µg/ml biotin + 1.5 µM thiamine). Cultures were grown to OD600 ~0.1 at 32°C, and then induced if necessary. Induction consisted of adding aTc to a final concentration of 100 ng/mL for ~3 minutes at ambient temperature, followed by 2 washes with MSC to remove aTc (Fig. 1C). Cells were allowed to grow until just prior to the production of the CI-repressed gene(s), then diluted to give ~1 cell per visual field when placed between a coverslip and 1.5% low melt MSC agarose. Growth of microcolonies was observed by fluorescence microscopy at 32ºC using a Leica DMIRB/E automated fluorescence microscope (Fig. 1D and Fig. S1). Cell-cycle period (doubling time) was 45±10min for all strains. Custom Visual Basic software was written to control the microscope and related equipment (Ludl motorized stage and Hamamatsu Orca II CCD camera), via ImagePro Plus and ScopePro packages (Media Cybernetics). In most cases, multiple fields of view were recorded simultaneously (in a loop). Typical intervals between subsequent exposures were 8~9 minutes. In the lambda-cascade strains, YFP fluorescence images were acquired only on alternate frames to reduce photo-bleaching. In the symmetric branch strains, YFP images were taken every frame.

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Cellular fluorescence values at time intervals when no CFP or CI-YFP molecules are produced (Fig. 2A) are consistent with negligible rates of protein degradation and photo-bleaching. This was confirmed by separate series of control experiments (data not shown). CI-YFP levels were diluted by cell growth (4) (see also ‘Math primer’, in downloadable data at http://www.weizmann.ac.il/mcb/UriAlon). Image analysis and data acquisition: Custom software was developed using MATLAB (The Mathworks, Inc.) to analyze time-lapse movie data. Analysis proceeds in several stages: First, segmentation of the microcolony was automatically performed on phase-contrast images (Fig. 1D, Fig. S1 and Fig. S4). The quality of the segmentation was checked interactively for each frame and poorly segmented cells were corrected or discarded. A custom tracking algorithm was then applied to the time series of segmented images to obtain a time course for each cell and its descendant lineages. This tracking analysis was also checked manually. Together, these procedures resulted in a lineage tree of the microcolony (Fig. S2) containing fluorescence information at each time-point (Fig. 2A).

Background and cellular auto-fluorescence values were subtracted from each channel and crosstalk from the cyan channel into the yellow channel was corrected for. The segmented image was used to collect the data from the fluorescence images, and the area of each cell at each time point was recorded as the number of pixels in the segmented cell region. The sum of the fluorescence intensity of these pixels was recorded in cyan (C) and yellow (Y) fluorescence channels (Fig 2A). In addition, the cell length (l, typical values are 3~4 microns) and width (w, narrowly distributed around 0.75 microns) were recorded, and cell volume calculated by modeling the cell as a cigar-shape cylinder of length (l-w) and radius (w/2), capped by two hemispheres of radius (w/2). Cell volumes typically varied from 1~2 µm3 to 2~3 µm3. Calibration by binomial errors in protein partitioning: In cell division events, a difference is observed between the fluorescence levels of the two daughter cells (Fig. 2A). We measured the total fluorescence of each of the two daughters after division, rescaled them to units of apparent number of molecules (see below), and calculated their sum and their difference (Fig. 2B). We compared the measured differences between the two daughter cells with a random, binomially generated daughter set. This set was sampled using an even binomial distribution from the measured sum of the two daughters. A Kolmogorov-Smirnov test implied that the daughter distribution was consistent with the binomial virtual daughter set, with a significance level of 80%. Thus, fluorescence partitioning during cell division appears binomial. According to the binomial model, the average number of particles received by each daughter (denoted by N1 and N2, such that N1+N2=Ntot) is half the number of particles in the parent, <N1>=Ntot/2, and their

standard deviation is 2/2

2

1 tottot

D NN

N =

−≡σ . To a first approximation, we assume

that all repressors occur in the cells as dimers, since cI is expected to dimerize in the range of concentrations used for induction (5) with a dissociation constant of ~10nM (6, 7). Let vy denote the CI-YFP fluorescence intensity reading given by one CI-YFP dimer in a cell, such that the measured fluorescence value is Y1=vy⋅N1. We expect that

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Dytot

ytoty

y vN

NvNv

NvYY

YYY

σ⋅≡

−⋅=

⋅−⋅=

+

−=

− 2

1

2

1

221

1

221

2222

and using the result for σD gives222

212

21 YYvNvv

YYy

totyDy

+⋅=⋅=⋅=

−

σ .

We grouped the individual division events according to total fluorescence (using an equal number of data points per bin), and calculated, for each group, the RMS difference in

fluorescence between two daughters (Fig. 2B). We fit these points to 2

21 YYvy

+⋅ with the

single free parameter vy, and so could convert the data to N1 and N2. Our results strongly suggest that the fluorescent units do indeed distribute according to a binomial distribution (Fig. 2B), although for larger numbers of molecules the standard deviation grows faster than a square root. This discrepancy may be due to multimerization into octamers (8) and larger aggregates, as well as other sources of measurement error, which would be expected to grow linearly. Apparent fluorescence of a CI-YFP monomer is found by dividing vy by 2. A strain that produces CFP and YFP from identical promoters (2) was used to find vc, the in vivo fluorescence of one CFP molecule. The values of vy and vc determined in this way were used to calibrate the amount of CI-YFP and of CFP in apparent numbers per cell, and thus to calculate the concentration of repressor in the cells in molar units and the production rates in molecules per minute. Errors in this calibration procedure are expected to originate from measurement errors (which are expected to grow linearly), uneven cellular divisions (in which the septum is off-center), and CI-YFP dimerization/multimerization. A more elaborate inference approach, which will be described elsewhere, results in a vy of the same order. Different estimates of vy agree to within a factor 2. Actual numbers of CFP and CI-YFP molecules may differ systematically from the apparent numbers, without affecting their ratios. Measurement accuracy and errors: Possible measurement errors in quantification of cellular fluorescence include errors in segmentation of the images and in calibration of the background and auto-fluorescence values. For each of these steps we compared several alternate quantification or calibration methods and assumptions. We found that the segmentation errors can contribute a relative error of a few percent, and calibration errors can contribute a systematic additive error on the order of 10 molecules per cell (of either CFP or YFP). These errors are demonstrated in Fig. 3B (black). The standard error in estimating the mean GRF is smaller than the marker size in Fig. 3A. The Hill function parameters were calculated separately for each alternate combination of methods. The error margins in Table 1 show the variation in these calculated values. Calculating production rates: To measure the average CFP production rate between movie frames, we took the difference in total CFP level between consecutive time points and divided by their separating time interval (8~9 minutes). Dependence on microenvironment: Growth in a microcolony is a complex process, in which cells are in contact with one another, may experience different local environments over time, and have been observed to generate complex patterns (9). We analyzed a movie in which three cells, containing different initial amounts of repressor, were grown simultaneously in the same field of

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view (Fig. S5A). The descendants of each initial cell increased CFP expression at different times, corresponding to different densities and to different stages of microcolony development. GRFs obtained from the descendants of each initial cell could be superimposed (Fig. S5B). Thus, the measured GRF appears to be robust to possible differences in growth environments within and between these microcolonies. It will be interesting to see whether other promoters may be specifically regulated by the local micro-environment of the cell. Correction for cell-cycle phase: Normalizing the production rate by the size of the cell did not reduce the spread of points for a given CI-YFP concentration (Fig. 3B), and a similar spread of data points was obtained by plotting the production rate of CFP versus either the total amount per cell or the concentration of CI-YFP. However, the production rate spread was reduced by accounting for the ‘age’ of the cell. For each cell we defined φ, the ‘phase’ in the cell-cycle, to be a number growing linearly in time from 0 at the cell's birth until 1 at the time of the cell's division. In exponential growth, the average number of copies, G, of any gene starts at M for a newly divided cell and grows to 2M, on average, for a cell about to divide (similar to Fig. 4B). We compared the production rates of ‘young’ cells (φ<0.15) to the production rate of ‘old’ cells (φ>0.85), and found that the spread of points for the ‘old’ cells coincides with the spread of points for the ‘young’ cells shifted by a factor of two in production rate, i.e. for the same concentration of CI-YFP, the ‘old’ cells produce twice as much CFP as the ‘young’ cells. The simple assumption that G=M·(1+φ), consistent with continuous DNA replication where a gene does not replicate at a specific phase in the cell-cycle, substantially reduced the spread in production rates. We used this method to normalize all production rates (shown in Fig. 3) to φ=0.5. Measuring repression-cooperativity without fluorescent protein fusions: The regulator dilution method results in an average reduction in regulatory protein concentration of two-fold at each division event. We re-analyzed the microcolony data ignoring the YFP fluorescence and assuming that the (‘unknown’) repressor were partitioned by half at each cell division event. Analyzed this way, the resulting values of n were within 10% of our previously measured values. Thus, the mean cooperativity (n) of any stable transcriptional regulatory protein can be obtained without fusing it to a fluorescent protein. Autocorrelation time of production rates: For each cell at each time point in the λ-cascade movies we calculated its production rate rank, compared to other cells with similar repressor concentration (or level, see below). For each pair of time points along a certain lineage (i.e. for one cell and all its ancestors), we recorded the rank at the early and the late time points and the time difference. We then calculated the average autocorrelation of the rankings as a function of the time difference t (Fig. 4E). Consistent results were obtained when ranking by bins with constant number of points or with constant repressor ranges, with different data subsets, and when using different quantification parameters, such as binning by repressor concentration or by repressor level. The autocorrelation function C(t), normalized to C(0)=1 at t=0, can be fit by a

sum of two exponentials, ( ) 21 22 21ττ

ttAAtC

−−⋅+⋅= , with A1~0.65, τ1~40 min, A2~0.35, and

τ2<5 min. This finding agrees with simulation results for a process with two sources of noise, one rapid and the other slow. Filtering out the rapid component in the production rates led to an

autocorrelation function of the form ( ) 12 τt

tC−

= , with τ1~40 min, for both data and simulations.

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Autocorrelations in the symmetric branch experiments: The difference between the YFP production rate and the CFP production rate was calculated at every time point for each cell, and was assigned a ranking compared to other cells at the same time point. The autocorrelation function was calculated for these rankings (Fig. 4E), yielding τintrinsic<10. The same procedure was applied to the difference between total YFP and total CFP protein at each time point, with τtotal=45±5 min. Similar results were obtained using the ratio of production rates (or of total proteins) rather than their differences. We obtained autocorrelation times of τ'intrinsic<10 min for the production rate ratios and τ'total=35±5 min for the total fluorescence ratios. Note that our time resolution is limited by the temporal resolution of measurements in the time-lapse experiments (<10 minutes). Folding and oxidation times of CFP and YFP were found to be < 10 minutes in E. coli. Supporting text Parameters of PR promoter repression: The dissociation constants and concentrations we obtain (Table 1) are comparable to previous estimates. In vitro binding assays indicate that half-maximal occupancy of the PR promoter occurs at repressor concentrations on the order of 10nM (10-12), although these values may be sensitive to parameters such as temperature (11). Total cellular λ repressor levels in lysogens have been estimated at about 140 copies of CI per cell (13), with measurements ranging from ~100 copies per cell (5, 14) to ~220 copies per cell (15). In vivo measurements indicate that half-maximal repression of the PR promoter occurs at repressor levels of roughly half that level (8), kd

PR~80nM. Previous experiments suggest that half-maximal repression of the OR2* mutant (designated as VN) occurs at repressor concentration (kd

VN) which are several times higher than kdPR (3, 16). Note that regulation of the

complete PR promoter in a bacteriophage lambda lysogen may differ significantly due to other effects such as looping interactions with operator sites at PL (8). Distribution of protein production rates: The protein production rates are distributed about the mean GRF (Fig. 3B). For each data point, with a repressor concentration R(t), we divided the measured protein production rate A(t) by the mean GRF value for that repressor concentration, f(R(t)), to obtain their ratio ρ(t)=A(t)/f(R(t)). The values of this ratio were distributed log-normally (Kolmogorov-Smirnov significance of 50%) rather than normally (Kolmogorov-Smirnov significance of 0.5%) and have a mean close to 1 with a standard deviation of 0.35; see Fig. S5. Similar results were obtained for the distribution of production rates A(R0) at a constant repressor concentration R0. Our findings suggest that, in a single cell, whose repressor concentration is R(t), the rate of production of a downstream protein corresponds to the value of the mean GRF, f(R(t)), modified by a noise term which is distributed log-normally (Fig. S5). This noise is not ‘white’, but rather has an autocorrelation time of one cell cycle (Fig. 4E). The production rate is further modified by an intrinsic noise process which has a short autocorrelation time.

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Supporting figures

Figure S1: Snapshots of a typical regulator dilution experiment using the OR2*-λ-cascade strain. Panels show the same microcolony as Fig. 1D, with greater time-resolution. CI-YFP protein is shown in red and CFP is shown in green. Times, in minutes, are indicated on snapshots. Insets show a selected cell lineage (outlined in white).

Figure S2: Lineage tree diagram of the microcolony shown in Fig S1. The microcolony begins with one cell. Each splitting point corresponds to a division event, and the two sister cells branch off from the parent cell. The highlighted lineage is the one outlined in Fig. 1D, Fig. S1, and Fig. 2A.

Figure S3: Variants of the PR promoter. The λ-phage PR promoter contains two neighboring binding sites, OR1 and OR2, which allow cooperative repression (3, 5, 8, 11, 12). The OR2* variant contains a single point mutation in OR2 (see methods).

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Figure S4: Analysis of fluorescence microscopy time-lapse images. Phase contrast images (left) are processed with a segmentation algorithm that identifies individual cells (right). Areas where cells grow out of the focal plane (center of microcolony) are discarded. Cell coloring is arbitrary. Cell dimensions and fluorescence are measured.

0 0.5 1 1.5 2 2.5

0.15

0.1

0.05

0

relative production rate

rela

tive

frequ

ency normal

log-normaldata

0 0.5 1 1.5 2 2.5

0.15

0.1

0.05

0

relative production rate

rela

tive

frequ

ency normal

log-normaldata

Figure S5: Distribution of protein production rates. A histogram of the protein production rates of the OR2* strain relative to the mean GRF (see supporting text). The log-normal distribution (solid red line) gives a better agreement with the data than the normal distribution (dashed black line). Figure S6 (next page): Local micro-environment has little detectable effect on this GRF. (A) Three separate wild-type-λ-cascade cell lineages, with different initial repressor concentration, grow into one microcolony. (B) The GRFs of the three lineages have small differences compared to other sources of variation in the system. The wild-type and OR2* mean GRFs are plotted as a guide to the eye (black lines).

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Figure S6 A

B

apparent CI-YFP concentration [a.u.] 101 102

102

CFP

pro

duct

ion

rate

[a.u

.]

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Online movies:

Movie S1: A time-lapse movie of the OR2*-λ-cascade microcolony shown in Fig. 1D and in Fig. 2A. Here CI-YFP protein, shown in red, can be seen diluting out from an initial cell as it grows into a microcolony. At sufficiently low repressor levels, CFP expression, shown in green, begins. Phase contrast images are shown in the background, in gray. The time between frames in this movie is ~18 minutes. (Note that saturating color values occur during rescaling of data for display and do not indicate saturation of the original images). Movie S2: A time-lapse movie of a wild-type-λ-cascade microcolony. Colors and the time between frames are as in movie S1. Movie S3: A time-lapse movie of a symmetric-branch microcolony, with 9 minutes between frames. Initially, (invisible) repressor levels are high and the cell fluorescence is low. As the colony grows and the repressor is diluted, YFP (shown in red) and CFP (shown in green) both turn on, and their superposition gives a yellow color. Some cells contain relatively higher levels of CFP (green cells) and other cells contain relatively higher levels of YFP (red cells). This property has a slow drift on the order of the cell-cycle time. Supporting references

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2002). 3. B. J. Meyer, R. Maurer, M. Ptashne, J Mol Biol 139, 163-94 (May 15, 1980). 4. N. Rosenfeld, U. Alon, J Mol Biol 329, 645-54 (Jun 13, 2003). 5. M. Ptashne, A Genetic Switch (Cell Press and Blackwell Science, ed. 2nd ed., 1992). 6. A. D. Johnson, C. O. Pabo, R. T. Sauer, Methods Enzymol 65, 839-56 (1980). 7. K. S. Koblan, G. K. Ackers, Biochemistry 30, 7817-21 (Aug 6, 1991). 8. I. B. Dodd et al., Genes Dev 18, 344-54 (Feb 1, 2004). 9. J. A. Shapiro, Annu Rev Microbiol 52, 81-104 (1998). 10. A. D. Johnson, B. J. Meyer, M. Ptashne, Proc Natl Acad Sci U S A 76, 5061-5 (Oct,

1979). 11. K. S. Koblan, G. K. Ackers, Biochemistry 31, 57-65 (Jan 14, 1992). 12. P. J. Darling, J. M. Holt, G. K. Ackers, J Mol Biol 302, 625-38 (Sep 22, 2000). 13. A. Levine, A. Bailone, R. Devoret, J Mol Biol 131, 655-61 (Jul 5, 1979). 14. V. Pirrotta, P. Chadwick, M. Ptashne, Nature 227, 41-4 (Jul 4, 1970). 15. L. Reichardt, A. D. Kaiser, Proc Natl Acad Sci U S A 68, 2185-9 (Sep, 1971). 16. R. Maurer, B. Meyer, M. Ptashne, J Mol Biol 139, 147-61 (May 15, 1980).