Vol 448 | 19 July 2007 | doi : 10.1038 / nature05951 LETTERS The effect of ancient population bottlenecks on human phenotypic variation Andrea Manica1 , William Amos1 , Francois Balloux2 & Tsunehiko Hanihara3 The origin and patterns of dispersal of anatomically modern humans are the focus of considerable debate1 3 . Global genetic analyses have argued for one single origin , placed somewhere in Africa4 7 . This scenario implies a rapid expansion , with a series of bottlenecks of small amplitude , which would have led to the observed smooth loss of genetic diversity with increasing distance from Africa . Analyses of cranial data , on the other hand , have given mixed results8 12 , and have been argued to support multiple origins of modern humans2 ,9,12 . Using a large data set of skull measurements and an analytical framework equivalent to that used for genetic data , we show that the loss in genetic diversity has been mirrored by a loss in phenotypic variability . We find evidence for an African origin , placed somewhere in the central/southern part of the continent , which harbours the highest intra-population diversity in phenotypic measurements . We failed to find evidence for a second origin , and we confirm these results on a large genetic data set . Distance from Africa accounts for an average 19 25 % of heritable variation in craniometric measurements -- a remarkably strong effect for phenotypic measurements known to be under selection . The origin of anatomically modern humans has been the focus of much heated debate1 ,3 . Recent large scale genetic analyses4 7 seem to support the idea that all modern humans originated from a single location -LRB- the ` single origin ' hypothesis -RRB- . More specifically , all studies point to Africa as the putative cradle of modern humans . If rapid , the expansion out of Africa would imply progressive loss of genetic diversity through a series of founder events -LRB- bottlenecks -RRB- , a prediction that has recently received empirical support4 6 . Heterozygosity declines monotonically with distance from east Africa , with South American populations carrying 64 % of the neutral variability -LRB- as measured from microsatellites -RRB- found in African populations . This view is further supported by some archaeological and anthropological evidence1 . However , studies of craniometric data have yielded mixed results8 12 , and the presence of archaic human-like traits in skulls that would be otherwise classified as Homo sapiens in several continents has been interpreted as evidence for multiple origins -LRB- the ` multiregional ' hypothesis -RRB- 2,12 . An important step towards an unequivocal answer regarding the number of origins of modern humans would be to analyse the phenotypic -LRB- cranial -RRB- measurements using the same approach used for genetic traits . The alternative models -LRB- single origin and multiregional -RRB- make clear predictions about how craniometric diversity should be distributed . Under the single origin model , we expect to find a monotonic decrease in phenotypic variability analogous to that seen for genetic traits -LRB- unless the sampling process is so strong as to destabilize canalization through the loss of genetic diversity -RRB- 13,14 . In contrast , multiple origins should lead to several clines , the magnitude of each cline being determined by the relative contribution of its origin . To test these predictions , we used an exceptional data set of 4,666 male skulls measured for 37 morphometric characteristics -LRB- Supplementary Table S1 -RRB- and drawn from 105 populations -LRB- Fig. 1 ; Supplementary Table S2 -RRB- 15,16 . A minimum sample size of 15 individuals was enforced -LRB- median size , 36 -RRB- and skulls older than 2,000 years were excluded to avoid any bias in the quality of the material . It is well known that some skull measurements correlate with climate , implying natural selection17 ,18 . Consequently , before considering Figure 1 | Origins of samples . Map of locations of populations from which male -LRB- blue -RRB- and female -LRB- red -RRB- skulls were collected . Locations from which skulls of both sexes were collected are marked in purple . 1 Department of Zoology , University of Cambridge , Downing Street , Cambridge CB2 3EJ , UK . 2Department of Genetics , University of Cambridge , Downing Street , Cambridge CB2 3EH , UK . 3Department of Anatomy , Saga Medical School , Saga 849-8501 , Japan . 346 2007 Nature Publishing Group NATURE | Vol 448 | 19 July 2007 LETTERS the effect of ancient demography , we investigated the effect of three key climatic variables on the within-population cranial variability : maximum and minimum temperature , and average annual precipitation . For each population , we estimated the mean standardized phenotypic variance19 and fitted it in a linear model with climate variables -LRB- maximum temperature , minimum temperature and precipitation , with all possible interactions -RRB- as predictors -LRB- see Methods -RRB- . Backwards stepwise elimination selected the interaction between maximum temperature and precipitation -LRB- DBayesian Information Criterion , DBIC 5 22.2 -RRB- as the best predictor of cranial variability . The minimal model including this interaction was used as the starting point for the investigation of any effect of ancient demography , effectively assuming that climate was the most parsimonious explanation for any global pattern , and that ancient demography had to explain variance that had not already been accounted for by climate . This is arguably a very conservative approach , given that a strong pattern of isolation by distance in craniometric inter-population differences has been found18 , and that these authors argued that selection through climate is insufficient to erase ancient demographic signals . We next searched the globe for the putative origin giving the strongest relationship between within-population phenotypic variability -LRB- corrected for climate -RRB- and distance on land5 ,20 -LRB- see Methods -RRB- . This strongest cline originates in central/southern Africa , and could be either a single origin or the main origin in a multiregional scenario -LRB- Figs 2a and 3 ; effect of distance from the centroid of the likely origins after correcting for climate : DBIC 5 212.5 ; R2 of plot against distance , 14.0 -RRB- . A similar analysis of the 789 autosomal neutral microsatellites from the 54 populations of the HGDP-CEPH panel21 ,22 , using heterozygosity as a measure of genetic variability , gives almost identical results -LRB- Fig. 2b ; showing patterns similar to those obtained by Ramachandran et al. 6 and Ray et al. 7 , who used previous versions of the HGDP-CEPH data set and somewhat different analytical approaches -RRB- . The only noticeable difference between the estimates based on phenotypic and genetic traits is that the latter does not include south Africa amongst the most likely origins . To test the multiregional hypothesis , we sought a second , nonAfrican origin capable of increasing the explanatory power of the model -LRB- see Methods -RRB- . Adding distances from other non-African origins did not improve our models -LRB- for either phenotypic or genetic traits -RRB- , supporting Ray et al. 7 , who used a spatially explicit stochastic population model and also failed to find evidence for the multiregional hypothesis . Our approach therefore suggests that a multiple origin is unlikely . However , we can not distinguish between single and multiple exoduses from Africa , because both scenarios would lead to a major cline from Africa . Depending on the exact timing and extent of the multiple exoduses , we could expect several subtly different patterns , and neither the genetic nor phenotypic data sets are currently large enough to investigate this level of detail . Also , very localized episodes of admixture between anatomically modern and archaic humans might go undetected if they left no signature in present day modern humans2 . How strong are the patterns for individual cranial measurements ? As we could not identify a precise location for the African origin of humans , we chose a centroid of the likely craniometric origins , and the possible influence of outliers was minimized by using robust regression23 -LRB- see Methods -RRB- . We considered both a model with distance as the only predictor , and one with a correction for climate . Out of 37 cranial measurements , 34 showed a decline in variability with distance from Africa -LRB- binomial test , P , 0.001 ; Supplementary Table S3 -RRB- , and 12 of these -LRB- 18 if we did not correct for climate -RRB- were significant after correction for multiple testing with a false discovery rate procedure24 . Although mean R2 was 6.3 % -LRB- 7.0 % if we did not correct for climate -RRB- , some measurements showed a strong demographic signal -LRB- Fig. 4 ; Supplementary Table S3 -RRB- . A further test of how reliable these results are is to repeat the analysis on an equivalent but smaller data set of female skulls , composed of 1,579 individuals from 39 populations -LRB- Supplementary Table S2 -RRB- . The results are very similar to those found in males -LRB- Supplementary Table S4 -RRB- , with a mean R2 of 9.1 % for distance -LRB- 8.9 % without correcting for climate -RRB- . Furthermore , slopes of measurement coefficient of variation over distance for females are almost identical to those obtained for males -LRB- best regression line : female slope for measurement x 5 1.00 3 male slope for measurement x , R2 5 0.77 , F1 ,36 5 124.9 , P , 0.001 -RRB- . Given that distance from Africa explains over 87 % of variance in heterozygosity at neutral microsatellite markers5 , the equivalent values for morphometric measurements might seem disappointing . However , phenotypes are only partially determined by genotypes , as the environment is also playing an important role . Heritability , h2 , defines the fraction of variance in a trait affected by genetics , and this represents an upper ceiling for the size of the demographic signal that can be detected . Estimates of heritability for cranial measurements are rare , 1.0 Phenotypic variance , corrected for climate 0.8 0.6 0.4 0.2 0.0 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 Distance from African origin -LRB- km -RRB- Figure 2 | Likely origin of anatomically modern humans . a , b , Maps showing the likely location of a single origin for phenotypic -LRB- a -RRB- and genetic -LRB- b -RRB- data . Lighter colours represent better fits of models of variability as predicted by distance from a location . The area in each panel containing the most likely origin is enclosed by a blue line . Areas of the world not investigated as possible origins -LRB- such as Iceland and Madagascar , which would require substantial land bridges to the main continents -RRB- are shown in grey . Figure 3 | Phenotypic variability versus distance from Africa . Relationship between mean phenotypic variability -LRB- corrected for climate -RRB- for male skulls and distance from the putative African origin -LRB- represented by the centroid of likely origins -RRB- . The solid line represents the best fit from the regression . 347 2007 Nature Publishing Group LETTERS NATURE | Vol 448 | 19 July 2007 a 0.05 0.04 0.03 0.02 0.01 0.00 0 10,000 20,000 30,000 b 0.10 0.08 0.06 0.04 0.02 0.00 0 10,000 20,000 30,000 2 . 3 . 4 . 5 . 6 . c 0.10 0.08 0.06 0.04 0.02 0.00 0 10,000 20,000 30,000 Distance from African origin -LRB- km -RRB- d CV in SSS 0.20 0.15 0.10 0.05 0.00 0 10,000 20,000 30,000 Distance from African origin -LRB- km -RRB- 7 . 8 . 9 . 10 . Figure 4 | Phenotypic variability of individual traits . Relationships between phenotypic variability for four measurements -LRB- expressed as coefficient of variation , CV , corrected for climate -RRB- from male skulls and distance from the putative African origin -LRB- represented by the centroid of locations of origins -RRB- . The measurements are : a , lambda-opisthion chord -LRB- OCC -RRB- ; b , nasion prosthion height -LRB- NPH -RRB- ; c , nasal height -LRB- NLH -RRB- ; and d , zygomaxillary subtense -LRB- SSS -RRB- . 11 . 12 . but values for 19 of the measurements included in our analysis have been recently derived25 , and these correlate significantly with the proportion of variance explained by distance from Africa -LRB- males r 5 0.56 , P 5 0.012 -RRB- . On average , R2/h2 5 0.20 -LRB- s.e. 5 0.06 -RRB- for males and R2 / h2 5 0.20 -LRB- s.e. 5 0.06 -RRB- for females -LRB- 0.24 6 0.06 and 0.25 6 0.06 , respectively , if we did not correct for climate -RRB- , indicating that the proportion of explained variance is at least a fifth of the heritability . Interestingly , this figure is similar to the 17 35 % of variance explained by distance from Africa for class I MHC genes which are under selection by infectious diseases26 , just as climatic -LRB- and potentially other -RRB- factors select for skull shape . Thus , after allowing for the impact of heritability and selection , the signal of ancient demography in human skull variability should properly be seen as remarkably strong . METHODS SUMMARY Thirty-seven morphometric cranial measurements -LRB- Supplementary Table S1 -RRB- were made on 4,666 male skulls drawn from 105 populations -LRB- Fig. 1 ; Supplementary Table S2 -RRB- 15,16 . After correcting for climate , we looked for the likely origin of human diversity by investigating the relationship between phenotypic diversity -LRB- scored as mean standardized phenotypic variance19 -RRB- and distances on land from locations across the globe . We then tested for the presence of a second origin by testing whether adding distances to putative locations improved the single origin model . We also assessed the effect of ancient demography on variability in individual measurements for both male skulls and an additional data set of 1,579 female skulls from 39 populations , and compared patterns found in the two sexes . Finally , we investigated the magnitude of the ancient demographic signal in the context of the heritability of individual measurements , as heritability provides an upper limit to any signature left by genetic factors . Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature . Received 8 January ; accepted 22 May 2007 . 1 . Mellars , P. Going east : New genetic and archaeological perspectives on the modern human colonization of Eurasia . Science 313 , 796 800 -LRB- 2006 -RRB- . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 21 . 22 . 23 . 24 . 25 . 26 . Trinkaus , E. Early modern humans . Annu . Rev. Anthropol . 34 , 207 230 -LRB- 2005 -RRB- . Mellars , P . Why did modern human populations disperse from Africa ca. 60,000 years ago ? A new model . Proc . Natl Acad . Sci . USA 103 , 9381 9386 -LRB- 2006 -RRB- . Liu , H. , Prugnolle , F. , Manica , A. & Balloux , F . A geographically explicit genetic model of worldwide human-settlement history . Am . J. Hum . Genet . 79 , 230 237 -LRB- 2006 -RRB- . Prugnolle , F. , Manica , A. & Balloux , F. Geography predicts neutral genetic diversity of human populations . Curr . Biol . 15 , R159 R160 -LRB- 2005 -RRB- . Ramachandran , S. et al. . Support from the relationship of genetic and geographic distance in human populations for a serial founder effect originating in Africa . Proc . Natl Acad . Sci . USA 102 , 15942 15947 -LRB- 2005 -RRB- . Ray , N. , Currat , M. , Berthier , P. & Excoffier , L. Recovering the geographic origin of early modern humans by realistic and spatially explicit simulations . Genome Res . 15 , 1161 1167 -LRB- 2005 -RRB- . Grine , F. E. et al. . Late Pleistocene human skull from Hofmeyr , South Africa , and modern human origins . Science 315 , 226 229 -LRB- 2007 -RRB- . Wolpoff , M. H. , Hawks , J. & Caspari , R. Multiregional , not multiple origins . Am . J. Phys . Anthropol . 112 , 129 136 -LRB- 2000 -RRB- . Brauer , G. , Collard , M. & Stringer , C. On the reliability of recent tests of the Out of Africa hypothesis for modern human origins . Anat . Rec . A 279 , 701 707 -LRB- 2004 -RRB- . Lahr , M. M . The multiregional model of modern human origins -- A reassessment of its morphological basis . J. Hum . Evol . 26 , 23 56 -LRB- 1994 -RRB- . Wolpoff , M. H. in The Human Revolution : Biological Perspectives in the Origins of Modern Humans -LRB- eds Mellars , P. & Stringer , C. -RRB- 62 108 -LRB- Princeton Univ. . Press , Princeton , 1989 -RRB- . Fowler , K. & Whitlock , M. C . The distribution of phenotypic variance with inbreeding . Evolution Int . J. Org . Evolution 53 , 1143 1156 -LRB- 1999 -RRB- . Frankham , R. Do island populations have less genetic variation than mainland populations ? Heredity 78 , 311 327 -LRB- 1997 -RRB- . Hanihara , T. & Ishida , H. Metric dental variation of major human populations . Am . J. Phys . Anthropol . 128 , 287 298 -LRB- 2005 -RRB- . Hanihara , T. & Ishida , H. Os incae : variation in frequency in major human population groups . J. Anat . 198 , 137 152 -LRB- 2001 -RRB- . Roseman , C. C. Detecting interregionally diversifying natural selection on modern human cranial form by using matched molecular and morphometric data . Proc . Natl Acad . Sci . USA 101 , 12824 12829 -LRB- 2004 -RRB- . Relethford , J. H. Boas and beyond : Migration and craniometric variation . Am . J. Hum . Biol . 16 , 379 386 -LRB- 2004 -RRB- . Relethford , J. H. & Blangero , J. Detection of differential gene flow from patterns of quantitative variation . Hum . Biol . 62 , 5 25 -LRB- 1990 -RRB- . Manica , A. , Prugnolle , F. & Balloux , F. Geography is a better determinant of human genetic differentiation than ethnicity . Hum . Genet . 118 , 366 371 -LRB- 2005 -RRB- . Rosenberg , N. A. Standardized subsets of the HGDP-CEPH human genome diversity cell line panel , accounting for atypical and duplicated samples and pairs of close relatives . Ann . Hum . Genet . 70 , 841 847 -LRB- 2006 -RRB- . Rosenberg , N. A. et al. . Genetic structure of human populations . Science 298 , 2381 2385 -LRB- 2002 -RRB- . Venables , W. N. & Ripley , B. D. Modern Applied Statistics with S -LRB- Springer , New York , 2002 -RRB- . Storey , J. D. & Tibshirani , R. Statistical significance for genomewide studies . Proc . Natl Acad . Sci . USA 100 , 9440 9445 -LRB- 2003 -RRB- . Carson , E. A. Maximum likelihood estimation of human craniometric heritabilities . Am . J. Phys . Anthropol . 131 , 169 180 -LRB- 2006 -RRB- . Prugnolle , F. et al. . Pathogen-driven selection and worldwide HLA class I diversity . Curr . Biol . 15 , 1022 1027 -LRB- 2005 -RRB- . Supplementary Information is linked to the online version of the paper at www.nature.com/nature . Acknowledgements We acknowledge J. Goudet for discussions . The Biotechnology and Biological Sciences Research Council provided financial support . Author Information Reprints and permissions information is available at www.nature.com/reprints . The authors declare no competing financial interests . Correspondence and requests for materials should be addressed to A.M. -LRB- am315@cam.ac.uk -RRB- . 348 2007 Nature Publishing Group doi : 10.1038 / nature05951 METHODS Data sets . Thirty-seven morphometric cranial measurements -LRB- Supplementary Table S1 -RRB- were measured in 6,245 skulls -LRB- 4,666 male and 1,579 female -RRB- , drawn from 105 and 39 populations for males and females , respectively -LRB- Fig. 1 ; Supplementary Table S2 -RRB- . Details of the measurements are provided elsewhere15 ,16 . Mid-oceanic populations were excluded because their origins are often unclear . Also excluded were samples over 2,000 years old , as deterioration might lead to biased estimates of phenotypic variability . Only the male data set was large enough to discriminate among potential origins of diversity . Consequently , the female data set was used for comparison when estimating the strength of the clines detected using male skulls . Genetic data come from the latest version of the HGDP-CEPH panel21 ,22 , which includes 971 individuals belonging to 54 populations and typed for 789 neutral autosomal microsatellites . Climate data -LRB- minimum and maximum temperature , and average precipitation -RRB- were obtained from WORDCLIM27 , as sets of global climatic GIS layers with a 30 arcsec resolution . Statistical analysis . Total within-population phenotypic variability was computed as the mean standardized phenotypic variance over all measurements . Following ref . 19 , this measure can be computed as the trace of the variance / covariance matrix of standardized values divided by the number of traits . Variability of individual measurements within each population was computed as the coefficient of variation -LRB- CV , the ratio of the standard deviation to the mean -RRB- . This dimensionless measure allows comparisons between different measurements . Realistic geographic distances between locations were computed as the shortest route through landmasses that avoid areas with a mean altitude over 2,000 m and assuming the following land bridges : a single connection between Africa and Eurasia via a route through the Sinai to the Levant , the Bering Strait between Eurasia and the Americas , and connections between the Malaysian Peninsula to Melanesia and Oceania5 ,20 . To model the effect of climate on craniometric measurements -LRB- male skulls only -RRB- , we fitted a linear model with mean standardized phenotypic variance as the response and three climatic variables and all their possible interactions as predictors . Starting from this full model , we then found a minimal model for climate by backwards stepwise elimination using the BIC28 . The presence of a primary cline in diversity was tested by fitting an additional predictor to the minimal climate model , namely distance from a range of potential origins distributed at intervals of 5 degrees latitude/longitude across the whole of Africa , Eurasia and Australia . As we effectively had to compare hundreds of similar models with only a slight difference in the values of the predictor variable -LRB- distances from different locations -RRB- , we used BIC to select origins that gave similarly good fits . Models within four units of the best model have `` considerable support `` 29 , thus providing a suitable envelope for the likely real origin . Having identified an African origin , we searched for a second origin by fitting distances from origins outside Africa as an additional predictor to the best African model . This approach was then repeated using the genetic data set , with heterozygosity as the response variable in a linear model . The strength of the relationship between variability of individual measurements and distance from Africa was explored by considering individual measurements in both males and females . Distances from a centroid of likely origins were fitted on top of the minimal climate model with the CV of measurements as individual responses . Visual inspection of the relationship between CV and geographic distance revealed outliers in several measurements . To account for heteroskedasticity without resorting to ad hoc removal of populations , we used robust regression with MM-estimators23 fitted in R30 using the robustbase package . This technique allows the estimation of linear models that are not affected by the outliers . We fitted models both with and without correcting for climate . The proportion of variance explained by distance from Africa when correcting for climate was estimated by subtracting the R2 of the model including distance and climate from the R2 of the climate model alone . Owing to the large number of nested tests , it is difficult to formulate exact P values . To provide a measure of goodness of fit , we computed local false discovery rates using the smoothing spline approach in ref . 24 to estimate g0 , the proportion of null P values -LRB- computations used the fdrtools package in R30 -RRB- . 27 . Hijmans , R. J. , Cameron , S. E. , Parra , J. L. , Jones , P. G. & Jarvis , A. Very high resolution interpolated climate surfaces for global land areas . Int . J. Climatol . 25 , 1965 1978 -LRB- 2005 -RRB- . 28 . Crawley , M. J. Statistical Computing : An Introduction to Data Analysis Using S-Plus -LRB- Wiley , London , 2002 -RRB- . 29 . Burnham , K. P. & Anderson , D. R. Model Selection and Inferences -LRB- Springer , New York , 1998 -RRB- . 30 . R Development Core Team -LRB- R Foundation for Statistical Computing , Vienna , 2006 -RRB- . 2007 Nature Publishing Group

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

human evolution phenotypic variation genetics population


Gene

Regulation

at

the

Single-Cell

Level

Nitzan

Rosenfeld

et

al.

Science

-LRB-

-RRB-

DOI

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REPORTS

Gene

Regulation

at

the

Single-Cell

Level

Nitzan

Rosenfeld

Jonathan

W.

Young

Uri

Alon

Peter

S.

Swain

Michael

B.

The

quantitative

relation

between

transcription

factor

concentrations

and

the

rate

of

protein

production

from

downstream

genes

is

central

to

the

function

of

genetic

networks

Here

we

show

that

this

relation

which

we

call

the

gene

regulation

function

-LRB-

GRF

-RRB-

fluctuates

dynamically

in

individual

living

cells

thereby

limiting

the

accuracy

with

which

transcriptional

genetic

circuits

can

transfer

signals

Using

fluorescent

reporter

genes

and

fusion

proteins

we

characterized

the

bacteriophage

lambda

promoter

PR

in

Escherichia

coli

A

novel

technique

based

on

binomial

errors

in

protein

partitioning

enabled

calibration

of

in

vivo

biochemical

parameters

in

molecular

units

We

found

that

protein

production

rates

fluctuate

over

a

time

scale

of

about

one

cell

cycle

while

intrinsic

noise

decays

rapidly

Thus

biochemical

parameters

noise

and

slowly

varying

cellular

states

together

determine

the

effective

single-cell

GRF

These

results

can

form

a

basis

for

quantitative

modeling

of

natural

gene

circuits

and

for

design

of

synthetic

ones

The

operation

of

transcriptional

genetic

circuits

-LRB-

-RRB-

is

based

on

the

control

of

promoters

by

transcription

factors

The

GRF

is

the

relation

between

the

concentration

of

active

transcription

factors

in

a

cell

and

the

Departments

of

Molecular

Cell

Biology

and

Physics

of

Complex

Systems

Weizmann

Institute

of

Science

Rehovot

Israel

for

Non-linear

Dynamics

Department

of

Physiology

McGill

University

Promenade

Sir

William

Osler

Montreal

Quebec

Canada

of

Biology

and

Department

of

Applied

Physics

Caltech

Pasadena

CA

USA

These

authors

contributed

equally

to

this

work

To

whom

correspondence

should

be

addressed

E-mail

melowitz@caltech.edu

rate

at

which

their

downstream

gene

products

are

produced

-LRB-

expressed

-RRB-

through

transcription

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

-LRB-

Fig.

-RRB-

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

-LRB-

-RRB-

determine

key

features

of

cellular

behavior

such

as

lysogeny

switching

-LRB-

-RRB-

developmental

cell-fate

decisions

-LRB-

-RRB-

and

oscillation

-LRB-

-RRB-

Its

properties

are

also

crucial

for

the

design

of

synthetic

genetic

networks

-LRB-

-RRB-

Current

models

estimate

GRFs

from

in

vitro

Fig.

Measuring

a

A

aTc

C

B

gene

regulation

tion

-LRB-

GRF

-RRB-

in

individual

CI-YFP

CFP

E.

coli

cell

lineages

-LRB-

A

-RRB-

Pc-TetR

The

GRF

is

the

dence

of

the

producaTc

tion

rate

of

a

target

Ptet-cIYFP

PR-CFP

promoter

-LRB-

y

axis

-RRB-

on

the

concentration

of

one

-LRB-

or

more

-RRB-

Repressor

Concentration

scription

factors

-LRB-

x

axTime

-LRB-

cell

cycles

-RRB-

is

-RRB-

-LRB-

B

-RRB-

In

the

l-cascade

D

strains

-LRB-

-RRB-

of

E.

coli

CI-YFP

is

expressed

from

a

tetracycline

promoter

in

a

TetR

background

and

can

be

induced

by

anhydrotetracycline

-LRB-

aTc

-RRB-

CIYFP

represses

production

of

CFP

from

the

PR

promoter

-LRB-

C

-RRB-

The

regulator

dilution

experiment

-LRB-

schematic

-RRB-

Cells

are

transiently

induced

to

express

CI-YFP

and

then

experiment

using

the

l-cascade

strain

-LRB-

see

fig

-RRB-

-LRB-

-RRB-

CI-YFP

protein

observed

in

time-lapse

microscopy

as

repressor

dilutes

out

during

cell

growth

is

shown

in

red

and

CFP

is

shown

in

green

Times

in

minutes

are

indicated

on

-LRB-

red

line

-RRB-

When

CI-YFP

levels

decrease

sufficiently

expression

of

the

cfp

target

snapshots

-LRB-

Insets

-RRB-

Selected

cell

lineage

-LRB-

outlined

in

white

-RRB-

Greater

time

gene

begins

-LRB-

green

line

-RRB-

-LRB-

D

-RRB-

Snapshots

of

a

typical

regulator

dilution

resolution

is

provided

in

fig

Total

CFP

per

cell

-LRB-

linear

scale

-RRB-

MARCH

VOL

SCIENCE

Total

YFP

per

cell

-LRB-

log

scale

-RRB-

Production

Rate

Downloaded

from

on

May

data

-LRB-

-RRB-

However

biochemical

parameters

are

generally

unknown

in

vivo

and

could

depend

on

the

environment

-LRB-

-RRB-

or

cell

history

-LRB-

-RRB-

Moreover

gene

regulation

may

vary

from

cell

to

cell

or

over

time

Three

fundamental

aspects

of

the

GRF

specify

the

behavior

of

transcriptional

circuits

at

the

single-cell

level

its

mean

shape

-LRB-

averaged

over

many

cells

-RRB-

the

typical

deviation

from

this

mean

and

the

time

scale

over

which

such

fluctuations

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

accuracy

In

order

to

address

all

three

aspects

it

is

necessary

to

observe

gene

regulation

in

individual

cells

over

time

Therefore

we

built

Bl-cascade

-LSB-

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

-LRB-

Fig.

-RRB-

These

strains

incorporate

a

yellow

fluorescent

repressor

fusion

protein

-LRB-

cI-yfp

-RRB-

and

a

chromosomally

integrated

target

promoter

-LRB-

PR

-RRB-

controlling

cyan

fluorescent

protein

-LRB-

cfp

-RRB-

In

order

to

systematically

vary

repressor

concentration

over

its

functional

range

-LRB-

in

logarithmic

steps

-RRB-

we

devised

a

Bregulator

dilution

-LSB-

method

Repressor

production

is

switched

off

in

a

growing

cell

so

that

its

concentration

subsequently

decreases

by

dilution

as

the

cell

divides

and

grows

into

a

microcolony

-LRB-

Fig.

-RRB-

We

used

fluorescence

time-lapse

microscopy

-LRB-

Fig.

fig

and

movies

and

-RRB-

and

computational

image

analysis

to

reconstruct

the

lineage

tree

-LRB-

family

tree

-RRB-

of

descent

and

sibling

relations

among

the

cells

in

each

microcolony

-LRB-

fig

REPORTS

-RRB-

For

each

cell

lineage

we

quantified

over

time

the

level

of

repressor

-LRB-

x

axis

of

the

GRF

-RRB-

and

the

total

amount

of

CFP

protein

-LRB-

Fig.

-RRB-

From

the

change

in

CFP

over

time

we

calculated

its

rate

of

production

-LRB-

y

axis

of

the

GRF

-RRB-

-LRB-

-RRB-

Regulator

dilution

also

provides

a

natural

in

vivo

calibration

of

individual

protein

fluorescence

Using

the

lineage

tree

and

fluorescence

data

we

analyzed

sister

cell

pairs

just

after

division

-LRB-

Fig.

-RRB-

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

-LRB-

-RRB-

Consequently

the

root-mean-square

error

in

CI-YFP

partitioning

between

daughters

increases

as

the

square

root

of

their

total

CIYFP

fluorescence

Using

a

one-parameter

fit

we

estimated

the

fluorescence

signal

of

individual

CI-YFP

molecules

-LRB-

Fig.

and

supporting

online

material

-RRB-

Thus

despite

cellular

autofluorescence

that

prohibits

detection

of

individual

CI-YFP

molecules

observation

of

partitioning

errors

still

permits

calibration

in

terms

of

apparent

numbers

of

molecules

per

cell

The

mean

GRFs

obtained

by

these

techniques

are

shown

in

Fig.

for

the

PR

promoter

and

a

point

mutant

variant

-LRB-

fig

-RRB-

These

are

the

mean

functions

obtained

by

averaging

individual

data

points

-LRB-

Fig.

-RRB-

in

bins

of

similar

repressor

concentration

indicating

the

average

protein

production

rate

at

a

given

repressor

concentration

Their

cooperative

nature

would

have

been

Bsmeared

out

-LSB-

by

population

averages

-LRB-

-RRB-

These

mean

GRF

data

provide

in

vivo

values

of

the

biochemical

parameters

underlying

transcriptional

regulation

Hill

functions

of

the

form

f

-LRB-

R

-RRB-

-LRB-

R/kd

-RRB-

n

are

often

used

to

represent

unknown

regulation

functions

-LRB-

-RRB-

Here

kd

is

the

concentration

of

repressor

yielding

half-maximal

expression

n

indicates

the

degree

of

effective

cooperativity

in

repression

and

b

is

the

maximal

production

rate

Hill

functions

indeed

fit

the

data

well

-LRB-

Fig.

and

Table

-RRB-

The

measured

in

vivo

kd

is

comparable

to

previous

estimates

-LRB-

-RRB-

-LRB-

see

supporting

online

text

-RRB-

The

significant

cooperativity

observed

-LRB-

n

-RRB-

may

result

from

dimerization

of

repressor

molecules

and

cooperative

interactions

between

repressors

bound

at

neighboring

sites

-LRB-

-RRB-

A

point

mutation

in

the

operator

-LRB-

-RRB-

-LRB-

fig

-RRB-

significantly

reduced

n

and

increased

kd

-LRB-

Fig.

and

Table

-RRB-

Note

that

with

similar

methods

it

is

even

possible

to

measure

effective

cooperativity

-LRB-

n

-RRB-

for

native

repressors

without

fluorescent

protein

fusions

-LRB-

-RRB-

We

next

addressed

deviations

from

the

mean

GRF

At

a

given

repressor

concentration

the

standard

deviation

of

production

rates

is

of

the

mean

GRF

value

Such

variation

may

arise

from

microenvironmental

differences

-LRB-

-RRB-

cell

cycle

dependent

changes

in

gene

copy

number

and

various

sources

of

noise

in

gene

expression

and

other

cellular

processes

-LRB-

-RRB-

We

compared

microcolonies

in

which

induction

occurs

at

different

cell

densities

-LRB-

-RRB-

The

results

suggested

that

the

measured

GRF

is

robust

to

possible

differences

among

the

growth

environments

in

our

experiments

-LRB-

fig

-RRB-

We

analyzed

the

effect

of

gene

copy

number

which

varies

twofold

over

the

cell

cycle

as

DNA

replicates

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

-LRB-

-RRB-

Thus

gene

dosage

is

not

compensated

Nevertheless

after

normalizing

production

rates

to

the

average

cell-cycle

phase

-LRB-

-RRB-

substantial

variation

still

remains

in

the

production

rates

and

their

standard

deviation

is

of

the

mean

GRF

-LRB-

Fig.

-RRB-

The

deviations

from

the

mean

GRF

show

a

lognormal

distribution

-LRB-

see

supporting

online

text

and

fig

-RRB-

These

remaining

fluctuations

may

arise

from

processes

intrinsic

or

extrinsic

to

gene

expression

Intrinsic

noise

results

from

stochasticity

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

proteins

-LRB-

-RRB-

Extrinsic

noise

is

the

additional

variation

originating

from

fluctuations

in

cellular

components

such

as

metabolites

ribosomes

and

polymerases

and

has

a

global

effect

-LRB-

-RRB-

Extrinsic

noise

is

often

the

dominant

source

of

variation

in

E.

coli

and

Saccharomyces

cerevisiae

-LRB-

-RRB-

To

test

whether

fluctuations

were

of

intrinsic

or

extrinsic

origin

we

used

a

Bsymmetric

branch

-LSB-

strain

-LRB-

-RRB-

that

produced

CFP

and

YFP

from

an

identical

pair

of

PR

promoters

-LRB-

Fig.

movie

-RRB-

The

difference

between

CFP

and

YFP

production

rates

in

these

cells

indicates

intrinsic

noise

in

protein

production

Eaveraged

over

to

intervals

-LRB-

-RRB-

suggesting

that

the

extrinsic

component

of

noise

is

dominant

and

contributes

a

variation

in

protein

production

rates

of

Our

measurements

provide

more

detailed

analysis

of

extrinsic

noise

in

two

ways

First

in

previous

work

-LRB-

-RRB-

extrinsic

noise

included

fluctuations

in

upstream

cellular

components

including

both

gene-specific

and

global

factors

Here

we

quantify

the

extrinsic

noise

at

known

repressor

concentration

and

so

extrinsic

noise

encompasses

fluctuations

in

global

cellular

components

such

as

polymerases

or

Fig.

Data

and

calibration

-LRB-

A

-RRB-

Fluorescence

intensities

of

individual

cells

are

plotted

over

time

for

the

experiment

of

Fig.

Red

indicates

CIYFP

which

is

plotted

on

a

logarithmic

y

axis

to

highlight

its

exponential

dilution

As

CI-YFP

is

not

produced

each

division

event

causes

a

reduction

of

about

twofold

in

total

CI-YFP

fluorescence

Green

indicates

CFP

which

is

plotted

on

a

linear

y

axis

to

emphasize

its

increasing

slope

showing

that

CFP

production

rate

increases

as

the

CI-YFP

levels

decrease

A

selected

cell

lineage

is

highlighted

-LRB-

also

outlined

in

Fig.

-RRB-

-LRB-

B

-RRB-

Analysis

of

binomial

errors

in

protein

partitioning

to

find

vy

the

apparent

fluorescence

intensity

of

one

independently

segregating

fluorescent

particle

-LRB-

-RRB-

Cells

containing

Ntot

copies

of

a

fluorescent

particle

-LRB-

total

fluorescence

Ytot

vy

I

Ntot

-RRB-

undergo

division

-LRB-

inset

-RRB-

If

each

particle

segregates

independently

and

the

number

of

copies

received

by

the

two

daughter

cells

are

distributed

binomially

and

satisfy

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

D

E

N

jN

pffiffiffiffiffiffiffiffi

Ntot

A

single-parameter

fit

thus

determines

the

value

of

vy

Here

we

plot

-LRB-

in

numbers

of

apparent

molecule

dimers

-RRB-

versus

Ntot

Blue

dots

show

the

scatter

of

individual

division

events

Crosses

-LRB-

red

-RRB-

show

the

root-mean-square

-LRB-

RMS

-RRB-

error

in

protein

partitioning

and

its

standard

error

The

expected

binomial

standard

deviation

is

shown

in

black

SCIENCE

VOL

MARCH

Downloaded

from

on

May

REPORTS

Fig.

The

GRF

and

its

A

B

fluctuations

-LRB-

A

-RRB-

The

mean

regulation

function

of

the

wild-type

l-phage

PR

promoter

-LRB-

blue

squares

-RRB-

and

its

variant

-LRB-

orange

circles

-RRB-

are

plotted

with

their

respective

standard

deviations

-LRB-

dashed/dotted

lines

-RRB-

Hill

function

approximations

-LRB-

using

parameters

wt

mean

GRF

from

Table

-RRB-

are

shown

production

rates

standard

dev

mean

GRF

-LRB-

solid

lines

-RRB-

-LRB-

B

-RRB-

Variation

in

fit

to

Hill

selected

lineage

mean

GRF

the

GRF

Individual

selected

lineage

standard

dev

points

indicate

the

instantameasurement

errors

fit

to

Hill

neous

production

rate

of

CFP

as

a

function

of

the

amount

of

CI-YFP

in

the

same

cell

for

apparent

cI-YFP

concentration

-LSB-

nM

-RSB-

apparent

cI-YFP

concentration

-LSB-

nM

-RSB-

all

cells

in

a

microcolony

of

the

l-cascade

strain

The

time

courses

of

selected

lineages

in

this

consecutive

data

points

along

a

trajectory

are

at

intervals

Typical

microcolony

are

drawn

on

top

of

the

data

showing

slow

fluctuations

measurement

errors

-LRB-

black

crosses

-RRB-

are

shown

for

a

few

points

Data

are

around

the

mean

GRF

CI-YFP

concentration

decreases

with

time

and

compensated

for

cell

cycle

related

effects

-LRB-

-RRB-

CFP

production

rate

-LSB-

apparent

molecules

-RSB-

CFP

production

rate

-LSB-

apparent

molecules

min

-RSB-

A

hypothetical

production

rate

D

Pc-TetR

aTc

E

PR-YFP

PR-CFP

Table

In

vivo

values

of

effective

biochemical

parameters

Molecular

units

are

estimated

using

binomial

errors

in

protein

partitioning

-LRB-

-RRB-

-LRB-

Fig.

-RRB-

which

may

have

systematic

errors

up

to

a

factor

Concentrations

are

calculated

from

apparent

molecule

numbers

divided

by

cell

volumes

estimated

from

cell

images

-LRB-

-RRB-

with

an

average

volume

of

T

-LRB-

for

which

nM

molecule/cell

-RRB-

Parameter

PR

PR

-LRB-

-RRB-

B

hypothetical

production

rate

total

noise

intrinsic

noise

C

hypothetical

production

rate

time

-LSB-

cell

cycles

-RSB-

n

-LRB-

degree

of

T

T

cooperativity

in

repression

-RRB-

T

T

kd

-LSB-

concentration

of

repressor

yielding

half-maximal

expression

-LRB-

nM

-RRB-

-RSB-

b

-LSB-

unrepressed

production

T

T

rate

-LRB-

molecules

I

I

-RRB-

-RSB-

time

-LSB-

min

-RSB-

Fig.

Fluctuations

in

gene

regulation

-LRB-

Left

-RRB-

Three

types

of

variability

observed

here

-LRB-

A

-RRB-

Fast

fluctuations

in

CFP

production

similar

to

those

produced

by

intrinsic

noise

-LRB-

B

-RRB-

Periodic

cell

cycle

dependent

oscillations

in

CFP

production

which

can

result

from

DNA

replication

-LRB-

C

-RRB-

Slow

aperiodic

fluctuations

such

as

extrinsic

fluctuations

in

gene

expression

-LRB-

D

-RRB-

Intrinsic

and

extrinsic

noise

can

be

discriminated

using

a

symmetric-branch

strain

-LRB-

-RRB-

of

E.

coli

containing

identical

chromosomally

integrated

l-phage

PR

promoters

controlling

cfp

and

yfp

genes

The

strain

also

expresses

nonfluorescent

CI-YFP

from

a

Tet-regulated

promoter

-LRB-

E

-RRB-

The

autocorrelation

function

of

the

relative

production

rates

in

the

l-cascade

strains

-LRB-

blue

squares

-RRB-

shows

that

the

time

scale

for

fluctuations

in

protein

production

is

tcorr

min

-LRB-

blue

-RRB-

The

difference

between

production

rates

of

YFP

and

CFP

in

the

symmetric

branch

strain

has

a

correlation

time

of

tintrinsic

G

min

-LRB-

red

-RRB-

The

data

and

correlations

presented

are

corrected

for

cell

cycle

related

effects

-LRB-

-RRB-

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

modeling

and

design

of

genetic

networks

In

cells

fast

and

slow

fluctuations

can

affect

the

operation

of

genetic

networks

in

dif

ferent

ways

Previous

experiments

-LRB-

-RRB-

used

static

Bsnapshots

-LSB-

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

-LRB-

Fig.

-RRB-

Fluctuations

can

be

characterized

by

their

autocorrelation

time

tcorr

-LRB-

-RRB-

The

VOL

magnitude

of

tcorr

compared

with

the

cellcycle

period

is

crucial

Fluctuations

longer

than

the

cell

cycle

accumulate

to

produce

significant

effects

whereas

more

rapid

fluctuations

may

Baverage

out

-LSB-

as

cellular

circuits

operate

-LRB-

-RRB-

In

these

data

three

types

of

dynamics

are

observed

-LRB-

Fig.

A

to

C

-RRB-

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

singlecell

lineages

departed

substantially

from

the

mean

GRF

over

relatively

long

periods

-LRB-

Fig.

-RRB-

with

tcorr

T

min

-LRB-

Fig.

-RRB-

This

value

is

close

to

the

cell

cycle

period

tcc

T

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

overexpression

will

likely

continue

for

roughly

one

cell

cycle

and

CFP

levels

will

accumulate

to

higher

concentrations

than

the

mean

GRF

would

predict

MARCH

SCIENCE

Downloaded

from

on

May

autocorrelation

of

production

rates

REPORTS

In

contrast

the

autocorrelation

of

the

intrinsic

noise

-LRB-

-RRB-

decays

rapidly

tintrinsic

G

min

tcorr

-LRB-

Fig.

-RRB-

Thus

the

observed

slow

fluctuations

do

not

result

from

intrinsic

noise

they

represent

noise

extrinsic

to

CFP

expression

-LRB-

see

supporting

online

text

-RRB-

The

concentration

of

a

stable

cellular

factor

would

be

expected

to

fluctuate

with

a

time

scale

of

the

cell

cycle

period

-LRB-

-RRB-

For

instance

even

though

intrinsic

fluctuations

in

production

rates

are

fast

the

difference

between

the

total

amounts

of

YFP

and

CFP

in

the

symmetric

branch

experiments

has

an

autocorrelation

time

of

ttotal

T

min

-LRB-

-RRB-

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

can

not

be

represented

by

a

single-valued

function

Slow

extrinsic

fluctuations

give

the

cell

and

the

genetic

circuits

it

comprises

a

memory

or

individuality

-LRB-

-RRB-

lasting

roughly

one

cell

cycle

These

fluctuations

are

substantial

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

fundamental

tradeoff

between

accuracy

and

speed

in

purely

transcriptional

responses

Accurate

cellular

responses

on

faster

time

scales

are

likely

to

require

feedback

from

their

output

-LRB-

-RRB-

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

necessary

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

-LRB-

-RRB-

References

and

Notes

M.

A.

Savageau

Biochemical

Systems

Analysis

-LRB-

AddisonWesley

Reading

MA

-RRB-

M.

Ptashne

A

Genetic

Switch

Phage

Lambda

and

Higher

Organisms

-LRB-

Cell

Press

and

Blackwell

Science

Cambridge

MA

ed

-RRB-

H.

H.

McAdams

L.

Shapiro

Science

-LRB-

-RRB-

E.

H.

Davidson

et

al.

Science

-LRB-

-RRB-

S.

S.

Shen-Orr

R.

Milo

S.

Mangan

U.

Alon

Nature

Genet

-LRB-

-RRB-

J.

E.

Ferrell

Jr.

E.

M.

Machleder

Science

-LRB-

-RRB-

M.

B.

Elowitz

S.

Leibler

Nature

-LRB-

-RRB-

T.

S.

Gardner

C.

R.

Cantor

J.

J.

Collins

Nature

-LRB-

-RRB-

A.

Becskei

B.

Seraphin

L.

Serrano

EMBO

J.

-LRB-

-RRB-

N.

Rosenfeld

M.

B.

Elowitz

U.

Alon

J.

Mol

Biol

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F.

J.

Isaacs

J.

Hasty

C.

R.

Cantor

J.

J.

Collins

Proc

Natl.

Acad

Sci

U.S.A.

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K.

S.

Koblan

G.

K.

Ackers

Biochemistry

-LRB-

-RRB-

P.

J.

Darling

J.

M.

Holt

G.

K.

Ackers

J.

Mol

Biol

-LRB-

-RRB-

R.

J.

Ellis

Trends

Biochem

Sci

-LRB-

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M.

Mirasoli

J.

Feliciano

E.

Michelini

S.

Daunert

A.

Roda

Anal

Chem

-LRB-

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Materials

and

methods

are

available

as

supporting

material

on

Science

Online

P.

Cluzel

M.

Surette

S.

Leibler

Science

-LRB-

-RRB-

G.

Lahav

et

al.

Nature

Genet

-LRB-

-RRB-

I.

B.

Dodd

et

al.

Genes

Dev

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-RRB-

B.

J.

Meyer

R.

Maurer

M.

Ptashne

J.

Mol

Biol

-LRB-

-RRB-

J.

A.

Shapiro

Annu

Rev.

Microbiol

-LRB-

-RRB-

M.

B.

Elowitz

A.

J.

Levine

E.

D.

Siggia

P.

S.

Swain

Science

-LRB-

-RRB-

P.

S.

Swain

M.

B.

Elowitz

E.

D.

Siggia

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

M.

Raser

E.

K.

O'Shea

Science

-LRB-

-RRB-

E.

M.

Ozbudak

M.

Thattai

I.

Kurtser

A.

D.

Grossman

A.

van

Oudenaarden

Nature

Genet

-LRB-

-RRB-

W.

J.

Blake

M.

K

rn

C.

R.

Cantor

J.

J.

Collins

Nature

-LRB-

-RRB-

H.

H.

McAdams

A.

Arkin

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

Paulsson

Nature

-LRB-

-RRB-

J.

L.

Spudich

D.

E.

Koshland

Jr.

Nature

-LRB-

-RRB-

P.

S.

Swain

J.

Mol

Bio

-LRB-

-RRB-

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.

is

supported

by

a

CASI

award

from

the

Burroughs

Wellcome

Fund

the

Searle

Scholars

Program

and

the

Seaver

Institute

U.A.

and

M.B.E.

are

supported

by

the

Human

Frontiers

Science

Program

P.S.S.

acknowledges

support

from

a

Tier

II

Canada

Research

Chair

and

the

Natural

Sciences

and

Engineering

Research

Council

of

Canada

N.R.

dedicates

this

work

to

the

memory

of

his

father

Yasha

-LRB-

Yaakov

-RRB-

Rosenfeld

Supporting

Online

Material

Materials

and

Methods

SOM

Text

Figs

to

References

and

Notes

Movies

to

October

accepted

February

science

Noise

Propagation

in

Gene

Networks

Juan

M.

Pedraza

and

Alexander

van

Oudenaarden

Accurately

predicting

noise

propagation

in

gene

networks

is

crucial

for

understanding

signal

fidelity

in

natural

networks

and

designing

noise-tolerant

gene

circuits

To

quantify

how

noise

propagates

through

gene

networks

we

measured

expression

correlations

between

genes

in

single

cells

We

found

that

noise

in

a

gene

was

determined

by

its

intrinsic

fluctuations

transmitted

noise

from

upstream

genes

and

global

noise

affecting

all

genes

A

model

was

developed

that

explains

the

complex

behavior

exhibited

by

the

correlations

and

reveals

the

dominant

noise

sources

The

model

successfully

predicts

the

correlations

as

the

network

is

systematically

perturbed

This

approach

provides

a

step

toward

understanding

and

manipulating

noise

propagation

in

more

complex

gene

networks

The

genetic

program

of

a

living

cell

is

determined

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

expression

because

some

of

the

components

in

these

circuits

are

present

at

low

numbers

which

makes

fluctuations

in

concentrations

unavoidable

-LRB-

-RRB-

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

Department

of

Physics

Massachusetts

Institute

of

Technology

Cambridge

MA

USA

To

whom

correspondence

should

be

addressed

E-mail

avano@mit.edu

experimental

studies

-LRB-

-RRB-

have

made

substantial

progress

identifying

the

factors

that

determine

the

fluctuations

in

the

expression

of

a

single

gene

However

how

expression

fluctuations

propagate

from

one

gene

to

the

next

is

largely

unknown

To

address

this

issue

we

designed

a

gene

network

-LRB-

Fig.

-RRB-

in

which

the

interactions

between

adjacent

genes

could

be

externally

controlled

and

quantified

at

the

single-cell

level

This

synthetic

network

-LRB-

-RRB-

consisted

of

four

genes

of

which

three

were

monitored

in

single

Escherichia

coli

cells

by

cyan

yellow

and

red

fluorescent

proteins

-LRB-

CFP

YFP

and

RFP

-RRB-

The

first

gene

lacI

is

constitutively

transcribed

and

codes

for

the

lactose

repressor

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

downregulates

the

transcription

of

the

third

gene

reported

by

YFP

The

fourth

gene

rfp

is

under

SCIENCE

VOL

MARCH

Downloaded

from

on

May

B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O B O O B O O O O O O O O O O O O O B O O O O O B O O B O O O O O O O O O O O O O O O B O O B O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O