alex talk1

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Stochastic gene expression from prokaryotes to eukaryotes and from steady-state to out-of-equilibrium Alexander van Oudenaarden Department of Physics, MIT http://web.mit.edu/biophysics avano@mit.edu

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Noise in gene expression can randomly flip a genetic switch: the lambda lysis-lysogeny decision Arkin, Ross and McAdams. Genetics 149, 1633 (1998)

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Biochemical reactions are intrinsically noisy The randomness is a natural consequence of the discreteness of molecules Describing the dynamics of a constitutively transcribed gene ? y mRNA concentration  transcription rate t time

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Noise can be observed in the expression of a single gene gfp LacI Pspac IPTG IPTG GFP  y y y Ozbudak et al., Nature Genetics 31, 69 (2002)Elowitz et al., Science 297, 1183 (2002)

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Biological Relevance of Noisy Gene Expression ? NOISE is BENEFICIAL Stochastic gene expression introduces a significant variability in mRNA and protein concentrations from cell-to-cell in an isogenic population. This might be beneficial for survival in fluctuating environments. NOISE is DETRIMENTAL Fluctuations in gene expression might impair faithful signal propagation in gene cascades and signal transduction pathways

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Part I Noise propagation in gene networks (Escherichia coli) Juan Pedraza, AvO Science 307, 1965 (2005)

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Stochastic gene expression from prokaryotes to eukaryotes and from steady-state to out-of-equilibrium

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Gene 1 Gene 2 Main topics of part I: - Experimentally measure how noise propagates in a gene cascade - Develop mathematical models that quantitatively describe and predict the noise properties A synthetic cascade in E. coli to probe noise propagation: Gene 0 Gene 3

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Gene 1 Gene 2 Related studies: Rosenfeld et al. Science 307, 1962 (2005) Hooshangi et al. PNAS 102, 3581 (2005) A synthetic cascade in E. coli to probe noise propagation

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The average signal does not reflect single cell behavior Gene 1 Gene 2

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... 3 color fluorescence microscopy image analysis 286 998 2217 1010 424 716 1519 1062 966 286 40 377 968 1293 1616 172 910 87 655 1512 115 1146 383 870 73 990 1097 1393 192 369 1722 19 476 1294 179 1950 951 690 127 301 817 1252 408 637 1069 2758 249 105 95 2630 468 352 1037 452 225 781 1362 75 339 45 184 463 1136 1229 96 1311 371 407 863 825 1150 2019 383 1064 709 559 1001 1651 865 790 755 1228 902 1833 2141 1320 239 179 418 1481 F1 ... ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ... # F2 F3 A typical data set (~ 5000 single cells; 3 colors/cell): ~ 15000 data points for one concentration of IPTG and ATC

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... 3 color fluorescence microscopy image analysis calculate correlations 286 998 2217 1010 424 716 1519 1062 966 286 40 377 968 1293 1616 172 910 87 655 1512 115 1146 383 870 73 990 1097 1393 192 369 1722 19 476 1294 179 1950 951 690 127 301 817 1252 408 637 1069 2758 249 105 95 2630 468 352 1037 452 225 781 1362 75 339 45 184 463 1136 1229 96 1311 371 407 863 825 1150 2019 383 1064 709 559 1001 1651 865 790 755 1228 902 1833 2141 1320 239 179 418 1481 F1 ... ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ... # F2 F3 Cij i = 1, 2, 3 j = 1, 2, 3 Correlations capture rich structure of 3D distributions ~ 15000 data points for one concentration of IPTG and ATC 1 correlation for one concentration of IPTG and ATC

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Auto correlations capture the cell-to-cell variability in the expression of a single gene : averaged over single cells in population For example, i = j = 1 (gene 1 is reported by CFP) (auto-correlation, coeficient of variation) (CFP)2 2

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... 286 998 2217 1010 424 716 1519 1062 966 286 40 377 968 1293 1616 172 910 87 655 1512 115 1146 383 870 73 990 1097 1393 192 369 1722 19 476 1294 179 1950 951 690 127 301 817 1252 408 637 1069 2758 249 105 95 2630 468 352 1037 452 225 781 1362 75 339 45 184 463 1136 1229 96 1311 371 407 863 825 1150 2019 383 1064 709 559 1001 1651 865 790 755 1228 902 1833 2141 1320 239 179 418 1481 F1 ... ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ... # F2 F3 (CFP)2 2 Single cell CFP fluorescence Cell count sCFP repeat for other colors and other IPTG and ATC concentrations

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i = j Autocorrelations Why are noise profiles qualitatively different for gene 1 and 2 ? What determines the shape of the profiles ?

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Cross correlations capture how variability in expression couples between different genes : averaged over single cells in population For example, i = 1; j = 2 (gene 1 is reported by CFP; gene 2 is reported by YFP)

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... 286 998 2217 1010 424 716 1519 1062 966 286 40 377 968 1293 1616 172 910 87 655 1512 115 1146 383 870 73 990 1097 1393 192 369 1722 19 476 1294 179 1950 951 690 127 301 817 1252 408 637 1069 2758 249 105 95 2630 468 352 1037 452 225 781 1362 75 339 45 184 463 1136 1229 96 1311 371 407 863 825 1150 2019 383 1064 709 559 1001 1651 865 790 755 1228 902 1833 2141 1320 239 179 418 1481 F1 ... ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ... # F2 F3

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... 286 998 2217 1010 424 716 1519 1062 966 286 40 377 968 1293 1616 172 910 87 655 1512 115 1146 383 870 73 990 1097 1393 192 369 1722 19 476 1294 179 1950 951 690 127 301 817 1252 408 637 1069 2758 249 105 95 2630 468 352 1037 452 225 781 1362 75 339 45 184 463 1136 1229 96 1311 371 407 863 825 1150 2019 383 1064 709 559 1001 1651 865 790 755 1228 902 1833 2141 1320 239 179 418 1481 F1 ... ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ... # F2 F3 repeat for other colors combinations and other IPTG and ATC concentrations

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i  j Cross-correlations Why determines the cross-correlation between gene 1 and 2 ? Why are C13 and C23 dependent on [IPTG] ?

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Modeling signal & noise transmission

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Transmitted noise depends on the logaritmic gain Two types of transmitted noise: 1. Transmitted intrinsic noise 2. Transmitted global noise (gene 1) (gene 2)

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Building up the noise

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Noise profile of gene 1 is mixture of intrinsic and transmitted noise Noise profile of gene 2 is dominated by the transmitted noise (profile resembles shape of H21) Interpretation of the noise profiles

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Crosscorrelations C13 and C23 are due to transmission of correlated global noise (independent of intrinsic noise) Interpretation of the noise profiles

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Why does C13 depend on H10 and therefore on [IPTG] ? global noise is correlated between gene 1 and 3 a global fluctuation resulting in increased expression of all genes (including gene 0) will lead to an increased repression of gene 1 depending on the coupling between gene 0 and 1 (H10) global noise couples genes even in the absence of a direct genetic interaction

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Global fit to means, autocorrelations and cross-correlations

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Predictive power of model (no fit parameters)

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Conclusions, Part I Noise in a gene is 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.

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Part II Noise amplification and correlation (Saccharomyces cerevisiae) Attila Becskei, Ben Kaufmann, AvO Nature Genetics 37, 937 (2005)

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Stochastic gene expression from prokaryotes to eukaryotes and from steady-state to out-of-equilibrium

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Holand et al. JBC 277, 14363 (2002) The majority of yeast transcription factorshave less than one mRNA/cell small number of mRNA molecules  huge fluctuations ?

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First problem: Most promoters are too weak for direct read-out direct read-out Solution: a synthetic signal and noise amplifier Elowitz et al. Science 297, 1183 (2002) Raser and O’Shea. Science 304, 1811 (2004) doxycycline Becskei, Boselli and AvO. Nature Cell Biology 6, 451 (2004) Becskei, Kaufmann and AvO. Nature Genetics 37, 937 (2005)

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Goal: determine input noise 1 of several weak promoters  = CV = standard deviation mean rtTA [dox] YFP input module response module ...

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What would you expect theoretically ? Paulsson. Nature 427, 415 (2004) Pedraza and AvO. Science 307, 1965 (2005) averaging constant logarithmic gain independent of input promoter !

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Input noise is found by globally fitting to the model Becskei, Kaufmann and AvO. Nature Genetics 37, 937 (2005)

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N Contribution of intrinsic input noiseshould depend on input signal experimental knob N: multiple Pinput-rtTA integrations

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N fully uncorrelated fully correlated Related study: Volfson et al., Nature, doi:10.1038 (2005)

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Output signal x2 (fluorescence) Output noise 2 N = 1 N = 2 N  5 Output noise is independent of N: noise from multiple promoter copies is strongly correlated PSWI6

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Output signal x2 (fluorescence) Output noise 2 ade2 ade2/ade2 5xade2 his3 2xhis3 his3/his3 Normalized noise 1 [dox]25% (mg/ml) Correlated noise depends on chromosomal position Becskei, Kaufmann and AvO. Nature Genetics 37, 937 (2005)

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Conclusions, Part II Although SWI6 promoter is one of weakest yeast promoters, noise is fully correlated between tandem copies Noise originates from rare events of promoter activation (not randombirth and deaths of mRNA molecules) and depends on chromosomal position

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Part III Noise in a circadian oscillator (Synechococcus elongatus) Jeff Chabot, Juan Pedraza, AvO

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Stochastic gene expression from prokaryotes to eukaryotes and from steady-state to out-of-equilibrium

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Cyanobacteria as a model system for circadian rhythms Kondo et al. (1993)

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Cyanobacteria as a model system for circadian rhythms Kondo et al. (1993)

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The circadian clock consists of only 3 proteins and can be reconstituted in vitro

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Circadian oscillations in Synechococcus elongatus PCC7942 Monitoring circadian oscillations in single cells using fluorescent proteins Related study: Mihalcescu et al., Nature 430, 81 (2004).

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Establishing fluorescence as a useful tool for exploring circadian rhytms in Synechococcus protein half-life YFP = 12.8 hrs protein half-life YFPLVA = 5.6 hrs Fluorescence (a.u.) Time in LL (hours) Time after IPTG removal (hours) Time after IPTG induction (hours) Fluorescence (a.u.) Fluorescence (a.u.) YFPLVA YFP

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deterministic model: R ~ 2.8 hr-1 P ~ 0.12 hr-1 Experimentally known: Since y(t) is known, kR(t) can be determined (in a.u.)

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Let’s use the same gene-doubling technique to determine correlation between expression fluctuations

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NS I & II fully correlated: (CV2)one copy = (CV2)two copies (s2)one copy = 4(s2)two copies NS I & II fully uncorrelated: (CV2)one copy = 0.5(CV2)two copies (s2)one copy = 2(s2)two copies

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Using this formalism q(t) can be extracted from the experiments [Rosenfeld et al. Science 307, 1962 (2005)]

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Global noise is consistent with global fluctuations in creation rate kR(t) N  P G  0.4

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Local noise is not consistent with intrinsic fluctuations For intrinsic noise:

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Conclusions, Part III Cell-to-cell variability was measured in cyanobacteria during a circadian period An out-of-equilibrium method was developed to extract the fluctuations introduced at the transcription level Data are consistent with a constant global noise and a time-varying local noise introduced at the transcription level

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Thanks ! Attila Becskei Ben Kaufmann $$$ NIH NSF Juan Pedraza Jeff Chabot