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Noise in gene expression networks?Ramu Anandakrishnan

March 14, 2006

Blah ..

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Shut up guys! I can’t hear what DNA it telling

me to do...

Rosenfeld et al.

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My goal

1. Share with you what I’ve learnt

2. Get clarification and answers to things I didn’t understand

3. Set the stage for my project

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Agenda

1. Some basic background

2. Gene regulation at the single-cell level, Rosenfeld et al.

3. Noise propagation in gene networks, Pedraza et al. (time permitting)

4. Some final thoughts

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Why is it important

• All biological organisms are essentially made up of proteins and use proteins to function

• We are a finely tuned machines requiring the EXACT right amount of the right type of protein, at the right time

• Proteins are produced through the gene expression process

• Slight variations or errors in the process can result in disease or even death

Understanding what causes variations (noise) in gene expression (protein production) can help prevent diseases .

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Gene expression process

• DNA to RNA Transcription– Activator and Repressor proteins control affinity to Start site– RNA polymerase attaches to Start site and locally cleaves DNA– mRNA s formed by stringing together nucleoside triphosphates. The reaction

is catalyzed by pyrophosphatase• RNA processing (eukaryotic cells)

– 5’ cap added to mRNA to prevent enzymatic degradation– Endonuclease cleaves 3’ end and poly(A) polymerase (a complex of proteins)

adds a poly(A) tail which specifies the correct number of A residues to add (does not require a template)

– Noncoding “introns” are removed by splicing • Protein Synthesis

– Specific aminoacyl-tRNA synthetase attach a specific amino acid to the transfer RNA (tRNA) which activates the tRNA

– Ribosomes, consisting of several different ribosomal RNA and more than 50 proteins, binds to the mRNA and the tRNA to accelerate protein synthesis

– Amino acids on the tRNA bind to form the polypeptide protein chain and the tRNA is released

• Protein Sorting and Secretion– Ribosome must carry mRNA to specific destinations– Protein moved to final destination, in some cases protected by transport vesicles and

Golgi complex ,

Gene expression in general is a very complex process with many opportunities for variances from the optimal outcome

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Controlled experiments

• Fluorescent Staining and Recombinant DNA

– Fuse gene for fluorescent protein (e.g. GFP) with gene for the protein of interest creating a “chimeric” protein gene

– Insert chimeric gene DNA into the cell, which then produces the chimeric protein

– The fluorescent dye lights up when the cell is illuminated

– Associated proteins can then be identified and counted

• Transcription Control

– Inducer concentration

– Mutation to inactivate repressor production

– Operator site mutation to prevent repressor binding

– Promoter site mutation to prevent RNA polymerase from initiating transcription

Biologists have devised ingenious ways of controlling and reporting the gene expression process to get data that can be analyzed

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Research

Basic research is like shooting an arrow into the air and, where it lands, painting a target.-- Homer Burton Adkins (1892-1949, American organic chemist)

I love fools' experiments; I am always making them -- Charles Darwin (1809-1882, British biologist)

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Gene regulation at the single cell level, Rosenfeld et al.*

• Analyzes noise in the Gene Regulation Function:Protein production rate = f (Transcription Factors)

• Variance separated into intrinsic and extrinsic noise

• Analyzes temporal aspect of noise

• λ-cascade strains of E. coli used to conduct controlled experiments

• Experiments designed to permit measurement of Rate of Production at an individual cell level instead of steady state quantity or averages for multiple cells

Temporal fluctuations due to extrinsic noise are large and long lasting, so must be taken into account for realistic modeling

* Gene regulation at the single-cell level, N Rosenfeld, JW Young, U Alon, PS Swain, MB Elowitz

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Experimental data

Conducted experiments designed to observe gene regulation in individual cells over time

λ-cascade strain of E. coli

Yellow fluorescent repressor fusion protein

Chromosomally integrated target promoter (PR) controlling

cyan fluorescent protein

Induced by anhydro-tetracycline

aTc used to initially induce production of cI-YFP, which then dilutes over time

as cells divide

TetR+ background represses YFP

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Data Calibration

Individual cI-YFP molecules can not be directly detected due to cellular autofluorescence, so it is indirectly estimated by fluorescence intensity

Number of copies of cI-YFP received by daughter cells follows a binomial distribution:

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Theoretical model

Gene Regulation Function (Hill function)

Production Rate =

The Hill function is often used to represent unknown regulation functions

Matlab plot for PR

0 1 2 3 4 5 6 7 8 9 10216

216.5

217

217.5

218

218.5

219

219.5

220

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Variance

The Hill function does fit the mean values, however it’s parameters are calculated from the data and the standard deviation is high (55%)

Standard deviation = 55%

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Explanation of variance – intrinsic and extrinsic noise

• Average CFP production rate for cells about to divide = 2x that of newly divided cells

• Why?

– True for all proteins?

– Need to make two of everything so each of the daughter cells will have enough to function?

– Cell grows twice as fast just before division?

• Production rates normalized to the average cell cycle phase. How?

• Normalized standard deviation = 40%

Even after normalizing for cell cycle phase standard deviation is high (40%)

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Explanation of variance – intrinsic and extrinsic noise

• Intrinsic noise (~20%)

– Caused by randomness in biochemical reactions

– Identical copies of genes would show different production rates

– Measured by comparing expression of two cells with identical levels of regulatory proteins

• Extrinsic noise (~35%)

– Resulting from fluctuations in levels of “cellular components such as metabolites, ribosomes and polymerases”, but not in the concentration of repressor

– Remaining variance after excluding intrinsic noise

– This must include variance due to cell cycle phase?

After separating out the effect of intrinsic noise (~20%), extrinsic noise represents 35% of variance

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Temporal analysis of intrinsic and extrinsic noise

• Autocorrelation function

– Correlation between observations at time i and i+m

– Rm = 1 indicates high correlated

• Intrinsic noise

– Decays rapidly, correlation time < 10 min

• Extrinsic noise

– Correlation time ~ 40 min, comparable to cell cycle times of ~ 45 min

Extrinsic noise varies over cell cycle time scales

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Conclusion

• Single-cell Gene Regulation Function can not be expressed by a single-valued function because slow extrinsic fluctuations give the cell a memory or individuality lasting roughly one cell cycle

• This implies that any accurate cellular response in faster time scales are likely to require a feedback loop

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Statistics

On the Gaussian curve:

Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact. -- Jules Henri Poincare (1854-1912) [French mathematician]

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Gene propagation in gene networks, Pedraza et al.*

• Studies propagation of noise from one gene to another in a network

• Synthetic network of four genes used to conduct controlled experiments

• Noise correlation model used to analytically calculate noise transfer from one gene to the next

• Demonstrated that transmitted noise has a logarithmic gain that depends on the interactions between upstream and downstream genes

Even though intrinsic noise may be low for each gene in the network, transmitted noise may be high due to correlated sources of noise

* Gene propagation in gene networks, JM Pedraza, A van Oudenaarden

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Experimental Data

IPTG and ATC inducers are used to regulate the expression of Gene 1 and Gene 2.

RepressorsInducers Not part of cascade

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Theoretical Model

The Langevin method can be used to analytically derive the correlation function for intrinsic and global noise

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Theoretical Model

The noise transfer gain, Hij is computed by fitting experimental data to the correlation function derived using the Langevin method

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Validation of the model

Parameters calculated by varying IPTG concentration, correctly predicted the impact of varying ATC concentration

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Conclusion

• Langevin method can be used to analytically predict noise in gene networks

• Noise has a correlated global component due to which fluctuation can be substantial despite low intrinsic noise in all components

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Noise

Noise \’noiz\ n 1: loud, confused or senseless shouting; 2 a: sound that lacks agreeable musical quality or is noticeably unpleasant; b: … ; c: an unwanted signal or disturbance interfering with the operation of a device or system; d: …

Noise in the gene expression network:

Is this really noise or a limitation of our model?

Maybe it is part of the “design” to make sure that the organism will die off over time and make way for the new and improved next generation?

Does it matter or are we talking about semantics?

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What happened to my hair?

1985 2006

Is it a result of accumulated errors from 20 years of “noisy” gene expression?