by Rosalind Allen

Regulatory networks

Biochemical noise

Slide 1: Cells with identical genes in identical environments can behave differently. This can be explained in terms of biochemical noise. Cover image by Elowitz et al from Science Volume 297 issue 5584. Reprinted with permission from AAAS. This figure may be used for non-commercial, classroom purposes only. Any other uses require the prior written permission from AAAS.

Slide 2: Computer simulation results for reaction A + B →C, starting with different numbers of A and B molecules.

CBA q Rate constant q is set to 1. Each simulation run is repeated five times (results shown in different colours) .

Slide 3: Image demonstrating that genetically and environmentally identical cells can show very different levels of gene expression. Cover image from <i>Science</i> Volume 297 issue 5584. Reprinted with permission from AAAS. This figure may be used for non-commercial, classroom purposes only. Any other uses require the prior written permission from AAAS.

Michael B Elowitz et al. 2002 Stochastic gene expression in a single cell Science 298 1183.

Slide 4: Illustration showing the effects on the two reporter proteins of fluctuations in the intracellular environment and of biochemical noise in transcription and translation. From Elowitz <i>et al</i> 2002 Stochastic Gene Expression in a Single Cell Science 297 1183. Reprinted with permission from AAAS. This figure may be used for non-commercial, classroom purposes only. Any other uses require the prior written permission from AAAS.

Intracellular environment fluctuates: this affects the two genes in the same way – the two colours are correlated.

Randomness of chemical reactions involved in protein production: this affects the two genes independently – the two colours are decorrelated.

Slide 5: The probability distribution p(N) (shown by the vertical bars) is changed by the protein production and degradation reactions.

Slide 6: The chemical master equation and probability distribution p(N) for the simple “one-step” model of protein expression.

)()()1()1()1(),(

NNpNkpNpNNkpdt

tNdp

Steady state: dp(N,t)/dt = 0 hence

kN

ek

NNp

!

1)(

k

NNk

N N 22

NkNN 1

Slide 7: Protein number probability distributions for one-step and two-step models of protein production.

Average number of protein molecules = 5

Average number of protein molecules = 100

For the two-step model, we assume that on average an mRNA produces five proteins, and we fix the transcription rate to get the same average number of proteins as in the one-step model.

Slide 8: An experimental system constructed by Yu et al. (2006) to visualise in real time the production of a single protein molecule in a cell. From Yu et al. 2006 Probing gene expression in live cells, one protein molecule at a time, Science 311 1600. Reprinted with permission from AAAS. This figure may be used for non-commercial, classroom purposes only. Any other uses require the prior written permission from AAAS.

“Venus” is a gene that encodes a yellow fluorescent protein; “tsr” encodes a peptide that anchors the fluorescent protein in the cell membrane.

Slide 9: Results showing the moment when individual protein molecules are produced in growing bacterial cells. From Yu et al. 2006 Probing gene expression in live cells, one protein molecule at a time, Science 311 1600. Reprinted with permission from AAAS. This figure may be used for non-commercial, classroom purposes only. Any other uses require the prior written permission from AAAS.

The appearance of individual protein molecules was monitored in growing cells over time. Yellow dots show individual protein molecules bound to the cell membrane.

The three plots show the rate of protein production (number of new proteins per 3 minute time interval) for three different cell “lineages”, which are illustrated on the right.