Systems biology meets synthetic biology:case study of metabolic effects of synthetic rewiring

Supplementary information

Josselin Noirel1 Saw Yen Ow1 Guido Sanguinetti1,2Phillip C. Wright1,*

18th May 2009

1 ChELSI Research Institute, The Sheffield Bioincubator, Department of Chemicaland Process Engineering, University of Sheffield, Mappin St, S1 3JD Sheffield,United Kingdom.

2 Department of Computer Science, 211 Portobello St, University of Sheffield, S1 4DPSheffield, United Kingdom.

* To whom correspondence should be addressed: p.c.wright@sheffield.ac.uk.

1 Supplementary information

1.1 Maximal-flux derivation at steady stateWe take again the simple toy pathway from Figure 2 (main text). We showed that ifsteady state is achieved,

[B]∞ =ATET1 k

(1)1 k

(1)2 (k

(2)−1 + k

(2)2 )

k(2)1

(ET2 (k

(1)−1 + k

(1)2 )k

(2)2 − ATk

(1)1 (ET1 k

(1)2 − ET2 k

(2)2 )) (S1)

Similarly, one can derive the flux d[C]/dt:

d[C]dt

= ET1k

(1)1 k

(1)2 A

T

k(1)1 A

T + k(1)−1 + k(1)2

(S2)

Interestingly, it does not depend on ET2 (or any of the second enzyme’s parameters, forthat matter) but does on ET1 and if steady state could always be achieved, maximal fluxwould be reached when ET1 is maximal. If we keep the total amount of enzymes constant:

ET1 + ET2 = ET

we would predict that maximal flux is attained when ET1 = ET and ET2 = 0. Obviously,when ET2 = 0, the overall flux must be zero. What happens is that when ET2 gets close to

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Supplementary Material (ESI) for Molecular BioSystemsThis journal is © The Royal Society of Chemistry 2009

zero, steady state cannot be attained because the threshold A∗ tends towards zero andtherefore the input AT ends exceeding A∗. As soon as AT ≥ A∗, B accumulates (as seenin the section ‘Ensuring flux balance’) and [B]∞ = +∞. Since the substrate of the secondenzyme is hyperconcentrated, the flux d[C]/dt is the v(2)max of the second enzyme, that is,

k(2)2 (ET − ET1 ) (S3)

Maximum flux is therefore attained when AT = A∗. So we can solve the equation

AT = (ET − ET1 )(k

(1)−1 + k

(1)2 )k

(2)2

k(1)1 (ET1 k

(1)2 − (ET − ET1 )k

(2)2 )

(S4)

We arrive at:ET∗1ET

= k(2)2 (k

(1)1 A

T + k(1)−1 + k(1)2 )

k(2)2 (k

(1)−1 + k

(1)2 ) + k

(1)1 A

T (k(1)2 + k(2)2 )

(S5)

The maximal flux depends on many parameters, including the input value AT . Wecan summarise this result with the following plot:

0 E1T * ET

AT

E1T

A*

Flu

x

As ET1 moves from zero to ET∗1 (the value for which AT equates the threshold A∗) theflux augments linearly and steady state is mathematically achievable. Above this value,E2 becomes limiting. The maximal flux is obtained at ET1 = ET∗1 , which will always begreater than 1/2 if k(1)2 = k

(2)2 .

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1.2 Supplementary figures

-1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Original value

p +

Figure S1: Newman et al.’s 2006 study presents a proteomic dataset obtained bymeasuring GFP fluorescence. The authors compared yeast cells grown in (a) rich and(b) minimal media. The dataset was made available as supplementary material andwas used to conduct a validation of MMG [20]. The dataset was copied and modified350 times into ‘mutant datasets’ (MD). For each MD, a datapoint x was removed soas to create 350 different MDs. MMG was run independently on each MD and used todetermine the probabilities p−, p+, and p0 for the missing datapoint to be down-regulated,up-regulated, and unchanged, respectively. These probabilities were then compared tothe original value x. Here is represented p+ as a function of x (log-ratio), it shows thathigh probabilities p+ of being up-regulated are associated with higher measurements x.This shows that genes predicted to up-regulated are likelier to be associated with highmeasurements in the original dataset.

3

Supplementary Material (ESI) for Molecular BioSystemsThis journal is © The Royal Society of Chemistry 2009

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

1.2

Time hours

OD

600

nm

Growth curve RU1012, RU1012 & plasmids

Figure S2: Growth curves of the strain RU1012 (red) and the engineered strain(blue). The time when the cells were harvested is indicated by a black circle.

1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Λ

Fre

quen

cy

Figure S3: MMG assumes that differential expression can be modelled by a positiveor negative exponential distribution, depending on whether one considers up- or down-regulation. The parameters of the exponential distribution were called λ− and λ+.Their values indicate the strength of differential expression, lower values hinting at morenoticeable changes. The posterior distributions of these parameters are represented here.Blue: λ−; magenta: λ+.

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b3926

b0351 b1241

b0356 b1241 b1478 b3589 b2097 b2925

b1779

b2096 b3137

b3919

b2926

b2095 b3132

b0114

b2297 b0823 b0903 b3114 b3951

0.85 0.90 0.95 1 1.05 1.10 1.15 1.20

0.850.900.9511.051.101.151.20

Up-regulation in the engineered strain (MS/MS data)

Down-regulation in the engineered strain (MS/MS data)p– , p0 , p+

A B

Figure S4: Up- and down-regulated networks labelled with the gene names ratherthan the enzyme descriptions.

Node p(−) p(0) p(+) Measurement Function

Down-regulated (in this study)477 0.63 0.37 0 -0.540 glycerol kinase2 0.64 0.36 0 -0.312 alcohol dehydrogenase class III509 0.60 0.40 0 -0.312 acetaldehyde-CoA dehydrogenase II9 0.69 0.31 0 -0.843 fructose-bisphosphate aldolase class I/II8 0.67 0.33 0 -0.785 triosephosphate isomerase7 0 0.43 0.57 +0.396 glyceraldehyde-3-phosphate dehydrogenase A99 0.35 0.33 0.31 NA glucitol/sorbitol-specific enzyme IIC component of PTS19 0.86 0.14 0 -1.247 phosphoglycerate kinase98 0.34 0.33 0.33 NA D-tagatose 1,6-bisphosphate aldolase

Up-regulated (in this study)400 0.56 0.44 0 -0.124 phosphate acetyltransferase503 0 0.45 0.55 +0.382 predicted pyruvate formate lyase3 0 0.54 0.46 +0.560 pyruvate dehydrogenase

Table S5: Re-analysis of the cis-1,2-dichloroethylene-degrading strain [18] basedon the networks identified in this study. The posterior probabilities are reported p(−),p(0), and p(+). The measurements from the 2006 study are reported in log2 ratios. ‘NA’indicates that the protein was not quantified.

1.3 Supplementary filesFile S6: QFluxConstant Mathematica notebook showing the dynamics of a toy enzymaticpathway. It can be viewed using MathematicaPlayer which may be downloaded fromhttp://www.wolfram.com/products/player/.

File S7: AllQuants Proteins quantified in this study. The file include the proteinname, the quantifications, and the error factors.

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Supplementary Material (ESI) for Molecular BioSystemsThis journal is © The Royal Society of Chemistry 2009

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