article.dvi

Systems biology of energetic and atomic costs in the yeast
transcriptome, proteome, and metabolome

Michael D Barton

, Bal´

azs Papp

, Daniela Delneri

, Stephen G Oliver

, Magnus Rattray

Casey M Bergman

Faculty of Life Sciences, University of Manchester, Manchester, M13 9PT, UK

Institute of Biochemistry, Biological Research Centre of the Hungarian Academy of Sciences, H-6726 Szeged, Hungary

School of Computer Science, University of Manchester, Manchester, M13 9PL, UK

Present address: Department of Biochemistry, University of Cambridge, Sanger Building, 80 Tennis Court Road, Cambridge, CB2

1GA, UK

Email: Michael D Barton - mail@michaelbarton.me.uk;

Corresponding author

Abstract

Background:

Every protein has a variable atomic and energetic cost to the cell based on the synthesis of its

constituent amino acids. Quantifying the cost of amino acid synthesis is challenging, however natural selection

is expected to favour the use of proteins whose constituents are cheaper to produce in terms of energetic and

atomic cost.

Results:

We develop a systems biology approach to estimate the cost of amino acid synthesis based on

genome-scale metabolic models, and directly investigate the effects of the cost of amino acid synthesis on

transcriptomic, proteomic and metabolomic data in Saccharomyces cerevisiae. We used our two new and six

previously reported measures of amino acid cost in conjunction with codon usage bias, tRNA gene number and

atomic composition to identify the factors that predict transcript, protein and free amino acid levels in the yeast

cell. While most previously reported cost measures are highly correlated, we find that our systems approach to

formulating the cost of amino acid synthesis produces a novel measure of cost, which explains similar levels of

variation in gene expression. Regardless of the measure used, the cost of amino acid synthesis is weakly

associated with transcript and protein levels, independent of codon usage bias. In contrast, energetic costs

explain a large proportion of variation in levels of free amino acids.

Conclusions:

In the economy of the yeast cell, the cost of amino acid synthesis correlates with transcript and

protein levels to a lesser degree than translational optimisation, whereas atomic and energetic cost plays a much

larger role in explaining levels in free amino acids. However, as there appears to be no single currency to

compute the cost of amino acid synthesis, a systems approach is necessary to uncover the full effects of amino

acid biosynthetic cost in complex biological systems that vary with cellular and environmental conditions.

Background

Everything in a living cell has a cost: from the energy needed to transform molecules against

thermodynamic equilibria, to the raw materials needed to produce the constituents of a new cell. Natural

selection may be expected to minimise such cellular costs, and evidence for adaptation to require less

energy and matter may exist at the molecular or cellular level. Testing this hypothesis requires answering

several questions about the meaning of cost in the cell, and how to measure it. For example, how does one

assign a biochemical price to a molecule whose state is dependent on changing environmental and cellular

conditions? Similarly, is it possible to separate different costs from one another, or from other molecular

constraints in the cell? Moreover, are biosynthetic costs the same at different levels of the gene expression

hierarchy? Knowing the answers to these questions is central to a systematic understanding of the chemical

forces that shape the composition of biomolecules, and how biomolecular composition relates to gene

expression at the transcriptional and post-transcriptional levels.

Craig and Weber [1] pioneered the quantitative analysis of cost at the cellular level to investigate the

effects on the synthesis and evolution of a small number of Escherichia coli proteins. These authors

estimated the cost of a protein as the sum of how many units of high energy phosphate bonds (e.g. ATP)

and reducing hydrogen atoms (e.g. NADPH) are diverted from the available energy pool to produce each

of the constituent amino acids from glucose, divided by the length of the protein. Akashi and Gojobori [2]

used a modified version of this approach to show in the chemoheterotrophic bacteria E. coli and Bacillus

subtilis

, that predicted gene expression levels based on codon usage bias show a negative correlation with

average protein cost. This work provided the first genome-wide evidence that evolution has optimised

prokaryotic cells to produce highly expressed proteins with less expensive amino acids, and established an

important link between the metabolism of a cell and the evolution of its genome sequence. Heizer et al. [3]

extended these findings to four additional prokaryotic species including photoautotrophs, demonstrating

that this cost optimisation occurs whether the source of energy is organic or inorganic. More recently,

Swire [4] used Craig and Weber's [1] cost values to generate a new cost measure for an amino acid based on

its usage in proteins as a function of overall protein cost computed from all other amino acids, and showed

that cost selection affects multiple prokaryotic, archaeal and eukaryotic genomes. Wagner [5] developed a

method similar to Craig and Weber [1] that includes the energetic costs of synthesising both mRNA and

protein for Saccharomyces cerevisiae, and showed that the cost of doubling gene expression after a gene

duplication is likely to be significant enough to be selected.

Seligmann [6] argued that, while the number of high energy molecules is an important part of the energetic

investment of synthesising an amino acid, this approach is unlikely to explain the entire investment made

by a cell when producing an amino acid. Instead, Seligmann [6] used the molecular weight of an amino acid

as a proxy for energetic costs, reasoning that this may take into account all the manifold effects of the

complexity of producing larger amino acids. Molecular weight also has the advantage of being constant

across species, and therefore can be used to test the cost selection hypothesis where the genome sequence is

available but the topology of amino acid synthetic pathways is unknown. Seligmann [6] used this to prove

on an individual protein basis, molecular weight is indeed minimised across a range of bacterial and

eukaryotic genomes. Estimating the cost of an amino acid based on its molecular weight also raises the

issue of the potential costs of the atomic content in biomolecules. In their seminal work, Mazel &

Marliere [7] showed in the cyanobacterium Calothrix that abundant proteins expressed under sulphur

limiting conditions are depleted for sulfur-containing cysteine and methionine residues. Baudouin-Cornu et

. [8] showed that enzymes in pathways scavenging sulphur, carbon, or nitrogen from the environment are

under-represented in terms of their atomic composition for that particular nutrient. Further research by

Bragg et al. [9] showed across 141 genomes that the sulphur content of the encoded protein varies widely

and is associated with environmental conditions of the species. All of these results indicate that atomic

composition may play an equally important role as biosynthetic cost in the evolution of protein sequence.

Even taking into consideration all of the atoms and energy required for protein synthesis accurately

predicted, this may not represent the true cost under all cellular or environmental conditions. Just as in

supply and demand economics, when a particular atom is scarce in the cell or environment, synthesis of

molecules abundant in this atom will be more expensive, in comparison to molecules where that atom is

under-represented. As an example of the effect of supply and demand in cellular economics, Varma et

al.

[10] showed in E. coli that the "shadow price" of using molecules involved in energy production changes

according to the availability of oxygen. As the availability of oxygen decreases, the cost of its use rises,

while the cost of ethanol use decreases as the energy to redox ratio become less efficient. The field of

metabolic control analysis takes a similar approach, estimating the importance of an entity in a system, by

perturbing a given parameter and determining the resultant change in flux in the rest of the

system [11, 12]. Carlson [13] demonstrated in silico the importance of supply and demand by illustrating

that E. coli will favour the expression of pathways using inexpensive proteins in stress inducing

environments. In this report, we use a systems biology approach based on Flux Balance Analayis (FBA)

similar to that of Varma et al. [10] to estimate cost of synthesising amino acids in the context of the

availability of nutrients. We first estimate the "relative" cost of synthesising an amino acid by examining

the sensitivity of growth rate to the required quantity of the amino acid per gram of biomass. We then

estimate a second "absolute cost" by multiplying the relative cost by the biomass requirement of the amino

acid in the FBA model. Similar to Varma at al. [10] where they examined the sensitivity of growth to

small increases in oxygen availability, we use in silico models estimate the effect of an increasing per gram

of biomass amino acid requirement has on the uptake of environmental nutrients. We calculated each of

these cost types for four nutrient limiting conditions (glucose, nitrogen, sulphur, and phosphorus) to

investigate how cost varies according to environmental conditions. As in previous studies [1, 36], we focus

on amino acid synthesis, because this allows us to analyse the effects of cost on gene expression.

Using our in silico systems approach, we analysed the joint effects of energetic and atomic costs on the

transcriptome, proteome and metabolome of S. cerevisiae. Our aim is to determine if there is measurable

relationship between biosynthetic cost and gene expression that could indicate a possible role for cost

minimisation as a selective pressure on genomic regulatory systems. Our results show that biosynthetic

cost and atomic composition do indeed have a measurable relationship with gene expression, but that the

effects of cost are dependent on the level at which the gene expression hierarchy is considered. Importantly,

we also analyse transcriptomic and proteomic data directly to study gene expression, whereas previous

work has used codon usage bias as a proxy for gene expression [2, 3, 14], examined atomic composition for

only a small set of expressed genes [15], or attempted to predict gene expression based on amino acid

composition without respect to biosynthetic cost [16]. By analysing the joint effects of cost and atomic

content together with other factors such as codon usage bias and genomic tRNA count together we are able

to account for any possible correlations between variables, and thereby assess the importance of each

independently. We show that our systems biology approach explains a significant proportion of variation in

gene expression levels, independent of codon usage bias, tRNA gene number or atomic content. Our

relative measure of cost is poorly correlated with previously reported measures of cost, but also explains a

comparable amount of gene expression, suggesting that no single measure currently captures all aspects of

biosynthetic cost. We also extend cost analysis to levels of free amino acid levels in the metabolome, an

aspect of cellular economics that has not been considered in previous research, but which provides intimate

an link to protein synthesis.

Results

A systems biology approach to estimating the cost of amino acid synthesis

To estimate the cost of synthesising an amino acid in S. cerevisiae, we used the in silico genome-scale

metabolic model created by Duarte et al. [17]. For each amino acid, the required quantity for growth was

altered and the effect on one of four nutrient uptake fluxes was measured. These uptake fluxes were

glucose, ammonium, sulphate and phosphate. The biomass production rate for the model was fixed at a

constant value. For each amino acid, a small percentage increase and decrease in requirement mmol of

amino acid per gram of biomass production was applied. This change was applied to the S

position the

stoichiometric matrix, where j corresponds to the biomass reaction, and i is the position of the amino acid

in the reaction. This allowed the cost of an amino acid relative to growth ("relative cost") to be measured

as the slope between the percentage change in amino acid requirement and the predicted uptake flux. A

per-molecule "absolute cost" was then calculated for each amino acid by multiplying the relative cost by

the biomass requirement in the FBA model. Details of the relationship between these two estimates of cost

are outlined in the Materials and Methods. An alternative method to estimate the cost of an amino acid

would be to fix nutrient influx and determine the effect on maximal growth rate, however our approach of

fixing biomass and minimising influx has that advantage of scaling each cost to the same growth rate,

which allows costs to compared on the same scale. The left hand side of Figure 1 shows previous costs

measures reported in the literature and our novel systems biology cost estimates. The right hand side

shows an agglomerative hierarchical clustering dendrogram of all cost measures listed in Table 1, based on

the Spearman's Rank correlation (Additional File 2). The correlation between absolute and relative costs

in S. cerevisiae and E. coli with Akashi and Gojobori's [2] energetic cost and molecular weight are also

shown in Additional File 3.

As expected if the limiting factor is the availability of atoms to create the molecule rather than energetic

limitation, we find that the absolute cost of an amino acid under S and N limitation is directly

proportional to the number of atoms of that nutrient in the molecule. The absolute costs of all amino acids

under P limitation are zero, in accordance with the fact that amino acids do not contain phosphate atoms.

Absolute cost estimates under glucose limitation have Spearman correlation coefficients greater than 0.8

with Akashi and Gojobori's [2] energetic cost, Craig and Weber's [1] energetic cost, Wagner's [5]

respiratory energetic cost, and molecular weight (Additional File 2). Wagner's [5] fermentative energy cost

and Craig and Weber's [1] biosynthetic complexity show lower coefficients of 0.522 and 0.65, respectively,

but are still significantly correlated. These results show our absolute cost measure under glucose limitation

is in good agreement with the previous manually-curated measures described in the literature, and indicate

that the most relevant measure of amino acids biosynthetic cost is most likely a function of energetic

limitation in yeast.

Our relative costs are can be viewed as the absolute cost of synthesising the amino acid, scaled by its use in

the proteome. For example, cysteine and methionine have the same absolute cost under sulphur limiting

conditions, but in relative terms the cost of methionine is much greater because it is used more in the

proteome. A similar pattern is also observed for histidine and lysine, whose rank order absolute costs switch

when scaled by proteome use. As expected, phosphate limitation does not shown any effect on the relative

cost of amino acid synthesis. Compared with previously reported cost measures, relative cost under glucose

limitation shows no significant correlation with any previously described cost measure (all p > 0.05). The

highest Spearman coefficient between relative cost under glucose limitation and any other literature

dataset is 0.077 (p = 0.49, with Wagner's [5] fermentative energetic cost), indicating that our relative cost

measure under glucose limitation has little in common previous descriptions of amino acid cost.

We used similar measures to calculate amino acid cost using the iJR904 model of the E. coli metabolic

network [18] to estimate the generality of our results between species and FBA models. Absolute costs of

synthesis are highly correlated between species under glucose limitation (Spearman R = 0.94, p = 0), as are

relative costs under glucose limitation (Spearman R = 0.74, p <0.001). The high correlation of absolute

cost is expected given the conservation of core metabolic pathways across species [19], whereas the lower

correlation of relative costs may arise from differences in amino acid composition of the proteome across

species. The estimated costs for E. coli are also included in Additional File 3 for illustrative purposes, and

demonstrate the general applicability of our method to any species with a genome-scale metabolic model.

The cost of amino acid synthesis on the yeast transcriptome, proteome and metabolome
Transcriptome

We investigated the capacity of absolute and relative cost under glucose limited growth, as well as each

previously reported cost measure, to explain transcript expression levels in each of the four nutrient

limiting environments from the S. cerevisiae dataset of Castrillo et al. [20] using multivariate regression.

The expression of each transcript was modelled as a function of the codon adaptation index (CAI) of the

coding sequence, average tRNA gene number, the mean energetic cost per residue of the protein, and the

mean atomic composition per residue of the protein. We included CAI and tRNA gene number in the

model since these factors are known to correlate with gene expression levels [21, 22], and allows us to

demonstrate an independent effect of cost that controls for these factors. We note that we do not imply

that CAI or genomic tRNA count are causal factors in gene expression, however these variables have been

shown to be correlated with both cost and/or gene expression [2, 22] , and we aim to consider the

importance of separately. Each of the selected cost types, was cycled as the cost variable in the regression

equation. Only the relative cost under glucose limitation was used, as this is the environment most relevant

to yeast [20, 23, 24] and the other costs under P, N and S limitation are proportional to atomic composition,

which is already included in the model. Table 2 shows the explanatory power for the full regression model

for each cost type in predicting transcript levels. All models explain 40% of the variation in transcript

levels across genes, with the difference in variation explained by the best and worst model being only 4.5%.

Using Akaike's Information Criterion (AIC) [25] the importance of the variables in the regression equation

was measured by removing each in turn, then comparing the goodness of fit with the model containing all

terms. Figure 2A compares the importance of each variable with other variables in the same model for

each cost type. Compared to characteristics of the encoded protein, the CAI of the transcript is at least

half an order of magnitude more important than the nearest explanatory variable, regardless of which cost

type is included. This result supports the well-established fact that codon bias correlates with gene

expression levels in growing yeast cells [21, 26, 27]. The dominant influence of CAI over other factors also

explains why the different cost types do not yield substantially different predictive power in the model. In

the molecular weight model which has the greatest explanatory power (42.2%), the most important

individual variable for predicting transcript level after CAI is cost, and carbon content is the third most

important. A general trend across all models is that the most important variable after CAI is either cost,

carbon content or nitrogen content. The importance of tRNA gene number on transcript levels appears

relatively fixed regardless of which cost is used. Finally average sulphur content appears the least

predictive measure of transcript levels.

Proteome

The importance of cost in explaining protein levels was also modelled using multivariate regression followed

by variable removal. To analyse the effect of cost on gene expression at the protein level, we used data

from Ghaemmaghami et al. [28], measuring antibody tap-tagged protein expression, since protein

expression levels from Castrillo et al. [20] were measured relative to a background (see Methods for

details). Table 2 illustrates the explanatory power of each cost model to predict protein expression levels.

As with the transcript data, each model explains approximately 40% of gene expression, and the

difference in explained variation between the best and worst model is very small (0.8%), relative to the

overall variance explained.

Figure 2B shows the relative importance of each factor in the multivariate regression model for protein

levels. This analysis illustrates similar trends to that of the transcript data where CAI is, by an order of

magnitude, the most important factor in the model. This is not unexpected given that in the original

paper, Ghaemmaghami et al. [28] showed Spearman R = 0.57 for the relationship between CAI and protein

expression. The best fit model uses absolute cost under glucose limited conditions, in which biosynthetic

cost, carbon content and nitrogen content all have a similar importance in explaining variation. Sulphur

content is again the least important variable. This is a similar trend to the transcript data where generally

(i.e. across all models) biosynthetic cost, carbon content and nitrogen content all play a similar importance

in explaining variation in gene expression levels, and sulphur content is the least important. However the

importance of tRNA gene number, and sulphur content are more variable than in the transcript data, and

in some instances their removal improves model parsimony, as indicated by a negative AIC.

Metabolome

The availability of comprehensive metabolomic data for S. cerevisiae from Castrillo et al. [20], allows us to

determine if atomic and energetic costs are important in maintenance of free amino acid levels in the cell.

Using similar multivariate regression and variable removal, we investigated the importance of each variable

in explaining free amino acid levels. We used the same factors as the previous two analyses, with the

exception of CAI (which is not applicable to amino acids). The main difference between analysis of the

metabolomic data and either the transcriptomic or proteomic data are fewer number of data points for free

amino acids versus those for transcripts and proteins. Table 2 shows how much of the variance in free

amino acid level is explained by each of the multivariate models. In contrast to transcript or protein levels,

cost type shows the greatest range in explaining variation in free amino acid levels, with R

coefficients

ranging from 76.7% for molecular weight, to 87.5% for relative cost under glucose limitation. The

explanatory power of these models at the metabolomic level are remarkable given that CAI was not

included, and are due only to the effects of energetic costs, atomic costs and genomic tRNA gene number.

Figure 2C shows the importance of each cost type in explaining free amino acid levels. The general trend

across these models in that all variables appear important, though there is more variability for carbon and

sulphur content. In particular under glucose limitation, carbon and sulphur content are less important and

therefore the explanation of free amino acid levels can be attributed to nitrogen content, tRNA gene

number, and the relative cost of amino acid synthesis.

Discussion

The principal achievements of this work are twofold. First, we developed a novel method to estimate the

cost of amino acid synthesis using a systems biology approach that incorporates sensitivity analysis and

flux balance analysis of genome-scale metabolic models. We compared our novel estimates of amino acid

costs to six measures reported in the literature and showed that absolute cost under glucose limitation is

highly correlated with previous cost measures, while relative cost under glucose limitation is not.

Furthermore we showed that our systems biology approach can be applied to calculate environment-specific

biosynthetic costs, which highlighted the effects of limiting elements of amino acid cost. Second, we

investigated the utility of energetic cost measures in conjunction with atomic costs and other factors to

analyse transcript, proteomic, and metabolomic data from S. cerevisiae. Our analysis shows that amino

acid costs do show an association with gene expression, but explain only a minor component of transcript

and protein levels relative to factors related to translational optimisation such as CAI. In contrast, we find

that energetic and atomic costs do explain a substantial degree of the variation in levels of free amino acids

in the metabolome.

No single currency for amino acid biosynthetic cost

Our systematic review and comparison of energetic cost types previously described in the literature (Table

1) shows that they are highly correlated with one another. Among previously reported measures, molecular

weight is the least related (Figure 1), which is expected since the other energetic cost measures are based

on manual curation of metabolic networks. This finding supports the view of Seligmann [6] that the

molecular weight of an amino acid includes investments by the cell that may not easily be estimated from

the metabolic network alone. Nevertheless, molecular weight and biosynthetic cost based on curated

metabolic networks are highly correlated (see also [6]). Of the two costs estimated from a glucose limited

state, which is probably most relevant to yeast biology, our absolute cost measure correlates with those

previously described in the literature, confirming previous cost measures and validating our general

approach to estimating biosynthetic cost. Our absolute cost measure, like all previously reported cost

measures (with the exception of Wagner's fermentative measure [5]), points to tryptophan as being the

most expensive amino acid for the cell to produce (Table 1). Tryptophan is considered expensive because

of its complex double ring structure and the number of high energy molecules required for its synthesis and

is (along with methionine) unusual in that it is encoded by only one codon in the genetic code.

In contrast to our absolute cost in glucose limitation, the corresponding relative cost shows little

relationship with any previously described cost metric under the same conditions, and provides a novel

perspective on how to measure the cost of amino acid biosynthesis. Under glucose limitation, relative cost

shows leucine and lysine to be the most expensive amino acids and tryptophan is estimated as one of the

cheapest, in contrast to other previously reported cost measures (see above). Our relative cost measure

reflects the absolute cost of synthesising the amino acid, scaled to its use in the proteome. Therefore

although a tryptophan molecule may be expensive to produce individually, its low usage in the proteome

makes it cheaper to maintain overall at the cellular level. An interesting observation is that carbon limited

relative cost and nitrogen limited relative cost are correlated (Spearman R = 0.63, p = 0.003). We

speculate that this may be a possible selective advantage as any mutations to minimise biosynthetic cost

under carbon limiting conditions would also have an effect to minimise cost under nitrogen limiting

conditions content at the same time, and vice versa.

To test whether absolute or relative cost may have shaped the long-term evolution of yeast genes, we

compared the cost of each amino acid estimated under glucose limitation with their proportional usage in

the genome (Figure 3). It is important to note that our relative costs are estimated using dry weight amino

acid biomass composition in the FBA model, not amino acid usage in the genome, and therefore these two

datasets are not intrinsically correlated. We find a high correlation between relative cost and amino acid

usage in the genome (Spearman R = 0.65, p = 0.0021), but not for absolute cost (Spearman R = -0.37, p

=0.1053). This result supports the observation that certain amino acids in S. cerevisiae are more likely to

appear in highly expressed proteins noted by Jansen & Gerstein [29], who suggested that this could be

related to their cost of synthesis. An interesting exception to the relationship between glucose limited

relative cost and usage in the genome is that serine does not follow the proportional use versus cost trend.

Serine was also previously identified as an outlier in an analysis of the relationship between cost and rates

of amino acid substitution [30]. We speculate that there are biological reasons why serine may be less

costly than expected relative to other amino acids based on it usage in yeast genes. Serine is involved in

nucleic acid synthesis, as well as that of glycine and cysteine, therefore additional demand for serine may

be buffered by the many pathways to which it is linked. Alternatively, the low cost and the fact that six

codons encode this amino acid may permit serine to be used at relatively high abundance in unconstrained

positions of proteins.

While it is clear that no single measure may fully capture all aspects of the cost of amino acid synthesis, we

believe our systems biology method for computing amino acid cost has a number of advantages over

previous methods. Given a genome-scale FBA model, computationally generated cost measures require no

manual curation and allow cost calculations that are more explicitly replicable. Moreover, use of a

computational model allows costs to be calculated under a variety of nutrient conditions, permitting a

more flexible approach to exploring costs under different cellular and environmental conditions.

Additionally, we believe our approach takes into account the whole cellular state, including all simulated

reactions and metabolites, not just those between substrates and products in amino acid metabolism.

Furthermore, as more information is included in genome scale models, the in silico predictions of amino

acid cost may come to more closely represent their costs in vivo. In particular the inclusion of

thermodynamic constraints in the S. cerevisiae model, as has been done in E. coli [31], would be of

particular relevance when estimating amino acid biosynthetic cost. Possible drawbacks are that a

species-specific FBA model must be available to perform the analysis, though our results shows that

absolute cost of synthesis is conserved across species, while relative requirements may vary. Secondly the

FBA estimated cost of an amino acid may be dependent on the objective function used in the model, for

example do we assume that the S. cerevisiae growth strategy is to maximise biomass, or another function

such as to maximise ATP yield? Work by Schuetz et al. [32] on this problem showed that the biological

relevance of the objective function is dependent on the environment considered. The analysis of the

transcript and proteomic data showed relatively little difference difference depending on the which cost

measure was used. Therefore, we would expect that further detailed objective function investigation would

have little impact on these results. In the analysis of the metabolic data the importance of object function

may be more relevant, as the metabolome will likely very sensitive to changes in the environment. Future

work could therefore address how costs vary between organisms that have evolved and adapted their

proteome to markedly different environmental conditions, with specific analysis of organisms that would

likely have different objective functions given the environment. In addition it may also be interesting to

consider the impact of different flux optima on determining amino acid cost. Of particular relevance to this

is an exhaustive study of flux optima by Reed and Palsson [33] which showed that a significant portion of

network flexibility associated with different optima is observed in energy metabolism, which could point to

variability in amino acid cost dependent on the flux distribution phenotype.

Translational optimisation over cost minimisation

At the transcript and protein levels, our models explain approximately 40% of the the variation in

expression (Table 2). Overall, codon usage bias is the most important factor for explaining variance in gene

expression levels, and the other factors only show a limited impact on model fit. Therefore, of the variance

in gene expression explained by our models, the majority is due to optimisation of the coding sequence for

translation rather than cost minimisation. Nevertheless, we can demonstrate a small effect of amino acid

cost on transcript and protein levels that is independent of codon usage bias (Table 2, Figure 2).

Importantly, the rank ordering of these constraints on gene expression could not be made in previous

studies that used codon usage bias as a proxy for gene expression levels [2]. A secondary role for cost on

gene expression is consistent with the results of Dekel at al. [34] who compared the benefit of increased

enzymatic activity, versus the cost of expressing the protein, in terms of the benefit to growth rate. These

authors showed that the expression of the lac operon attenuated to the optimal concentation given the

environmental lactose concentation, indicating that expression levels are a more significant factor than any

optimisation of a per molecule cost. The small effect of the cost regardless of which cost measure is used in

the model may also be expected, as we have shown that they are all highly correlated, and therefore little

variance occurs between each measure. The exception to this is the relative cost measure under glucose

limited conditions which shows no correlation with previous measures, yet still explains a significant degree

of variation in gene expression levels. This indicates that the physiological maintenance of amino acids in

the the proteome, and not just their absolute cost, is an important factor in considering the cost of gene

expression.

For the analysis of the metabolomic data, the variation in the R

values between models is much greater

than observed at the transcript or protein levels. One possible explanation for this is the reduced number

of data points (N = 184 [20]), compared with the large transcript (N = 36264 [20]) and protein (N =

2204 [28]) data sets used in the previous analyses. In contrast to transcript and protein levels, the model

that explained the greatest variation in free amino acid levels was based on our relative cost measure,

demonstrating the value of this model for interpreting energetic investment at the metabolomic level. This

is of interest as the relative cost relates cost of amino acid synthesis to its usage in the proteome, therefore

highlighting a possible link between the maintenance of a free amino acid levels proportional to their usage

in the genome.

Conclusions

We have conducted a systematic investigation of the hypothesis that the cost of synthesising amino acids

has shaped the evolution of protein primary structure and gene expression in yeast. Our analysis indicates

that cost plays a role, but not as large as might be expected given that a predicted 80% [5] of the cellular

ATP budget is devoted to protein synthesis. Instead our research shows that codon usage bias, and

therefore translational efficiency is a more dominant factor in the evolution of gene expression. We believe

this indicates that the optimisation of translation outweighs any benefits that would be gained from the

use of cheaper amino acids. This is further illustrated by our analysis of the metabolomic data where the

cost measure that shows the greatest explanatory power, is highly correlated with the usage of amino acids

in the proteome.

Materials and Methods

Simulating a genome scale model of metabolism

The S. cerevisiae and E. coli genome scale models are each a matrix detailing the stoichiometry of a set of

metabolic reactions, that is the ratios of metabolites used and produced in each reaction. Each model

matrix S is of size m × n, where m is the total number of metabolites, and n is the total number of

metabolic reactions. The position S

in the matrix gives the coefficient of metabolite i in reaction j. A

positive value indicates the metabolite is produced, while a negative value indicates the metabolite is

consumed. A value of 0 indicates the metabolite does not participate in the reaction.

Flux balance analysis of a genome scale model aims to solve the equation S · v = 0 using linear

programming, where v is a vector of predicted flux distributions, i.e. reaction rates, and therefore is of

length n. Multiple solutions may exist for v, and a biologically relevant reaction is usually optimised, such

as production of biomass, or ATP. Additional constraints may be placed on the model, such that certain

fluxes may not be negative indicating that the reaction may only proceed in the forward direction. Setting

additional constraints on the reactions that move nutrients from the external to the internal of the cell can

also be used the simulate the availability of different nutrients in the environment.

A systems biology approach to estimating the cost of amino acid synthesis

Flux balance analysis was performed using the COBRA toolbox [35] and the lpsolve library [36], running in

the MATLAB environment. The genome scale models used were iND750 for S. cerevisiae [17] and iJR904

for E. coli [18]. Costs between species and environment models were compared by fixing biomass flux to a

constant value. The units used in the model are mmol of reactant per gram of biomass per hour.

For each of the twenty amino acids, which are all included in the biomass reaction, we altered in turn the

requirement of each for the production of biomass, for position S

in stoichiometric matrix where i is the

position of the amino acid, and j is the biomass reaction. This ranged from a 0.0002% increase in

requirement, to a -0.0002% decrease, at 0.0001% intervals. For each perturbation biomass production flux

was fixed at 0.05, and the model solved to maximise one of the four input fluxes glucose, ammonium,

sulphate, and phosphate. The figure 0.05 was choosen as an arbitrary value for biomass flux, as it was

much smaller than the possible magnatude of the intake fluxes (-1000) as to make them unbounded, and as

shown, our results using this value are consistent with previous estimates of amino acid cost. Maximising

uptake flux of a given nutrient is the equivalent of finding the solution with the minimal flux of that

molecule into the cell. The aim of this was to simulate the expense of the amino acid under a given

nutrient limiting environment, but also scaled each cost to the same growth rate. The relative cost for a

given amino acid, under a given nutrient limitation, was then estimated as the slope between amino acid

requirement (x) and the corresponding nutrient uptake flux (U ), at the level of requirement defined in the

model (x

). As the relative cost is estimated from a percentage change in amino requirement, this can be

scaled to an absolute per molecule cost by multiplication of 100/x

. The proofs for this relationship are

shown below. The code used in this analysis is available in the supplementary materials.

Absolute Cost

x 0

= U (x)

Relative Cost

U x

1 +

100

x 0

100

(x)

Determination of transcript, protein, and amino acid characteristics

The Codon Adaptation Index (CAI) for each S. cerevisiae gene was taken from Wall et al. 2005 [37], tRNA

gene number was taken from Akashi [22]. Previously reported amino acid energetic costs were obtained

from Craig & Weber [1], Akashi & Gojobori [2], Wagner [5], and Seligmann [6]. For each gene, the average

tRNA gene number, energetic cost, or atomic cost was computed as the sum of the count or cost over the

encoded protein, divided by the length, excluding stop codons. Prior to analysis, each these variables was

transformed by the natural logarithm, then scaled to have the the same mean and variance. This was to

reduce any over-variation and heteroscedasticity biasing model estimation. Scaling was performed by

subtracting the mean, then dividing by the root mean square for each data set. For the metabolomic data

set, a small constant (0.0001) was added to sulphur content so that this variable could be logged.

Determining explanatory power of factors in transcript, protein, and metabolite data

Multiple regression was used to measure the importance of atomic and energetic cost on transcript and

protein expression using the R statistical computing language [38]. For each data set, a multiple regression

model was fitted. The measured quantities of the transcript, protein, or metabolite was treated as the

response variable, and atomic cost, energetic cost, and the CAI (if applicable) were used as explanatory

variables. Atomic cost consisted of three independent variables: carbon, nitrogen and sulphur content.

Experimental conditions that differed among replicates in the datasets were treated as fixed effects in the

model, and included as interaction terms. Initially, all possible interaction terms were considered and

automated step-wise regression used to remove superfluous interaction terms based on a penalised

log-likelihood score, Akaike's Information Criterion (AIC) [25].

To estimate the importance of each of the equation parameters, the data set was modelled without the

variable in question, and then compared to the model containing all terms, again using AIC. For example,

to estimate the importance of nitrogen in the Castrillo et al. 2007 [20] data set, the data were first

modelled using all factors - environment, dilution rate, CAI, tRNA gene count, energetic cost, nitrogen,

carbon and sulphur content. The importance of nitrogen was then determined by repeating the data

modelling with the same variables, except nitrogen content. The contribution of nitrogen content to

explain the variation in models was then estimated from the difference in the model without nitrogen with

the model containing all terms. This process was performed for all factors in the equation, and then

repeated for all energetic cost estimates as the cost variable in the equation.

Experimental data

Experimental transcriptomic, proteomic and metabolomic data used in this analysis are from Castrillo et

. 2007 [20], and an additional proteomic dataset is from Ghaemmaghami et al. 2003 [28]. Briefly, the

Castrillo et al. 2007 [20] experiments continuously cultured S. cerevisiae using a chemostat under four

nutrient limiting conditions and three (two for protein data) dilution rates, for a total of twelve (eight for

protein) different experimental conditions. The transcript data produced from replicate microarray

analysis of total RNA, which were processed by robust multi-array (RMA) quantile normalisation [39].

Proteomic data was produced using Isotope Tags for Relative and Absolute Quantification (iTRAQ)

LC-MS/MS and standardised relative to a standard pool sample and normalised by median absolute

deviation. Metabolomic data was obtained by GC/TOF-MS, and also normalised using median absolute

deviation, missing values were inferred from replicates in the same conditions.

As the protein data from Castrillo et al. [20] measured up/down regulation of a protein against a

background, which is not suitable as a measure of absolute protein expression levels, we instead used data

from Ghaemmaghami et al. 2003 [28] for our analyses of cost on protein expression. This reasoning was

borne out by the small explanatory power (R

3%) for any cost measure model using the protein data

from Castrillo et al. [20]. Protein expression data from Ghaemmaghami et al. 2003 [28] is based on tandem

affinity purification (TAP) of TAP-tagged S. cerevisiae ORFs. Expression levels for each protein were

determined using antibody-tag based quantification. These data were converted to absolute protein

molecules per cell using a purified E. coli INFA-TAP construct standardised against the range of yeast

TAP tag protein observations.

For the model analysis, metabolite levels were mean averaged in each experimental condition to prevent

pseudo-replication of observations. Protein and metabolite levels were logged then scaled. Transcript levels

were scaled, but not logged as they were logged already in the original processing. The reasons for this are

the same as above, as is the scaling method.

Authors contributions

MDB performed the research. MDB, MR and CMB analysed the data. BP contributed ideas and methods

to the development of the systems biology cost measures. DD and SGO provided supervision. MDB and

CMB wrote the manuscript. All authors read, revised and approved the final manuscript.

Acknowledgements

We thank Nick Gresham, Simon Oliver and Markus Herrgard for help implementing the COBRA toolbox;

Nick Gresham and Adam Huffman for support of the University of Manchester Faculty of Life Sciences

Bioinformatics Beowulf cluster; Evangelos Simeonidis for discussion of flux balance analysis; Leo Zeef, Juan

Castrillo, Pinar Pir and Andy Hayes for helpful discussion of the transcriptomic, proteomic and

metabolomic datasets; and Hans Westerhoff, Sam Griffiths-Jones, Simon Whelan and Laurence Hurst for

their critical comments on this work. This work is funded by NERC Ph.D. studentship

NER/S/R/2005/13609 to MDB, NERC advanced fellowship NE/B500190/1 to DD, NER/T/S/2001/00343

to SGO, and BBSRC grant BB/C008219/1 to SGO, MR, and CMB and others. This is a contribution

from the Manchester Centre for Integrative Systems Biology [40].

References

1. Craig CL, Weber RS: Selection costs of amino acid substitutions in ColE1 and ColIa gene clusters

harbored by Escherichia coli . Mol Biol Evol 1998, 15(6):774776.

2. Akashi H, Gojobori T: Metabolic efficiency and amino acid composition in the proteomes of

Escherichia coli

and Bacillus subtilis. Proc Natl Acad Sci U S A 2002, 99(6):36953700.

3. Heizer EMJ, Raiford DW, Raymer ML, Doom TE, Miller RV, Krane DE: Amino acid cost and codon-usage

biases in 6 prokaryotic genomes: a whole-genome analysis. Mol Biol Evol 2006, 23(9):16701680.

4. Swire J: Selection on synthesis cost affects interprotein amino acid usage in all three domains of

life. J Mol Evol 2007, 64(5):558571.

5. Wagner A: Energy costs constrain the evolution of gene expression. J Exp Zoolog B Mol Dev Evol

2007, 308(3):322324.

6. Seligmann H: Cost-minimization of amino acid usage. J Mol Evol 2003, 56(2):151161.

7. Mazel D, Marli`ere P: Adaptive eradication of methionine and cysteine from cyanobacterial

light-harvesting proteins. Nature 1989, 341(6239):245248.

8. Baudouin-Cornu P, Surdin-Kerjan Y, Marli`ere P, Thomas D: Molecular evolution of protein atomic

composition. Science 2001, 293(5528):297300.

9. Bragg JG, Thomas D, Baudouin-Cornu P: Variation among species in proteomic sulphur content is

related to environmental conditions. Proc Biol Sci 2006, 273(1591):12931300.

10. Varma A, Boesch BW, Palsson BØ: Stoichiometric interpretation of Escherichia coli glucose

catabolism under various oxygenation rates. Appl Environ Microbiol 1993, 59(8):24652473.

11. Fell D: Understanding the control of metabolism. Portland Press 1997.

12. ter Kuile BH, Westerhoff HV: Transcriptome meets metabolome: hierarchical and metabolic

regulation of the glycolytic pathway. FEBS Lett 2001, 500(3):169171.

13. Carlson RP: Metabolic systems cost-benefit analysis for interpreting network structure and

regulation. Bioinformatics 2007, 23(10):12581264.

14. Das S, Ghosh S, Pan A, Dutta C: Compositional variation in bacterial genes and proteins with

potential expression level. FEBS Letters 2005, 579(23):52055210.

15. Bragg JG, Wagner A: Protein carbon content evolves in response to carbon availability and may

influence the fate of duplicated genes. Proc Biol Sci 2007, 274(1613):10631070.

16. Raghava GP, Han JH: Correlation and prediction of gene expression level from amino acid and

dipeptide composition of its protein. BMC Bioinformatics 2005, 6:5959.

17. Duarte NC, Palsson BØ, Fu P: Integrated analysis of metabolic phenotypes in Saccharomyces

cerevisiae

. BMC Genomics 2004, 5:6363.

18. Reed JL, Vo TD, Schilling CH, Palsson BØ: An expanded genome-scale model of Escherichia coli K-12

(iJR904 GSM/GPR). Genome Biol 2003, 4(9).

19. Brauer MJ, Yuan J, Bennett BD, Lu W, Kimball E, Botstein D, Rabinowitz JD: Conservation of the

metabolomic response to starvation across two divergent microbes. Proc Natl Acad Sci U S A 2006,
103(51):1930219307.

20. Castrillo JI, Zeef LA, Hoyle DC, Zhang N, Hayes A, Gardner DC, Cornell MJ, Petty J, Hakes L, Wardleworth

L, Rash B, Brown M, Dunn WB, Broadhurst D, O'Donoghue K, Hester SS, Dunkley TP, Hart SR, Swainston
N, Li P, Gaskell SJ, Paton NW, Lilley KS, Kell DB, Oliver SG: Growth control of the eukaryote cell: a
systems biology study in yeast. J Biol 2007, 6(2):44.

21. Ikemura T: Correlation between the abundance of yeast transfer RNAs and the occurrence of the

respective codons in protein genes. Differences in synonymous codon choice patterns of yeast
and Escherichia coli with reference to the abundance of isoaccepting transfer RNAs. J Mol Biol
1982, 158(4):573597.

22. Akashi H: Translational selection and yeast proteome evolution. Genetics 2003, 164(4):12911303.

23. DeRisi JL, Iyer VR, Brown PO: Exploring the metabolic and genetic control of gene expression on a

genomic scale. Science 1997, 278(5338):680686.

24. Brauer MJ, Saldanha AJ, Dolinski K, Botstein D: Homeostatic adjustment and metabolic remodeling

in glucose-limited yeast cultures. Mol Biol Cell 2005, 16(5):25032517.

25. Akaike H: A new look at the statistical model identification. Automatic Control, IEEE Transactions on

1974, 19(6):716723.

26. Brockmann R, Beyer A, Heinisch JJ, Wilhelm T: Posttranscriptional expression regulation: what

determines translation rates? PLoS Comput Biol 2007, 3(3).

27. Jansen R, Bussemaker HJ, Gerstein M: Revisiting the codon adaptation index from a whole-genome

perspective: analyzing the relationship between gene expression and codon occurrence in yeast
using a variety of models. Nucleic Acids Res 2003, 31(8):22422251.

28. Ghaemmaghami S, Huh WK, Bower K, Howson RW, Belle A, Dephoure N, O'Shea EK, Weissman JS: Global

analysis of protein expression in yeast. Nature 2003, 425(6959):737741.

29. Jansen R, Gerstein M: Analysis of the yeast transcriptome with structural and functional

categories: characterizing highly expressed proteins. Nucl. Acids Res. 2000, 28(6):14811488.

30. Hurst LD, Feil EJ, Rocha EPC: Protein evolution: Causes of trends in amino-acid gain and loss.

Nature

2006, 442(7105):E11E12.

31. Feist AM, Henry CS, Reed JL, Krummenacker M, Joyce AR, Karp PD, Broadbelt LJ, Hatzimanikatis V,

Palsson BØ: A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that
accounts for 1260 ORFs and thermodynamic information. Mol Syst Biol 2007, 3.

32. Schuetz R, Kuepfer L, Sauer U: Systematic evaluation of objective functions for predicting

intracellular fluxes in Escherichia coli. Mol Syst Biol 2007, 3.

33. Reed JL, Palsson B Genome-scale in silico models of E. coli have multiple equivalent phenotypic

states: assessment of correlated reaction subsets that comprise network states. Genome Res 2004,
14(9):17971805.

34. Dekel E, Alon U: Optimality and evolutionary tuning of the expression level of a protein. Nature

2005, 436(7050):588592.

35. Becker SA, Feist AM, Mo ML, Hannum G, Palsson BØ, Herrgard MJ: Quantitative prediction of cellular

metabolism with constraint-based models: the COBRA Toolbox. Nat Protoc 2007, 2(3):727738.

36. lp solve: http://sourceforge.net/projects/lpsolve.

37. Wall DP, Hirsh AE, Fraser HB, Kumm J, Giaever G, Eisen MB, Feldman MW: Functional genomic

analysis of the rates of protein evolution. Proc Natl Acad Sci U S A 2005, 102(15):54835488.

38. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for

Statistical Computing, Vienna, Austria 2006, [http://www.R-project.org]. [ISBN 3-900051-07-0].

39. Bolstad BM, Irizarry RA, Astrand M, Speed TP: A comparison of normalization methods for high

density oligonucleotide array data based on variance and bias. Bioinformatics 2003, 19(2):185193.

40. Manchester Centre For Integrative Systems Biology T: http://www.mcisb.org/.

Figures

Figure 1 - Comparison of amino acid cost estimates.

Amino acid cost estimates are shown as barcharts on the left hand side. Each barchart axis shows the

minimum and maximum value of each cost type, rounded to three significant figures. The correlations

between costs are compared in a dendrogram on the righthand side computed by complete agglomerative

clustering using Spearman's Rank correlation distance between data sets (see Additional File 2).

Figure 2 - Comparison of models and variable explanatory effects for transcript, protein and
metabolite data.

A multiple regression model was fitted to explain transcript, protein and metabolite levels using carbon,

nitrogen, sulphur and cost and CAI codon adaptation index (CAI). Each variable was then removed from

the model and effect on model explanatory power was measured using Akaike's Information Criterion

(AIC). Eight different cost effects described in the text were used as the cost explanatory variable.

Figure 3 - Comparison of absolute and relative cost of amino acid biosynthesis and the percentage use
in the yeast genome.

`Loess' smoothing is used to indicate trend line.

Tables

Table 1 - Predicted amino acid cost estimates

Datasets taken from the literature are indicated with reference. The Akashi & Gojobori [2], Craig & Weber

energy [1], and the two Wagner [5] data sets are based on the curation of the number of high-energy

molecules used during synthesis, where a defined ratio is used to convert them into a single measures:

usually ATP. The Craig & Weber 'steps' measure [1] is based on the number of the number of biosynthetic

steps between central metabolism and the produced amino acid. Molecular weight is in Daltons. Our cost

measures are the slope of the relationship between the amino acid requirement for growth and nutrient

uptake flux.

Amino acid

cere-

visiae
Absolute

cere-

visiae
Relative

Akashi &
Gojobori
(2002)

Craig

Weber
(1998)
Energy

Craig

Weber
(1998)
Steps

Wagner
(2005)
Fermen-
tative

Wagner
(2005)
Respira-
tory

Molecular
Weight

ala

0.00474

0.002174

11.7

12.5

14.5

89.1

arg

0.0132

0.00212

27.3

18.5

20.5

174.2

asn

0.00746

0.000757

14.7

18.5

132.1

asp

0.00586

0.00173

12.7

15.5

133.1

cys

0.0071

0.000047

24.7

24.5

26.5

121.2

gln

0.00874

0.00092

16.3

9.5

10.5

146.2

glu

0.0082

0.00247

15.3

8.5

9.5

147.1

gly

0.0029

0.000845

11.7

14.5

75.1

his

0.01386

0.000918

38.3

155.2

ile

0.01146

0.002205

32.3

131.2

leu

0.01146

0.00339

27.3

131.2

lys

0.01246

0.003562

30.3

18.5

146.2

met

0.01186

0.0006

34.3

18.5

36.5

149.2

phe

0.0174

0.00233

165.2

pro

0.0094

0.00155

20.3

12.5

14.5

115.1

ser

0.00468

0.000865

11.7

14.5

105.1

thr

0.0065

0.001243

18.7

21.5

119.1

trp

0.02264

0.000645

74.3

78.5

75.5

204.2

tyr

0.0168

0.001715

56.5

181.2

val

0.00908

0.0024

23.3

117.2

Table 2 - Adjusted R

coefficients for multiple regression models

The R

describes the fit of the model with tRNA gene count, and all atomic, and energetic factors to

experimental data. CAI is also included in the model for transcript and protein data. Each row represents

the specific cost factor used in that model.

Cost type

Castrillo

2007 Tran-

scripts

Ghaemmaghami
et al

. 2003 Pro-

teins

Castrillo et al.
2007

Metabo-

lites

S. cerevisiae

Absolute

0.389

0.406

0.782

S. cerevisiae

Relative

0.383

0.408

0.875

Akashi & Gojobori (2002)

0.398

0.405

0.805

Craig & Weber (1998) Energy

0.416

0.40

0.835

Craig & Weber (1998) Steps

0.375

0.404

0.866

Wagner (2005) Respiratory

0.382

0.405

0.822

Wagner (2005) Fermentative

0.377

0.407

0.851

Molecular Weight

0.422

0.405

0.767

Additional Files

Additional file 1 -- Amino acid costs

Amino acid cost data sets used in the analysis.

Additional file 2 -- Amino acid cost correlations

Spearman's rank correlations between cost data sets.

Additional file 3 - Comparison of the genome scale model derived cost data sets.

Comparison of estimated amino acid cost with number of ATP and NADPH molecules used in synthesis

(left), and molecular weight (right). On the y axis are the amino acid costs estimated using flux balance

analysis. Both S. cerevisiae and E. coli measures are included to illustrate correlation of cost estimates

between species. Estimated cost values have been been rescaled around their mean value to allow

comparisons across species. The trends in each plot are drawn using `loess' smoothing.

Additional file 4 -- Tablulated transcript data set

The transcript data from Castrillo et al. 2007 tabulated with cost, atomic composition, tRNA gene number

and CAI.

Additional file 5 -- Tabulated protein data set

The protein data from Ghaemmaghami et al. 2003 tabulated with cost, atomic composition, tRNA gene

number and CAI

Additional file 6 -- Tabulated metabolite data set

The metabolite data from Castrillo et al. 2007 tabulated with cost, atomic composition, and tRNA gene

number.

Additional file 7 -- Matlab code to estimate amino acid cost

The Matlab and COBRA [35] code used to estimate amino acid cost in this analysis.