Uniform direction of change in levels of complex subunits
In an experiment reported by Newman et. al. [24], the abundance of yeast proteins was compared between two states: YEPD (rich), and SD (minimal) by measuring cells' fluorescence due to GFP-tagging of individual proteins. Based on these measurements, Newman et. al. [24] assigned each protein to one of three classes: Rich-State proteins (proteins whose concentration in SD condition is significantly lower than the one in YEPD), Minimal-State proteins (YEPD concentrations are significantly lower than those in SD), and Constant proteins (no significant difference in concentrations observed). Out of about 6,000 yeast proteins, more than 2,000 were classified. 232 proteins are minimal-state, 684 are rich-state, and 1298 are constant. Integration of this data on protein levels with the collection of protein complexes (downloaded from MIPS[28] website, [see Additional file 1]) generates interesting observations.
In the following, we present a number of results relating abundance and noise levels of complex subunits. All of these results are then analyzed in terms of a simple toy-model of complex formation, and are shown to be different manifestations of complex production efficiency.
We first extract the number of complexes with uniform change, i.e., complexes in which all identified proteins belong to the same class. Excluding complexes with three or less identified subunits, 426 complexes are available for analysis (complexes with only few subunits might exhibit uniform change just by chance, masking any real trend. We have verified that our results remain qualitatively the same even when analyzing all complexes). There are 46 uniform change complexes, compared to 14 ± 4 complexes (P-value ≈ 10-15, see Methods) expected when randomly assigning proteins to classes – see Figure 1(a) for a graphical comparison of real and random complex make up [see Additional file 2]. In 26 of these complexes all proteins are constant, in 19 all are rich-state, and in one all are minimal-state (ubiquinol-cytochrome c reductase complex (bc1 complex), which is a component of the mitochondrial inner membrane electron transport chain[29]). Looking at the whole set of complexes, one also observes a clear tendency towards uniformity in direction of change (Figure 1(b)).
Larger decrease in the levels of more abundant proteins
The actual amount by which protein levels change is also of interest. Looking at the difference in protein levels between the SD state and the YEPD state as a function of the steady-state concentration in YEPD state[21] (Figure 2(a)), one clearly sees that the higher the protein levels are, the larger is the decrease in the minimal state, where increase is observed only for those proteins which are scarcely expressed in YEPD. For proteins with higher levels in YEPD, the correlation coefficient between the logarithm of the concentration and (level _yepd level _sd)/level _yepd is r = 0.1, P ≈ 10-4.
Lower noise in components of large complexes
Next, we study role of 'noise', that is, the cell-to-cell variation in protein levels, and its interplay with protein complexes production. Measurements of cell-to-cell variance in protein levels were also reported by Newman et. al. [24]. Noise is measured by the CV (coefficient of variation), the standard deviation of protein levels divided by the average, in percentage. In the absence of correlations between different individual proteins, one would expect the standard deviation to be proportional to the square root of the mean, or CV ∝ N-1/2 × 100%, where N is the average number of copies in a cell. In reality, it was shown[24] that the CV decreases with protein level, but much slower than N-1/2, reflecting the fact that production of multiple copies of a single protein is typically a correlated process.
We first note that proteins participating in a complex have significantly lower noise[30] as compared to other proteins (CV 19.7 vs. 21.5 for complex and non-complex proteins, respectively (in YEPD state). P < 10-14, t-test; [see Additional file 2]). Among the complex proteins, we find that components of large complexes (144 complexes with at least 15 subunits) exhibit a significantly lower noise (CV 18.52 vs. 19.07 ± 0.12, P ≈ 10-5). We note that the large complexes contain proteins of higher concentration compared to what is expected by chance (averaged log-concentration 8.7 vs. 8.57 ± 0.03, P ≈ 10-6), which can partly explain the lowered CV. However, the noise in components of large complexes is even lower than could be expected based on abundance alone (P ≈ 10-4, see Methods). This tendency holds even upon controlling for the large amount of essential proteins found in large complexes (P ≈ 0.003, see Methods [see Additional file 2]).
Lower noise in the least abundant protein in a complex
We then return to all complexes, and focus on the level of the least abundant protein in each complex. First we note that the concentration of these proteins (averaged over all complexes) is 36% higher (1,310 molecules/cell, averaged over all complexes with at least 4 identified subunits) than could be expected by chance (960 molecules/cell, P ≈ 10-8; see Methods), or due to the complexes having more similar subunit abundances than random [see Additional file 2]. As a result, the CV of the protein with minimal concentration, which is an indication of the typical possible loss (in percentage) of complexes due to noise in protein synthesis, is lower (20.7%, in comparison to 21.3% ± 0.2%, P ≈ 0.004). In addition, this remains true even when abundance and essentiality are controlled for (P ≈ 0.02, see Methods). In comparison, the protein of highest concentration in a complex does not have CV lower than expected by chance (in fact, it has (non-significantly) higher CV).
Thus, we conclude that for large complexes, as well as for the least abundant protein in each complex, significantly low noise levels are found. In both cases, it is also found that the low noise level is not only due to proteins having high abundance or being more essential than expected by chance.
Complex subunits have similar length
Another aspect of complex organization is revealed by studying protein and mRNA lengths. Recently, the entire yeast transcriptome has been sequenced[31], from which we extracted the full length of the mRNA molecules, UTRs included. We found that the lengths of transcripts that belong to the same complex tend to be more similar than expected by chance. To show this, we calculated the variance of the (logarithm of the) lengths (5' untranslated region length + open reading frame length + 3' untranslated region length) of genes that are subunits in a given complex. We consider again only those complexes with information on at least 4 subunits (there are 467 such complexes). The variance for real complexes is 0.27 (averaged), significantly lower than the randomly expected one (0.33 ± 0.013, P ≈ 10-7). We note that the results holds even if only the UTRs are considered, but the significance is much lower (P ≈ 0.05).
A negative correlation exist between protein abundance and length (see e.g. [32]). Also, proteins of same function tend to have similar length[33]. Thus, one may argue that the similarity between the transcript lengths of complex subunits is due to either their similar abundance or similar function. Therefore, we controlled for both abundance and function when shuffling the complexes [see Additional file 2]. The variance in the complexes randomized with control of abundance and function is indeed somewhat lower than for completely random shuffling (0.31 ± 0.012 vs. 0.33 ± 0.013), but is still significantly higher than that observed in real complexes (0.27, P ≈ 10-5).
Balance of protein translation activity and degradation rate
The concentration of a protein results from a balance between its rate of synthesis (translational activity[27], which, in turn, relates to its mRNA abundance and ribosome occupancy and density) and rate of degradation[26]. To identify the regulation strategies employed to achieve the uniformity in protein levels in a complex, it is interesting to study the relative contribution of each of these two factors.
According to the simplest model for the kinetics of protein synthesis[27], the logarithm of a protein's concentration is the sum of the logarithms of its translational activity and the its half life. Thus, the variance due to each of them can be computed independently. We find that both show lower variance in complexes than expected by chance. However, while the variance of the translational activity is 34% lower than expected (0.47 vs. 0.72 ± 0.03, P < 10-14), the variance of the half life is only 10% lower than expected, and less significant (1.24 vs. 1.38 ± 0.08, P = 0.05). Thus, it seems that the half life plays a less significant role in the regulation for efficient complex synthesis.