Introduction

The close link between growth rate and fitness, coupled with the sensitivity of growth to genetic and environmental perturbations, has made growth rate among the most-studied phenotypes in biology. Studies of growth have provided evidence for the functions of specific genes, when knockouts halt or slow growth in some environmental conditions but not others [1,2], and have uncovered programs of responses to diverse conditions such as nutrient limitation, exposure to antibiotics, heat, or osmotic shock [3-5]. However, most techniques can reliably distinguish growth rate differences only on the order of 10%–20% [3]. Moreover, laboratory perturbations generating fitness effects large enough to measure by these techniques may induce a general stress response [6,7] or another response that confounds perturbation-specific effects on growth. More precise growth rate measurements require substantial cell culturing, frequent dilution, high replicate numbers, and many generations of exponential growth. The most precise techniques can distinguish growth rates differences as small as 0.5–1% [2,4,8].

This precision pales in comparison to that of natural selection, which can efficiently distinguish between lineages whose growth rate differs by roughly the inverse of the effective population size, which for many animals exceeds 10⁵ and for microbes can exceed 10⁸. For example, a mutation causing a fitness defect of 0.01% in popular microbial model organisms such as E. coli or budding yeast will be undetectable in the laboratory using any present-day method, but is virtually certain to be evolutionarily lethal to the mutant lineage. Weak selection on traits conferring tiny fitness differences contributes critically to evolutionary variation, underlying widespread phenomena such as codon bias [9] and evolutionary rate differences between genes and genomic regions [10].

To extend the reach of empirical studies into milder fitness regimes will require substantial improvements and, likely, nontraditional approaches. One strategy is exemplified by the recent demonstration of hyper-precise measurements of the mass of single cells [11,12]; such approaches, however, are not well-suited to measuring differences in cell doubling time over large numbers of cells under arbitrary growth conditions, the typical aim of a fitness assay. In this study, we explore a fundamentally different method to quantifying cell growth that extracts instantaneous growth rate from instantaneous gene expression [13].

In budding yeast cultures with growth rate differences of 15% or greater, about a quarter of the genome is expressed in a growth-rate-dependent fashion [6,7]. Indeed, many regulatory responses appearing during cell stresses appear to be a secondary response to slowed growth rather than to any specific stress [6]. Growth-rate differences induced by heat shock or nutrient limitation in both batch and chemostat cultures have been reliably predicted by monitoring expression of these growth-dependent genes [6,13]. We reasoned that such a response to growth would provide an attractive, general signal that could be exploited for inferring smaller growth differences than can presently be measured by cell counting. Here, we probe the sensitivity and generality of this growth-rate prediction technique.

Building on previous efforts [14], we monitor protein abundances rather than transcript abundances. Using relative protein abundance measurements obtained via whole-proteome mass spectrometry, we search for proteins that demonstrate growth-dependent expression in strains with mild (1%) growth defects induced by protein misfolding. The levels of these proteins constitute a proteomic growth-rate “speedometer” that rivals other growth assays in precision, distinguishing growth rate differences of less than half a percent. Proteomic growth quantitation is especially promising given frequent advances in mass spectrometry that allow for greater sensitivity at lower cost [15] and higher throughput [16], while offering the opportunity to study growth-related phenomena that involve only post-transcriptional processes. However, we find that one growth model does not fit all studies. In fact, there is surprisingly little overlap between the growth-predictive proteins we detect and those previously found to be correlated with altered growth rate [6,7,14]. This result suggests that budding yeast’s response to growth rate depends on the growth-altering perturbation. It also offers the possibility that some subtle growth perturbations can be studied free of the confounding influence of a systemic growth-rate response.

Results

All of the growth perturbations we study were induced by intracellular protein misfolding, and have been quantified previously by competitive growth of paired strains in batch culture, monitoring relative cell counts by flow cytometry [4] to extract growth-rate differences (Figure 1A). To monitor relative protein abundance between paired strains—each pair including one unperturbed strain (expressing a wild-type protein) and one growth-perturbed strain (expressing a misfolded variant of the same protein) — we used stable-isotope labeling of amino acids in cell culture (SILAC) [17], and quantified labeled/unlabeled protein ratios in 1:1 mixtures of total protein harvested from these paired strains during exponential growth (Table S1). A total of five pairs of strains are included in this study, including a control pairing in which both strains are uninduced (Table 1).

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Figure 1. Constructing a proteomic growth model.

(A) The average % growth rate difference relative to the ‘wt’ strain in each pair (figure produced using previously published data) [4]. Error bars show +/- one standard deviation. (B) Log relative protein abundance measurements vs. growth rate for 3 example proteins. ‘NDE1’ is repressed in strains with decreased growth rate. ‘RPP2A’ is unresponsive to changing relative growth rates. ‘HSP82’ is induced in strains with decreased growth rate. Colors correspond to strain pairs in (A). Error bars show +/- one standard deviation. (C) Slopes for three example proteins from (B) multiplied by a conversion factor (see Methods S1) to allow direct comparison between our slopes (across relative % growth differences; grey) and slopes found previously (across absolute growth differences; black) [6]. We use unconverted slopes to predict growth differences. Error bars display +/- standard error on the slope.

https://doi.org/10.1371/journal.pone.0075320.g001

To assemble a set of proteins whose levels predict relative growth rate, we regressed relative protein abundance on growth-rate difference (Figure 1B), retained proteins measured across three or more strain pairs, sorted these proteins by goodness-of-fit (R²) values, and used slopes from the best fitting proteins to predict the growth differences between paired strains (Figure 1C). Prediction error, the square root of the sum of the squared deviations between the predicted and measured growth differences across all five strain pairs, sharply increases when we include more than 53 proteins (Figure 2A). Therefore, we use the 53 proteins for which R² ≥ 0.367 to predict growth (Table 2). Previous models use abundance measurements from a comparable number of transcripts (72) to predict growth rate [6,13].

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Figure 2. A proteomic growth model predicts small growth defects induced by protein misfolding.

(A) To select the set of proteins that best correlate with growth, we chose an R² cutoff of 0.367, or 0.371 for a set that excludes UPR-cyto proteins (inset). (B) The predicted growth differences between paired strains, when each pair is held out from the dataset used to calibrate the proteomic growth model, fall within one standard deviation of each experimental measurement [4]. The UPR-cyto excluding model generates similar predictions (inset). Both models’ predictions have smaller standard deviations (vertical error) than growth measurements (horizontal error).

https://doi.org/10.1371/journal.pone.0075320.g002

To test the accuracy of our technique, we repeat the above procedure five times, each time holding out data from one of the strain pairs and predicting the growth rate of the held-out pair only. The predicted growth-rate differences for held-out pairs fall within one standard deviation of each experimental measurement (Figure 2B). This technique’s precision, derived from as few as two replicate measurements per perturbation (Table 1), exceeds that of repeated multi-day measurements of competitive fitness by flow cytometry [4]: for held-out data, the average standard deviation on predictions is 0.24% while the average standard deviation on experimental measurements is 0.41% (Figure 2B).

To further estimate the expected error on our growth rate predictions, we reassembled the set of growth predictive proteins 100 times, each time holding out 30% of the data, regressing relative protein abundance on growth rate for the remaining 70%, sorting these proteins by goodness-of-fit (R²) values, and using the best fitting proteins to predict the growth differences from the held-out data. The average standard deviations over 100 trials range from 0.09–0.14% per paired strain, with an average standard deviation across pairs of 0.12% (Figure S1), smaller than the average standard deviation on the most precise experimental measurements [2,4]. These results indicate that growth rates of greater precision can be extracted from proteomic data than from state-of-the-art competition assays. This technique’s predictions match the measured values to within experimental error (Figure 2B), suggesting they are accurate as well as precise.

Surprisingly, the proteins for which expression best predicts growth in our study are not functionally similar to those found in previous screens for transcriptomic [6,7,14] and proteomic [14] signatures of growth rate. For example, the set of growth-predictive proteins does not include many ribosomal proteins (Table 2; Table S2). Instead, 19 out of 53 growth-predictive proteins are components of the cytosolic unfolded protein response (UPR-cyto) [4,18,19], which is provoked in yeast by low-level protein misfolding (Table 2; Table S2). Additionally, the proteomic response to growth perturbation by intracellular misfolding is of a greater absolute magnitude than expected given previously described growth-rate responses [6,7] (Figure 1C; Figure S2; Table S3). These results suggest that the previously described growth-rate response (GRR) [7] is not the dominant response of cells during the misfolding stimulus, nor the most predictive of the resulting growth differences in this condition. However, the possibility remains that the GRR is not absent, but merely less-predictive than the stimulus-specific response [Hashimoto & Airoldi; ‘A linear model framework for genome-scale functional analysis’; unpublished manuscript]. We performed three additional analyses to test this possibility.

First, we assembled a set of growth-predictive proteins while excluding UPR-cyto proteins [4]. This set consists of 36 proteins (Table S4), accepts proteins with R² > 0.371 (Figure 2A; inset), and is slightly less accurate than the original set at predicting growth rate; 4 of 5 predicted growth-rate differences fall within one standard deviation of each experimental measurement (Figure 2B; inset). This set of growth-predictive proteins also has high precision—the average standard deviation on its predictions is 0.38—but it does not provide substantial evidence of a GRR. Gene ontology analysis demonstrates that functions enriched among GRR proteins (e.g. environmental stress response and ribosome biogenesis) [6,7,14] are not overrepresented among these 36 proteins.

To survey a greater number of proteins that correlate with growth, we performed a likelihood ratio test (LRT), approximating the probability distribution of the log-likelihood ratio statistic using Wilks’ theorem. This LRT is less stringent in that it allows monotonic (rather than strictly linear) relationships with growth, and it includes proteins that are detected in two or more (rather than three or more) strain pairs. Using a P-value cutoff of 0.05, we detected 163 proteins for which abundances covary with growth differences induced by protein misfolding (Table S5). The biological processes overrepresented among these 163 proteins have little overlap with the biological processes that comprise the GRR [7] or the related environmental stress response (ESR) [5] (Table S6).

The 71 proteins that positively covary with growth in this dataset are significantly enriched for aerobic respiration and oxidative metabolism, but these gene functions negatively covary with growth in previous studies where growth was limited by glucose concentration [6,7,14]. This enrichment remains when we repeat LRT while requiring proteins be detected in a minimum of 3 or 4 strain pairs (Tables S7 & S8). Also inconsistent with GRR expectations, ribosome-related functions are not overrepresented among proteins that positively covary with growth.

Of 92 proteins that negatively covary with growth, only 7 (8%) are ESR-induced genes, while previous studies found greater overlap: 116/367 or 32% of growth-repressed transcripts [6] and 34/88 or 39% of growth-repressed proteins [14]. Of the top 50 most strongly growth-repressed, ESR-induced genes from table S1 in Brauer, et al. 2008, only HSP104, a UPR-cyto component, correlates with growth in this analysis.

One possible reason for the failure to detect a GRR or ESR is that expected changes in protein abundance, given the very mild growth perturbations studied here, may be too small to distinguish from experimental error. To determine the expected abundance difference for every protein in each strain pair, we inverted growth rate predictions from previous work in which the GRR was defined. Briefly, we obtained slopes from a linear regression of transcript levels on growth [7] and multiplied each slope by the growth rate difference between paired strains (quantified previously [4]) as well as by a correction factor that converts relative to absolute growth differences (see Methods S1). For any protein, if the resulting estimated difference in abundance is larger than the observed error on our replicate mass spectrometry experiments, we have the power to detect the expected protein-level response to our growth perturbation. Although we are using transcript levels to predict protein levels, multiple groups have measured a generally direct (1:1 on average, despite substantial variation between specific genes) relationship between mRNA and proteins changes [16,20].

In each set of paired strains, less than 65% of the GRR proteins expected to mount a significant response to our growth perturbations do so. Most demonstrate a weaker response than expected, while other proteins respond (some significantly) opposite expectations (Figure 3A). Ribosomal proteins, which on the basis of GRR studies we expect to be down-regulated in slower-growing strains, also fail to show the expected response (Figure 3B). In general, we see a poor fit between our observed protein abundances and the expectations we generated from previous studies [7] (Figure S2).

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Figure 3. Most classes of proteins do not respond to small growth perturbations induced by protein misfolding.

Expected differences in protein abundance levels are inferred from transcript data [7] (A & B) or from our proteomic data when each strain pair is held out (C), while assuming a linear response to growth. Only proteins for which we expect a significant response are plotted (i.e., proteins for which the expected fold change +/- observed error does not include 1.0 with p < 0.05). Fold changes in abundance are shown for the misfolded protein-expressing (growth-perturbed) member of each strain pair relative to the wt-expressing strain, colors represent positive (green) or negative (red) correlations with faster growth, and horizontal lines represent median values. (A) Most GRR proteins do not show the expected response to our growth perturbation. (B) Ribosomal proteins do not significantly or consistently differ in abundance between paired strains, even when the relative growth difference between strains exceeds 3% (YFPm4). (C) UPR-cyto protein abundance levels match expectations. Note that YFPm4 generates a smaller expected median UPR-cyto response despite inducing a larger growth defect because it contains data from only 2 replicate experiments and the most responsive proteins were not sampled.

https://doi.org/10.1371/journal.pone.0075320.g003

However, the observed changes in UPR-cyto protein levels match expectations generated from held-out data (Figure 3C). We calculated the expected abundance change for each UPR-cyto protein in each strain pair by obtaining slopes from regressions of protein level on growth while holding out one strain pair at a time, and multiplying each slope by the growth-rate difference of the held-out pair. Using this linear model to predict protein abundances for held-out data, we were not able to predict changes in abundance for any other group of proteins (Figure S3). Together, the above results demonstrate that cells respond to mild growth rate differences induced by protein misfolding with a perturbation-specific response to growth.

Discussion

Relative protein abundance measurements from strains with small differences in relative growth rates – an order of magnitude smaller than in previous studies [6,13] – reveal a set of proteins that respond linearly to growth defects. By monitoring the levels of these proteins, we can predict the growth rate of cells in batch culture to within a fraction of a percent. The proteomic model that we construct predicts growth with a precision that rivals the best growth quantitation techniques [2,4,8], requires significantly less cell culturing, and is poised to improve as mass spectrometry rapidly becomes more sensitive and higher throughput [15,16].

However, we find that proteomic growth models are not independent of the perturbations that induce growth rate differences. Proteins that predict growth in one study may not exhibit growth dependence in other conditions. This unexpected result suggests that, in yeast, growth rate is not inextricably linked to the levels of any set of proteins (not even ribosomes). The pathways that set the pace of cell division may differ depending on the growth-altering stimulus. For example, perhaps intracellular misfolding slows growth without producing the molecular signals that induce a GRR. Alternatively, it may be that a GRR (or ESR) is only induced after absolute growth drops below a threshold level.

Proteomic growth quantitation provides snapshots of how cellular content changes with tiny growth-rate adjustments. Additionally, proteomic models can estimate growth rate repeatedly over short timescales, detecting differences not only in steady-state growth rate, but also in the time needed to achieve steady-state growth after environmental insult. As technology advances, properly validated proteomic growth models might allow prediction of even smaller growth differences than can be measured using traditional techniques. The ability to study small (yet evolutionarily profound) growth differences grants access to biological regimes that have been obscured by the brutal perturbations often required to produce detectable growth effects. In these regimes, new biology surely awaits.

Materials and Methods

Supporting Information

Acknowledgments

We are grateful to John Neveu for assistance with mass spectrometry, to Daniel L. Hartl, Naomi Ziv, Mark Siegal, and David Gresham for helpful discussions, and to Chris Marx and John Wakeley for providing comments on an earlier version of this manuscript.