The Product neutrality function defining genetic interactions emerges from mechanistic models of cell growth
- Department of Biology, Stanford University, United States
- Department of Biochemistry and Molecular Medicine, University of Montreal, Canada
- Chan Zuckerberg Biohub, United States
Figures
Figure 1
High-throughput gene deletion experiments in budding yeast support a Product neutrality function for double-mutant fitness.
(A) Budding yeast mutant fitness is defined as the colony growth rate relative to that of wild-type cells. Schematic illustration of epistasis in growth rate and of different laws proposed in the literature. λ denotes the growth rate, and W the fitness. (B–D) For each double mutant, we plot the residual of the fitness predicted from the indicated model against the fitness of the fittest of the two separate single mutants (maximum single-mutant fitness). Dots indicate the median for 10 equally spaced bins between 0.5 and 1. (E) Box plots for the distributions of the residuals for the three neutrality functions as a function of the maximum single-mutant fitness. A thick line denotes the median, and boxes denote the 25th and 75th percentiles of the distributions. The data plotted here represents a subset of the entire Synthetic Genetic Array (SGA) dataset, corresponding to the Deletion Mutant Array (DMA) at 30°C.Appendix 1—figures 1 and 2 report results for the other subdatasets.
Figure 2
The Product neutrality function describes interactions between genes associated with two distinct biological processes.
(A) Schematic illustration of the analysis process. We first select two different Gene Ontology (GO) biological processes and extract the double mutants in the Synthetic Genetic Array (SGA) dataset associated with them. Then, we compute the median residual for each pair of biological processes and each neutrality function. (B–D) Median residual for the Minimum, Product, and Additive neutrality functions as a function of the maximum single-mutant fitness. Each line denotes mutations to a different pair of distinct GO biological processes. The majority of biological process pairs closely follow the Product model.
Figure 3
A bacterial growth model partially supports the Product neutrality function.
(A) Schematic of the bacterial growth model by Scott and Hwa. Growth rate is defined by the translation flux, which is itself equal to the metabolic flux. The cell partitions its proteome so as to maximize growth rate. (B) Mutations are modeled such that they affect either of the parameters, separately. Values of and in the mutant are indicated with primes and are sampled from a uniform distribution from 0 to their value in wild-type cells. indicates the corresponding growth rate. The analytical expression of the double-mutant fitness consists of the Product model with a perturbation. (C–E) For each sampled double mutant, we plot the residual of the fitness predicted from the indicated model against the fitness of the fittest of the two separate single mutants (maximum single-mutant fitness). Dots indicate the median for 10 equally spaced bins between 0.5 and 1. (F) Box plots for the distributions of the residuals for the three models and the model in (C) as a function of the maximum single-mutant fitness. A thick line denotes the median, and boxes denote the upper and lower quartiles of the data. The analytical model in (B), named Scott–Hwa and shown in red, is exact.
Figure 4
The Product neutrality function accurately predicts fitness for many pairs of parameters in a more complex cell growth model.
(A) Schematic of the growth model from Weiße et al., 2015. This model includes nutrient intake, metabolism, transcription, and translation. (B) Schematic of the mutational analysis. For each pair of parameters α and β, mutations are modeled such that they affect either of the parameters, separately. Then, the median residual is computed for each neutrality function and they are subsequently reported for every pair of parameters considered. For each parameter pair, we report the mean deviation of the simulated double mutants from (C) the Product neutrality function and (D) the analytical expression of the double-mutant fitness under the Scott–Hwa model. Only parameter pairs corresponding to two different biological processes are considered. Those corresponding to the same process are grayed out. Parameter pairs involving translation () are the ones described best by the Scott–Hwa model, while the others are better described by the Product neutrality function.
Figure 5
Nonlinear kinetics drive deviations from the Product neutrality function in the Weiße model.
(A) A subset of parameter pairs we analyzed follows the Product model very closely. We derived an analytical approximation of the growth rate and the double-mutant fitness for these pairs and found that the deviation from the product law is governed by nonlinear kinetics. (B) In the case of the parameter pair , we show that the deviation from the Product model is driven by the Michaelis–Menten constant associated with transcription (see Supporting Information). (C) Tuning the value of γ impacts how good of an approximation the Product neutrality function is for this and other parameter pairs (see text). This analysis validates the analytical approximation and highlights how nonlinear kinetics, in this case Michaelis–Menten kinetics, can drive deviations from the Product neutrality function.
Appendix 1—figure 1
Double-mutant fitnesses are best described by the Product neutrality function in the Synthetic Genetic Array (SGA) dataset.
Box plots for the distributions of the residuals for the three neutrality functions as a function of the maximum single-mutant fitness. Each plot corresponds to a different subset of the SGA dataset. Namely, they correspond to the first set of query mutants (see Methods) crossed to different types of mutant arrays in different temperature conditions (A) Deletion Mutant Array at 26°C. (B) Temperature Sensitive Array at 26°C. (C) Temperature Sensitive Array at 30°C. Thick line denotes the median, and boxes denote the 25th and 75th percentiles of the distributions. The Product neutrality function models the data consistently better than the others.
Appendix 1—figure 2
Double-mutant fitnesses are best described by the Product neutrality function in the Synthetic Genetic Array (SGA) dataset.
Box plots for the distributions of the residuals for the three neutrality functions as a function of the maximum single-mutant fitness. Each plot corresponds to a different subset of the SGA dataset. Namely, they correspond to the second set of query mutants (DAmP, see Methods) crossed to different types of mutant arrays in different temperature conditions (A) Deletion Mutant Array at 30°C. (B) Temperature Sensitive Array at 26°C. (C) Temperature Sensitive Array at 30°C. Thick line denotes the median, and boxes denote the 25th and 75th percentiles of the distributions. The Product neutrality function models the data consistently better than the others.
Appendix 1—figure 3
Larger deviations from the Product neutrality function characterize gene pairs affecting the same GO biological process.
(A) Schematic illustration of the analysis process for double mutants where both mutations affect the same GO biological process. We first select two different GO biological processes and extract the double mutants in the Synthetic Genetic Array (SGA) dataset associated with them. Then, we compute the median residual for each pair of biological processes and each neutrality function. (B–D) Median residual for the Minimum, Product, and Additive neutrality functions as a function of the maximum single-mutant fitness. Each line denotes mutations to a single GO biological process. We see larger deviations from the Product model than in Figure 2. (E) Histogram of the SGA dataset after extracting pairs affecting either two different (inter) or the same (intra) GO biological process. Large residuals are much more likely when both mutations affect the same GO biological process.
Appendix 1—figure 4
The Scott–Hwa model with no feedback follows a Minimum neutrality function.
Box plots for the distributions of the residuals for the model of Scott–Hwa model with no feedback as a function of the maximum single-mutant fitness. A thick line denotes the median, and boxes denote the upper and lower quartiles of the data. The absence of feedback due to resource competition in the model of Scott–Hwa model with no feedback results in a Minimum neutrality function.
Appendix 1—figure 5
Large deviations from the Product neutrality function characterize beneficial mutations.
Box plots for the distributions of the residuals for the different neutrality functions for beneficial mutations as a function of the minimum single-mutant fitness. Thick lines denote the median, and boxes denote the upper and lower quartiles of the data. Deviations from the Product neutrality function derived in Derivation of the double-mutant fitness can be unbounded.
Appendix 1—figure 6
Eleven parameters exhibit negative impact on growth rate upon mutation in the Weiße model.
Among the initial 21 parameters, 13 were kept as candidates for a mutational analysis. Two of them , associated with the metabolic sector, do not have any impact on growth rate upon mutation, likely because this sector is not limiting for growth in that parameter range. The others have a negative impact upon mutation.
Appendix 1—figure 7
Deviations from the Product neutrality function in the Weiße model are captured by the γ approximation.
Box plots for the distributions of the residuals for all models considered in this paper, for two example parameter pairs (A: , B: ). A thick line denotes the median, and boxes denote the upper and lower quartiles of the data. The Gamma model, in purple, denotes the derivation in Figure 5A. It captures the small deviations from the Product neutrality function.
Appendix 1—figure 8
Tuning γ impacts how good an approximation the Product neutrality function is for multiple parameter pairs in the Weiße model.
The analysis of Figure 5C, illustrating the impact of γ on a single parameter pair () is here extended to other parameter pairs to demonstrate the validity of the mechanistic interpretation. (A) ; (B) ; (C). In all cases, we see that decreasing γ results in better alignment with the Product model.
Tables
Appendix 1—table 1
GO biological processes used in the analysis.
| GO biological process name | GO biological identifier |
|---|---|
| DNA integration | GO:0015074 |
| DNA recombination | GO:0006310 |
| DNA repair | GO:0006281 |
| Ascospore formation | GO:0030437 |
| Cell cycle | GO:0007049 |
| Cell division | GO:0051301 |
| Cell wall organization | GO:0071555 |
| Cellular response to DNA damage stimulus | GO:0006974 |
| Cellular response to oxidative stress | GO:0034599 |
| Chromatin remodeling | GO:0006338 |
| Chromatin silencing at telomere | GO:0006348 |
| Chromosome segregation | GO:0007059 |
| Cytoplasmic translation | GO:0002181 |
| Endocytosis | GO:0006897 |
| Endoplasmic reticulum to Golgi vesicle-mediated transport | GO:0006888 |
| Fungal-type cell wall organization | GO:0031505 |
| Intracellular protein transport | GO:0006886 |
| Intracellular signal transduction | GO:0035556 |
| mRNA splicing, via spliceosome | GO:0000398 |
| Macroautophagy | GO:0016236 |
| Maturation of SSU-rRNA from tricistronic rRNA transcript | GO:0000462 |
| Meiotic cell cycle | GO:0051321 |
| Mitochondrial translation | GO:0032543 |
| Negative regulation of transcription by RNA polymerase II | GO:0000122 |
| Positive regulation of transcription by RNA polymerase II | GO:0045944 |
| Proteasome-mediated ubiquitin-dependent protein catabolic process | GO:0043161 |
| Protein folding | GO:0006457 |
| Protein import into nucleus | GO:0006606 |
| Protein phosphorylation | GO:0006468 |
| Protein targeting to vacuole | GO:0006623 |
| Protein transport | GO:0015031 |
| Protein ubiquitination | GO:0016567 |
| Pseudohyphal growth | GO:0007124 |
| rRNA methylation | GO:0031167 |
| rRNA processing | GO:0006364 |
| Reciprocal meiotic recombination | GO:0007131 |
| Regulation of transcription by RNA polymerase II | GO:0006357 |
| Regulation of transcription, DNA-templated | GO:0006355 |
| Ribosomal large subunit biogenesis | GO:0042273 |
| Sporulation resulting in formation of a cellular spore | GO:0030435 |
| Transcription by RNA polymerase II | GO:0006366 |
| Transcription elongation from RNA polymerase II promoter | GO:0006368 |
| Translational termination | GO:0006415 |
| Transmembrane transport | GO:0055085 |
| Transposition, RNA-mediated | GO:0032197 |
| Ubiquitin-dependent protein catabolic process | GO:0006511 |
| Vesicle-mediated transport | GO:0016192 |
Appendix 1—table 2
Model parameters from Weiße et al., 2015, obtained either from the literature or from parameter optimization.
| Description | Default value | Unit | |
|---|---|---|---|
| External nutrient | 104 | [molecs] | |
| mRNA-degradation rate | 0.1 | [min−1] | |
| Nutrient efficiency | 0.5 | None | |
| Ribosome length | 7459 | [aa/molecs] | |
| Length of non-ribosomal proteins | 300 | [aa/molecs] | |
| Max. transl. elongation rate | 1260 | [aa/min molecs] | |
| Transl. elongation threshold | 7 | [molecs/cell] | |
| Max. nutrient import rate | 726 | [min−1] | |
| Nutrient import threshold | 1000 | [molecs] | |
| Max. enzymatic rate | 5800 | [min−1] | |
| Enzymatic threshold | 1000 | [molecs/cell] | |
| Max. ribosome transcription rate | 930 | [molecs/min cell] | |
| Max. enzyme transcription rate | 4.14 | [molecs/min cell] | |
| Max. q-transcription rate | 948.93 | [molecs/min cell] | |
| Ribosome transcription threshold | 426.87 | [molecs/cell] | |
| Non-ribosomal transcription threshold | 4.38 | [molecs/cell] | |
| q-Autoinhibition threshold | 152,219 | [molecs/cell] | |
| q-Autoinhibition Hill coeff. | 4 | None | |
| mRNA–ribosome binding rate | 1 | [cell/min molecs] | |
| mRNA–ribosome unbinding rate | 1 | [min−1] | |
| Total cell mass | 108 | [aa] |
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The Product neutrality function defining genetic interactions emerges from mechanistic models of cell growth
eLife 14:RP105265.
https://doi.org/10.7554/eLife.105265.3
