Thirty-two codons in FOS and JUN were mutated using NNS primers (S = G or C), that is replacing the wild-type codon by one of 31 or 32 mutant codons (if the wild-type codon ends in A or T, all 32 codons on the primer are mutagenic) able to encode all 20 amino acids plus one stop. Assuming equal representation of all variants, replacing 32 positions by one of 32 codons leads to 1024 combinations. However, because 17/32 codons in wild-type FOS end in G or C, there are 1007 unique variant sequences each present at a frequency of 1/1024 and one wild-type sequence present at a frequency of 17/1024. Similarly, there are 24 codons in wild-type JUN ending in G or C. There are thus 1000 unique variants each present at a frequency of 1/1024 and one wild-type sequence present at a frequency of 24/1024. Consequently, when combined, the resulting library design encodes 1,007,000 unique double codon mutants each present at a frequency of 1/1024², 1007 unique single FOS codon mutants each present at a frequency of 24/1024², 1000 unique single JUN codon mutants each present at a frequency of 17/1024² and one wild-type sequence present at a frequency of 17 × 24/1024². The frequency of double amino acids mutants where both amino acids can be encoded by a single possible codon substitution each is thus equal to the frequency of double codon mutants, that is f_low = 1/1024² = 9.5×10⁻⁷. All the volumes for all reaction and culturing conditions, as well as the number of reads obtained through deep sequencing, were determined to ensure that no amino acid variant would be lost throughout the library construction process, the competition assay, the sequencing libraries preparation and the sequencing itself. Since some amino acids are encoded by a single codon, these frequencies where calculated using the codon as the unit. Additionally, the competition had to be run for a number of generations that had to be not too low, to ensure correct enrichment for strongly interacting variants, but also not too high, to ensure that the weakly interacting variants could still be quantified.

The mutagenic PCR steps caused no bottlenecks because the picomoles of mutagenic primers used in the reactions represented ~1×10¹² molecules. The Gibson assembly was also performed with picomoles of FOS and JUN variants to ensure that inefficient assembly would not create a bottleneck. Following the recommendations of Fowler et al. (2014), we targeted at least 10/f_low ≈ 10⁷ bacterial and yeast transformants. Post-transformation selections (i.e. selection of transformants, before the actual competition) and competitions were performed in 1 L so that there were ~500 cells per variant when inoculating at an OD_600nm of 0.05 (cell density of 10⁷ cells / OD/ mL x 0.05 OD x 1000 mL x f_low ≈ 500). Two cycles of competition from an OD of 0.05 to 1.6 would thus lead to 10 population generations. An estimation of three to four generations of background growth (i.e. where weakly interacting variant grow as fast as strongly interacting variant at the beginning of the competition because of non-depleted cellular resources), leads to six to seven generations of effective competition. Under these settings, a non-functional variant (i.e. a variant that interact so weakly that the cell cannot grow) would decrease in frequency by 1/2⁶ to 1/2⁷ ≈ 64 to 128 fold. A sequencing depth of 100 × 1/f_low ≈ 10⁸ reads per replicate input or output would thus lead to an average of 100 reads per variant in the input and ~1 read per dead variant in the output. A high number of reads is important to limit noise from stochastic sampling during cluster formation on the sequencing flow cell. However, as described below, the six samples libraries were sequenced on a single lane of an Illumina HiSeq 2500 for an average of ~4.1×10⁷ reads per sample, which was found to be enough for good quality data. The culture volume of 1 L also ensures that no bottleneck is created during DNA extraction (cell density of 10⁷ cells / OD/ mL * minimum of 1 OD x 1000 mL x f_low ≈ 10⁴ cells per variants). Finally, we needed to run a large number of PCR reactions per sample for the preparation of sequencing libraries to ensure that the libraries were amplified from enough template molecules. A lower number of template molecules would increase the probability of several reads coming from the same initial PCR template molecule hence biasing the measurement of variant frequency in the population. Targeting 10⁸ reads per sample, we decided to use 20 times more template molecules in the PCR reactions, that is a total of 2 × 10⁹ per sample.

Mutagenic NNS primers were ordered from Sigma-Aldrich. One forward and one reverse primer were designed per codon, with 15 nt upstream and 15 nt downstream of the target codon.

PCR1 template DNA fragments encompassing the whole coding sequences but lacking one or the other universal/flanking primer binding sites were prepared by restriction digestion in order to limit the amplification of wild-type sequences from the template DNA carried over from PCR1 to PCR2 by the two universal primers. All templates were prepared by digesting pGD012 with BsrGI and Cfr10I (FOS 5’ template), BspHI (JUN 5’ template) or BamHI and NheI (FOS and JUN 3’ templates) and gel purified.

Since carried-over templates can still anneal and overlap-extend during PCR2, PCR1 was performed with a low template concentration. Specifically, two PCR reactions were set up per target codon, one using the 5’ template, the reverse mutagenic primer corresponding to the target codon and the 5’ universal primer (OGD145 and OGD138 for FOS and JUN mutagenesis, respectively) and another one using the 3’ template, the forward mutagenic primer corresponding to the target codon and the 3’ universal primer (OGD137 and OGD148, respectively). PCR reactions were performed with Kapa HiFi HotStart DNA polymerase (Kapa Biosystems, Wilmington, Massachusetts) according to manufacturer’s protocol in 25 μL with 0.15 fmol of template DNA and 7.5 pmol of each primer and using a melting temperature of 58˚C and an extension time of 1 min for 15 cycles. This resulted in two PCR fragments per target codon that overlap over 33 bp. The 5’ fragment started 169 or 142 bp upstream of the CYC promoter (for FOS and JUN, respectively) and encompassed the CYC promoter, DHFR fragment, linker and first half of the gene until 15 bp downstream of the target codon. The 3’ fragments started 15 bp upstream of the target codon and encompassed the rest of gene and a fragment of the CYC terminator (the 3’ and 5’ fragments for FOS and JUN, respectively, overlapping over 40 bp for Gibson assembly).

The two overlapping PCR products of each target codon were then pooled together (20 μL each) and purified using QIAEX II beads as follows. 120 μL of QX1 buffer, 1.5 μL of beads and 10 μL of 3 M NaOAc were added to the 40 μL of PCR mix. The mixtures were vortexed, incubated 10 min at room temperature and spun for 2 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R. The beads were washed twice with 100 μL of buffer PE and the DNA fragments were eluted in 30 μL buffer EB after a 45 min room temperature incubation.

The second PCRs were performed with Kapa HiFi HotStart DNA polymerase (Kapa Biosystems, Wilmington, Massachusetts) according to manufacturer’s protocol in 25 μL with 10 μL of the eluted DNA fragments, 7.5 pmol of each universal primer (OGD137-OGD145 or OGD148-OGD138 for FOS and JUN, respectively) and using a melting temperature of 53˚C and an extension time of 1 min 30 s for 15 cycles. 3 μL of the PCR product of each target codon were analyzed on an agarose gel to ensure the correct overlap extension. The concentrations of the PCR products of correct size were estimated by four replicate measurements for each target codon using Quant-iT PicoGreen dsDNA Assay Kit (Life Technologies, Carlsbad, California) according to manufacturer’s protocol and corrected by the intensity ratio of the correct band over the whole well measured on the agarose gel. The 32 PCR products corresponding to the same gene were then pooled at equimolar ratio, resulting in two libraries of mutated PCR products at target codon positions, one for FOS and one for JUN.

The backbone was amplified by PCR using Q5 Hot Start High-Fidelity DNA Polymerase (New England Biolabs, Ipswich, Massachusetts) according to the manufacturer’s protocol in 8 × 50 μL with 2 ng of pGD012 template DNA and 22.5 pmol of each primer (OGD144 and OGD153) per 50 μL reaction and using a melting temperature of 58˚C and an extension time of 2 min 30 s for 24 cycles.

The two mutated PCR product libraries overlapped each other over 40 bp in the CYC terminator. They also each overlapped upstream of the promoter with the backbone over 40 bp. These Gibson assembly junctions were chosen to minimize the effect of indels on protein activity that can result from incorrect assembly. All three DNA fragments were gel purified using the QIAquick gel extraction kit (Qiagen, Netherlands) and dialyzed to remove extra salt using nitrocellulose membranes with 0.025 μm pores (Merck Millipore). The three fragments were assembled by Gibson assembly in 800 μL with 1.2 pmol of backbone fragment and 3 pmol of each of the mutated gene fragments. The master mix was split into 16 × 50 μL reactions and incubated 17 hr at 50˚C. The 16 reactions were then pooled back, purified on column using QIAquick PCR purification kit (Qiagen, Netherlands), eluted in 2 × 30 μL of EB buffer, concentrated down to 29 μL in a speedvac and stored at −20˚C until use.

Test transformations revealed that a 2X dilution gave the highest number of transformants. 5 μL of concentrated DNA assembly were thus diluted with 5 μL of distilled water and transformed in two batches into NEB 10-beta Electrocompetent E. coli as follows. For one batch, four transformations were set up by mixing 1 μL of DNA to 25 μL of competent cells in a 0.1 cm Gene Pulser Cuvette (Bio-Rad, Hercules, California) chilled on ice. The four mixtures were electroporated using a Gene Pulser Xcell (Bio-Rad, Hercules, California) at 2.0 kV, 200 Ω and 25 μF. After each electroporation, the cells were immediately re-suspended in 1 mL SOC medium (provided by the manufacturer) warmed to 37˚C and the cuvettes were rinsed with another 1 mL of the same medium. The four electroporations were then pooled together and incubated for 30 min at 37˚C. After this recovery period, 10 μL were diluted 100 X in the same medium and 10 μL were plated on pre-warmed LB +Amp Petri dishes and incubated for ~16 hr at 37˚C. The remaining ~7.7 mL of cells were added to 200 mL of pre-warmed LB +400 μg/mL in 1L flasks and incubated for ~16 hr at 37˚C under constant agitation at 200 rpm. This resulted in a total of 11.6e6 transformant per batch. Each batch of 200 mL was then split in four 50 mL Falcon tubes, cells were harvested by centrifugation for 15 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R and pellets were stored at −20˚C for later use. One pellet of each batch was then thawed and plasmid DNA was extracted using Qiagen Plasmid Midi Kit. The two batches were then pooled at equimolar ratio to form the plasmid DNA library.

Yeast transformation was performed in triplicates in parallel following a modified version of the protocol found in Melamed et al. (2013). First, a glycerol stock of the BY4742 strain was streaked to single colonies on YPD Petri dishes and incubated at 30˚C for 2 days. For each replicate, a whole colony was resuspended in 25 mL YPDA and grown overnight to saturation at 30˚C under constant agitation at 200 rpm. The next day, three flasks of 700 mL of pre-warmed YPDA were inoculated with each of the pre-culture at a starting OD_600nm of 0.125 and incubated at 30˚C under constant agitation at 200 rpm. After 6 hr 30 min of incubation, the cells were harvested by centrifuging 5 min at 3000 g in a Avanti J-26 XP Centrifuge using a JLA 8.1000 rotor (Beckman-Coulter, Brea, California). Cells were washed once with 250 mL sterile distilled water, re-suspended in 25 mL SORB, transferred to 50 mL Falcon tubes and completed to 50 mL with SORB. The cells were harvested by centrifugation 5 min at 3000 g in an Eppendorf Centrifuge 5810 R, re-suspended in 34.3 mL SORB and incubated at room temperature on a wheel for 30 min. Meanwhile, 2.2 mL of 10 mg/mL salmon sperm DNA (Agilent Technologies, Santa Clara, California) were thawed, boiled for 5 min in a heating block and cooled on ice for 2 min. When the cells were ready, 56 μg of plasmid DNA library and 700 μL salmon sperm DNA were added to each replicate and mixed by inverting the tubes six times. Each trans replicate was then split in 4 × 8.75 mL in 50 mL Falcon tubes for a total of 12 tubes, to which 35 mL of plate mixture were added. The Falcon tubes were incubated at room temperature for 30 min on a SSM4 mini seesaw rocker (Stuart Equipment, United Kingdom) at 30 oscillations/min. Then, 3.5 mL of DMSO were added to each tube and mixed in by inverting the tubes six times. The cells were heat-shocked for 20 min at 42˚C in a water bath. To homogenize the temperature faster, the tubes were inverted after 30 s, 1 min, 2 min 30 s, 5 min, 7 min 30 s, 10 min and 15 min. The cells were then harvested by centrifugation for 5 min at 1791 g (3000 rpm) in an Eppendorf Centrifuge 5810 R (Eppendorf, Hamburg, Germany). The supernatant was first poured out of the tubes, the tubes were then quick-spun for 10 s to bring the remaining liquid down, which was then removed by aspiration with a vacuum pump. The cells from each tube were re-suspended in 10 mL of pre-warmed recovery medium. The four tubes of the same replicate were pooled together and added to 1.4 L of pre-warmed recovery medium in 5 L flasks. Recovery medium were incubated for 1 hr at 30˚C under constant agitation at 200 rpm. The cells were then harvested by centrifugation at 3000 g for 5 min in a Avanti J-26 XP Centrifuge using a JLA 8.1000 rotor (Beckman-Coulter, Brea, California), washed once with 200 mL of SC –ura and added to 1.4 L of SC –ura in 5 L flasks. After homogenization by stirring, 10 μL were platted on SC –ura Petri dishes and incubated for ~48 hr at 30˚C to measure transformation efficiency. The liquid cultures were grown to saturation for ~48 hr at 30˚C under constant agitation at 200 rpm. This transformation resulted in 19.88 × 10⁶, 19.32 × 10⁶ and 16.52 × 10⁶ transformants for replicates 1, 2 and 3.

After the first cycle of post-transformation selection, a second selection cycle was performed for each replicate by inoculating 1 L of SC –ura/ade/met at a starting OD_600nm of 0.1 with the saturated culture and growing it to exponential phase (OD_600nm of ~1–1.2) for 12 hr 30 min at 30˚C in 5 L flasks under constant agitation at 200 rpm. To start the first cycle of the competition, the volume of culture necessary to inoculate 1 L of competition medium at an OD_600nm of 0.05 was centrifuged for 5 min at 3,000 g in an Eppendorf Centrifuge 5810 R. Cells were re-suspended in 10 mL of competition medium containing methotrexate and added to 1 L of the same medium and incubated at 30˚C in 5 L flasks under constant agitation at 200 rpm. Meanwhile, the remainder of the cultures were harvested by centrifugation for 5 min at 3,000 g in a Avanti J-26 XP Centrifuge using a JLA 8.1000 rotor (Beckman-Coulter, Brea, California), washed with distilled water, transferred to 50 mL Falcon tubes and the pellets were stored at −20 for later use. After ~20 hr 50 min of growth, the three replicates reached an OD_600nm of 1.57, 1.60 and 1.53 respectively. A second cycle of competition was performed in the same conditions by diluting back the cultures to an OD_600nm of 0.05 in 1L of competition medium. The remainder of the cultures were harvested and stored as described above. After 16 hr of growth, the cultures reached an OD_600nm of 2.66, 2.49 and 2.55, respectively. The whole cultures were harvested and stored as described above.

The cell pellets of the second post-transformation selection cycle (i.e. input population) and second competition cycle (i.e. output population) were first thawed at room temperature, re-suspended in 10 mL of DNA extraction buffer, frozen for 10 min in an ethanol/dry ice bath and thawed for 10 min in a 62 water bath. After an additional freeze/thaw cycle, 10 g of acid-washed, 425–600 μm glass beads (Sigma-Aldrich, St. Louis, Missouri) and 10 mL of Phenol/Chloroform/Isoamyl alcohol 25:24:1 equilibrated in 10 mM Tris-HCl, 1 mM EDTA, pH 8.0 were added to each tube. Cells were lysed by vortexing for 10 min and the aqueous phase containing the total DNA was separated by centrifuging for 20 min at 3,184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Hamburg, Germany). Another extraction was performed by adding 11 mL of Phenol/Chloroform/Isoamyl alcohol 25:24:1 equilibrated in 10 mM Tris-HCl, 1 mM EDTA, pH 8.0, vortexing 2 min and centrifuging 20 min at 3,184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany). The aqueous phase was transferred to a new tube and nucleic acids were precipitated by adding 1/10 vol of 2M NaCl and 2.2 volumes of pre-chilled absolute ethanol and incubating for 30 min at −20˚C. NaCl was used instead of NaOAc to limit SDS precipitation. Nucleic acids were pelleted by centrifugation for 30 min at 3,184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany) pre-chilled at 4˚C. The supernatants were removed and the pellets were put at 37˚C until dry and then re-dissolved in 6 mL of 10 mM Tris-HCl, 1 mM EDTA, pH 8.0. The dissolution was extremely slow, and after an overnight incubation at room temperature, the pellets were still not completely dissolved. The solution was thus centrifuged for 15 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany) to pellet the non-dissolvable material and the supernatants were transferred to new 14 mL Falcon tubes. RNAs were digested by adding 50 μL of RNAseA 10 mg/ml and incubating for 30 min at 37˚C followed by a 2 hr incubation at room temperature. DNA was then extracted by adding 6 mL of Phenol/Chloroform/Isoamyl alcohol 25:24:1 equilibrated in 10 mM Tris-HCl, 1 mM EDTA, pH 8.0. After centrifugation 10 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R, the interphases were still thick and two other Phenol/Chloroform/Isoamyl alcohol 25:24:1 extractions were performed in the same way followed by an extraction with chloroform alone. DNA was precipitated by adding 600 μL of 2M NaCl and 13.2 mL of pre-chilled absolute ethanol and incubating for 20 min at −20˚C and then pelleted by centrifugation 30 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany) pre-chilled at 4˚C. To remove excess salt, 8 mL of 70% ethanol was poured on top of the pellets and incubated for 30 min at room temperature. After centrifugation 30 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany), the supernatant was removed, the tubes were sealed with an air-breathable seal and the pellets were let to dry overnight at room temperature. The next day, the dried DNA pellets were dissolved in 1 mL of 10 mM Tris-HCl, pH 8.0. The three replicates from competition cycle two appeared to be cloudy. To remove the non-dissoluble material, the six samples were centrifuged 5 min at 3184 g (max speed) in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany) and the supernatants were transferred to 1.5 mL Eppendorf tubes (Eppendorf, Germany).

The sequencing libraries were constructed by two consecutive PCR reactions using a method adapted from Levy et al. (2015). The first PCR was designed to amplify the region of interest, that is from directly upstream of the first mutated codon in FOS to directly upstream of the first mutated codon in JUN (the two genes are in head-to-tail orientation). The first PCR also added Unique Molecular Barcodes (UMIs) and the first half of the illumina adapter sequences. A small number of cycles of the first PCR would limit the number of differently barcoded molecules that derive from the same template molecule. The second PCR would then add the remainder of the Illumina adapter sequences.

Plasmid concentrations in the total DNA extractions were first quantified by qPCR using primer pair OGD241-OGD242 that bind in ori region of the plasmid. For each six samples of each of the cis and trans libraries, respectively, 4 and 48 PCRs were performed using Q5 Hot Start High-Fidelity DNA Polymerase (New England Biolabs, Ipswich, Massachusetts) according to manufacturer’s protocol in 50 μL reactions with 4.2 × 10⁷ molecules of plasmid from the DNA extraction, 25 pmol of primers OGD237 and OGD238, and a melting temperature of 66˚C (previously determined by temperature gradient), an extension time of 30 s or 1 min, respectively, for four cycles. A total of 2 × 10⁹ molecules of plasmids were then used to prepare the sequencing libraries from each sample. Excess primers were removed by adding 2 μL of ExoSAP-IT (Affymetrix, Santa Clara, California) and incubating for 20 min at 37˚C followed by an inactivation for 15 min at 80˚C. This step was necessary because these 60 nt primers are not efficiently removed by the following column purification step. The 48 PCRs of each sample of the trans library were then pooled and purified using eight Qiagen PCR purification kit (Qiagen, Netherlands) columns per sample. According to manufacturer’s protocol, one column is able to bind 10 μg of DNA, which corresponds to ~8×10⁸ genomes. Eight columns were then used to ensure that they are not saturated by the genomic DNA carried over from the DNA extraction. The DNA was eluted in 2 × 50 μL of EB buffer (provided by the manufacturer) and pooled for each sample. The eluted DNA was then split into 24 PCR reactions per, which were performed using Kapa HiFi HotStart DNA polymerase (Kapa Biosystems, , Wilmington, Massachusetts) according to manufacturer’s protocol in 50 μL with 15 pmol of illumina adapter primers. The reverse primers carried a different index for each of the six samples of the same library. For this PCR step, Kapa was chosen over Q5 because it was less efficient in the first PCR reactions (higher optimal melting temperature) and thus would lead to a lower re-barcoding of amplicons with new UMIs present on primers from the first PCR reaction that would have been carried over. Each sample was loaded on an agarose gel to check for correct amplification. A strong non-specific band of lower size was observed, which seemed to gradually disappear as the number of cycles in the first PCR was increased. However, increasing the number of cycles would increase the probability of producing amplicons with different UMIs that derived from the same original template molecule. The number of cycles in the first PCR was thus kept to four and the band of correct size was extracted by gel purification from each sample. To this end, the 24 PCRs of each sample were pooled, concentrated on four Qiagen PCR purification kit (Qiagen, Netherlands) columns per sample and each eluted with 2 × 50 μL of EB buffer (provided by the manufacturer). The bands of correct size were then purified on 2% agarose gel starting from 100 μL of each sample using 10 μL QIAEX II beads (Qiagen, Netherlands) according to manufacturer’s protocol and eluted in 20 μL EB buffer. DNA concentration was determined by picogreen in triplicates and the six samples were pooled at equimolar ratio. The pooled sample was sequenced in a single lane of an Illumina HiSeq2500 with 125 bp paired-end reads at the EMBL Genomics Core Facilities in Heidelberg, Germany.

A total of 245,676,608 read pairs were obtained from the lane. However, ~30% corresponded to adaptor sequences and had to be discarded. The high adaptor sequence reads level was probably due to the non-specific PCR amplification during the sequencing library preparation despite the gel purification. Sequencing data was filtered using homemade Perl scripts. Paired reads for which one of the two variable regions had an average Phred score below or equal to 20 were also discarded. Additionally, paired reads were also filtered-out if they had i) one or more non-resolved bases (Ns) in the variable or UMI regions, ii) more than one mutated codon in each gene’s variable region or iii) if the mutated codon ended in an A or T (since these were not encoded by the NNS mutagenic primers). These non-designed substitutions could have occurred during the library construction process before the competition and thus lead to accurate PPI score. However, their low frequency suggested they were more likely to be the results of amplification errors during sequencing library preparations and/or sequencing errors and were thus filtered-out in the interest of stringency and higher quality. These filtering steps resulted in between 1.08 and 1.42 × 10⁷ usable reads per replicate input and output.

To estimate sequencing errors, we measured the per base error probability in the constant region upstream of the variable regions of FOS and JUN that were used as primer annealing sites for library amplification. These sequences should be 100% wild type and any mutations called should be the result of a sequencing error. We estimate the probability of a base to be wrongly called to be 0.0019 for the forward read and 0.0058 for the reverse read, averaged across the six samples (three replicates inputs and outputs). Sequencing errors do not seem to affect the downstream estimate of PPI scores as filtering reads at a Phred score of 30, 35 or additionally filtering out reads where at least one of the called mutations had a Phred score below 30 (>90% of the wrongly called mutations in the constant region had a Phred score below 30 compared to <25% of the correctly called bases) led to PPI scores that were highly correlated to the ones calculated using the above filters (Figure 1—figure supplement 1A).

The frequency of each variant in each sample was then calculated by counting the number of unique UMIs associated to each unique amino acid variant (wild-type (WT), single or double mutant) divided by the total number of unique UMI per variant in the corresponding sample. First, nucleotide sequences were converted to amino acid sequences and the UMIs of different nucleotide variants coding for the same amino acid sequences were summed up. PPI scores were then calculated for each variant according to the formula provided in Figure 1B.

Variants with zero UMI in any of the three outputs were filtered out. Even though variants with lethal mutations could be expected to go to 0, they cannot go further down while their actual frequency in the population is still decreasing (e.g. they could still not be detected even if sequencing 10X or 100X deeper). Their PPI scores thus reach a boundary that is a function of the input UMI count as illustrated in Figure 1—figure supplement 1B. These variants could be misidentified as having intermediate effects or even neutral effects while they are actually lethal. On the contrary, variants with at least one UMI in each replicate output have been consistently detected. Hence, even though the estimate of their PPI score might be associated to a high error due to the stochasticity of low read counts, their actual PPI score should lie within a range around the estimates (e.g. sequencing 10X or 100X deeper would lead to read counts of ~10 or ~100, respectively).

Variants with low input UMIs are also typically associated with a higher error due to stochastic effects. Moreover, these variants are biased toward intermediate or neutral effect due to the PPI score boundary (Figure 1—figure supplement 1B). We thus filtered out variants with less than 10 UMIs in any of the three input replicates. The WT and variants containing stop codons were also excluded from downstream analyses.

In PCA, cells that do not express the DHFR fragments or express protein fusions that do not interact can initially divide for a few generations. This background growth is probably the result of intracellular stores of folate and other metabolites that can be used for growth before they are depleted. To correct for batch effects in this background growth, PPI scores were corrected to align the mode of the detrimental variants (left most mode in the bimodal distribution of PPI scores), which is assumed to correspond to the background growth. This mode was identified in each replicate using the R density function. PPI scores were then aligned to the maximal value of this mode across replicates to avoid the possibility of getting negative values for variants with PPI scores in the left-hand tail of the distribution. This was done according to the following formula, which keeps the WT PPI score as one in all replicates:

where m is the mode in the corresponding replicate and M is the maximal value of the modes across all replicates.

To ensure that growth rate measured by deep sequencing in our assay agree with actual growth rate, we reconstructed 14 variants (one wild-type interaction and 13 single mutants) chosen randomly across the range of PPI scores and measured their growth rate individually in a TECAN plate reader (TECAN, Switzerland). The 14 mutants were constructed individually by OE-PCR in the same way as the large-scale library but using fixed sequence mutagenic primers instead of NNS primers (Supplementary file 5). Each clone was sequence-confirmed and transformed in yeast using a scaled-down version of the transformation protocol used for the large-scale assay.

Two colonies of each variant were grown overnight in 100 μL of SC –ura/ade/met medium at 30C in microtiter plate with constant shaking. The next day, precultures were diluted to an OD_600nm of 1 and 5 uL was added to a final volume of 100 μL of MTX medium in a microtiter plate. Growth curve were measured in a TECAN infinite M200 (TECAN, Switzerland) with OD_600nm measurements every 15 min for 50 hr.

PPI scores were calculated in a similar way than the ones from the large-scale assay. For each variant, the number of doubling was calculated between the beginning of the assay and the time point at which the wild-type interaction reached its maximal growth rate (approximating the point at which cells were harvested in the large-scale assay). The PPI score was then calculated as the number of doublings of a variant relative to the number of doubling of the wild-type.

Thresholds based on the distributions of PPI scores averaged across replicates were used to classify variants as detrimental (PPI score <= 0.64), intermediate (0.64 < PPI scores<=0.96), neutral (0.96 < PPI scores<=1.04) or strengthening (PPI scores > 1.04). Additionally, one sample t-tests were performed to test the difference of the mean PPI score of each variant across replicates from the WT PPI score of 1. False discovery rates were controlled using the Benjamini-Hochberg method as implemented in the R function p.adjust. The p-value threshold to call variants significantly different from WT was set so that the FDR was inferior to 0.05. The robustness of all downstream analyses was analyzed by varying these PPI score thresholds.

Fos and Jun single mutant effects were predicted at each of the 32 mutated positions from amino acid features retrieved from the amino acid index database (Kawashima et al., 2008). Only features without any missing value for the 20 amino acids were considered. PPI score of mutations at each position were predicted with each feature independently using R’s built-in lm function.

The differences in PPI scores between identical mutations at the same position in Fos and Jun were assessed using a paired t-test. False discovery rates were controlled using the Benjamini-Hochberg method as implemented in the R function p.adjust. The enrichment for mutations that had an intermediate effect in either protein was tested using Fisher’s exact test.

Multiplicative genetic interactions were computed as the difference between the PPI scores measured for the double mutant and the multiplicative expectation, that is the product of the PPI scores of the two corresponding single mutants. This was done independently in each of the three replicates, and an average genetic interaction score was calculated for each variant. A one-sample t-test was performed to test whether this average was significantly different from 0. FDRs were computed as follows. In each of 10,000 permutations, the genetic interaction scores were randomized within replicates independently. The one-sample t-test was then performed again. At any given p-value threshold, hits in the permutated data can be considered as false discoveries that are significant just by chance by randomly drawing values from this distribution of genetic interaction scores. At each p-value observed in the original data, the FDR was hence computed in each permutated data set as the number of false discoveries divided by the total number of discoveries in the real data. The standard error of the average FDR was then computed in the same way at each p-value threshold, but was negligible (2.5e⁻⁵ at a FDR of 0.2).

The thermodynamic model was built by fitting the quadratic solution for the dissociation constant, K_D, of the interaction:

with AB being the concentration of the dimeric complex, A_F the concentration of the free form of protein A, B_F the concentration of the free form of protein B, A_T the total concentration of protein A and B_T the total concentration of protein B.

Assuming that the growth rate of a cell expressing a variant is directly proportional to the concentration of protein complex so that

with n being the number of generations during competition. Cells with variants harboring lethal mutations such as stops are still able to grow for a few generations at the beginning of the competition, even in the presence of methotrexate, as highlighted by the mode of the peak of detrimental variants in Figure 3A. This background growth might be allowed before the depletion of intracellular stores of tetrahydrofolate or downstream metabolites. We hence introduced a parameter b to account for background growth. PPI score (PPI) can then be expressed as

Replacing (3) in (1),

With ${\displaystyle K=\frac{b}{A{B}_{wt}}}$, ${\displaystyle X=\frac{\frac{b}{A{B}_{wt}}+\frac{A_T}{A{B}_{wt}}}{\frac{b}{A{B}_{wt}}+1}}$ and ${\displaystyle Y=\frac{\frac{b}{A{B}_{wt}}+\frac{B_T}{A{B}_{wt}}}{\frac{b}{A{B}_{wt}}+1}}$

Equation (4) expresses ΔG (or, more accurately, its approximation in arbitrary units) as a function of PPI scores with the terms ${AB}_{wt}$, $X$, $Y$ and $K$. The smallest of the two terms $X$ and $Y$ represents the maximal PPI score, including background growth, that a variant can achieve when all the molecules of the limiting factor are in complex and assuming no change in total abundance (multiplying both side of the fraction by AB_wt returns back to equation 3 with A_T or B_T replacing AB).

It is more practical to express PPI score as a function of ΔΔG rather than ΔG:

The PPI score of the wild-type is one by definition, and ${AB}_{wt}$ cancels out from the numerator and the denominator, leading to

Rearranging Equation (5),

Equation (6) is a quadratic equation with two solutions but a single relevant solution (the other root would lead to PPI scores higher than the maximum dictated by the free parameters):

According to the null expectation, the ΔΔG of a double mutant d is the sum of the ΔΔG of the two corresponding single mutants s1 and s2 (Horovitz, 1996), such that

Replacing Equation (8) in Equation (7) leads to:

Equation (9) represents the thermodynamic model that predicts the PPI score of the double mutant as a function of the PPI scores of the two corresponding single mutants and has three free parameters$\frac{A_T}{{AB}_{wt}}$, $\frac{B_T}{{AB}_{wt}}$ and$\frac{b}{{AB}_{wt}}$.

The model was fitted to the data with an exhaustive parameter search from 1.1 to 2 with a step of 0.01 for$\frac{A_T}{{AB}_{wt}}$ and $\frac{B_T}{{AB}_{wt}}$ and from 0.3 to 1.2 with a step of 0.001 for $\frac{b}{{AB}_{wt}}$. These intervals were chosen based on the distribution of PPI scores, for example a background growth of > 1.2 would not make sense since it would mean that everything is background growth. As can be seen in Figure 3—figure supplement 2A, it is fair to assume that the optimal fit lies within these intervals. In the cases where one or both single mutants had a PPI score, respectively, below or above the bottom or top asymptotes defined by equation (7) and illustrated on Figure 3D, equation (9) would give infinite or aberrant (negative) values. The corresponding predicted double mutant PPI score was hence set to the minimal and maximal values, respectively, allowed by the function ((${\displaystyle \frac{b}{A{B}_{wt}}}$)/($\frac{b}{{AB}_{wt}}$+1) and min($\frac{A_T}{{AB}_{wt}}$, $\frac{B_T}{{AB}_{wt}}$)/($\frac{b}{{AB}_{wt}}$+1), respectively).

For the trans library alone (first part of the paper), the model was fitted on the three replicates pooled together and the parameter set leading to the lowest percentage of variance explained between the observed and predicted double mutants PPI scores was then chosen. To ensure that the model was not over-fitting, a Monte-Carlo cross-validation was performed as follow. One half of the Fos and Jun single mutants were randomly sampled and the corresponding double mutants were used as a fitting set. The double mutants corresponding to the other halves of the Fos and Jun single mutants constituted the test set, to ensure independency of the two sets. The model was then fitted with an exhaustive parameter search from 1.1 to 1.6 with a step of 0.01 for$\frac{A_T}{{AB}_{wt}}$ and $\frac{B_T}{{AB}_{wt}}$ and from 0.3 to 1 with a step of 0.01 for $\frac{b}{{AB}_{wt}}$. The procedure was repeated 1000 times and the median value of the three fitted free parameters matched the values obtained from fitting the model on the whole dataset, indicating no over-fitting. The median of the proportion of variance explained for the 1000 test sets differed by only 0.001 with a standard error of 1.2 × 10⁻⁴ across the 1000 random samples (Figure 3—figure supplement 2B).

Genetic interaction scores for the three replicate of each double mutant were calculated as the difference between the observed and the predicted PPI scores and averaged across the three replicates. To test whether the genetic interaction scores were significantly different from 0, a one-sample t-test was performed. p-Values were then corrected using a permutation procedure as described above for genetic interactions calculated from the multiplicative model.

Enrichments for cases of either strong positive or strong negative genetic interactions (absolute genetic interaction score > 0.1 and FDR < 0.2) were tested using Fisher’s exact test. FDRs were controlled independently for enrichment in positive and negative genetic interactions and for each feature tested. Significant enrichments or depletions were determined at an FDR of 10%. Distance between mutated positions were measured from the crystal structure (pdb 1fos, [Glover and Harrison, 1995]). The smallest distance between side chain atoms was used. The robustness of these enrichments was tested by repeating this analysis using different absolute genetic interaction score cut-offs.

For the cis library, FOS was mutated by doped oligonucleotide synthesis instead of using NNS mutagenic primers, which would have required an iterative mutagenic process. A doping rate of 2.1% was chosen to maximize the frequency of double nucleotide mutants at 0.274, or 6.66 × 10⁻⁶ for each of the 41,040 double mutants. Accounting for ~ 25% of non-workable, indel-containing sequences, f_low was estimated at ~ 5×10⁻⁶. Using the same rule of thumb than for the trans library, we targeted 10/f_low = 2 × 10⁶ transformants in bacteria and yeast. Selections and competitions were performed in 200 mL in order to have a bottleneck size and a number of generations similar to the trans library during the competition assay (cell density of 10⁷ cells / OD/ mL * 0.05 OD * 200 mL * f_low ≈ 500 cells per variant). However, the six samples (three replicates input and output) were still sequenced on a whole lane, leading to expected increase in coverage per double mutant (~30M reads per library * f_low ≈ 200 reads per sample). A total of 2 × 10⁸ template molecules per sample were targeted for the sequencing library preparation.

The doped oligonucleotide was purchased from TriLink and cloned into pGD012 by Gibson assembly. The backbone fragment was prepared as for the trans library. The upstream FOS fragment and terminator + JUN fragment were amplified by PCR using using Kapa HiFi HotStart DNA polymerase (Kapa Biosystems, Wilmington, Massachusetts) according to the manufacturer’s protocol, each in 4 × 50 μL with 1 ng of pGD012 template DNA and 15 pmol of each primer (OGD145-OGD271 and OGD138-OGD272) per 50 μL reaction and using a melting temperature of 63˚C and 58˚C, respectively, and an extension time of 1 min for 24 cycles. The PCR products of correct sizes were purified on agarose gel using QIAEX II (Qiagen, Netherlands) beads according to manufacturer’s protocol, using 10 μL beads and eluted in 2 × 20 μL of EB buffer. The doped oligonucleotide was prepared by complementary strand synthesis using Q5 Hot Start High-Fidelity DNA Polymerase (New England Biolabs, Ipswich, Massachusetts) according to manufacturer’s protocol with 12 pmol of template doped oligonucleotide and 12.5 pmol of primer OGD270 per 25 μL reaction. A temperature gradient of 12 reactions between 50˚C and 72˚C was first performed to determine the optimal hybdrization temperature, with an extension time of 30 s and 32 cycles to make sure all complementary strands are synthesized. Melting temperature didn’t seem to affect specificity and the double stranded DNA from the first eight reactions were each purified on a lane of an E-gel SizeSelect 2% (Invitrogen, Carlsbad, California), pooled and then concentrated on minElute column (Qiagen, Netherlands) according to manufacturer’s protocol and eluted in 2 × 10 μL EB buffer.

The four fragments were assembled by Gibson assembly in 50 μL with 137.5 fmol of backbone fragment, 343.75 fmol (2.5X) of each of the upstream and downstream fragments and 1.375 pmol (10X) of the double stranded doped oligonucleotide. After a 24 hr incubation at 50˚C, the reaction was dialyzed for 1 hr on nitrocellulose membranes with 0.025 μm pores (Merck Millipore, Burlington, Massachusetts). A single batch of transformation was realized as described for the trans library and pooled for 25 min recovery (to account for the time it takes to do all eight electroporations and ensure cells from the first electroporation didn’t divide yet). After this recovery period, 2 μL were diluted 100 X in the same medium and 100 μL were plated on pre-warmed LB + Amp Petri dishes and incubated for ~16 hr at 37˚C. The remaining ~ 16 mL of cells were added to 400 mL of pre-warmed LB + 400 μg/mL in 1L flasks and incubated for ~16 hr at 37˚C under constant agitation at 200 rpm. This resulted in a total of ~1.75×10⁶ transformants. The cells were harvested and the plasmids were extracted as described for the trans library.

The transformation protocol was further optimized between the transformation of the trans and cis libraries and scaled down for the latter since it is of lower complexity. First, a glycerol stock of the BY4742 strain was streaked to single colonies on YPD Petri dishes and incubated at 30˚C for 2 days. For each replicate, a whole colony was re-suspended in 20 YPDA for the cis and trans libraries, respectively, and grown overnight to saturation at 30˚C under constant agitation at 200 rpm. The next day, three flasks of 175 mL of pre-warmed YPDA were inoculated with each of the pre-culture at a starting OD_600nm of 0.3 and incubated at 30˚C under constant agitation at 200 rpm. After 4 hr of incubation, the cells were harvested by centrifuging for 5 min at 3000 g in an Avanti J-26 XP Centrifuge using a JLA 8.1000 rotor (Beckman-Coulter, Brea, California). Cells were washed once with 50 mL sterile distilled water, re-suspended in 10 mL SORB, transferred to 50 mL Falcon tubes and completed to 25 mL with SORB. The cells were harvested by centrifugation 5 min at 3000 g in an Eppendorf Centrifuge 5810 R (Eppendorf, Germany), re-suspended in 8.6 mL SORB and incubated at room temperature on a wheel for 30 min. Meanwhile, 1.1 mL of 10 mg/mL salmon sperm DNA (Agilent Technologies, Santa Clara, California) were thawed, boiled for 5 min in a heating block and cooled on ice for 2 min. When the cells were ready, 3.5 μg of plasmid DNA library, 175 μL salmon sperm DNA and 35 mL of plate mixture were added to each replicate and mixed by inverting the tubes six times. The Falcon tubes were incubated at room temperature for 30 min on a SSM4 mini seesaw rocker (Stuart Equipment, United Kingdom) at 30 oscillations/min. Then, 3.5 mL of DMSO were added to each tube and mixed in by inverting the tubes six times. The heat-shock procedure was identical as for the trans library. The cells from each tube were re-suspended in 10 mL of pre-warmed recovery medium and added to 350 mL of pre-warmed recovery medium in 1 L flasks. Recovery medium were incubated for 1 hr at 30˚C under constant agitation at 200 rpm. The cells were then harvested by centrifugation at 3000 g for 5 min in a Avanti J-26 XP Centrifuge using a JLA 8.1000 rotor (Beckman-Coulter, Brea, Californi), washed once with 25 mL of SC –ura, respectively, and added to 350 mL of SC –ura in 2 L flasks. After homogenization by stirring, 10 μL were platted on SC –ura Petri dishes and incubated for ~48 hr at 30˚C to measure transformation efficiency. The liquid cultures were grown to saturation for ~48 hr at 30˚C under constant agitation at 200 rpm. This transformation resulted in 1.17 × 10⁷, 9.6 × 10⁶ and 1.09 × 10⁷ transformants for replicates 1, 2 and 3, respectively.

The competition was performed in the same way as for the trans library, except for the following minor changes. The post-transformation selection cycle and the two cycles of competition were performed in 200 mL in 500 mL flasks (the cis library is of lower complexity hence smaller volumes are sufficient). The first cycles of competition were grown to an OD_600nm of 1.585, 1.615 and 1.65 for the three replicates, respectively. The second cycle of competition was inoculated at an OD_600nm of 0.1 and the three replicates were harvested at an OD_600nm of 1.475, 1.59 and 1.49, respectively. Finally, 150 mL of the post-transformation selection and competition cultures were harvested at the end of the cycles for DNA extraction.

The cis library was processed in the same way as the trans library, except for the following minor changes. Because the DNA was extracted from 150 mL instead of 1 L cultures, all the volumes were scaled down by 0.15 X. Cell lysis and the two phenolic extractions were performed the same way. In between the processing of the two different libraries, the protocol was simplified and improved to get rid of the residual SDA and impurities more efficiently. DNA was first precipitated in the same way as previously but using 0.1 volumes of 3 M NaOAc instead of 2 M NaCl. After pelleting and drying overnight, the pellets were re-suspended in 900 μL TE buffer. As for the trans samples, the pellets didn’t re-suspend well and a lot of insoluble material remained. The samples were treated with 7.5 μL RNAseA 10 mg/ml and incubated 30 min at 37˚C. DNA was then purified using 75 μL QIAEX II beads (Qiagen, Netherlands) per sample following the manufacturer’s protocol. DNA was eluted in 2 × 187.5 75 μL after 5-min incubation at 60˚C.

The preparation of the cis library for sequencing was performed the same way as for the trans library, except for the following minor changes. First, only the Fos region was amplified, from directly upstream of the first mutated codon to directly downstream of the last mutated codon. For the first round of PCR, only 4 × 50 μL reactions per sample were performed, with 50 × 10⁶ molecules of plasmid in each reaction and primers OGD277 and OGD278 at a melting temperature of 56˚C and an extension time of 30 s. The four PCRs from the same sample were pooled and purified using 12 μL (6 μg) QIAEX II beads (Qiagen, Netherlands). The eluted DNA was then split into two PCR reactions per sample, which were performed in the same way as for the trans library. The two PCRs of each sample were then pooled but not further concentrated. Relative DNA concentrations were measured as for the trans library but directly from the PCR reactions. The six samples were then pooled at equimolar ratio and the correct band was purified from 100 μL on a 1% agarose gel using 4 μL of QIAEX II beads (Qiagen, Netherlands). The pooled library was sequenced in a single lane of an Illumina HiSeq2500 with 125 bp paired-end reads at the EMBL Genomics Core Facilities in Heidelberg, Germany.

A total of 262,393,254 read pairs were obtained from the lane, with ~ 12% adapter sequences. However, these were not filtered at this step. Paired-end reads, which were overlapping over the full length of the variable region, were assembled using PEAR version 0.9.6 (Zhang et al., 2014) with a p-value threshold for correct assembly of 0.05, a maximum and minimum fragment length of 150 nt, and a minimum overlap size of 100 nt. These parameters force the assembly of sequences of the unique expected length. An average of 30% and 20% of the paired end reads from the three input and output libraries, respectively, were not assembled and filtered out. These included the adapter sequences and indels (resulting from the <100% coupling efficiency inherent to DNA synthesis). Additionally, assembled reads with Ns in any part of the sequence were filtered out. These filtering steps resulted in between 3.0 and 3.7 × 10⁷ usable reads per replicate input and output.

PPI scores were calculated in the same way as for the trans library. However, all amino acid variants with more than two substitutions were filtered out along with amino acid substitution that require more than one nucleotide substitution from the WT sequence. This was required because double amino acids mutants for which one or both of the two mutated codons were more than one nucleotide away from the WT codon had a lower sequencing coverage and were hence less reliable. However, frequencies were calculated accounting for the total number of different UMIs of the corresponding replicate, that is accounting for all the other variants present in the sequenced population including those with more than two mutations. As for the trans library, variants with less than 10 UMIs in any of the three input replicates or without any UMI in any of the three output replicates were filtered out at this step. The WT and variants containing stop codons were also excluded from downstream analyses.

For a fair comparison of mutation effects and genetic interaction patterns between the two libraries, all analyses for the trans library were repeated after filtering out all variants for which the amino acid substitutions require more than one nucleotide change from the WT amino acid.

The mode of detrimental variants was adjusted in the same way as for trans library to correct for batch effects in background growth. The two libraries, that is the cis and the restricted trans, were adjusted to the same value, that is the maximal value of the mode across the three replicates of the two libraries.

Classification was performed using the same cut-offs as for the non-restricted trans library. However, FDR was re-computed for the restricted trans library to take into account the ~8 x decrease in the number of tests.

The differences in double mutants effects and pattern of genetic interactions in the cis and trans libraries can be the result of i) biases in double mutant compositions of the two libraries even after restricting the trans library to amino acid substitutions reachable through single nucleotide changes; ii) differences in single mutant effect distributions, that is combining two Fos single mutants has a different multiplicative and thermodynamic expectation than combining one Fos and one Jun; and iii) differences in structural genetic interactions in cis and trans. To control for the two effects, the two libraries were sub-sampled as follows to match the effects of their single mutant distributions. For each of 1000 sub-samplings, the two libraries were each binned in two dimensions according to the PPI scores of their constituting single mutants. Each dimension was binned into 20 evenly spaced bins from the lowest to the highest single mutants PPI score measured in the two libraries (0.477 and 1.082, respectively). For the cis library, the two single mutants constituting each double mutant were assigned to one or the other dimension randomly in each sub-sampling. For each two-way bin, the double mutants belonging to the library that was the most represented in the bin were randomly sub-sampled to match the number of double mutants belonging to the same bin in the other library. This resulted in identical distributions of single mutants PPI scores according to these binning breaks.

Double mutants from each of the 1000 sub-sampled libraries of matched single mutant effects were classified using the same class definitions as above. The proportions of each class in each library averaged over the 1000 matched sub-samples were reported. The p-value corresponds to the proportion of matched sub-samples where the differences between the two libraries were in the opposite direction than the averages.

The same thermodynamic model as above (Equation 9) was fitted. All fitting procedures were performed after pooling the three replicates in the same model. To test whether the same model with the same parameter would fit both the cis and trans libraries, the model was first fitted on both libraries independently. These libraries were the original ones, that is before matching single mutant distributions (but the restricted trans library). The two fitting procedures converged to similar parameters that had an almost identical predictive power when tested on the other library than the one it was fitted on. To test whether the differences in the distribution of single mutant effects between the two libraries would affect the fitting, this was repeated on the 1000 matched, sub-sampled libraries. This confirmed that the model was robust to and independent of these differences. The parameters and genetic interaction scores used in subsequent analyses were thus the ones from the model fitted on the two libraries pooled together.

Genetic interaction scores were calculated as the difference between the observed double mutants PPI scores and the ones predicted by the thermodynamic model. The significance of genetic interactions was tested using a one-sample t-test. The FDR at each p-value threshold was then calculated independently for the two libraries to account for the differences in the p-value distributions that might be partly the consequences of different levels of noise or technical artifacts in the two libraries. This was performed as explained above using 10,000 permutations.

The proportion of the non-random variance in the double mutants PPI scores explained by the model for each library was calculated first for the original libraries. The proportion of total non-random variance was calculated as the average of the squared Pearson’s correlation coefficients between the double mutant PPI scores of each pair of the three replicates of a given library. The proportion of non-random variance explained by the model was then calculated as the percentage ovariance explained by the model divided by the proportion of total non-random variance.

To test whether this proportion of non-random variance explained by the model is independent of the differences in single mutant effects, this was repeated on 1000 libraries sub-sampled to match their distribution of single mutants effects. The proportion of total non-random variance was recalculated in each sub-sample because they might differ since the double mutant compositions differ. The model was not re-fitted on each sub-sample since it was demonstrated above that this does not vary significantly. The proportion of non-random variance explained by the model was then recalculated and averaged across the 1000 matched sub-samples.

To compare the proportion of structural positive and negative genetic interactions in cis and trans, the same p-value threshold was chosen in the two libraries instead of the same FDR because identical variants with identical effect sizes and identical levels of noise, that is variants that would have identical p-values after the t-test, could otherwise be significant in one but not in the other library due to different FDR adjustments. The average proportion of true cases of genetic interactions was then estimated in each library as the total number of significant cases of either positive or negative genetic interactions multiplied by one minus the average FDR calculated by permutation at any given p-value threshold.

To ensure that the higher prevalence of both positive and negative genetic interactions is not the consequence of different single mutant effect sizes in the two libraries, this analyses was repeated on the 1000 libraries randomly sub-sampled to match their distributions of single mutants effects. In each sub-sample, FDRs were re-computed using 10,000 permutations as explained above. The proportion of both positive and negative genetic interactions was then computed in each sub-sample using the FDR averaged over the 1000 randomizations.

Enrichments for cases of either strong positive or strong negative genetic interactions (absolute genetic interaction score > 0.1 and FDR < 0.2) were tested by Fisher’s exact test as described above for the non-restricted trans library alone. For this analysis, different p-value thresholds leading to the same FDR in the two libraries were used to minimize the differences in noise levels between the two libraries.

• Ben Lehner

• Ben Lehner

• Ben Lehner

• Ben Lehner

• Ben Lehner

• Ben Lehner

• Ben Lehner

• Ben Lehner