Synthetic Lethality between Gene Defects Affecting a Single Non-essential Molecular Pathway with Reversible Steps

Systematic analysis of synthetic lethality (SL) constitutes a critical tool for systems biology to decipher molecular pathways. The most accepted mechanistic explanation of SL is that the two genes function in parallel, mutually compensatory pathways, known as between-pathway SL. However, recent genome-wide analyses in yeast identified a significant number of within-pathway negative genetic interactions. The molecular mechanisms leading to within-pathway SL are not fully understood. Here, we propose a novel mechanism leading to within-pathway SL involving two genes functioning in a single non-essential pathway. This type of SL termed within-reversible-pathway SL involves reversible pathway steps, catalyzed by different enzymes in the forward and backward directions, and kinetic trapping of a potentially toxic intermediate. Experimental data with recombinational DNA repair genes validate the concept. Mathematical modeling recapitulates the possibility of kinetic trapping and revealed the potential contributions of synthetic, dosage-lethal interactions in such a genetic system as well as the possibility of within-pathway positive masking interactions. Analysis of yeast gene interaction and pathway data suggests broad applicability of this novel concept. These observations extend the canonical interpretation of synthetic-lethal or synthetic-sick interactions with direct implications to reconstruct molecular pathways and improve therapeutic approaches to diseases such as cancer.


TABLE OF CONTENTS
Section S1 Page 16 Section S2 Page 21 Section S3 Page 27 Section S4 Page 29 Table S1 Page 31  cerevisiae and humans catalyzing individual steps in the forward (green shaded) and backwards (red shaded) reactions are indicated. The designation of the substrate, intermediates, and products, as well as reaction steps (k 1 , k -1 , k 2 , k -2 , k 3 ) relating to the models in Figures 3, 4, 6, and Figure S2 in Text S1 are indicated in light blue with grey shading. It is presently unclear, which of the intermediates in the srs2 rad54 double mutant, Rad51-ssDNA filament or D-loops or both, are toxic but this has no effect on the present discussion. The reversion of extended D-loops channels recombination events to synthesis-dependent strand annealing (not depicted in Figure S1 in Text S1). In this case, the displaced invading strand anneals with the second end of the DSB to always generate non-crossover outcomes. DSBs can also be repaired by non-homologous endjoining (NHEJ) or single-strand annealing (SSA), whereas replication gaps could be processed by translesion synthesis (TLS) or fork regression (FR). These compensatory pathways are labeled as k 3 in the modeling diagrams.  Figure S1 in Text S1 that enables kinetic proof-reading. In this case the repair product P is irreversibly transformed to the final repaired state R. The scheme represents a simplified version of the pathway depicted in Figure S1 in Text S1 using the same abbreviations. The difference between two models of homologous recombination DNA repair presented in Figure 3 and S2 is the presence of an irreversible step to a final repaired product in the latter. In the case of DNA repair, this might be justified: the enzymes regulating the backward reactions should not be able to cause DNA damage. However, in other contexts, the relevance of a last irreversible step might be less obvious (see Discussion and Figure 8). The presence of a last irreversible step modifies several but not all cell fates in Figure 6 (verified by comparing numerical simulations for the two models and varying the parameter k 4 ). First, the normal wildtype models are not affected. Second, the bpSL and wrpSL scenario are not affected. Those genetic scenarios whose cell fates can be reversed in the presence of the last irreversible step are shown as hexagons in Figure S4A in Text S1 and indicated in Figure S4B in Text S1. In these cases, the effect of timing starts playing the most crucial role and the simple analysis of only steady state values is not sufficient. At a short time scale, the dynamics of the two models can be practically indistinguishable, while being very different at longer time scales (see above). In particular, this is the case for scenario 8 (F2↓) and scenario 13 of Figure 6 (F2↓F1↑) (see also Figure S4 in Text S1). Thus, for making predictions from these simulations, one needs to estimate more precisely the T dam and T tox delays (time intervals during which the DNA damage and the toxicity can be tolerable) that become crucial parameters in the cell fate decisions. Figure S4. Relationships between wild type, single and double mutant model modifications.
The probability of complete repair of DNA damage can serve as a measure of fitness for the different genetic models. For genetic scenarios affecting two genes the strength of the interaction between knock-outs or overexpression conditions are measured by the deviation from the multiplicative model ε = W ab -W a W b , where W a and W b are the fitness values for single condition (knockout or overexpression) and W ab is the fitness with a knockout and overexpression. A) The nodes correspond to the simulations from Figure 6. The node border style shows viability as defined from the steady state of repaired DNA (value P s , formula (4)). Hexagonal nodes denote those lethal scenarios which can be rescued by the addition of the last irreversible pathway step (see Figure S2 in Text S1).   and CDC14 (FEAR complex phosphatase) [1,2]. Cdc5 Polo kinase is dependent on prior phosphorylation (priming) by other kinases, often cyclin-dependent kinases (CDK), using its Polo domain, a phospho-epitope binding motif, to bind to the primed protein substrate [3]. The phosphatase Cdc14 also functions in cell cycle regulation in conjunction with Cdc5 [4].
Mutations in CDCD14 and CDC5 were shown to have a synthetic negative interaction, an observation not [1] easily explained by a mechanism proposing that Cdc5 and Cdc14 target the same residue for phosphorylation or dephosphorylation. Such a mechanism would predict mutual suppression. The wrpSL mechanism, however, is consistent with the observed negative interaction. Importantly, this system also fulfills a further prediction of wrpSL, in that Cdc14 overexpression shows an alleviating interaction with a cdc5 mutation [2]. This example highlights that wrpSL can also be applied to essential pathways with hypomorphic mutations ( Figure 5).

Mechanism of recombination and single pathway synthetic lethal interactions.
Homologous recombination (HR) is an important mechanism to maintain genome integrity [1].
HR plays a fundamental role in meiosis generating genetic diversity and ensuring accurate chromosome segregation. HR is a central DNA repair pathway of complex DNA damage such as double-stranded breaks (DSB), interstrand crosslinks (ICL), and single-stranded DNA gaps. The stalling or collapse of replication forks requires HR to complete DNA synthesis during S-phase in cycling cells. HR is of particular importance in cancer biology for its dual significance in tumor suppression and cancer therapy [2]. Key HR factors, such as BRCA1, BRCA2, RAD51C, and BLM, have been identified as tumor suppressors (Table S1). Moreover, induction of DNA damage in cancer therapy by ionizing radiation (IR), interstrand crosslinks, topoisomerase inhibitors and alkylating agents leads to DNA damage that are HR substrates.
The key reaction of HR is homology search and DNA strand invasion catalyzed by the Rad51-ssDNA filament ( Figure S1 in Text S1) [1]. In order to assemble Rad51-ssDNA filaments, the DNA damage (DSB or gaps) must be processed to reveal ssDNA of sufficient length. The eukaryotic ssDNA binding protein RPA immediately covers available ssDNA, and mediator proteins such as the Rad51 paralogs Rad55-Rad57 and Rad52 in yeast (Rad51B/C/D, XRCC2/3, BRCA2 in humans) are required for Rad51-ssDNA filament formation. After strand invasion, Rad54 is required to turnover the Rad51-dsDNA product complex to allow access by DNA polymerases to the 3'-end of the invading strand. The ensuing DNA synthesis restores the missing DNA leading to the formation of junction intermediates that require either one of two pathways for processing to repaired end products. One pathway, double Holliday junction dissolution, involves the helicase Sgs1 (human BLM) in association with the type 1A topoisomerase Top3 (human TOPOIIIα) and the specificity factor Rmi1 (human RMI1/2). The second pathway involves cleavage of junction molecules and is defined by the endonuclease Mus81-Mms4 (human MUS81-EME1) [3]. Hence, the recombination pathway bifurcates in this last step into two pathways, one Sgs1/BLM-dependent, the other Mus81-dependent ( Figure S1 in Text S1).
While the above discussion summarizes accurately the forward reactions in the HR pathway, it has become clear that dedicated motor proteins and DNA helicases catalyze specific backwards reactions that either antagonize recombinational repair outright or channel intermediates into specific sub-pathways ( Figure S1 in Text S1). The paradigm for an anti-recombinase is the Saccharomyces cerevisiae Srs2 helicase, which serves to repress recombination [4][5][6].
Biochemical analysis uncovered a satisfying mechanism for anti-recombination by showing that Srs2 dissociates Rad51 from ssDNA [7,8]. Candidates for equivalent activities in humans are FBH1, FANCJ, and RECQ5 [9][10][11]. This identifies the Rad51-ssDNA filament as a reversible intermediate in recombination (Figure S1 in Text S1, corresponds to I in Figure 2). Another reversible intermediate is the D-loop ( Figure S1 in Text S1, corresponds to I in Figure 2), which is formed by the Rad51-ssDNA filament and dissociated by the Mph1 protein [12] and possibly Sgs1 [13][14][15]. In humans, FANCM and RTEL1 exhibit such an activity [16,17]. D-loop reversal is anti-recombinogenic per se. However, reversion of an extended D-loop ( Figure S1 in Text S1 after DNA synthesis from the invading strand) does not prevent recombination, but channels recombination to the synthesis-dependent strand annealing (SDSA) pathway, which always lead to a non-crossover outcome. In fact, mutations in RTEL1 show the expected increase crossover formation during Caenorhabditis elegans meiosis [18]. Thus the extended D-loop could be viewed as a reversible intermediate, but the reaction could equally be a direct forward step to SDSA ( Figure S1 in Text S1, corresponds to P in Figure 2).
Synthetic lethality between various single gene mutations within the recombinational DNA repair pathway has been observed in budding yeast. Of particular interest are cases where the synthetic lethality was demonstrated to be recombination-dependent, meaning the synthetic lethality was suppressed by a third mutation disabling an early stage of the recombination pathway. Examples include the following double mutants: srs2 rad54, mph1 mus81 or mph1 mms4, srs2 sgs1 [19][20][21][22][23][24], and the synthetic lethal interaction between mus81 or mms4 and sgs1 or top3 or rmi1 in yeast [25] with similar observations being reported in Drosophila [26]. The recombination-dependent synthetic lethality involving Sgs1 are more complex, because of the multiple roles of Sgs1-Top3-Rmi1 in DSB repair including DSB resection, joint molecule disruption, and double Holliday junction dissolution ( Figure S1 in Text S1) [27]. Both Mus81-Mms4 and the Sgs1-Top3-Rmi1 complex function in the processing of late recombination intermediates ( Figure S1 in Text S1), the genetic situation resembles within-pathway synthetic lethality involving parallel forward pathways ( Figure 2B2). In this case, the recombination pathway bifurcates into alternate routes of product formation ( Figure S1 in Text S1). The twist is that a complete recombination defect in yeast is not lethal per se, suggesting that toxic intermediates, accumulating in the double mutant, cause lethality. Alternatively, the role of Sgs1 in disrupting joint molecules [13][14][15] could be the cause for the synthetic lethality with mus81 [25], which would conform to the mechanism of within-reversible-pathway synthetic lethality. Likewise, it is unclear which role of Sgs1 leads to its synthetic lethality with Srs2, D-loop disruption or double Holliday junction dissolution. The role of Sgs1 in DSB resection is quite redundant with other helicases and nucleases [28,29], and this function does not appear to limit recombinational repair, as suppression of late defects in for example Rad54, Mus81-Mms4 would have been expected by mutations in Sgs1. where square brackets denote the probability of the corresponding molecular state (a number between 0 and 1). The following system of equations describes the time evolution of the model system:    (1) is

Supplemental
In our interpretation of synthetic interactions, the incomplete knock-down of one of the enzymes then A=0). We will not consider triple mutants in our analysis.
The general solution (3) includes one particular case when the compensatory pathway is much faster than the S → I → P cascade itself. Hence, DNA is repaired practically only through the compensatory pathway. In mathematical terms this corresponds to the case 1 3 k k >> . In our numerical simulations we will consider that the compensatory pathway is relatively slow, hence 3 1 k k >> . This will always be correct except for the F1↓ mutation ( , which should be treated separately. The requirement of a relatively slow compensatory pathway is not essential for most of our conclusions (see the parametric study in Figure 5). In particular, the kinetic trapping mechanism due to inactivation of the second forward reaction (F2) and first backwards reaction (R1) (Figure 3) is always valid, although there could be a kinetic difference in the accumulation of the toxic intermediate.
Let us introduce notations for the relative speed of the compensatory pathway 3 r , forward/backward rate ratios 1 r and 2 r for the reactions 1 and 2, and the ratio of backward rates b r : Then, from (3) From these conditions it follows qualitatively that for cell death from toxicity, three requirements should be satisfied simultaneously: For cell death from unrepaired DNA damage it is enough that .
When the DNA repair pathway functions normally, we assume that both the S → I and I → P reactions are more efficient in the forward direction. In mathematical language, this is formulated

B. Conditions for various cellular fates in the toy model
The five kinetic rates of the model can be grouped into three control parameters, r 1 , r 2 and b r r × 3 , determining the cell viability (see (5) and (6)). Depending on whether they are large or small, the pathway can be found in one of the following states: Normal Robust (state NR), Normal Fragile (state NF), Compensated (state C), death due to DNA Damage (state DD) and Death due to Toxic intermediates (state DT) (Figure 4). The most sensitive parameter is the forward/backward rate ratio for the reaction I↔P, . Since we assume that the compensatory pathway is relatively slow and ). In the normal fragile state NF, one single null mutation disrupting the pathway at the downstream I↔P step (single deletion of F2, Figure 6, row 8 and Figure S4 in Text S1) can lead to lethal consequences. In the normal robust state NR, the cell can resist to disruption of the I↔P step by utilizing the compensatory path and switching to the compensated state C (Figure 6, row 7 and Figure S4 in Text S1).
We define that if in the steady state it is more probable to find the system in the toxic intermediate state than in any other states then it causes cell death due to the toxic stress (state DT). If in the steady state it is more probable to find the systems in the unresolved DNA damage state then cell death is due to DNA damage (state DD). The forward/backward rate ratio ). Let us denote it as mode normal robust (NR). The upper row situation is implemented when these rates are comparable or the first is smaller than the second ( ). This is denoted as normal fragile (NF).
Single gene knock-out or over-expression can change one or two of the ratios 3 2 1 , , r r r , b r (for example, eliminating F1 affects both 1 r and 3 r ). Hence, it corresponds to the change of a cell shown in the Figure 4. As a result, changing cell fate from survival to death by changing the activity of a single enzyme is possible in both the NR and NF states by changing the 2 r ratio. This is possible by either disrupting the downstream forward step ( 0 2 = k , knocking-out F2) or significantly increasing the backward rate (