Rapid-SL identifies synthetic lethal sentences with an arbitrary cardinality


A number of human pathogenic microorganisms exhibit multidrug resistance, which poses a serious challenge in the era of global healthcare1.2. Most of these species benefit from multiple pathogenicity factors (i.e. production of antigens) and broad drug resistance mechanisms (i.e. antibiotic target mutations). Therefore, disrupting the activity of just a single gene in these microorganisms does not guarantee stopping their growth or the biosynthesis of virulence factors. In addition, targeting the essential responses or genes in some pathogens may lead to a significant increase in biofilm-associated responses. This implies that single essential genes may not be suitable targets for these types of microorganisms3. In contrast, multi-target drugs and combinatorial therapeutics synergistically impress the systematic activities of the microorganisms; hence they have been suggested to be much more potent and show less drug resistance than single targets4.

Computational Systems Biology proposes powerful methods to address biomedical questions (eg, human disease metabolism, identification of potential drug targets) via a multidisciplinary, systems-level study that considers multifaceted interactions among many elements in biological networks5. Constraint-based models (CBMs) are very influential in this regard. These models are successfully employed as operational mathematical representations of genome-scale metabolic models (GEMMs) by imposing the relevant context- and state-specific constraints on genome-scale metabolic network reconstructions (GENREs). CBMs can comprehensively analyze metabolic activities and study the physiological properties of biological systems. Through the use of CBMs, systematic analyzes can be performed by applying the powerful class of computational techniques available in the Constraint-Based Reconstruction and Analysis (COBRA) toolbox6,7,8.

Because in silico studies save significant time and costs, these methods are widely used to identify the various effects of reaction and gene knockouts on the flux distribution of the metabolic networks of interest. These knockout studies can be conducted to identify new drug targets from three perspectives9: (a) Targeting of virulence factors3(b) metabolite-centric targeting10,11,12and (c) target essential responses and genes13,14,15,16,17. The last perspective is known as the most common way to identify potential drug targets and is not limited to the deletion of just one reaction or one gene. Synthetic lethal (SLs) are pairs of nonessential responses or genes that are deleterious to an organism when disrupted simultaneously18. Similarly, as the number of targets increases, higher order (n > 2) synthetic lethal sets can be obtained18.

We should note that although the identification of higher-order synthetic lethal phrases may introduce new targets for the use of different drugs in the design of combinatorial therapeutics, this approach is not common in practice19. However, certainly not intended, this concept may have already been used for many drug combination strategies. An example of this strategy is the combination of daptomycin, cefoperazone and doxycycline to eradicate Borrelia burgdorferiB. by loss of membrane potential and inhibition of energy metabolism, cell wall peptidoglycan synthesis and protein synthesis20. There are other examples in cancer therapy such as the combination of BRAF and EGFR inhibitors potently affecting AKT, MEK and ERK signaling proposed for colon cancer patients with BRAF mutations19. In the cases mentioned, combinatorial therapeutics led to more effective effects compared to monotherapies due to the synergistic effects on different functionalities of the cells.

Two approaches are used to computationally identify SLs: exhaustive search and search space reduction. The exhaustive search is straightforward and has been used in some studies17:21, but applying this approach to identify higher-order SLs, especially when the cardinality of SLs is greater than three, is not feasible due to computational time issues. Based on the available computational resources, we estimated that the required computational time for the exhaustive search would be over 180 days to obtain all quadruple SLs Escherichia coli with iAF126022 GMM. Therefore, other methods are required to handle such problems by reducing the search space. Depending on the proposed criteria used to reduce the search space, some of these methods can only find a fraction of the higher-order SLs18while some other methods aim to find all SLs23,24,25,26,27,28.

One of these methods, called “SL Finder”, performs an optimization-based search for the complete and targeted identification of SLs18. To reduce the search space, this method uses flux coupling analysis29 to include just one of the fully coupled reactions in the knockout list. This approach was used to discover all double and triple SLs and to perform targeted identification of some quadruple and quintuple SLs for iAF1260 GENRE E. coli.

Instead, MCSEnumerator finds intervention strategies by enumerating the elementary modes of the dual network30 of the corresponding metabolic network23. This is a powerful approach, especially for metabolic engineering applications. Further improvements were made to this approach to preserve the generalized framework of MCSEnumerator and to speed up the dual computations24,25,26. MCSEnumerator was applied to find all double to quintuple SLs in iAF126023. However, the computation time for SLs with higher cardinalities increases exponentially, and therefore the search procedure has to be stopped after a predefined number of SLs has been found or a time limit has been reached. Alternatively, in this post, we propose a targeted enumeration algorithm aimed at increasing search efficiency.

Fast-SL is a powerful algorithm that drastically reduces the search space by cleaning up the search space of reactions that are guaranteed not to produce SLs27. Fast-SL calculates a flux distribution that maximizes the growth rate by using a minimum value for the sum of fluxes (({l}_{1})-norm) to identify flux-carrying reactions. In the next step, the algorithm searches only these flow-carrying reactions and their combinations to identify SLs within a reduced search space. The authors reported the identification of 127 new synthetic lethal genes in E. coli, which was not found by SL Finder. Also, Fast-SL outperforms MCSEnumerator by finding the same SLs about four times faster. Fast-SL provided a valuable idea for finding SLs in a reduced search space, but implementing this method has two main disadvantages. First, the authors developed different methods to obtain the SLs with different cardinalities up to quadruple SLs. Therefore, in order to obtain SLs with more than four targets in each set, an entirely new method must be developed for each cardinality. Consequently, following in the footsteps of the implementation in the original Fast-SL, the process becomes extremely complicated and requires labor-intensive work to develop. The second disadvantage is that Fast-SL lacks an organized search method; Therefore, several duplicate cases are explored in the original Fast-SL. This leads to serious problems when searching for SLs with high cardinalities.

Logical transformation of the model (LTM) is another technique used in this field. This method changes the stoichiometry matrix (i.e. the S-matrix) by adding pseudometabolites and reactions to account for the gene-protein-response associations (GPRs).28. However, the LTM method increases the size of the S-matrix, which in turn increases the problem size. Therefore, more linear programming problems (LPs) need to be solved to find SLs. Therefore, this method becomes extremely time consuming to perform knockouts on higher order SLs.

As mentioned earlier, drug resistance is a major concern and identifying new drug targets based on the concept of synthetic lethality may be an appropriate solution to this problem. However, a comparison of the effects of the different synthetic lethal sets on the metabolic network and its functionalities shows that some of the sets with higher cardinalities can have stronger and deeper effects on the network. For example, we can divide the synthetic lethal sets into two types: (a) SLs that produce auxotrophic strains, and (b) SLs that produce strains that lack essential functionalities. The first type of SLs results in strains that are able to restore growth when the missing nutrients are supplied. In contrast, the strains obtained in the second group cannot restore their growth even if additional components are provided in the growth medium. We expect the second group of SLs to work more effectively and allow us to target targets that pathogens have a harder time resisting. Based on our in silico observations, higher order SLs give us more of these more effective SLs.

The purpose of the current work is to develop a comprehensive and simple re-implementation of the Fast-SL algorithm to facilitate the identification of higher-order SLs. We call our implementation Rapid SLwhich involves two main steps that are executed iteratively based on the depth-first search algorithm (DFS).31: (1) identifying the seed space (i.e. reactions with non-zero fluxes) and (2) searching within the seed space to find the solutions. The main difference between this new implementation and the original Fast-SL is the splitting of the search process into multiple branches. This branching allows for an awkward parallelism32 and prevents double case testing. This reduces the search space by around 35-60% compared to Fast-SL. However, in the modern drug discovery process, target identification is typically the first step. Therefore, as in the case of Fast-SL, further analysis of Rapid-SL results as a biological hypothesis is required to arrive at an approved drug.

To examine the performance of the developed method, we compared the results of Rapid-SL and Fast-SL for three microorganisms. We then presented three applications for Rapid-SL that could be effective for targeting higher-order SLs, especially when the cardinality of SLs is greater than four targets. Accordingly, we can: (1) search a specific list of reactions selected in accordance with a biological context, (2) apply graph-based search methods, and (3) selectively enumerate the SLs among the DFS branches. Based on our in silico experiments in the current work, over 9000 eightfold (n = 8) SL reactions were reported E. coliwith iAF1260 GEMM. We hope that the identification of higher-order synthetic lethal sets using efficient tools like Rapid-SL will pave the way for the systematic development of effective combinatorial therapeutics in future studies.


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