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Conceived and designed the experiments: ZX ZH. Performed the experiments: TKW. Analyzed the data: ZX XF TKW ZH. Contributed reagents/materials/analysis tools: ZX ZH. Wrote the paper: ZX XF TKW ZH.
Prevention of the initiation of biofilm formation is the most important step for combating biofilm-associated pathogens, as the ability of pathogens to resist antibiotics is enhanced 10 to 1000 times once biofilms are formed. Genes essential to bacterial growth in the planktonic state are potential targets to treat biofilm-associated pathogens. However, the biofilm formation capability of strains with mutations in these essential genes must be evaluated, since the pathogen might form a biofilm before it is eliminated. In order to address this issue, this work proposes a systems-level approach to quantifying the biofilm formation capability of mutants to determine target genes that are essential for bacterial metabolism in the planktonic state but do not induce biofilm formation in their mutants. The changes of fluxes through the reactions associated with the genes positively related to biofilm formation are used as soft sensors in the flux balance analysis to quantify the trend of biofilm formation upon the mutation of an essential gene. The essential genes whose mutants are predicted not to induce biofilm formation are regarded as gene targets. The proposed approach was applied to identify target genes to treat Pseudomonas aeruginosa infections. It is interesting to find that most essential gene mutants exhibit high potential to induce the biofilm formation while most non-essential gene mutants do not. Critically, we identified four essential genes, lysC, cysH, adk, and galU, that constitute gene targets to treat P. aeruginosa. They have been suggested by existing experimental data as potential drug targets for their crucial role in the survival or virulence of P. aeruginosa. It is also interesting to find that P. aeruginosa tends to survive the essential-gene mutation treatment by mainly enhancing fluxes through 8 metabolic reactions that regulate acetate metabolism, arginine metabolism, and glutamate metabolism.
Biofilms have been frequently associated with human diseases such as osteomyelitis , chronic wound infections ,  and cystic fibrosis , as they facilitate the survival of pathogens in hostile environments. It is reported that nearly 65% of all nosocomial infections in the USA are associated with biofilms . When exposed to stress, such as that imposed by antibiotic treatments or limited nutrients, pathogens adhere to each other to form biofilms for the purpose of survival . The development of biofilms generally comprises the following four stages, i.e., the initial attachment of planktonic pathogens to a surface, the accumulation of biofilms through the production of extracellular polysaccharide substance (EPS) that interconnects and transiently immobilizes biofilm cells, the maturation of biofilm architecture, and the dispersal of single cells from the biofilm . The first few stages play a key role in treating the biofilm-associated pathogens, as the ability of pathogens to resist antibiotics is significantly enhanced once they form biofilms , . Therefore, significant effort in the biofilm research community has been devoted to the investigation of bacterial metabolism and signaling which are involved in the transition from planktonic growth to biofilm growth , .
Elucidating the mechanisms of biofilm formation is far from trivial: hundreds of highly interacted molecules such as metabolites, metabolic enzymes, and signaling proteins are involved in regulating this process. Most current research is focused on the experimental investigation of the impact of individual molecules, such as regulators, on biofilm formation , . This is insufficient for characterizing the biofilm formation process, as a systems-level characterization of interactions between molecules involved in biofilm formation is required to fully understand biofilm formation mechanisms and thus manipulate the metabolism of microorganisms in biofilms. Genome-scale metabolic modeling has been commonly used for systemically studying microorganism metabolism, as evidenced by its wide application in identifying genes that are essential for the growth of Escherichia coli , Staphylococcus aureus , Mycobacterium tuberculosis , Acinetobacter baumannii , and Pseudomonas aeruginosa . A recent study by Thiele and her coworkers  shows the first systems biology approach to identifying candidate drug targets for treating P. aeruginosa in biofilms. This approach mainly applies single/double gene inhibition simulations to determine the growth of P. aeruginosa in specific microenvironments that imitate microbial communities associated with biofilm formation. However, certain issues have not been addressed in this approach, including the quantification of the trend for mutants to form biofilms, and the identification of metabolic reactions that facilitate biofilm formation in mutants. This forms the motivation of this work, that is, to consider the trend of biofilm formation for mutants in the identification of drug-target genes.
Here, we propose an approach to identifying drug targets against a biofilm-forming pathogen, by identifying genes that satisfy two requirements: 1) these genes are crucial for the growth of the pathogen in the planktonic state, that is, the mutation of any of these genes can eliminate the planktonic pathogen; and 2) the inhibition of the function of these genes does not induce biofilm formation.
In particular, we first use the essential planktonic-growth genes presented in Oberhardt et al., 2008  as the initial set of genes satisfying the first requirement, and further, from the initial set, identify genes also satisfying the second requirement. We perform the search by pinpointing a set of biofilm associated reactions from the genes that are reported to be positively related to P. aeruginosa biofilm formation in Müsken et al., 2010 , and using the flux changes through these reactions as soft-sensors to quantify the impact of the mutation of each gene from the initial set on biofilm formation. The rationale for the use of biofilm-associated reactions is that a large enhancement of fluxes (i.e., activity levels) through these reactions reflects a large potential for a mutant to form biofilms. Specifically, to obtain the flux changes through biofilm-associated reactions, we simulate the metabolism of a gene mutant via flux balance analysis (FBA) , and sample the biofilm-associated reaction fluxes via the artificially-center-hit-and-run method (ACHR), an efficient sampling approach for a linearly constrained space . In addition, metabolic reactions whose fluxes significantly increase in most mutants can be determined and regarded as reactions that facilitate biofilm formation. P. aeruginosa is chosen as the reference pathogen in this work, because P. aeruginosa is one of the leading causes of nosocomial infections in hospitalized patients and P. aeruginosa is resistant to a wide array of antibiotics by forming biofilms during chronic infections , .
The key innovation of the proposed approach is to take the biofilm formation of a single mutant into account when identifying gene targets to treat biofilm-associated pathogens. While the detail of the proposed approach is given in the Material and Methods section, an example is shown in Figure 1 to illustrate the steps for the identification of drug targets that impair the growth of P. aeruginosa without inducing biofilm formation. The genes positively associated with biofilm formation (obtained from Müsken et al., 2010  for P. aeruginosa in LB medium) are first overlaid with the P. aeruginosa metabolic network to identify reactions associated with biofilm formation (Figure 1, Step 1). The metabolic model presented in Oberhardt et al., 2008 , which contains 1056 genes and 883 metabolic reactions, is used in this work, as it is the most comprehensive metabolic model for P. aeruginosa and it has been used to correctly predict catabolism of various substrates such as amino acids and common sugars via flux balance analysis. Further, we quantitatively evaluated the impact of the mutation of each essential planktonic-growth gene (obtained from Oberhardt et al., 2008  for P. aeruginosa in LB medium, including the PA1756 gene) on biofilm associated reactions, by calculating relative activity changes of these reactions via Steps 2 and 3. The obtained relative activity change profile quantitatively suggests the capability of a mutant to form biofilms, that is, large values for the changes imply a potential induction of the mutant's biofilm formation. In Step 4, the similarity in the shape and magnitude of relative activity profiles is used to categorize the essential planktonic-growth genes  into different clusters. The clusters of essential planktonic-growth genes whose mutants have low potential to induce biofilm formation are identified as drug-target genes (such as PA1756), because the mutation of these genes can eliminate planktonic pathogens. Metabolic reactions whose activity levels significantly increase in most single mutants are identified in Step 5. These reactions illustrate how P. aeruginosa adjusts its metabolism to form biofilms upon the mutation of genes essential for planktonic growth
A set of biofilm-associated metabolic reactions are obtained via Step 1 in Figure 1. The experimental data of genetic determinants of P. aeruginosa biofilm have been presented in Müsken et al., 2010 . 394 genes are reported to be positively associated with biofilm formation, and 64 of them are involved in the metabolic network. None of these 64 genes are essential for bacterial growth in the planktonic state. Flux balance analysis showed that inhibition of 37 of these 64 genes doesn't affect bacterial growth rate. These genes are thus not directly involved in the bacterial biomass synthesis. Fluxes of reactions associated with these 37 genes are the ideal virtual sensors that monitor the trend of P. aeruginosa to form biofilms, as these genes are only associated with biofilm formation. The 39 reactions associated with these 37 genes are considered as biofilm-associated reactions (see Table 1).
It can be seen from Table 1 that the biofilm-associated reactions are mainly involved in the consumption of nitrite, the regulation of acetate, tricarboxylic acid (TCA) circle, the generation of carbon dioxide and ammonia, iron metabolism, the regulation of hydrogen peroxide, arginine metabolism, the production of glutamate, pyrimidine metabolism, and oxidative phosphorylation. While these reactions were identified by overlaying the 37 genes that are reported to be associated with biofilm formation in Müsken et al., 2010  onto the metabolic network of P. aeruginosa, their important role in biofilm formation is further confirmed by the following independent evidence:
Given the above biofilm-associated reactions, we obtained a relative activity change profile of these reactions for each single mutant of the 136 essential planktonic-growth genes obtained from Oberhardt et al., 2008  (via Steps 2 and 3), and, subsequently, based upon the similarity in relative activity change profiles for different single mutants, went through Step 4 to hierarchically categorize the essential planktonic-growth genes into six different clusters (as shown in Figure 2). Clusters 1 and 2 are located in one branch, while the other four clusters are associated with the other branch. The hierarchical clustering algorithm allows us to further separate genes in each cluster into different groups according to the similarity in their relative activity change profiles. The genes associated with each group shown in Figure 2 are listed in Table 2.
The profiles of relative activity change for the mutants of the representative groups for different clusters are shown in Figure 3. Figure 3 (A) and (B) show the profiles for the mutants of the PA0945 (from Group 1, Cluster 1) and PA5038 genes (from Group 25, Cluster 1), respectively. The profiles of these two mutants are used to represent the whole spectrum of Cluster 1, because, although they are from the two groups (Groups 1 and 25) with the lowest similarity in the cluster, their profiles of relative activity change in Figure 3 (A) and (B) are similar, suggesting that the single mutations of genes in Cluster 1 have similar impacts on biofilm-associated reactions and thus potentially on biofilm formation. Figure 3 (C) through (G) show the relative activity change profiles of representative groups from Clusters 2 through 6, respectively. Since there is only one group (actually one gene per group) associated with each of these clusters, these groups are regarded as the representatives of the corresponding clusters (as shown in Figure 2).
Single mutants of genes from different clusters have different potentials to induce biofilm formation. As shown in Figure 3 (A) and (B), the activity levels of certain biofilm-associated reactions have significant increases upon the mutation of a gene from Cluster 1, suggesting that the gene mutants from Cluster 1 might form biofilms and in turn prevent the elimination of P. aeruginosa. The comparison of Figure 3 (C) to Figure 3 (A) and (B) shows that mutants from Cluster 2 might still form biofilms but to a lesser extent. In particular, the mutant from Cluster 2 (PA4031) and those from Cluster 1 (PA0945 and PA5038) have similar relative activity changes in the biofilm-associated reactions Rxn#1 through Rxn#32, but the mutant from Cluster 2 has much smaller changes in Rxn#33 through Rxn#39 than those from Cluster 1. Interestingly, as shown in Table 2, there are totally 132 essential genes associated with Cluster 1 and Cluster 2, while only the remaining four are from Clusters 3 through 6, suggesting that the mutation of most essential planktonic-growth genes might induce the formation of biofilms. Therefore, not every essential planktonic-growth gene is a good target to treat biofilm-associated pathogens.
The mutation of any gene from Clusters 3 through 6 might not induce biofilm formation, as approximately 96% of the biofilm-associated reactions for these mutants are of small relative activity changes (e.g. most less than 0.5). In addition, the relative activity changes of certain biofilm-associated reactions are reversed and have negative values. Even though the amplitudes of these negative relative fold changes are minor (e.g., most less than 0.5), the metabolic activities are not distributed in the direction for promoting biofilm formation for the mutants from Clusters 3 through 6. Therefore, the four genes in these clusters, i.e., PA0904 (lysC), PA1756 (cysH), PA3686 (adk), and PA2023(galU), are regarded potential gene targets to treat P. aeruginosa, because they are essential to planktonic P. aeruginosa and their mutants might not induce biofilm formation.
Experimental data were collected from the literature to validate the aforementioned prediction results, which shows that the mutants from Clusters 1 and 2 might induce biofilm formation while the mutants from Clusters 3 through 6 might not. The essential genes contained in Clusters 1 and 2 are mainly involved in vitamin and cofactor synthesis, amino acid catabolism, cell wall synthesis, central metabolism, the membrane transport system, nucleotide synthesis, nucleotide salvage, and lipid synthesis. The involvement of these genes in the aforementioned biological systems is listed in the Table S1. The mutants of some genes in Cluster 1 have been reported to form biofilms. For example, the inhibitor of the enzyme encoded by the glmU gene (Group 4) is able to enhance the formation of biofilms of P. aeruginosa PAO1 . Another example is given that the pgsA null mutant (Group 4) of E. coli activates the Rcs signal transduction pathway that is crucial for E. coli biofilm formation . In addition, the down-regulation of the following six essential genes, i.e., pyrH (Group 6), tktA (Group 22), tpiA (Group 19), rpiA (Group 24), dapD (Group 4), and rmlA (Group 4), is reported as the driving force for Streptococcus biofilm formation .
As seen from Figure 3, the activity levels of all the biofilm-associated reactions are small for the genes from Clusters 3 through 6, i.e., PA0904 (lysC), PA1756 (cysH), PA2023(galU), and PA3686 (adk). Hence, they are regarded as ideal gene targets to treat P. aeruginosa infections because the inactivation of any of them can kill the planktonic pathogen cells but cannot promote the switch from planktonic growth to biofilm formation. The following experimental evidence further confirms these four genes are good targets to treat biofilm-associated P. aeruginosa:
An interesting finding by inspecting Figure 3 (A) through (C) is that certain biofilm-associated reactions have significantly increased activity levels (e.g., more than three-fold) upon the single mutations of all the three representative genes from Cluster 1 and Cluster 2, i.e., PA0945 (purM), PA5038 (aroB), and PA4031 (ppa). This implies that, although these metabolic reactions are all associated with biofilm formation, certain parts of them are more likely to be utilized by P. aeruginosa upon the stress such as that imposed by the mutation of essential planktonic growth genes.
Therefore, we analyzed the relative activity changes of each biofilm-associated reaction across all single mutants, and categorized the 39 biofilm-associated reactions into two types: 1) the reactions with minor increase of activity levels for most essential mutants and 2) those with significant activity increase. Figure 4 (A) and (B) show the typical relative activity changes of two biofilm-associated reactions: a minor-increase reaction (Reaction Rxn# 1) and a “significant-increase” reaction (Reaction Rxn# 4). The relative activity changes of other biofilm-associated reactions are similar to either the one for Rxn# 1 or that for Rxn# 4 (data not shown). Reactions associated with each of the two types of reactions are listed in Table 3.
The “significant-increase” type of reactions have significant increases in activity levels for the mutants of most essential genes, and might reveal the underlying mechanisms for biofilm formation when P. aeruginosa is treated by the antimicrobial agents that attack the essential genes. It can be seen from Table 3 that these reactions are mainly involved in acetate metabolism (mainly via Rxn# 4 and 35), arginine metabolism (mainly via Rxn#27 and 34), glutamate metabolism (mainly via Rxn# 5 and 36), the regulation of hydrogen peroxide (mainly via Rxn# 22), and the phosphate transport (mainly via Reaction Rxn #28). These findings are supported by existing experimental data listed as follows.
While all the aforementioned experiments focus on the investigation of the impact of individual metabolic modules on biofilm formation, this work represents the first mathematical modeling approach for the systemic identification of the underlying metabolic mechanisms that facilitate biofilm formation of single-mutants.
The formation of biofilms facilitates the survival of disease-causing pathogens in hostile environmental conditions. Therefore, preventing the pathogen's transition from the planktonic state to the biofilm growth mode is one of the most important steps to treat biofilm-associated pathogens. Since the metabolism of pathogens is determined by the interaction of hundreds of metabolic reactions, genes, and enzymes, systems biology approaches can facilitate gene target identification for preventing the planktonic to biofilms transition. In this work, a systems-level analysis approach was presented to answer the following question that still remains unanswered, that is, how to mathematically quantify the capability of a pathogen to form biofilms upon the mutation of a specific gene. The fluxes through the reactions associated with an essential planktonic-growth gene are limited to 10% of their nominal values in flux balance analysis to mimic the mutation of the gene in this work. Although the approach used here is a partial shutdown instead of a complete gene-knockout mutation, it better reflects the response of pathogens to the treatment of antimicrobial agents, which generally cannot immediately eliminate the biological functions of the target genes. The mutant might form biofilm before antimicrobial agents completely eliminate the bacterial metabolism. In addition, the pathogen might be treated by a sub-inhibition dose, which can be mimicked by setting the allowable fluxes to 10% of their nominal values. The terminology “mutant” or “mutation” is still used in this work, although an in silico partial shutdown mutation is performed to identify gene targets from those essential planktonic-growth genes of P. aeruginosa.
Based upon the results in this work, it is interesting to hypothesize that the mutations of essential genes are more likely to induce P. aeruginosa biofilm than those of non-essential ones. For essential genes, the mutations of 132 out of the 136 essential planktonic-growth genes were predicted to induce biofilm formation, and the down-regulation of 8 of them, i.e., pyrH, tktA, tpiA, rpiA, dapD, and rmlA , glmU , and pgsA , has been experimentally proven to be positively correlated with biofilm formation. In contrast, we find that only two out of 920 non-essential mutants might induce biofilm formation, when applying the proposed approach to evaluate the biofilm formation capability of mutants of the nonessential genes in the P. aeruginosa model reported by Oberhardt et al., 2008 . For the 920 non-essential genes, we have followed the experiment approaches presented in Ueda et al., 2009 , to carry out comprehensive screening experiment for altered biofilm mutants from the PA14 non-redundant transposition mutant library (Liberati et al., 2006, ). The library contains 835 of the 920 non-essential genes, and of these 835 mutants, 823 have been verified not to induce biofilm formation (data can be provided upon request). While we predicted a lower number of mutants that form biofilms (i.e., two by prediction versus 12 by experiment), this is probably because we use a conservative approach in mimicking partial shutdown mutation, in which a reaction that is catalyzed by multiple enzymes is not inhibited for single mutants, but on the whole the results were verified for the vast majority of the bacteria with mutations in non-essential genes. The potential reason for explaining the hypothesized strong biofilm formation capability of most essential mutants is that the mutation of an essential planktonic-growth gene might cause limited nutrient uptakes, which strongly enhance biofilm formation , and make the pathogen feel the stress, which is reported as one of the major driving forces for biofilm formation . On the contrary, when a non-essential gene is inhibited, the pathogen does not feel very much stress, because non-essential genes are not crucial for the biomass synthesis. This hypothesis as well as the findings of the biofilm formation phenotypes of single mutants forms the foundation for the further experimental investigation.
This work was mainly focused on investigating the biofilm formation capability of single mutants, as the single gene inhibition is easier to implement than the multiple gene inhibition. While it is possible to apply the proposed approach to multiple-mutants, the ACHR sampling approach needs to be upgraded to improve the computational efficiency. It takes approximately 15 minutes to obtain 20,000 samples of fluxes of the biofilm-associated reactions upon the mutation of a single gene for a desktop computer with Intel Core i5 2.5 GHz CPU and 8 GB RAM. Since 920 nonessential genes have been reported in Oberhardt et al., 2008 , it is very time-consuming to study the biofilm formation ability of all possible multiple-mutants. Nevertheless, the study of the impact of the multiple-gene mutation on biofilm formation is an interesting topic for the future research.
To the best knowledge of the authors, this work represents the first systems-level approach to incorporate the quantification of biofilm formation capability in evaluation of genes as the targets to treat biofilm-associated pathogens. Four essential planktonic-growth genes, i.e., PA0904 (lysC), PA1756 (cysH), PA3686 (adk), and PA2023(galU), were identified as the potential gene targets to treat P. aeruginosa, as the mutation of any of these genes can eliminate the pathogen without inducing biofilm formation. This finding is implied by existing experimental data. Based upon the relative activity change of biofilm-associated reactions over all the single mutants, it is interesting to find that the fluxes of approximately 8 biofilm-associated reactions significantly increase for most single essential mutants. They are mainly associated with acetate metabolism, arginine metabolism, and glutamate metabolism. All these findings can be used to generate hypotheses for experiment design. In addition, the proposed approach can be applied to identify gene targets for treating any other biofilm-associated pathogen if the genes positively associated with biofilm formation have been identified and the metabolic model has been developed for the pathogen.
In this section, the systems-level approach whose outline is shown in the illustrative example (Figure 1) is described. This approach is used to quantify the biofilm formation capability of single essential mutants, cluster essential genes according to the biofilm formation capacity of their mutants, and systematically identify the metabolic reactions whose activity levels significantly increase for most single essential mutants. The detail of the proposed approach is shown step by step as follows.