Effect of Microbial Interactions on Performance of Community Metabolic Modeling Algorithms: Flux Balance analysis (FBA), Community FBA (cFBA) and SteadyCom

Effect of Microbial Interactions on Performance of Community Metabolic Modeling Algorithms: Flux Balance analysis (FBA), Community FBA (cFBA) and SteadyCom | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effect of Microbial Interactions on Performance of Community Metabolic Modeling Algorithms: Flux Balance analysis (FBA), Community FBA (cFBA) and SteadyCom Maryam Afarin, Fereshteh Naeimpoor This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4226944/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract To explore the impact of microbial interactions on outcomes from three prevalent algorithms (Flux Balance Analysis (FBA), community FBA (cFBA), and SteadyCom) analyzing microbial community metabolic networks, five toy community models representing common microbial interactions were designed. These include commensalism, mutualism, competition, mutualism-competition, and commensalism-competition. Various scenarios, considering different biomass yields and substrate constraints, were examined for each type. In commensal communities, all algorithms consistently produced similar results. However, changes in biomass yields and substrate constraints led to variable abundances and community growth rates within a broad range (0.33 to 0.8 and 2 to 5, respectively). For competitive communities, all algorithms predicted growth of fastest-growing member. To comply with the natural coexistence of members, suboptimal solutions over optimal point are recommended. FBA faced challenges in modeling mutualism, consistently predicting growth of only one member. Although cFBA and SteadyCom resulted in a lower community growth rate, coexistence of both members were satisfied. In toy models with dual interactions, more realistic outcomes were achieved contrary to purely competitive model as the dependency fosters the coexistence which was missing in the competitive only scenarios. These findings emphasize the importance of algorithm choice based on specific microbial interaction types for reliable community behavior predictions.​ Microbial Community Metabolic Modeling Microbial Interaction SteadyCom cFBA FBA Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction A group of microorganisms is known as a microbial community when they coexist in a specific physical place and effectively interact through metabolic and signaling relationships [1]. Over the years, numerous microbial communities have been formed naturally in soil, aquatic environments as well as in the human gut. Microbial consortia have also been used in food production by fermentation, e.g. cheese and soy sauce [2]. Remarkably, diverse roles can be performed by microbial communities found in nature, many of which can be used for environmental, industrial, and medical purposes. For example, soil microbial communities have the capability to degrade various contaminants. Similarly, activated sludge, a natural complex microbial community, has been employed for wastewater treatment for many years [3]. Formation of microbial communities and the abundance of each member in the community are influenced by environmental abiotic factors, such as the type and availability of substrate. Microbial communities exhibit higher stability under environmental changes compared to single-species. which has been attributed to the existing interactions among the members and their dynamic behavior [4]. Interactions within a microbial community can be beneficial, neutral, or even detrimental to individual community members. Based on the impacts of one member on another, microbial interactions in a community have been categorized into six general types [1]. The schematic of a microbial community and the potential interactions are given in Figure 1. Since natural microbial communities may not always exhibit sufficient effectiveness for industrial applications, synthetic microbial communities are needed to be constructed to technically exploit the various benefits of community. Numerous synthetic microbial communities have so far been designed for the production of various human health-related products (such as antibiotics), valuable chemical compounds, and bioremediation purposes [5-7]. However, many of these synthetic communities are generated by either member elimination from the existing communities or randomly configuring certain candidate species with desired features. The integration of computer tools and genome-scale data has provided scientists with the advantage of studying the metabolic behavior of microbial communities and individual microorganisms using systems biology. This provides the ability to identify the limitations in microbial systems and prediction of quantitative changes in much less time and in a cost-effective manner as compared to the experimental examination [8]. Hence, improved design of synthetic microbiomes requires metabolic modeling of microbial communities, which, in turn, necessitates the use of single-species metabolic networks of the community members. Metabolic models of single species are reconstructed by utilizing scientific literature, biochemical information, and genomic annotations of the microorganisms. Once a metabolic network is reconstructed, it can be converted into a mathematical representation, allowing mathematical and computational analysis [9]. Flux balance analysis (FBA), a mathematical modeling technique employing linear programming to optimize a metabolic objective function (MOF) such as biomass or product formation, utilizes mass balances on intracellular metabolites under pseudo steady state assumption. FBA was initially developed and successfully applied to numerous single species [10-12]. Mathematical formulation of FBA in the form of an optimization problem is given in Eqs. 1-3 [13]: where S ij , v , v j , C, R, M, LBj and UBj represent the stoichiometric coefficient of metabolite i in reaction j , vector of unknown fluxes, flux of reaction j , vector of objective function coefficients, set of reactions, set of metabolites, minimum and maximum flux values for reaction j , respectively. Modeling microbial communities is more complex compared to single species modeling due to the presence of microbial interactions among community members. In addition to the detailed metabolic model for each individual member, pools of shared metabolites should be considered to allow exchange of metabolites as well as members interactions. Microbial community metabolic modeling can be broadly categorized into three frameworks as presented in Figure 2: supra microorganism, compartmentalization, and dynamic analysis. The choice of framework depends on factors such as the number of community members, the importance of considering interactions among them, and the availability of information [14]. Having a community metabolic model, simulations can be carried out to predict the behavior of the community using various algorithms developed in the last decade. These algorithms include FBA for community [8], OptCom [15], d-OptCom [16], cFBA [17], SteadyCom [18] and COMETS [19]. For considering the dynamic behavior of the community, d-OptCom and COMETS were developed, while OptCom and SteadyCom are well-suited for pseudo-steady-state analyses and have broad applications [15, 16, 18, 19]. These algorithms offer valuable tools for analyzing and understanding the behavior of microbial communities. An overview of the assumptions and formulations of FBA for community, cFBA and SteadyCom are illustrated in Figure 3. FBA can similarly be exploited for communities by considering a linear combination of individual member targets. This formulation has been utilized in various studies, including investigations of gut microbiome [20], the exploration of interactions between different tissues in humans and plants [21] and the optimization of chemical production [22]. While member abundances are crucial characteristics of microbial consortia, they have not been considered in most simulating algorithms. However, the development of cFBA has addressed this limitation by enabling the prediction of relative species abundances in addition to calculating the maximum community growth rate at balanced growth (equal growth rates of members). As can be seen in Figure 3, the cFBA formulation is nonlinear due to the multiplication of abundances by the fluxes. This nonlinear problem is solved by iteratively fixing the abundances in each step and solving the linearized problem to obtain the maximized growth rate. By plotting µ vs. x, one can identify the highest community growth rate. cFBA has been successfully applied to simulate a community consisting of three species involved in methane production and acetogenesis during anaerobic digestion for biogas production [23]. Since the sub-problems to be solved in cFBA increase exponentially with the number of organisms, SteadyCom reformulated cFBA to overcome this issue. Using the same assumption of balanced growth of members, an innovative concept called 'aggregate flux' was introduced by SteadyCom (see Figure 3) and the aggregate fluxes were used as new variables alongside the unknown community growth rate. The aggregate flux of reaction j of member k ( V j k = v j k .X k ,) considers the contribution of total biomass of member k rather than v j k which shows the rate of reaction j per unit biomass of member k . This also applies to biomass formation reaction of each member where growth rate of each member (µ k = µ) should be multiplied by its mass fraction ( X k ) to provide the overall biomass formation rate of member k , rendering the problem nonlinear. SteadyCom iteratively tests fixed values of community growth using a specified interval and solves LP problems maximizing the total community biomass ( X = summation of X k ) such that X becomes larger and smaller than 1 gram. Following this, a non-derivative-based root-finding algorithm is employed to determine the community growth rate leading to X = 1. The algorithm's efficacy was validated through the results of a community composed of four E. coli mutants, each with auxotrophy for two amino acids while each one is an exporter for one amino acid and in terms of microbial interactions, the setup consisted of four mutualistic pairs, with each involving two members, as well as two competitive interactions, both of which lacked mutualistic interactions [18]. SteadyCom has been successfully utilized to predict the behavior of microbial communities ranging from two-membered systems [24] to more complex, populated communities [24-27]. Since community algorithms have different ruling logic, it seems necessary to probe the dissimilarities in results obtained by application of these algorithms to the same community. In addition to the exploited algorithm, the results may be influenced by the type of existing interactions in the community. For instance, competition interaction has been reported to give results which are not in accord to real-world. Therefore, we aimed to separately investigate the performance of community algorithms (SteadyCom, FBA, and cFBA) in simulating important interactions in biotechnological applications by constructing five toy models representing the most common community interactions, namely, mutualism, commensalism, competition, competition-mutualism, and competition-commensalism. Application of different algorithms to communities with various microbial interactions alongside analysis of the results can provide insights into the dissimilarity of results as well as effectiveness of each algorithm in simulating different types of interactions. 2. Materials and Methods Based on the experience gained from working in the domain of metabolic modeling of microbial communities, it became evident that the algorithms used to solve microbial community models do not always provide reasonable solutions for all types of interactions. To address this issue and to determine the appropriate algorithm for analyzing each type of microbial interaction, simplified toy models covering five common interactions were designed and utilized. This approach was chosen due to the impracticality of using genome-scale models with their extensive network size for investigation and comparison of the results. To represent the five common microbial community interactions of commensalism, competition, mutualism, commensalism-competition and mutualism-competition, five two-member (m 1 and m 2 ) toy communities termed T1 to T5, respectively, were constructed using the compartmentalization framework as depicted in Figure 4. Among the 10 metabolites A to J in these models, A and/or E serve as the external substrate(s), each with a limited availability. Uptake rates of these substrates were restricted by fixing their values in all simulations as environmental constraints. Metabolites J and H act as unlimited substrates in the communities T1, T2, and T4. C and/or D were regarded as the shared metabolites that could be exchanged between members. In all toy communities, F and G represented the biomass of m1 and m2, respectively, and the total community biomass was obtained by summation of F and G. The remaining metabolites (B and I) were the internal metabolites within the networks of the individual members. These communities were analyzed using the three simulation algorithms of FBA, cFBA, and SteadyCom. To address the likely challenges in simulations, diverse scenarios were considered for each community according to real situations in natural communities and our experiences working with these algorithms. Additionally, these scenarios aimed to assess the algorithms' ability to uphold their claimed features, such as balanced growth – a fundamental principle in cFBA and SteadyCom. The details for various runs are provided in Table 1. The runs are distinguished by two altering conditions: the equality/inequality of biomass yields of the two members (as indicators of relative growth rates of single species) and the uptake rate of the specialized substrate for each member. Equal biomass yields equal to 1 were chosen to model communities with closely matched species, while unequal biomass yields were used to simulate communities with dissimilar members (microalgae and bacteria). To adjust biomass yield of members, the stoichiometric coefficient of metabolite F (biomass of m1) or G (biomass of m2) in the relevant biochemical reaction network was altered. Setting the coefficients of F(G) at 1 resulted in biomass yield for m1(m2) being equal to 1 on its specialized substrate A(E), while biomass yield equal to 2 was obtained by setting the relevant coefficient equal to 2. This means that a distinct metabolic network should be envisioned for toy models T1-T5 in cases with unequal biomass yields. Therefore, toy models T1-T5 shown in Figure 4 only illustrates the cases with the biomass yields for m1 and m2 being equal to 1.Three biomass yield cases (a: yield of m1 = yield of m2 = 1, b: yield of m1 = 2 = 2×yield of m2, and c: vice versa of b) were considered for each community. Additionally, different fixed uptakes rates of A and/or E where applicable were used to simulate the scarcity of substrates while the exchange flux of metabolites J, C, H, and D were unconstrained. Overall, 6 and 14 runs were performed with equal and unequal yields, respectively. Table 1. Designed computer experiments (runs) and their conditions using toy models (T1-T5). Interaction type * Run code: model-run no. Conditions Interaction type * Run code: model-run no. Conditions Coeff. of Subs. uptake rate (mmol/h) Coeff. of Subs. uptake rate (mmol/h) F G A E F G A E Cm T1-1 1 1 -1 -1 M T3-2 2 1 -1 -1 T1-2 1 1 -2 -1 T3-3 1 2 -1 -1 T1-3 2 1 -1 -1 T3-4 2 1 -2 -1 T1-4 1 2 -1 -1 T3-5 2 1 -1 -2 T1-5 2 1 -2 -1 Cm-Cp T4-1 1 1 -1 - T1-6 1 2 -2 -1 T4-2 2 1 -1 - Cp T2-1 1 1 -1 - T4-3 1 2 -1 - T2-2 2 1 -1 - M-Cp T5-1 1 1 -1 - T2-3 1 2 -1 - T5-2 2 1 -1 - M T3-1 1 1 -1 -1 T5-3 1 2 -1 - * Cm: Commensalism, M: Mutualism, Cp: Competition It should be noted that the external fluxes in FBA and cFBA are expressed in mmol/h/gCom (millimoles per hour per gram dry weight of community), while in SteadyCom, fluxes are expressed in mmol/h. This distinction arises due to taking one gram of community biomass in FBA and cFBA, while SteadyCom allows the user to adjust this value, though its default value is 1. Given that, the total biomass in SteadyCom was set at 1 gram in our runs and hence the unit of external fluxes in this method aligns with the other two in mmol/h/gCom. Furthermore, the internal fluxes in SteadyCom are in mmol/h, corresponding to the aggregate flux, which results from the multiplication of flux by the biomass of each member. Due to the default assumption of a total community biomass of 1 gram, the unit of internal fluxes in SteadyCom becomes mmol/h/gCom. In contrast, the internal fluxes in cFBA are mmol/h per gdw of each individual member. In the results section therefore we multiplied these fluxes by the abundance of the respective member (grams of member per 1 gram of community biomass). This leads to the unit of reported internal fluxes being mmol/h/gCom. Finally, the internal fluxes in FBA are expressed as mmol/h/gCom. In sum, despite these varying units across different methods, all fluxes are comparable in results section. Since we assumed a total community biomass of 1 gram for all runs, the unit of fluxes are simplified and expressed as mmol/h. 3. Results and Discussions Results obtained from application of the three computational algorithms to two-member models T1-T5 will be separately discussed based on the type of microbial interactions. For each interaction, the effect of conditions (see Table 1) on community behavior will be investigated. Furthermore, the results obtained by application of each algorithm will be compared with those of the other two algorithms under the same conditions. A complete set of results for runs in Table 1 is provided in supplementary material. 3.1. Commensal Community (T1) Commensalism, a beneficiary interaction for one member in community, can be found in various natural microbial ecosystems such as biogas-producing microbial communities or the gut microbiome. Toy model T1 consisting of members m1 and m2 with specialized and limited substrates A and E, respectively, has been designed as a community that exclusively features the commensal interaction with growth of m2 relying on m1 through the shared metabolite C. This commensal community was analyzed using FBA, cFBA and SteadyCom under six different conditions (runs T1-1 to T1-6 in Table 1). Comparisons of the results obtained via application of these algorithms showed identical results for each run as given in Table 2. In all runs of commensal community, the cFBA results indicate that there is a unique optimal solution, and for other x m1 values, the system becomes infeasible. Table 2. Identical results of commensal community obtained by FBA, cFBA and SteadyCom algorithms However, alterations were observed in the results of different runs due to the dissimilar conditions. In case of T1-1 with equal fluxes of A and E and equal biomass yields of 1, results show equal fluxes of F and G, community growth rate of 2 h -1 and equal mass fraction of members (0.5). Two fold increase in uptake of A in T1-2 (compared to T1-1) resulted in higher flux of F alongside constant flux of G due to the unchanged flux of E, triggering higher community growth rate (3 h -1 ). To counterbalance the higher growth rate at constant flux of G, mass fraction of m2 lessened and this in turn increased the mass fraction of m1 (0.67). Since the increased production flux of C by m1 in case T1-2 could not be taken up by m2, C was exchanged with exterior as compared to T1-1 showing no exchange of C. This shows that higher supply of a dedicated substrate to a member with other conditions remaining constant will result in higher community growth rate and increased mass fraction of that member to comply with the equality of members’ growth rates. Cases T1-3,4 consider commensal communities with one member having higher biomass yield on its dedicated substrate than the other member while other conditions remained the same as case T1-1. Of these two cases, explanations are only given for case T1-4 where yield of biomass formation for m2 on E was increased by two fold by setting the coefficient of G equal to 2 compared to case T1-1. This resulted in a higher flux of G with no change in flux of F and hence a higher community growth rate of 3 h -1 . To satisfy the equality of growth rates, mass fraction of m2 was enlarged while that of F was reduced. One can therefore conclude that increasing biomass yield of one member results in the enlargement of its mass fraction provided that other conditions are unchanged. This also applies to the case T1-3 where biomass yield of m1 was doubled and its mass fraction was increased. Case T1-5 was a case similar to T1-3 with respect to biomass yield and other conditions apart from uptake flux of A by m1 was doubled. Figure 5 depicts the flux distribution of T1-5 where fluxes of F and C were doubled while flux of G remained unchanged due to unaltered flux of E, all compared to fluxes in T1-3. To comply with the higher community growth rate of 5 h -1 as a result of higher overall production of F and G, mass fraction of m2 decreased and this resulted in an increase in mass fraction of m1. Since consumption of C by m2 was constrained by the limited availability of E, a part of produced C by m1was released to exterior. The effect of variation of uptake rate of A at constant biomass yields on flux distribution can be analyzed by comparison of the results of cases T1-3 and T1-5. It can be seen that doubling the flux of A in T1-5 compared to T1-3 resulted in increased mass fraction of m1 alongside a higher community growth rate. This also applies to the cases of T1-1 and T1-2 as well as cases T1-4 and T1-6 with equal values of biomass yields and doubled supply of A. As can be seen in Table 2, mass fraction of m1 and community growth rates both increased. Altogether in commensal community, different biomass yields of members and different supply of substrates significantly affected the flux distribution, member abundances and community growth rate. However, the performance of the three algorithms used for flux analysis were reasonable and the same results were obtained for each case. 3.2. Competitive Community (T2) Competition is a prevalent interaction in various communities, particularly in industrial applications of microbial consortia, such as wastewater treatment. Competition for limited substrate is a challenging interaction for metabolic analysis and algorithms have been developed to confront the existing difficulties. Model T2 (see Figure 4) represents a community with competition as the sole interaction in which growth of both members rely on the limited substrate A. Community growth rates obtained by cFBA algorithm at varying mass fraction of m1 for case T2-1 plotted in Figure 6A show the same community growth rate of 1 h -1 across all abundances. In other words, the maximum growth rate of competitive community with equal biomass yields can be achieved at all mass fractions. This is a case where the corresponding linear programming problem show multiple optimal solutions resulting in the same optimized value of the objective function despite showing different solutions (fluxes and mass fractions). By application of FBA and SteadyCom algorithms, identical fluxes as given in Figure 6D were obtained. Actually, this solution was one of the multiple solutions obtained via cFBA in which substrate A was completely consumed by m1, leading to zero production rate of G (biomass of m2). This at first may seem contradictory with equal growth rates of members ( μ = μ 1 = μ 2 ) assumed in SteadyCom. However, it can be explained by the fact that the variables in SteadyCom are aggregate fluxes. Considering V biomass, m2 = μ x m2 as aggregate biomass formation flux of m2, one can perceive that zero value of V biomass, m2 could be as a result of zero x m2 , not zero value of μ 2 and hence μ 1 = μ 2 can be satisfied even in this special solution. In fact, this is only one of the multiple solutions of case T2-1 leading to maximal community growth rate. Actually, SteadyCom terminates by finding the first optimal solution and the reasonable optimal answer might sometimes lay in the middle of the range of multiple optimal solutions. It should however be mentioned that the SteadyCom in COBRA toolbox of Matlab has provided an option called "BMcon" allowing preset values of members biomass which can be used to obtain a more realistic solution. Flux distribution of case T2-2(3) with members having unequal biomass yields given in Figure 6E(F) show that all three algorithms promoted only the growth of member with the higher biomass yield (m1 for T2-2 and m2 for T2-3), leading to the complete consumption of substrate A by this member. Figure 6B(C) presenting the cFBA results for T2-2(3), shows the monotonic escalation of community growth rate with mass fraction of m1(m2) until reaching its highest value at x m1 = 1(x m2 =1) beating one member. Similar to the previous case, more realistic suboptimal solutions can be found by using "BMcon" command at fixed biomass values. The occurrence of zero abundance in SteadyCom had also been previously reported by some researchers [25, 27]. In simulation of gut microbiota using a 28-species community by SteadyCom, results indicated that only five/six species had non-zero abundances in different diet scenarios while other members were omitted [25] The members with low biomass yields exhibited zero abundances, similar to our cases T2-2,3. Mutualism and commensalism were reported as the dominant interactions of remaining members while the interactions of omitted species were not specified. According to our results, competition in their case might be a contributing factor in zero abundances of most members. In another study on chronic wound microbiota, a 12-species community was simulated by SteadyCom and five members with zero abundances were reported [27]. However, the specific type of interactions for omitted members were not reported. Competitive communities with equal biomass yields are susceptible to showing multiple optimal solutions which can only be visualized by plotting the growth rate vs. mass fraction (such as Figure 6D) using cFBA. SteadyCom and FBA algorithms terminate by finding the first feasible solution and may sometimes produce less reasonable answers, such as the elimination of a member. As in natural competitive communities, it is expected that all members would coexist even with varying biomass levels. Incorporation of experimental data/general knowledge of member abundances into simulations can help refine the results and enhance their biological relevance. To achieve a more realistic solution in SteadyCom, the "BMcon" option can be utilized. When the biomass yields of members are unequal, all three algorithms generate a result where only one member would remain. This outcome aligns with the objective function of maximizing growth, which results in the member with a larger biomass yield monopolizing the substrate. Since maximizing growth might not accurately represent the goals of competitive communities in reality, a suboptimal solution could offer a more realistic outcome or alternatively experimental data on member abundances may be incorporated to allow better mirror real-world results. 3.3. Mutualistic Community (T3) Mutualistic interaction refers to a symbiotic relationship between two members relying on each other for growth. This interaction often coexists with other types of interactions in microbial communities. The toy model T3, depicted in Figure 4, exemplifies the mutualism interaction facilitated through the exchange of metabolites C and D as the sole form of interaction within this toy model while A or E functions as specialized substrate for each member. The interdependence of these members resulted in distinct outcomes. Five different conditions were examined in cases of T3-1 to T3-5 to consider the effect of variations on biomass yields and substrates uptake rates. Coexistence of the two members in this model is expected since the shared metabolites D and C are required for growth of m1 and m2, respectively, in addition to the dedicated substrates A and E. FBA results are firstly described and discussed for the examined cases as these were inconsistent with the results obtained via cFBA and SteadyCom. In all cases, FBA showed the growth of only one member (m1 in most cases and m2 in T3-3) while the other member showed no growth. This means that the growing member obtains the required shared metabolites (C or D) by the non-growing member (see Figures S11-S15 of supplementary material). Actually, the member showing no growth consumed its dedicated substrate to solely provide the metabolite required for the other member’s growth. Consequently, the community biomass was solely derived from the biomass reaction of the growing member. Community growth rate of 1 1/h was obtained for case T3-1 with biomass yields of 1, while this was 2 1/h for all other runs in which biomass yield of one member was 2. In case T3-4 (T3-5) where extra substrate A (E) were taken up, release of shared metabolite C (D) by community to exterior environment was observed. Although donation of the required metabolites by a non-growing member in a microbial community to other members has previously been reported when using FBA algorithm, the type of interaction leading to this situation was not specified [18]. Results obtained by cFBA and SteadyCom algorithms for mutualistic community under different conditions are illustrated in Table 3. Where more reasonable results for this type of interaction were predicted by these two algorithms. In run T3-1 with equal biomass yields and equal dedicated substrate availabilities, both cFBA and SteadyCom algorithms demonstrated non-zero abundances for the two members, though one was much lower. Similar to previously discussed cases, cFBA allowed visualization of the existing multiple optimal solutions at x m1 (mass fraction of m1 in community) ranging from 0.001 up to 0.999 (see Figure 7A) and outside this range the system becomes infeasible, while SteadyCom gave only one optimal solution at x m1 = 0.001. Table 3. Comparison of the results of mutualistic community (T3) predicted by cFBA and SteadyCom algorithms under different conditions For cases T3-2,3,4,5 with unequal biomass yields, identical unique solutions were obtained by cFBA and SteadyCom, while FBA predicted different results. Community growth rate obtained by FBA was slightly higher compared to other algorithms as FBA led to no growth of the member with lower biomass yield while balanced growth assumption of the other algorithms enforced growth of that member, though at a small rate, lowering the community growth rate. This reveals that coexistence of both members in community may not result in a higher community growth rate, but it aligns more closely with reality. Although the same maximized community growth rate of 1.998 h -1 was obtained for cases T3-2,3, abundance of the member with higher biomass yield was higher than that of the other member (see Figure 7B,C). Results of case T3-4 were identical to those of T3-2, apart from C being released by community to exterior at a rate of 1 mmol/h/gCom in case T3-4 due to doubling the uptake of A. Case T3-5 having double uptake rate of E with other conditions being unchanged compared to case T3-2 led to the decreased community growth rate alongside the decreased x m1 , the release of D as community product and higher and lower exchange rates of C and D by m2 and m1, respectively. In summary, FBA was found an inappropriate choice for analyzing the metabolic network of a mutualistic community due to providing the required shared metabolite by the non-growing member. SteadyCom and cFBA were shown to provide reasonable identical results and hence appear to be suitable methods for simulating mutualistic interaction. Comparing our findings to a study described in the introduction section that reported favorable outcomes using the SteadyCom method [18], reveals interesting insights. The community investigated in that study involved both mutualistic and competitive interactions. Similar to our results in a mutualistic community, they obtained reasonable outcomes when compared to FBA. It is noteworthy that in their study, competition did not revolve around a limited external substrate. Consequently, the reported results in that context were considered plausible. 3.4. Commensal-Competitive Community (T4) In real cases, a combination of interactions as opposed to single interactions, with the simplest being the dual interaction, could occur which needs consideration. Commensal-competitive community is an important case among the communities with dual interactions where members compete for the same substrate while a metabolite formed by one member is necessary for the growth of another member. Designed community T4 (see Figure 4) represents a simple commensal-competitive community with both members requiring substrate A and metabolite C, produced by m1, being necessary for growth of m2. This community was examined under three different conditions, the results of which are presented in Figure 8. Figure 8A illustrates the variation of community growth rate with x m1 obtained via cFBA for case T4-1 having equal yields. System was feasible only for a range of x m1 ≥ 0.5 where a unique maximized community growth rate of 1 h -1 was attained, suggesting the existence of multiple optimal solutions. By increasing x m1 within this range, metabolite C was concurrently released as product of m1. The same optimized community growth rate of 1 h -1 was found by SteadyCom and FBA however different values of 1 and 0.5 for x m1 were predicted, respectively. Comparison of these results with cFBA plot (Figure 8A) shows that the results obtained by SteadyCom and FBA for case T4-1 lies at the limits of optimal range of x m1 obtained by cFBA and hence only represent one of the optimal solutions. In case T4-2 where biomass yield of m1 was doubled, cFBA resulted in feasible solutions for x m1 ≥ 0.667 with an increasing trend of community growth rate with x m1 , leading to the highest rate of 2 h -1 by dominance of m1 at x m1 =1. Flux distribution predicted by FBA and SteadyCom were as predicted by cFBA which is given in Figure S16. As mentioned in Section 3-2, the balanced growth assumption was satisfied despite observing zero mass fraction of m2. By doubling biomass yield of m2 in run T4-3, all algorithms led to a community growth rate of 1.5 (1/h) with substrate A being equally shared between members as presented in Figure 8B. The same x m1 (0.33) was obtained by SteadyCom and cFBA however the community growth rate was lower compared to case T4-2. This can be explained by the fact that commensalism demands the growth of m1 to provide metabolite C for growth of m2 with higher biomass yield. This in turn diminishes the maximized growth rate of community as the member with lower yield should also grow alongside the other member. Overall, competitive interaction in commensal-competitive community supports the dominance of independent member provided that it has the higher biomass yield on the shared substrate. On the contrary, when dependent member has higher biomass yield, commensalism forces this member to obtain a shared metabolite produced by the other member and hence both members coexist. 3.5. Mutualistic-Competitive Community (T5) Among the communities with dual microbial interaction, mutualistic-competitive community is another important type observed in various natural and industrial microbial communities, including yogurt-producing microbiomes. To investigate this type of dual interactions, community T5, as depicted in Figure 4 was designed in which growth of m1 depends on m2 and vice versa in addition to competence of m1 and m2 for the common limited substrate A. Three cases T5-1,2,3 with equal and unequal biomass yields were considered. Overall, results were similar to those of mutualistic community (T3). In all examined cases, FBA predicted growth of only one member obtaining its essential metabolite by the non-growing member. However, SteadyCom and cFBA both predicted the growth of both members, though at various extents. cFBA plot of case T5-1 (Figure S18) with equal yields showed the existence of multiple optimal solutions at optimal community growth rate of 0.5 h -1 and x m1 ranging from very low values (0.0005) up to values close to 1 (0.9995). By applying SteadyCom, one optimal solution was obtained at x m1 = 0.9995 which lies within the multiple optimal solutions. For cases with unequal yields (T5-2,3), cFBA plots (Figures S19,20) showed increasing and decreasing trends of the community growth rate with x m1 for cases with doubled biomass yields of m1 (case T5-2) and m2 (case T5-3), respectively. Therefore, cFBA predicted a unique optimal solution for case T5-2 (T5-3) at x m1 = 0.9995 (x m1 = 0.0005). The same results were obtained by SteadyCom due to the existence of unique solutions for cases T5-2,3. Compared to results obtained by FBA, optimal community growth rate obtained by SteadyCom and cFBA were slightly lower (0.9995 1/h compared to 1 1/h) due to metabolites C and D being produced by growing member as opposed to non-growing member in FBA. Overall, the performance of the three algorithms for simulating competition alongside mutualism were almost similar to that of mutualistic community. SteadyCom algorithm showing zero aggregate fluxes for one member under equal yields in community with solely competitive interaction, led to the more realistic coexistence of both members for competition alongside mutualism. 4. Conclusion To assess and compare the performances of three commonly used microbial community algorithms (FBA, cFBA, and SteadyCom) in simulating the behavior of communities, five toy models were constructed each representing one of the most common microbial interactions. Results showed distinct capabilities of algorithms in simulating the diverse microbial interactions. The three algorithms equally performed when applied to the commensal community with a unique solution under all examined conditions. Challenges were faced by application of these algorithms to competitive community. At equal biomass yield of members, multiple optimal solutions were obtained using cFBA algorithm. However, SteadyCom and FBA could give only one of these solutions lying at a point with zero abundance of one member (growth of only one member) which was misleading. Despite the balanced growth assumption in cFBA and SteadyCom, application of these two algorithms to communities with unequal biomass yields still faces limitations in depicting the coexistence of both members (zero abundance of one member), though balanced growth assumption was mathematically satisfied and the uniqueness of solution was confirmed by cFBA plot. In natural ecosystems however competitive communities often exhibit simultaneous growth of members as a result of higher-level strategies. Other constraints, objective functions or a combination of the two may govern the natural communities instead of taking the community growth rate as the objective function. This indicates that further research and development are necessary to enhance the accuracy and reliability of community metabolic modeling algorithms for competitive interactions. Of course, suboptimal solutions which are more reasonable and biologically plausible can be attained by fixing the abundances at specified experimental values. Simulation of mutualistic community by cFBA and SteadyCom led to growth of both members in community due to the balanced growth assumption and dependence of members on each other, while FBA led to no growth of the member providing the necessary metabolite for the growth of the other member and this in turn allowed slightly higher community growth rate. Incorporation of commensal interaction into a competitive community demonstrated improved modeling performance with FBA compared to competitive alone communities. In the context of a community with equal biomass yields of members, cFBA showed multiple optimal solutions while FBA and SteadyCom produced only one these solutions. On the contrary to FBA resulting in presence of all members, SteadyCom led to one member with zero abundance not matching the reality. By introducing mutualism to competitive community, the results closely resembled those of the mutualistic community. Similarly, FBA exhibited less reasonable results due to the production of metabolites from non-growing members. On the other hand, cFBA and SteadyCom provided lower community growth rate in comparison to FBA in scenarios with unequal biomass yields however both members coexisted in the community. Altogether, when using SteadyCom, it is crucial to examine the existence of multiple optimal solutions since more reasonable answers may exist. In scenarios where only a single unreasonable solution exists, incorporating experimental or scientific knowledge about community abundances may be valuable in obtaining a suboptimal yet more reasonable solution. Declarations Acknowledgments This research did not receive any specific grant from funding agencies. Conflict of Interest Statement The authors declare that they have no conflict of interest. Data Availability Statement All data generated or analyzed during this study, including a comprehensive set of models and results, are available in the supplementary material accompanying this published article. References Faust K, Raes J (2012) Microbial interactions: from networks to models. Nat Rev Microbiol 10:538-550. https://doi.org/10.1038/nrmicro2832 Qian X, Chen L, Sui Y, Chen C, Zhang W, Zhou J, Dong W, Jiang M, Xin F, Ochsenreither K (2020) Biotechnological potential and applications of microbial consortia. Biotechnol adv 40:107500. https://doi.org/10.1016/j.biotechadv.2019.107500 Eng A, Borenstein E (2019) Microbial community design: methods, applications, and opportunities. Curr opin biotechnol 58:117-128. https://doi.org/10.1016/j.copbio.2019.03.002 Michael LS, Kargi F (2002) Bioprocess engineering: basic concepts. Prentice-Hall International, Upper Saddle River, NJ, USA. 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Front genet 8:88. https://doi.org/10.3389/fgene.2017.00088 Zomorrodi AR, Maranas CD (2012) OptCom: a multi-level optimization framework for the metabolic modeling and analysis of microbial communities. PLoS comput biol 8:e1002363. https://doi.org/10.1371/journal.pcbi.1002363 Zomorrodi AR, Islam MM, Maranas CD (2014) d-OptCom: dynamic multi-level and multi-objective metabolic modeling of microbial communities. ACS synth biol 3:247-257. https://doi.org/10.1021/sb4001307 Khandelwal RA, Olivier BG, Röling WF, Teusink B, Bruggeman FJ (2013) Community flux balance analysis for microbial consortia at balanced growth. PloS one 8:e64567. https://doi.org/10.1371/journal.pone.0064567 Chan SHJ, Simons MN, Maranas CD (2017) SteadyCom: predicting microbial abundances while ensuring community stability. PLoS comput biol 13:e1005539. https://doi.org/10.1371/journal.pcbi.1005539 Harcombe WR, Riehl WJ, Dukovski I, Granger BR, Betts A, Lang AH, Bonilla G, Kar A, Leiby N, Mehta P (2014) Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics. Cell reports 7:1104-1115. https://doi.org/10.1016/j.celrep.2014.03.070 Heinken A, Thiele I (2015) Anoxic conditions promote species-specific mutualism between gut microbes in silico. Appl environ microbiol 81:4049-4061. https://doi.org/10.1128/AEM.00101-15 Bordbar A, Feist AM, Usaite-Black R, Woodcock J, Palsson BO, Famili I (2011) A multi-tissue type genome-scale metabolic network for analysis of whole-body systems physiology. 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Supplementary Files ESM1.docx ESM2.xls ESM3.xls ESM4.xls ESM5.xls ESM6.xls ESM7.xlsx ESM8.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 14 Jul, 2024 Reviews received at journal 13 Jul, 2024 Reviewers agreed at journal 04 May, 2024 Reviewers agreed at journal 26 Apr, 2024 Reviewers invited by journal 18 Apr, 2024 Editor assigned by journal 08 Apr, 2024 Submission checks completed at journal 08 Apr, 2024 First submitted to journal 06 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4226944","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":289054836,"identity":"c65b9053-c120-4a54-894f-d7976bb31755","order_by":0,"name":"Maryam Afarin","email":"","orcid":"","institution":"Iran University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Maryam","middleName":"","lastName":"Afarin","suffix":""},{"id":289054837,"identity":"1c262482-a0b2-4fad-856e-31849a886153","order_by":1,"name":"Fereshteh Naeimpoor","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYBAC9gYgkcBgwwMT4MGtFqbiAFhLGlAlMylaGBgOM8C0EAY80s0PHzzMOS9jcP78AYYfNQwy5g2EtMgcMzZI3Habx+BGMgNjzzGgwAECWuwlEswkIFqADuNtYOCRIOgwifTvPxK3neMxOH+YgfEvcVpyzBgStx3gMTiQzMBMpC05xUCHJfNI3kg2OCxzTIIoh238+HObnT3f+YMPH76psbEnqAUFHGBgIE3DKBgFo2AUjAIcAADFNDa4TugjhAAAAABJRU5ErkJggg==","orcid":"","institution":"Iran University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Fereshteh","middleName":"","lastName":"Naeimpoor","suffix":""}],"badges":[],"createdAt":"2024-04-06 10:29:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4226944/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4226944/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54587059,"identity":"d873e7b0-608c-45de-847b-c1d405db29c1","added_by":"auto","created_at":"2024-04-12 16:03:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":123955,"visible":true,"origin":"","legend":"\u003cp\u003eTypical interactions in a microbial community\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/f2ac1416ce3d1cca1ebb2ad0.png"},{"id":54586592,"identity":"4adcd1ae-a5b5-44a1-a4dc-2a396a7e2d00","added_by":"auto","created_at":"2024-04-12 15:55:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":96285,"visible":true,"origin":"","legend":"\u003cp\u003eCommunity metabolic modeling frameworks and simulating algorithms\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/2179ac6be089b94c1195988e.png"},{"id":54586593,"identity":"fd51bd10-d4c1-48cf-89dd-e4d7b6459497","added_by":"auto","created_at":"2024-04-12 15:55:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":154005,"visible":true,"origin":"","legend":"\u003cp\u003eCommunity analysis algorithms characteristics and formulation\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/b091706fd7db26152b1e8987.png"},{"id":54586598,"identity":"4093b61d-581a-48a9-8d5a-8ff72a847ddb","added_by":"auto","created_at":"2024-04-12 15:55:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":114553,"visible":true,"origin":"","legend":"\u003cp\u003eScheme of the five toy models T1 to T5 representing important interactions in a microbial community\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/e6719c9b4b26d0eeb678a383.png"},{"id":54586596,"identity":"6f1f444b-e244-4a88-a15d-39251d7bd97b","added_by":"auto","created_at":"2024-04-12 15:55:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":31869,"visible":true,"origin":"","legend":"\u003cp\u003eIdentical flux distribution obtained by FBA, cFBA and SteadyCom for commensal community T1-5\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/10c5241a91d4246eb24d144b.png"},{"id":54587061,"identity":"ab0c6ad8-0bbb-422e-b8aa-067d48a83d50","added_by":"auto","created_at":"2024-04-12 16:03:24","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":123353,"visible":true,"origin":"","legend":"\u003cp\u003eResults of competitive community; Growth rate vs. x\u003csub\u003em1\u003c/sub\u003e diagram for finding maximum m by cFBA for runs T2-1 (A), T2-2 (B), T2-3 (C), flux distributions for runs T2-1 (D), T2-2 (E), T2-3 (F), identical results was obtained by FBA, cFBA and SteadyCom\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/3a12d08e655d4e71cd607616.png"},{"id":54587063,"identity":"2ad033e4-9e52-46cb-a135-30c795744fbf","added_by":"auto","created_at":"2024-04-12 16:03:24","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":94525,"visible":true,"origin":"","legend":"\u003cp\u003eResults of mutualistic community, growth rate vs. x\u003csub\u003em1\u003c/sub\u003e diagram for cases T3-1 (A) and T3-2 (B) obtained by cFBA as well as flux distribution obtained by cFBA and SteadyCom and cFBA for case T3-2 (C).\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4226944/v1/347fb8eaadf7ae67bb63d7d3.png"},{"id":54586591,"identity":"ba15f936-1ac9-48c7-913f-856a1a6f3edc","added_by":"auto","created_at":"2024-04-12 15:55:23","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":68880,"visible":true,"origin":"","legend":"\u003cp\u003eResults of commensal-competitive community, growth rate and release of metabolite C vs. x\u003csub\u003em1\u003c/sub\u003e by cFBA for case T4-1 (A); 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Over the years, numerous microbial communities have been formed naturally in soil, aquatic environments as well as in the human gut. Microbial consortia have also been used in food production by fermentation, e.g. cheese and soy sauce [2]. Remarkably, diverse roles can be performed by microbial communities found in nature, many of which can be used for environmental, industrial, and medical purposes. For example, soil microbial communities have the capability to degrade various contaminants. Similarly, activated sludge, a natural complex microbial community, has been employed for wastewater treatment for many years [3].\u003c/p\u003e\n\u003cp\u003eFormation of microbial communities and the abundance of each member in the community are influenced by environmental abiotic factors, such as the type and availability of substrate. Microbial communities exhibit higher stability under environmental changes compared to single-species. which has been attributed to the existing interactions among the members and their dynamic behavior [4]. Interactions within a microbial community can be beneficial, neutral, or even detrimental to individual community members. Based on the impacts of one member on another, microbial interactions in a community have been categorized into six general types [1].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe schematic of a microbial community and the potential interactions are given in Figure 1. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSince natural microbial communities may not always exhibit sufficient effectiveness for industrial applications, synthetic microbial communities are needed to be constructed to technically exploit the various benefits of community. Numerous synthetic microbial communities have so far been designed for the production of various human health-related products (such as antibiotics), valuable chemical compounds, and bioremediation purposes [5-7]. However, many of these synthetic communities are generated by either member elimination from the existing communities or randomly configuring certain candidate species with desired features. The integration of computer tools and genome-scale data has provided scientists with the advantage of studying the metabolic behavior of microbial communities and individual microorganisms using systems biology. This provides the ability to identify the limitations in microbial systems and prediction of quantitative changes in much less time and in a cost-effective manner as compared to the experimental examination [8]. Hence, improved design of synthetic microbiomes requires metabolic modeling of microbial communities, which, in turn, necessitates the use of single-species metabolic networks of the community members.\u003c/p\u003e\n\u003cp\u003eMetabolic models of single species are reconstructed by utilizing scientific literature, biochemical information, and genomic annotations of the microorganisms. Once a metabolic network is reconstructed, it can be converted into a mathematical representation, allowing mathematical and computational analysis [9]. Flux balance analysis (FBA), a mathematical modeling technique employing linear programming to optimize a metabolic objective function (MOF) such as biomass or product formation, utilizes mass balances on intracellular metabolites under pseudo steady state assumption. FBA was initially developed and successfully applied to numerous single species [10-12]. Mathematical formulation of FBA in the form of an optimization problem is given in Eqs. 1-3 [13]:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003eS\u003csub\u003eij\u003c/sub\u003e\u003c/em\u003e, \u003cem\u003ev\u003c/em\u003e,\u003cem\u003e\u0026nbsp;v\u003csub\u003ej\u003c/sub\u003e\u003c/em\u003e, C, R, M, \u003cem\u003eLBj\u003c/em\u003e and \u003cem\u003eUBj\u003c/em\u003e represent the stoichiometric coefficient of metabolite \u003cem\u003ei\u003c/em\u003e in reaction \u003cem\u003ej\u003c/em\u003e, vector of unknown fluxes, flux of reaction \u003cem\u003ej\u003c/em\u003e,\u003cem\u003e\u0026nbsp;\u003c/em\u003evector of objective function coefficients, set of reactions, set of metabolites, minimum and maximum flux values for reaction \u003cem\u003ej\u003c/em\u003e, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eModeling microbial communities is more complex compared to single species modeling due to the presence of microbial interactions among community members. In addition to the detailed metabolic model for each individual member, pools of shared metabolites should be considered to allow exchange of metabolites as well as members interactions. Microbial community metabolic modeling can be broadly categorized into three frameworks as presented in Figure 2: supra microorganism, compartmentalization, and dynamic analysis. The choice of framework depends on factors such as the number of community members, the importance of considering interactions among them, and the availability of information [14].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHaving a community metabolic model, simulations can be carried out to predict the behavior of the community using various algorithms developed in the last decade. These algorithms include FBA for community [8], OptCom [15], d-OptCom [16], cFBA [17], SteadyCom [18] and COMETS [19]. For considering the dynamic behavior of the community, d-OptCom and COMETS were developed, while OptCom and SteadyCom are well-suited for pseudo-steady-state analyses\u0026nbsp;and have broad applications [15, 16, 18, 19].\u0026nbsp;These algorithms offer valuable tools for analyzing and understanding the behavior of microbial communities.\u003c/p\u003e\n\u003cp\u003eAn overview of the assumptions and formulations of FBA for community, cFBA and SteadyCom are illustrated in Figure 3. FBA can similarly be exploited for communities by considering a linear combination of individual member targets. This formulation has been utilized in various studies, including investigations of gut microbiome [20], the exploration of interactions between different tissues in humans and plants [21] and the optimization of chemical production [22].\u003c/p\u003e\n\u003cp\u003eWhile member abundances are crucial characteristics of microbial consortia, they have not been considered in most simulating algorithms. However, the development of cFBA has addressed this limitation by enabling the prediction of relative species abundances in addition to calculating the maximum community growth rate at balanced growth (equal growth rates of members). As can be seen in Figure 3, the cFBA formulation is nonlinear due to the multiplication of abundances by the fluxes. This nonlinear problem is solved by iteratively fixing the abundances in each step and solving the linearized problem to obtain the maximized growth rate. By plotting \u0026micro; vs. x, one can identify the highest community growth rate. cFBA has been successfully applied to simulate a community consisting of three species involved in methane production and acetogenesis during anaerobic digestion for biogas production [23].\u003c/p\u003e\n\u003cp\u003eSince the sub-problems to be solved in cFBA increase exponentially with the number of organisms, SteadyCom reformulated cFBA to overcome this issue. Using the same assumption of balanced growth of members, an innovative concept called \u0026apos;aggregate flux\u0026apos; was introduced by SteadyCom (see Figure 3) and the aggregate fluxes were used as new variables alongside the unknown community growth rate. The aggregate flux of reaction \u003cem\u003ej\u003c/em\u003e of member \u003cem\u003ek\u003c/em\u003e (\u003cem\u003eV\u003csub\u003ej\u003c/sub\u003e\u003csup\u003ek\u0026nbsp;\u003c/sup\u003e= v\u003csub\u003ej\u003c/sub\u003e\u003csup\u003ek\u003c/sup\u003e.X\u003csup\u003ek\u003c/sup\u003e\u003c/em\u003e,) considers the contribution of total biomass of member \u003cem\u003ek\u003c/em\u003e rather than \u003cem\u003ev\u003csub\u003ej\u003c/sub\u003e\u003csup\u003ek\u003c/sup\u003e\u003c/em\u003e which shows the rate of reaction \u003cem\u003ej\u003c/em\u003e per unit biomass of member \u003cem\u003ek\u003c/em\u003e. This also applies to biomass formation reaction of each member where growth rate of each member (\u0026micro;\u003cem\u003e\u003csup\u003ek\u0026nbsp;\u003c/sup\u003e\u003c/em\u003e= \u0026micro;) should be multiplied by its mass fraction (\u003cem\u003eX\u003csup\u003ek\u003c/sup\u003e\u003c/em\u003e) to provide the overall biomass formation rate of member \u003cem\u003ek\u003c/em\u003e, rendering the problem nonlinear. SteadyCom iteratively tests fixed values of community growth using a specified interval and solves LP problems maximizing the total community biomass (\u003cem\u003eX\u003c/em\u003e = summation of \u003cem\u003eX\u003csup\u003ek\u003c/sup\u003e\u003c/em\u003e) such that \u003cem\u003eX\u003c/em\u003e becomes larger and smaller than 1 gram. Following this, a non-derivative-based root-finding algorithm is employed to determine the community growth rate leading to X = 1. The algorithm\u0026apos;s efficacy was validated through the results of a community composed of four \u003cem\u003eE. coli\u003c/em\u003e mutants, each with auxotrophy for two amino acids while each one is an exporter for one amino acid and in terms of microbial interactions, the setup consisted of four mutualistic pairs, with each involving two members, as well as two competitive interactions, both of which lacked mutualistic interactions [18]. SteadyCom has been successfully utilized to predict the behavior of microbial communities ranging from two-membered systems [24] to more complex, populated communities [24-27].\u003c/p\u003e\n\u003cp\u003eSince community algorithms have different ruling logic, it seems necessary to probe the dissimilarities in results obtained by application of these algorithms to the same community. In addition to the exploited algorithm, the results may be influenced by the type of existing interactions in the community. For instance, competition interaction has been reported to give results which are not in accord to real-world. Therefore, we aimed to separately investigate the performance of community algorithms (SteadyCom, FBA, and cFBA) in simulating important interactions in biotechnological applications by constructing five toy models representing the most common community interactions, namely, mutualism, commensalism, competition, competition-mutualism, and competition-commensalism. Application of different algorithms to communities with various microbial interactions alongside analysis of the results can provide insights into the dissimilarity of results as well as effectiveness of each algorithm in simulating different types of interactions.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cp\u003eBased on the experience gained from working in the domain of metabolic modeling of microbial communities, it became evident that the algorithms used to solve microbial community models do not always provide reasonable solutions for all types of interactions. To address this issue and to determine the appropriate algorithm for analyzing each type of microbial interaction, simplified toy models covering five common interactions were designed and utilized. This approach was chosen due to the impracticality of using genome-scale models with their extensive network size for investigation and comparison of the results.\u003c/p\u003e\n\u003cp\u003eTo represent the five common microbial community interactions of commensalism, competition, mutualism, commensalism-competition and mutualism-competition, five two-member (m\u003csub\u003e1\u003c/sub\u003e and m\u003csub\u003e2\u003c/sub\u003e) toy communities termed T1 to T5, respectively, were constructed using the compartmentalization framework as depicted in Figure 4.\u003c/p\u003e\n\u003cp\u003eAmong the 10 metabolites A to J in these models, A and/or E serve as the external substrate(s), each with a limited availability. Uptake rates of these substrates were restricted by fixing their values in all simulations as environmental constraints. Metabolites J and H act as unlimited substrates in the communities T1, T2, and T4. C and/or D were regarded as the shared metabolites that could be exchanged between members. In all toy communities, F and G represented the biomass of m1 and m2, respectively, and the total community biomass was obtained by summation of F and G. The remaining metabolites (B and I) were the internal metabolites within the networks of the individual members.\u003c/p\u003e\n\u003cp\u003eThese communities were analyzed using the three simulation algorithms of FBA, cFBA, and SteadyCom. To address the likely challenges in simulations, diverse scenarios were considered for each community according to real situations in natural communities and our experiences working with these algorithms. Additionally, these scenarios aimed to assess the algorithms\u0026apos; ability to uphold their claimed features, such as balanced growth \u0026ndash; a fundamental principle in cFBA and SteadyCom.\u003cbr\u003e\u0026nbsp;The details for various runs are provided in Table 1. The runs are distinguished by two altering conditions: the equality/inequality of biomass yields of the two members (as indicators of relative growth rates of single species) and the uptake rate of the specialized substrate for each member. Equal biomass yields equal to 1 were chosen to model communities with closely matched species, while unequal biomass yields were used to simulate communities with dissimilar members (microalgae and bacteria). To adjust biomass yield of members, the stoichiometric coefficient of metabolite F (biomass of m1) or G (biomass of m2) in the relevant biochemical reaction network was altered. Setting the coefficients of F(G) at 1 resulted in biomass yield for m1(m2) being equal to 1 on its specialized substrate A(E), while biomass yield equal to 2 was obtained by setting the relevant coefficient equal to 2. This means that a distinct metabolic network should be envisioned for toy models T1-T5 in cases with unequal biomass yields. Therefore, toy models T1-T5 shown in Figure 4 only illustrates the cases with the biomass yields for m1 and m2 being equal to 1.Three biomass yield cases (a: yield of m1 = yield of m2 = 1, b: yield of m1 = 2 = 2\u0026times;yield of m2, and c: vice versa of b) were considered for each community. Additionally, different fixed uptakes rates of A and/or E where applicable were used to simulate the scarcity of substrates while the exchange flux of metabolites J, C, H, and D were unconstrained. Overall, 6 and 14 runs were performed with equal and unequal yields, respectively.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;1. Designed computer experiments (runs) and their conditions using toy models (T1-T5).\u003c/p\u003e\n\u003cdiv align=\"Left\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"528\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.416666666666666%\" rowspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eInteraction type\u003csup\u003e*\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.712121212121213%\" rowspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eRun code: model-run no.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"30.87121212121212%\" colspan=\"5\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eConditions\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.272727272727273%\" rowspan=\"13\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.090909090909092%\" rowspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eInteraction type\u003csup\u003e*\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.090909090909092%\" rowspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eRun code: model-run no.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.545454545454547%\" colspan=\"5\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eConditions\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.435736677115987%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoeff. of\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.8213166144200628%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.84012539184953%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eSubs. uptake rate (mmol/h)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.808777429467085%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoeff. of\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.8213166144200628%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"27.272727272727273%\" colspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003eSubs. uptake rate (mmol/h)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"9.748427672955975%\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.748427672955975%\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.830188679245283%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.465408805031446%\"\u003e\n \u003cp\u003e\u003cstrong\u003eA\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.465408805031446%\"\u003e\n \u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.320754716981131%\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.547169811320755%\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.830188679245283%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.522012578616351%\"\u003e\n \u003cp\u003e\u003cstrong\u003eA\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.522012578616351%\"\u003e\n \u003cp\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.679611650485437%\" rowspan=\"6\" valign=\"top\"\u003e\n \u003cp\u003eCm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.932038834951456%\"\u003e\n \u003cp\u003eT1-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.019417475728155%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.019417475728155%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.7475728155339805%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.932038834951456%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.932038834951456%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.320388349514563%\" rowspan=\"4\" valign=\"top\"\u003e\n \u003cp\u003eM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.320388349514563%\"\u003e\n \u003cp\u003eT3-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.990291262135922%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"4.660194174757281%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.7475728155339805%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.349514563106796%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.349514563106796%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003eT1-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.650485436893204%\"\u003e\n \u003cp\u003eT3-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.737864077669903%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.825242718446602%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003eT1-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.650485436893204%\"\u003e\n \u003cp\u003eT3-4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.737864077669903%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.825242718446602%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003eT1-4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.650485436893204%\"\u003e\n \u003cp\u003eT3-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.737864077669903%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.825242718446602%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003eT1-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.739130434782608%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.739130434782608%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9565217391304348%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003e-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.434782608695652%\" rowspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003eCm-Cp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.434782608695652%\"\u003e\n \u003cp\u003eT4-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.826086956521739%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.217391304347826%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9565217391304348%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.347826086956522%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.347826086956522%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003eT1-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.650485436893204%\"\u003e\n \u003cp\u003eT4-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.737864077669903%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.825242718446602%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.777301927194861%\" rowspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003eCp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003eT2-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.638115631691649%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.638115631691649%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9271948608137044%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003e\u003csup\u003e-\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.278372591006423%\"\u003e\n \u003cp\u003eT4-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.708779443254818%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.139186295503212%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9271948608137044%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.207708779443255%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.207708779443255%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003eT2-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.739130434782608%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.739130434782608%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9565217391304348%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.434782608695652%\" rowspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003eM-Cp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.434782608695652%\"\u003e\n \u003cp\u003eT5-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.826086956521739%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.217391304347826%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9565217391304348%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.347826086956522%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.347826086956522%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003eT2-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.524271844660194%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.16504854368932%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.650485436893204%\"\u003e\n \u003cp\u003eT5-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.737864077669903%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.825242718446602%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"2.1844660194174756%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.436893203883495%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"11.777301927194861%\" valign=\"top\"\u003e\n \u003cp\u003eM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003eT3-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.638115631691649%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.638115631691649%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9271948608137044%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.850107066381156%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"10.278372591006423%\"\u003e\n \u003cp\u003eT5-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"7.708779443254818%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"5.139186295503212%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"1.9271948608137044%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.207708779443255%\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.207708779443255%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"100%\" colspan=\"15\" valign=\"top\"\u003e\n \u003cp\u003e\u003csup\u003e*\u0026nbsp;\u003c/sup\u003eCm: Commensalism, M: Mutualism, Cp: Competition\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIt should be noted that the external fluxes in FBA and cFBA are expressed in mmol/h/gCom (millimoles per hour per gram dry weight of community), while in SteadyCom, fluxes are expressed in mmol/h. This distinction arises due to taking one gram of community biomass in FBA and cFBA, while SteadyCom allows the user to adjust this value, though its default value is 1. Given that, the total biomass in SteadyCom was set at 1 gram in our runs and hence the unit of external fluxes in this method aligns with the other two in mmol/h/gCom.\u003c/p\u003e\n\u003cp\u003eFurthermore, the internal fluxes in SteadyCom are in mmol/h, corresponding to the aggregate flux, which results from the multiplication of flux by the biomass of each member. Due to the default assumption of a total community biomass of 1 gram, the unit of internal fluxes in SteadyCom becomes mmol/h/gCom. In contrast, the internal fluxes in cFBA are mmol/h per gdw of each individual member. In the results section therefore we multiplied these fluxes by the abundance of the respective member (grams of member per 1 gram of community biomass). This leads to the unit of reported internal fluxes being mmol/h/gCom. Finally, the internal fluxes in FBA are expressed as mmol/h/gCom. In sum, despite these varying units across different methods, all fluxes are comparable in results section. Since we assumed a total community biomass of 1 gram for all runs, the unit of fluxes are simplified and expressed as mmol/h.\u003c/p\u003e"},{"header":"3.\tResults and Discussions ","content":"\u003cp\u003eResults obtained from application of the three computational algorithms to two-member models T1-T5 will be separately discussed based on the type of microbial interactions. \u0026nbsp;For each interaction, the effect of conditions (see Table 1) on community behavior will be investigated. Furthermore, the results obtained by application of each algorithm will be compared with those of the other two algorithms under the same conditions. A complete set of results for runs in Table 1 is provided in supplementary material.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e3.1. Commensal Community (T1)\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eCommensalism, a beneficiary interaction for one member in community, can be found in various natural microbial ecosystems such as biogas-producing microbial communities or the gut microbiome. Toy model T1 consisting of members m1 and m2 with specialized and limited substrates A and E, respectively, has been designed as a community that exclusively features the commensal interaction with growth of m2 relying on m1 through the shared metabolite C. \u0026nbsp;This commensal community was analyzed using FBA, cFBA and SteadyCom under six different conditions (runs T1-1 to T1-6 in Table 1). Comparisons of the results obtained via application of these algorithms showed identical results for each run as given in Table 2. In all runs of commensal community, the cFBA results indicate that there is a unique optimal solution, and for other x\u003csub\u003em1\u003c/sub\u003e values, the system becomes infeasible.\u003c/p\u003e\n\u003cp\u003eTable 2. Identical results of commensal community obtained by FBA, cFBA and SteadyCom algorithms\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n\u003cp\u003eHowever, alterations were observed in the results of different runs due to the dissimilar conditions. In case of T1-1 with equal fluxes of A and E and equal biomass yields of 1, results show equal fluxes of F and G, community growth rate of 2 h\u003csup\u003e-1\u003c/sup\u003e and equal mass fraction of members (0.5). Two fold increase in uptake of A in T1-2 (compared to T1-1) resulted in higher flux of F alongside constant flux of G due to the unchanged flux of E, triggering higher community growth rate (3 h\u003csup\u003e-1\u003c/sup\u003e). To counterbalance the higher growth rate at constant flux of G, mass fraction of m2 lessened and this in turn increased the mass fraction of m1 (0.67). Since the increased production flux of C by m1 in case T1-2 could not be taken up by m2, C was exchanged with exterior as compared to T1-1 showing no exchange of C. This shows that higher supply of a dedicated substrate to a member with other conditions remaining constant will result in higher community growth rate and increased mass fraction of that member to comply with the equality of members\u0026rsquo; growth rates.\u003c/p\u003e\n\u003cp\u003eCases T1-3,4 consider commensal communities with one member having higher biomass yield on its dedicated substrate than the other member while other conditions remained the same as case T1-1. Of these two cases, explanations are only given for case T1-4 where yield of biomass formation for m2 on E was increased by two fold by setting the coefficient of G equal to 2 compared to case T1-1. This resulted in a higher flux of G with no change in flux of F and hence a higher community growth rate of 3 h\u003csup\u003e-1\u003c/sup\u003e. To satisfy the equality of growth rates, mass fraction of m2 was enlarged while that of F was reduced. One can therefore conclude that increasing biomass yield of one member results in the enlargement of its mass fraction provided that other conditions are unchanged. This also applies to the case T1-3 where biomass yield of m1 was doubled and its mass fraction was increased.\u003c/p\u003e\n\u003cp\u003eCase T1-5 was a case similar to T1-3 with respect to biomass yield and other conditions apart from uptake flux of A by m1 was doubled. Figure 5 depicts the flux distribution of T1-5 where fluxes of F and C were doubled while flux of G remained unchanged due to unaltered flux of E, all compared to fluxes in T1-3. To comply with the higher community growth rate of 5 h\u003csup\u003e-1\u0026nbsp;\u003c/sup\u003eas a result of higher overall production of F and G, mass fraction of m2 decreased and this resulted in an increase in mass fraction of m1. Since consumption of C by m2 was constrained by the limited availability of E, a part of produced C by m1was released to exterior.\u003c/p\u003e\n\u003cp\u003eThe effect of variation of uptake rate of A at constant biomass yields on flux distribution can be analyzed by comparison of the results of cases T1-3 and T1-5. It can be seen that doubling the flux of A in T1-5 compared to T1-3 resulted in increased mass fraction of m1 alongside a higher community growth rate. This also applies to the cases of T1-1 and T1-2 as well as cases T1-4 and T1-6 with equal values of biomass yields and doubled supply of A. As can be seen in Table 2, mass fraction of m1 and community growth rates both increased.\u003c/p\u003e\n\u003cp\u003eAltogether in commensal community, different biomass yields of members and different supply of substrates significantly affected the flux distribution, member abundances and community growth rate. However, the performance of the three algorithms used for flux analysis were reasonable and the same results were obtained for each case.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e3.2. Competitive Community (T2)\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eCompetition is a prevalent interaction in various communities, particularly in industrial applications of microbial consortia, such as wastewater treatment. Competition for limited substrate is a challenging interaction for metabolic analysis and algorithms have been developed to confront the existing difficulties. Model T2 (see Figure 4) represents a community with competition as the sole interaction in which growth of both members rely on the limited substrate A.\u003c/p\u003e\n\u003cp\u003eCommunity growth rates obtained by cFBA algorithm at varying mass fraction of m1 for case T2-1 plotted in Figure 6A show the same community growth rate of 1 h\u003csup\u003e-1\u003c/sup\u003e across all abundances. In other words, the maximum growth rate of competitive community with equal biomass yields can be achieved at all mass fractions. This is a case where the corresponding linear programming problem show multiple optimal solutions resulting in the same optimized value of the objective function despite showing different solutions (fluxes and mass fractions). By application of FBA and SteadyCom algorithms, identical fluxes as given in Figure 6D were obtained. Actually, this solution was one of the multiple solutions obtained via cFBA in which substrate A was completely consumed by m1, leading to zero production rate of G (biomass of m2).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;This at first may seem contradictory with equal growth rates of members (\u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e = \u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e\u003csub\u003e1\u0026nbsp;\u003c/sub\u003e=\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e\u003csub\u003e2\u003c/sub\u003e) assumed in SteadyCom. However, it can be explained by the fact that the variables in SteadyCom are aggregate fluxes. Considering V\u003csub\u003ebiomass, m2\u003c/sub\u003e = \u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e x\u003csub\u003em2\u003c/sub\u003e as aggregate biomass formation flux of m2, one can perceive that zero value of V\u003csub\u003ebiomass, m2\u003c/sub\u003e could be as a result of zero x\u003csub\u003em2\u003c/sub\u003e, not zero value of \u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e\u003csub\u003e2\u003c/sub\u003e and hence \u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e\u003csub\u003e1\u003c/sub\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e=\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003cspan style=\"text-align: start;color: rgb(0, 0, 0);background-color: rgb(255, 255, 255);font-size: 11px;\"\u003e\u0026mu;\u003c/span\u003e\u003csub\u003e2\u003c/sub\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e can be satisfied even in this special solution. In fact, this is only one of the multiple solutions of case T2-1 leading to maximal community growth rate. Actually,\u0026nbsp;\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e\u003cspan dir=\"LTR\"\u003eSteadyCom terminates by finding the first optimal solution and the reasonable optimal answer might sometimes lay in the middle of the range of multiple optimal solutions.\u0026nbsp;\u003c/span\u003e\u003cspan dir=\"LTR\"\u003eIt should however be mentioned that the SteadyCom in COBRA toolbox of Matlab has provided an option called \u0026quot;BMcon\u0026quot; allowing preset values of members biomass which can be used to obtain a more realistic solution.\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eFlux distribution of case T2-2(3) with members having unequal biomass yields given in Figure 6E(F) show that all three algorithms promoted only the growth of member with the higher biomass yield (m1 for T2-2 and m2 for T2-3), leading to the complete consumption of substrate A by this member. Figure 6B(C) presenting the cFBA results for T2-2(3), shows the monotonic escalation of community growth rate with mass fraction of m1(m2) until reaching its highest value at x\u003csub\u003em1\u003c/sub\u003e = 1(x\u003csub\u003em2\u003c/sub\u003e=1) beating one member. Similar to the previous case, more realistic suboptimal solutions can be found by using \u0026quot;BMcon\u0026quot; command at fixed biomass values.\u003c/p\u003e\n\u003cp\u003eThe occurrence of zero abundance in SteadyCom had also been previously reported by some researchers\u0026nbsp;[25, 27]. In simulation of gut microbiota using a 28-species community by SteadyCom, results indicated that only five/six species had non-zero abundances in different diet scenarios while other members were omitted\u0026nbsp;[25]\u0026nbsp;The members with low biomass yields exhibited zero abundances, similar to our cases T2-2,3. Mutualism and commensalism were reported as the dominant interactions of remaining members while the interactions of omitted species were not specified. According to our results, competition in their case might be a contributing factor in zero abundances of most members. In another study on chronic wound microbiota, a 12-species community was simulated by SteadyCom and five members with zero abundances were reported\u0026nbsp;[27]. However, the specific type of interactions for omitted members were not reported.\u003c/p\u003e\n\u003cp\u003eCompetitive communities with equal biomass yields are susceptible to showing multiple optimal solutions which can only be visualized by plotting the growth rate vs. mass fraction (such as Figure 6D) using cFBA. SteadyCom and FBA algorithms terminate by finding the first feasible solution and may sometimes produce less reasonable answers, such as the elimination of a member. As in natural competitive communities, it is expected that all members would coexist even with varying biomass levels. Incorporation of experimental data/general knowledge of member abundances into simulations can help refine the results and enhance their biological relevance. To achieve a more realistic solution in SteadyCom, the \u0026quot;BMcon\u0026quot; option can be utilized.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWhen the biomass yields of members are unequal, all three algorithms generate a result where only one member would remain. This outcome aligns with the objective function of maximizing growth, which results in the member with a larger biomass yield monopolizing the substrate. Since maximizing growth might not accurately represent the goals of competitive communities in reality, a suboptimal solution could offer a more realistic outcome or alternatively experimental data on member abundances may be incorporated to allow better mirror real-world results.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e3.3. Mutualistic Community (T3)\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eMutualistic interaction refers to a symbiotic relationship between two members relying on each other for growth. This interaction often coexists with other types of interactions in microbial communities. The toy model T3, depicted in Figure 4, exemplifies the mutualism interaction facilitated through the exchange of metabolites C and D as the sole form of interaction within this toy model while A or E functions as specialized substrate for each member. The interdependence of these members resulted in distinct outcomes. Five different conditions were examined in cases of T3-1 to T3-5 to consider the effect of variations on biomass yields and substrates uptake rates. Coexistence of the two members in this model is expected since the shared metabolites D and C are required for growth of m1 and m2, \u0026nbsp;respectively, in addition to the dedicated substrates A and E.\u003c/p\u003e\n\u003cp\u003eFBA results are firstly described and discussed for the examined cases as these were inconsistent with the results obtained via cFBA and SteadyCom. In all cases, FBA showed the growth of only one member (m1 in most cases and m2 in T3-3) while the other member showed no growth. This means that the growing member obtains the required shared metabolites (C or D) by the non-growing member (see Figures S11-S15 of supplementary material). Actually, the member showing no growth consumed its dedicated substrate to solely provide the metabolite required for the other member\u0026rsquo;s growth. Consequently, the community biomass was solely derived from the biomass reaction of the growing member. Community growth rate of 1 1/h was obtained for case T3-1 with biomass yields of 1, while this was 2 1/h for all other runs in which biomass yield of one member was 2. In case T3-4 (T3-5) where extra substrate A (E) were taken up, release of shared metabolite C (D) by community to exterior environment was observed. Although donation of the required metabolites by a non-growing member in a microbial community to other members has previously been reported when using FBA algorithm, the type of interaction leading to this situation was not specified [18].\u003c/p\u003e\n\u003cp\u003eResults obtained by cFBA and SteadyCom algorithms for mutualistic community under different conditions are illustrated in Table 3. Where more reasonable results for this type of interaction were predicted by these two algorithms.\u003c/p\u003e\n\u003cp\u003eIn run T3-1 with equal biomass yields and equal dedicated substrate availabilities, both cFBA and SteadyCom algorithms demonstrated non-zero abundances for the two members, though one was much lower. Similar to previously discussed cases, cFBA allowed visualization of the existing multiple optimal solutions at x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003e(mass fraction of m1 in community) ranging from 0.001 up to 0.999 (see Figure 7A) and outside this range the system becomes infeasible, while SteadyCom gave only one optimal solution at x\u003csub\u003em1\u003c/sub\u003e = 0.001.\u003c/p\u003e\n\u003cp\u003eTable 3. Comparison of the results of mutualistic community (T3) predicted by cFBA and SteadyCom algorithms under different conditions\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eFor cases T3-2,3,4,5 with unequal biomass yields, identical unique solutions were obtained by cFBA and SteadyCom, while FBA predicted different results. Community growth rate obtained by FBA was slightly higher compared to other algorithms as FBA led to no growth of the member with lower biomass yield while balanced growth assumption of the other algorithms enforced growth of that member, though at a small rate, lowering the community growth rate. This reveals that coexistence of both members in community may not result in a higher community growth rate, but it aligns more closely with reality. Although the same maximized community growth rate of 1.998 h\u003csup\u003e-1\u003c/sup\u003e was obtained for cases T3-2,3, abundance of the member with higher biomass yield was higher than that of the \u0026nbsp;other member (see Figure 7B,C). Results of case T3-4 were identical to those of T3-2, apart from C being released by community to exterior at a rate of 1 mmol/h/gCom in case T3-4 due to doubling the uptake of A. Case T3-5 having double uptake rate of E with other conditions being unchanged compared to case T3-2 led to the decreased community growth rate alongside the decreased x\u003csub\u003em1\u003c/sub\u003e, the release of D as community product and higher and lower exchange rates of C and D by m2 and m1, respectively.\u003c/p\u003e\n\u003cp\u003eIn summary, FBA was found an inappropriate choice for analyzing the metabolic network of a mutualistic community due to providing the required shared metabolite by the non-growing member. SteadyCom and cFBA were shown to provide reasonable identical results and hence appear to be suitable methods for simulating mutualistic interaction.\u003c/p\u003e\n\u003cp\u003eComparing our findings to a study described in the introduction section that reported favorable outcomes using the SteadyCom method [18], reveals interesting insights. The community investigated in that study involved both mutualistic and competitive interactions. Similar to our results in a mutualistic community, they obtained reasonable outcomes when compared to FBA. It is noteworthy that in their study, competition did not revolve around a limited external substrate. Consequently, the reported results in that context were considered plausible.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e3.4.\u003c/strong\u003e \u003cstrong\u003eCommensal-Competitive Community (T4)\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eIn real cases, a combination of interactions as opposed to single interactions, with the simplest being the dual interaction, could occur which needs consideration. Commensal-competitive community is an important case among the communities with dual interactions where members compete for the same substrate while a metabolite formed by one member is necessary for the growth of another member. Designed community T4 (see Figure 4) represents a simple commensal-competitive community with both members requiring substrate A and metabolite C, produced by m1, being necessary for growth of m2. This community was examined under three different conditions, the results of which are presented in Figure 8.\u003c/p\u003e\n\u003cp\u003eFigure 8A illustrates the variation of community growth rate with x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003eobtained via cFBA for case T4-1 having equal yields. System was feasible only for a range of x\u003csub\u003em1\u003c/sub\u003e \u0026ge; 0.5 where a unique maximized community growth rate of 1 h\u003csup\u003e-1\u0026nbsp;\u003c/sup\u003ewas attained, suggesting the existence of multiple optimal solutions. By increasing x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003ewithin this range, metabolite C was concurrently released as product of m1. The same optimized community growth rate of 1 h\u003csup\u003e-1\u003c/sup\u003e was found by SteadyCom and FBA however different values of 1 and 0.5 for x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003ewere predicted, respectively. Comparison of these results with cFBA plot (Figure 8A) shows that the results obtained by SteadyCom and FBA for case T4-1 lies at the limits of optimal range of x\u003csub\u003em1\u003c/sub\u003e obtained by cFBA and hence only represent one of the optimal solutions. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn case T4-2 where biomass yield of m1 was doubled, cFBA resulted in feasible solutions for \u0026nbsp;x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003e\u0026ge; 0.667 with an increasing trend of community growth rate with x\u003csub\u003em1\u003c/sub\u003e, leading to the highest rate of 2 h\u003csup\u003e-1\u003c/sup\u003e by dominance of m1 at x\u003csub\u003em1\u003c/sub\u003e=1. Flux distribution predicted by FBA and SteadyCom were as predicted by cFBA which is given in Figure S16. As mentioned in Section 3-2, the balanced growth assumption was satisfied despite observing zero mass fraction of m2. By doubling biomass yield of m2 in run T4-3, all algorithms led to a community growth rate of 1.5 (1/h) with substrate A being equally shared between members as presented in Figure 8B. The same x\u003csub\u003em1\u003c/sub\u003e (0.33) was obtained by SteadyCom and cFBA however the community growth rate was lower compared to case T4-2. This can be explained by the fact that commensalism demands the growth of m1 to provide metabolite C for growth of m2 with higher biomass yield. This in turn diminishes the maximized growth rate of community as the member with lower yield should also grow alongside the other member.\u003c/p\u003e\n\u003cp\u003eOverall, competitive interaction in commensal-competitive community supports the dominance of independent member provided that it has the higher biomass yield on the shared substrate. On the contrary, when dependent member has higher biomass yield, commensalism forces this member to obtain a shared metabolite produced by the other member and hence both members coexist.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003e3.5.\u003c/strong\u003e \u003cstrong\u003eMutualistic-Competitive Community (T5)\u003c/strong\u003e\u003c/h2\u003e\n\u003cp\u003eAmong the communities with dual microbial interaction, mutualistic-competitive community is another important type observed in various natural and industrial microbial communities, including yogurt-producing microbiomes. To investigate this type of dual interactions, community T5, as depicted in Figure 4 was designed in which growth of m1 depends on m2 and vice versa in addition to competence of m1 and m2 for the common limited substrate A.\u003c/p\u003e\n\u003cp\u003eThree cases T5-1,2,3 with equal and unequal biomass yields were considered. Overall, results were similar to those of mutualistic community (T3). In all examined cases, FBA predicted growth of only one member obtaining its essential metabolite by the non-growing member. However, SteadyCom and cFBA both predicted the growth of both members, though at various extents.\u003c/p\u003e\n\u003cp\u003ecFBA plot of case T5-1 (Figure S18) with equal yields showed the existence of multiple optimal solutions at optimal community growth rate of 0.5 h\u003csup\u003e-1\u003c/sup\u003e and x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003eranging from very low values (0.0005) up to values close to 1 (0.9995). \u0026nbsp;By applying SteadyCom, one optimal solution was obtained at x\u003csub\u003em1\u003c/sub\u003e= 0.9995 which lies within the multiple optimal solutions. For cases with unequal yields (T5-2,3), cFBA plots (Figures S19,20) showed increasing and decreasing trends of the community growth rate with x\u003csub\u003em1\u003c/sub\u003e for cases with doubled biomass yields of m1 (case T5-2) and m2 (case T5-3), respectively. Therefore, cFBA predicted a unique optimal solution for case T5-2 (T5-3) at x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003e= 0.9995 (x\u003csub\u003em1\u0026nbsp;\u003c/sub\u003e= 0.0005). The same results were obtained by SteadyCom due to the existence of unique solutions for cases T5-2,3. Compared to results obtained by FBA, optimal community growth rate obtained by SteadyCom and cFBA were slightly lower (0.9995 1/h compared to 1 1/h) due to metabolites C and D being produced by growing member as opposed to non-growing member in FBA.\u003c/p\u003e\n\u003cp\u003eOverall, the performance of the three algorithms for simulating competition alongside mutualism were almost similar to that of mutualistic community. SteadyCom algorithm showing zero aggregate fluxes for one member under equal yields in community with solely competitive interaction, led to the more realistic coexistence of both members for competition alongside mutualism.\u003c/p\u003e"},{"header":"4.\tConclusion","content":"\u003cp\u003eTo assess and compare the performances of three commonly used microbial community algorithms (FBA, cFBA, and SteadyCom) in simulating the behavior of communities, five toy models were constructed each representing one of the most common microbial interactions. Results showed distinct capabilities of algorithms in simulating the diverse microbial interactions.\u003c/p\u003e\n\u003cp\u003eThe three algorithms equally performed when applied to the commensal community with a unique solution under all examined conditions. Challenges were faced by application of these algorithms to competitive community. At equal biomass yield of members, multiple optimal solutions were obtained using cFBA algorithm. However, SteadyCom and FBA could give only one of these solutions lying at a point with zero abundance of one member (growth of only one member) which was misleading. Despite the balanced growth assumption in cFBA and SteadyCom, application of these two algorithms to communities with unequal biomass yields still faces limitations in depicting the coexistence of both members (zero abundance of one member), though balanced growth assumption was mathematically satisfied and the uniqueness of solution was confirmed by cFBA plot. In natural ecosystems however competitive communities often exhibit simultaneous growth of members as a result of higher-level strategies. Other constraints, objective functions or a combination of the two may govern the natural communities instead of taking the community growth rate as the objective function. This indicates that further research and development are necessary to enhance the accuracy and reliability of community metabolic modeling algorithms for competitive interactions. Of course, suboptimal solutions which are more reasonable and biologically plausible can be attained by fixing the abundances at specified experimental values.\u003c/p\u003e\n\u003cp\u003eSimulation of mutualistic community by cFBA and SteadyCom led to growth of both members in community due to the balanced growth assumption and dependence of members on each other, while FBA led to no growth of the member providing the necessary metabolite for the growth of the other member and this in turn allowed slightly higher community growth rate.\u003c/p\u003e\n\u003cp\u003eIncorporation of commensal interaction into a competitive community demonstrated improved modeling performance with FBA compared to competitive alone communities. In the context of a community with equal biomass yields of members, cFBA showed multiple optimal solutions while FBA and SteadyCom produced only one these solutions. On the contrary to FBA resulting in presence of all members, SteadyCom led to one member with zero abundance not matching the reality.\u0026nbsp;\u003cbr\u003e\u0026nbsp;By introducing mutualism to competitive community, the results closely resembled those of the mutualistic community. Similarly, FBA exhibited less reasonable results due to the production of metabolites from non-growing members. On the other hand, cFBA and SteadyCom provided lower community growth rate in comparison to FBA in scenarios with unequal biomass yields however both members coexisted in the community.\u003c/p\u003e\n\u003cp\u003eAltogether, when using SteadyCom, it is crucial to examine the existence of multiple optimal solutions since more reasonable answers may exist. In scenarios where only a single unreasonable solution exists, incorporating experimental or scientific knowledge about community abundances may be valuable in obtaining a suboptimal yet more reasonable solution.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analyzed during this study, including a comprehensive set of models and results, are available in the supplementary material accompanying this published article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eFaust K, Raes J (2012) Microbial interactions: from networks to models. 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J appl microbiol127:1576-1593. https://doi.org/10.1111/jam.14421\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bioprocess-and-biosystems-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Bioprocess and Biosystems Engineering](https://www.springer.com/journal/449)","snPcode":"449","submissionUrl":"https://submission.nature.com/new-submission/449/3","title":"Bioprocess and Biosystems Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Microbial Community, Metabolic Modeling, Microbial Interaction, SteadyCom, cFBA, FBA","lastPublishedDoi":"10.21203/rs.3.rs-4226944/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4226944/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo explore the impact of microbial interactions on outcomes from three prevalent algorithms (Flux Balance Analysis (FBA), community FBA (cFBA), and SteadyCom) analyzing microbial community metabolic networks, five toy community models representing common microbial interactions were designed. These include commensalism, mutualism, competition, mutualism-competition, and commensalism-competition. Various scenarios, considering different biomass yields and substrate constraints, were examined for each type. In commensal communities, all algorithms consistently produced similar results. However, changes in biomass yields and substrate constraints led to variable abundances and community growth rates within a broad range (0.33 to 0.8 and 2 to 5, respectively). For competitive communities, all algorithms predicted growth of fastest-growing member. To comply with the natural coexistence of members, suboptimal solutions over optimal point are recommended. FBA faced challenges in modeling mutualism, consistently predicting growth of only one member. Although cFBA and SteadyCom resulted in a lower community growth rate, coexistence of both members were satisfied. In toy models with dual interactions, more realistic outcomes were achieved contrary to purely competitive model as the dependency fosters the coexistence which was missing in the competitive only scenarios. These findings emphasize the importance of algorithm choice based on specific microbial interaction types for reliable community behavior predictions.​\u003c/p\u003e","manuscriptTitle":"Effect of Microbial Interactions on Performance of Community Metabolic Modeling Algorithms: Flux Balance analysis (FBA), Community FBA (cFBA) and SteadyCom","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-12 15:55:17","doi":"10.21203/rs.3.rs-4226944/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-14T08:12:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-13T17:38:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"22193157757882139142120976072265615310","date":"2024-05-04T22:45:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7aa94efd-e56c-4967-b73d-a0bb00bab3b3","date":"2024-04-26T08:27:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-18T15:42:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-09T01:49:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-09T01:49:37+00:00","index":"","fulltext":""},{"type":"submitted","content":"Bioprocess and Biosystems Engineering","date":"2024-04-06T10:27:18+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bioprocess-and-biosystems-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Bioprocess and Biosystems Engineering](https://www.springer.com/journal/449)","snPcode":"449","submissionUrl":"https://submission.nature.com/new-submission/449/3","title":"Bioprocess and Biosystems Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6e7ca814-e5a5-40b8-816e-cdd5df884837","owner":[],"postedDate":"April 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-07-30T01:09:54+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-12 15:55:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4226944","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4226944","identity":"rs-4226944","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}