Integrated Knowledge-based Reverse Engineering of Metabolic Pathways

Transcription

1 Integrated Knowledge-based Reverse Engineering of Metabolic Pathways Shuo-Huan Hsu, Priyan R. Patkar, Santhoi Katare, John A. Morgan and Venkat Venkatasubramanian School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA Abstract A framework for reverse engineering of metabolic pathways is proposed. It is driven by the knowledge of the reaction stoichiometry and constraints from flux balance analysis. For a desired product, the framework predicts the theoretical yield of the product, and generates all the possible reaction network topologies capable of producing the maximal theoretical yield. Two rules are used to select the most useful pathways. The first one is ATP yield. The pathways with higher ATP production are valued because they are energetically favorable. The second rule is calculating the number of gene knockouts, which indicates the cost of engineering the organism. Based on these two criteria, this framework can generate several pathway candidates for the metabolic engineer to enhance the yield of the product secreted by an organism. We illustrate the entire procedure for ethanol production. Keywords: Reverse engineering, metabolic pathways, flux balance analysis, multiple solutions, theoretical yield 1. Introduction Traditional model building procedures such as postulating an hypothesis to explain data, translating the hypothesis into a model, validating the model against limited data and manual refinement of hypothesis based on model-data mismatch are too slow in the era of bioinformatics and systems biology. The pace of data generation warrants automated tools that can aid a human expert in these tasks. A rational automated methodology is required as against the traditional guess-and-test procedure. This is particularly important because systematic understanding of the dynamics of a cell requires reverse engineering of metabolic networks - construction and subsequent analysis of the interactions of cellular species from transciptome, proteome and metabolic data. The large number of species, their interactions and variability based on the environment make this task particularly difficult. The problem of automating the process of constructing metabolic pathways has received considerable attention in the literature. Since it is difficult to get the dynamic metabolic data of the cells from the experiment until now, the knowledge of steady state condition Author to whom all correspondence should be addressed. venkat@ecn.purdue.edu, Phone: (765) , Fax: (765)

2 can provide useful results. Synthesis of metabolic pathways using artificial intellgence (AI) was first addressed in 1988 (Seressiotis and Bailey, 1988). Given the database of enzyme and substrate description, the AI search algorithms can identify the qualitative feasible pathways (Mavrovouniotis et al., 1990). Graph theoretical approaches have been applied to constructing a metabolic or reaction network (Arita, 2000, Seo et al., 2001, Fan et al., 2002). The graph theory based approaches require the stoichiometric information only and can enumerate all possible pathways. However, the algorithm is efficient for relatively small networks. Another valuable method of steady state analysis is Flux Balance Analysis, FBA (Varma and Palsson, 1993a), which formulates the problem as a linear program. FBA requires the information about the stoichiometric ratio of each reaction, requirements for growth, and the measurement of a few strainspecific parameters. FBA is based on the fact that the metabolic transients are typically rapid compared with the rates of cellular growth and environmental changes. Therefore, the pseudo-steady state assumption is applied, and leads the following flux balance equation: S v = 0 (1) where S is the matrix containing the stoichiometric ratios of the metabolic reactions and v is the flux vector. In general, this equation is underdetermined since the number of fluxes normally exceeds the number of metabolites. The problem can be solved as a linear program to obtain a rational solution by specifiying an obective such as maximizing the organism growth, maximizing the yield of a metabolite, etc. There are several applications of FBA, such as finding minimal reaction sets under different environments (Burgard et al., 2001), estimating the performance subect to gene addition or deletions (Burgard and Maranas, 2001), testing hypothesized metabolic obective functions (Burgard and Maranas, 2003). It is also possible that there are multiple solutions for the same obective value. Lee et al. (2000) proposed an algorithm to enumerate all possible linear programming solutions. Therefore, we can only expect the upper/lower bound of the fluxes from the analysis. We propose a framework to construct metabolic pathways with the theoretical yields based on the flux balance analysis. The multiple solutions are also discussed, and we propose an alternative way to enumerate the solutions. We apply rules for the screening of the candidate pathways that reduce the number of candidates to a reasonably small value. The procedure is illustrated using ethanol production as an example. 2. Prediction of theoretical yields using FBA In typical flux balance analysis, the obective is usually maximizing the flux of biomass production. This is perceived to be an evolutionary obective for an organism. However, there can be other rational choices for the obective, for example, maximizing the flux of a certain metabolite or ATP. Since the quantity of interest here is the theoretical yield of some product P, the obective function is set to be the maximization of the flux v p, constrained by the flux v s of a certain substrate S. The theoretical yield can be represented by v p /v s. For convenience in formulating the problem, we assume the

3 substrate flux v s = -1 (the negative sign indicates the consumption of the metabolite). The complete formulation is as follows: max v v s s i i i s, p subect to s v s v s v v s ATP, 0, = = 1 v v R i M i M i M ATP,min irr i r p (2) where s i is the stoichiometric coefficient of the i th metabolite in the th reaction, v is the flux of the th reaction, M i is the set of internal metabolites, M r is the set of reactants other than the substrate, M p is the set of products, R irr is the set of irreversible reactions. The matrix S = {s i } represents the reaction network structure. The second to last equation in (2) satisfies the constraint that a minimum level of ATP is required for maintenance and therefore for the survival of the organism. Eq. (2) is a linear porgram, which can be solved efficiently by commercial software such as CPLEX. 3. Enumeration of multiple topologies with the same theoretical yield It has been shown in the literature that there are multiple solutions for the optimal yield (Phalakornkule et al., 2000, Lee et al., 1997). Such alternative optimal networks can be important to metabolic engineers from the point of view of design. We introduce a new integer variable set y = {y }, where y indicates whether the th reaction is active or not. 1 if v 0 y = (3) 0 otherwise Then it is possible to visit the (k+1) st constraint successively: alternate optimum by adding the following y 1 (4) y, k where = { } y is k th alternate optimum. The set of successive constraints given by k y. k Eq. (4) ensure that the (k+1) st optimal solution y k+1 is different from all the previously visited optima y 1, y 2,..., y k. This constraint is nonlinear, and therefore the entire optimization problem becomes a mixed-integer-nonlinear program (MINLP). In general,

4 global optimality cannot be guaranteed for a nonlinear optimization problem. Therefore if the constraint (4) can be rewritten as a linear constraint, the problem can be simplified to an MILP, which can then be solved to global optimality. We define the set N k as follows: { 1} N (5) = y = k, k Then Eq. (4) can be written as a linear contraint by introducing Eq. (5): N k y y N 1 (6) k J \ Nk N is the cardinality of the set N k k. Additional constraints need to be included to ensure that all reactions are irreversible. The rationale for doing so arises from Eq. (3), where we enforce y = 0 if and only if v = 0. Then, if any reaction is actually reversible, it is decomposed into two irreversible reactions, the forward and the reverse. Therefore, the following constraints are added to the linear program: ε v y Ev (7) y y 1 (8) p + q where ε is a small positive number and E is a large number. Reaction p is a reversible reaction, which is decomposed into the corresponding forward and reverse reactions, whose fluxes are y p and y q respectively. The constraint given by Eq. (8) ensures that only one direction of the reversible reaction is active. The iterative procedure to enumberate the multiple optima is described as follows: Step 1: Solve the linear program (Eq. (2), (7) and (8)), and get the first optimum, y 1. Step k: Add constraint (6) to the linear program and resolve it to get y until the obective value decreases. Once all the optimal pathways have been obtained, different criteria can be used to discriminate between them. For instance, it is important to calculate the ATP production of all the optimal pathways. A pathway producing more ATP is a favorable choice over other optima because it is energetically more productive. Another important consideration can be the difficulty or effort required to genetically engineer a candidate pathway topology. If the topology is easy to engineer, the engineered strain can be made relatively fast, which means this pathway is practically obtainable. The number of genes to knockout or add can be used a measure of the genetic engineering cost or effort associated with the pathway. k

5 No. of pathways moles ATP/mole glucose Fig. 1 ATP production distribution of different topologies G6P G6P G6P F6P 6PG F6P F16bP F16bP 2K3D6PG DHAP GAP DHAP GAP GAP 3PG 2PG 3PG 3PG PEP glucose 2PG PEP PYR AcCoA EtOH glucose (a) Yield of EtOH = 2 Yield of ATP = 2 2PG PEP PYR AcCoA EtOH glucose (b) Yield of EtOH = 2 Yield of ATP = 1 FUM MAL SUC PYR AcCoA OAA succoa CIT AKG EtOH ICT (c) Yield of EtOH = 1.76 Yield of ATP = 4 Fig. 2 Different pathways for producing ethanol (Unit of yield: moles product/mole glucose) 4. Case study: Ethanol production in E. coli E. coli is a common host organism for the biosynthesis of many products due to its wellknown physiology and ease of genetic engineering. Therefore, we have selected E. coli as the host. Only the reactions in the central metabolism of E. coli are considered and we maximize the flux of ethanol given 1 mole of glucose. The theoretical yield of ethanol fermentation is 2 moles ethanol/mole glucose without ATP maintenance. We identified 86 different optimal topologies using the proposed algorithm for maximizing the ethanol flux without ATP maintenance. Fig. 1 shows the ATP production distribution for the different topologies. The maximum ATP flux among the solutions is 2 moles ATP/mole glucose. The framework identifies five different pathways with this maximum ATP flux, but their topologies are quite similar with the only differences being the use of different cofactors for certain reactions. Figs. 2(a) and 2(b) show two different topologies for producing ethanol, corresponding to the two well studied glycolysis pathways, EMP (Embden-Meyerhof-Parnas) and ED (Entner-Doudoroff) pathways. By including a maintenance cost of 4 ATP moles per mole of glucose as reported by Varma and Palsson (1993b), the theoretical yield reduces to 1.76, and only one optimal

6 pathway is obtained, which is shown in Fig. 2(c). This pathway includes the TCA cycle, which is used to generate ATP to satisfy the maintenance constraint. 5. Conclusion We have proposed a framework to construct the pathways with maximal yield of a certain product based on the flux balance analysis and multiple solution enumeration technique for MILP. This framework successfully identifies various pathways for producing ethanol, including the simplest linear pathway that has been applied in the industry for many years. The ATP maintenance constraint is added to estimate the real maximum yield. This constraint usually reduces the yield of the product because some of the carbon is used to produce ATP. This framework can be applied on metabolic pathway design. By calculating the knockouts for all the different topologies, it is possible to find the most economic one that has the ability to secrete the desired product. It is also possible to add some genes from other organisms into E. coli genome, and predict the yield of the engineered strain. However, because this framework is based on the flux balance analysis model, it doesn t include any regulatory information. The prediction is always maximal yield; however the actual yield from the experiment could significantly differ from the prediction because of gene regulation. Therefore, this framework is useful for yieldlimited products. References Arita, M. (2000) Simulation Practice and Theory, 8, Burgard, A. P. and Maranas, C. D. (2001) Biotechnology and Bioengineering, 74, Burgard, A. P. and Maranas, C. D. (2003) Biotechnology and Bioengineering, 82, Burgard, A. P., Vaidyaraman, S. and Maranas, C. D. (2001) Biotechnology Progress, 17, Fan, L. T., Bertok, B. and Friedler, F. (2002) Computers and Chemistry, 26, Lee, J., Goel, A., Ataai, M. M. and Domach, M. M. (1997) Applied and Environmental Microbiology, 63, Lee, S., Phalakornkule, C., Domach, M. M. and Grossmann, I. E. (2000) Computers and Chemical Engineering, 24, Mavrovouniotis, M. L., Stephanopoulos, G. and Stephanopoulos, G. (1990) Biotechnology and Bioengineering, 36, Phalakornkule, C., Fry, B., Zhu, T., Kopesel, R., Ataai, M. M. and Domach, M. M. (2000) Biotechnology Progress, 16, Seo, H., Lee, D.-Y., Park, S., Fan, L. T., Shafie, S., Bertok, B. and Friedler, F. (2001) Biotechnology letters, 23, Seressiotis, A. and Bailey, J. E. (1988) Biotechnology and Bioengineering, 31, Varma, A. and Palsson, B. O. (1993a) Journal of Theoretical Biology, 165, Varma, A. and Palsson, B. O. (1993b) Journal of Theoretical Biology, 165,