Our work focuses on the optimization of hepatocyte functionality using mathematical programming techniques to model the metabolic state of cultured hepatocytes used for BAL devices. The metabolic network and constraints of measured fluxes considered in this work are based on a prior reconstruction of the hepatic metabolic network [1]. We consider this network in the context of available experimental data under several culture conditions [1]: (a) high/ low insulin preconditioned unsupplemented plasma cultures (HIP/ LIP), and (b) high/ low insulin preconditioned, amino acid-supplemented plasma cultures (HIP_AA/LIP_AA).
Many methods have been developed to study the properties of metabolic networks, including metabolic flux analysis (MFA), flux balance analysis (FBA), metabolic control analysis (MCA), and metabolic pathway analysis with elementary modes (EM) and extreme pathway (EP) [2]. These approaches enable the characterization and understanding of cellular metabolism given a limited set of extracellular measurements and can provide rational guidelines to manipulate (“engineer”) metabolic pathways. Recently, a mixed-integer linear programming (MILP) methodology has been developed that results in the determination of all alternative optimal solutions that exist due to experimental error and limited measurements [3,4]. In order to better understand the metabolic network of cultured hepatocytes, we perform a comprehensive study using and comparing a number of existing analysis frameworks: FBA, EM, the logic-based programming approach developed by Sharma et al. 2005 [5], as well as the MILP based approach to determine the number of alternative optimal solutions. Moreover, we develop a number of mathematical programming tools to enable better understanding of the hepatocyte metabolic functionality.
The first aim of this work is to identify the effects of the individual reaction and amino acid exchange flux deletions on the optimal values of urea production in the overall hepatocyte metabolic network. Urea production is commonly measured as an indicator of hepatocyte functionality and is used as a cellular objective in this work, as has been done previously [5]. A bi-level, nonlinear program based on FBA is developed for minimizing the sum-squared difference between the experimental fluxes and the optimal solution, while maximizing the urea production. The bi-level program becomes a single-level nonlinear optimal problem by including both the primal and dual constraints with an equality constraint forcing their objective values to be the same [6]. Under the constraint of reaction/amino acid deletion in the bi-level program, the optimal value of objective is obtained. The ratio of optimal urea production in the absence versus presence of a reaction of interest (R) is calculated and used to determine the effect of each individual reaction and amino acid exchange flux. The hepatic network becomes infeasible by deleting the TCA cycle in all of the conditions. By deleting reactions 16, 17 and 43, (reaction 16 is the transformation of ornithine into citrulline, reaction 17 is the transformation of citrulline and aspartate into arginine and fumarate, and reaction 43 is the transformation of asparagine into oxaloacetate), the network becomes infeasible in HIP_AA, and urea production is significantly decreased (<0.04) compared with the urea values in HIP, LIP and LIP_AA conditions. Regarding the amino acid deletion in the supplementation, we determined that arginine deletion will decrease the urea production whereas the deletion of ornithine and/or glutamate secretion will result in increasing urea production, though not significantly, in all of the conditions. In addition to these three amino acids, alanine, glutamine, proline and tryptophan exert a significant effect on the urea production that varies depending on the experimental conditions.
In order to elucidate the results from the bi-level program, the second aim of this work is to evaluate the most important pathways for urea production by calculating the weights of all the elementary modes. The elementary modes of the hepatocyte metabolic network are first obtained using FluxAnalyzer [7], which implements the iterative algorithm described by Schuster et al. [8]. There are three modes (mode 3, 27 and 28) that involve the urea production in a total of 32 elementary modes. Since any self-consistent flux distribution can be expressed as a linear combination of elementary modes, the flux distributions obtained by the bi-level program are used to calculate the weights of elementary modes. It is thus determined that more than 70% of urea is produced in mode 27, which includes the TCA cycle and reactions 16, 17 and 43 (as described before), under all of the conditions. The results obtained by the bi-level optimization can be well justified by inspection of this mode. For example, if ornithine secretion is deleted, more ornithine is directed back to TCA cycle producing more urea, as predicted by the optimization model.
The hepatic central metabolic network considered is complex, involving 45 internal metabolites and 77 reactions. Thus, it may exhibit multiple flux distributions that can fulfill metabolites balances and measured constraints with the same value of urea. By using the MILP program described by Lee, 2000 [3], we found that there exist a number of different fluxes distributions in all of the cultured conditions, which will reveal the various scenarios. It is also determined that a unique solution can be identified by improving the accuracy of some measurements or performing additional measurements. For example, there exist 25 different flux distributions with 40 adjusted fluxes for the LIP_AA condition. But if we can reduce the measurement error of glucose flux and cholesterol ester uptake, and measure the reactions involving glycogen production and tryptophan uptake, only one solution will be obtained, thus reducing the ambiguity of FBA.
When multiple deletions are considered simultaneously, which can be achieved using the logic-based mathematical programming approach proposed by Sharma et al., 2005 [5], we calculated the minimal reaction sets required to maintain the mass balance and the maximal value of urea production in the different cultured hepatocytes. We found that the minimal reaction set includes arginine uptake, urea production and ornithine output, which is the same set of reactions involved in the elementary mode 3. Thus although it seems like mode 27 is the pathway most commonly used by the cell to produce urea, alternative routes can be obtained if the target is to minimize the pathways involved.
The long-term objective of this work is to determine the conditions that result in the optimum cell functionality that can be used in BAL devices. The computational modeling provides a number of insights that, if experimentally validated, would be of utility in the design and operation of devices based on living hepatocytes. For instance, amino acid supplementation protocols can be tuned based on the results of deletion analysis (“first aim”), and this is trivial to test experimentally. An interesting fundamental question is whether a specific functionality (here, urea production) can be optimized in practice by focusing the flux through a single, most efficient pathway, or rather whether distributing the flux across all available pathways is more effective. Since there are only three pathways (elementary modes) to produce urea in the hepatic metabolic network, each pathway can be modulated, for example using siRNA technology. Thus, by combining computational pathway analysis tools with experimental pathway manipulation tools, we hope to ultimately impart higher and more robust functionality for cultured hepatocytes used in living cell devices.
Reference:
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