Novel Quantitative Tools for Engineering Analysis of Hepatocyte Cultures used in Bioartificial Liver Systems

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1 Noel Quantitatie Tools for Engineering Analysis of Hepatocyte Cultures used in Bioartificial Lier Systems M. Ierapetritou *, N. Sharma and M. L. Yarmush Department of Chemical & Biochemical Engineering Rutgers, the State Uniersity of New Jersey Piscataway, NJ Abstract Study of hepatic metabolism is important in the context of basic biology, disease diagnosis and seeral biotechnological applications such as deelopment of bioartificial support systems. In the current paper, we hae utilized mathematical programming techniques to optimize the biochemical enironment of hepatocyte cultures towards a desired effect of increased albumin and urea synthesis. Also, we hae obtained a set of solutions corresponding to different obecties in the metabolic framework. These studies demonstrate an initial step towards generating a systematic approach to hepatocyte cultures and towards optimizing different parameters for an extracorporeal deice based on real-time conditions. Keywords: metabolic flux analysis, linear programming optimization, hepatocytes 1. Introduction Lier disease treatment has been greatly improed by the eolutionary deelopment of lier transplantation. Howeer, approximately 30,000 patients die each year from endstage lier disease in the United States alone. The extracorporeal bioartificial lier (BAL) is a promising new technology for the treatment of lier failure, but significant technical challenges remain in order to deelop systems with sufficient processing capacity and of manageable size. During BAL operation, hepatocytes are exposed to plasma from the patient, at which time they are prone to accumulate intracellular lipids and exhibit poor lier-specific functions. Consequently understanding the mechanistic underpinnings responsible for these metabolic transformations is of critical significance. Prior studies in this direction hae used Metabolic Flux Analysis (MFA) to quantify the changes in intracellular pathway fluxes of primary rat hepatocytes in response to low-insulin preconditioning and amino acid supplementation (Chan et al. 2003a). More recently, Chan et. al (2003b) used multiariate analysis using Fisher Discriminant Analysis (FDA) and Partial least squares (PLS) to predict the factors that alter the metabolic states. Howeer, the latter studies do not identify factors that can maximize or minimize a desired obectie. * Author to whom correspondence should be adressed: marianth@sol.rutgers.edu

2 In this context, we hae deeloped a noel computational framework that will 1) enable the systematic determination of the parameters that lead to an optimized performance of hepatocyte cultures in bioartificial lier deices, 2) the most important pathways responsible for metabolic changes, and 3) the consideration of an infinite number of alternaties that can lead to complete noel treatments of the cell cultures. 2. Methods 2.1 Metabolic flux analysis Metabolic flux analysis is a useful methodology to characterize the differential actiation of metabolic pathways in hepatocyte cultures. Thus, based on a metabolic reaction network prealent in hepatocytes, intracellular reaction fluxes are estimated by mass balance around each intracellular metabolite and extracellular flux measurements. This technique is ery useful to identify key pathways that are sensitie to enironment changes by obiating the use of radiolabeled isotopes for flux distributions in networks. (Lee K et. al 1999) The current model consists of mass balances around 45 intracellular metabolites with 76 reactions/ reaction fluxes (Lee K et. al, 2000). The sum of fluxes to and from the metabolite pools was assumed to be zero (pseudo steady-state assumption): S * r = 0 (1) where the matrix S contains the stoichiometric coefficients for the arious blocks of reactions. Each element S i of S is the coefficient of metabolite i in reaction, and each r of ector r is the net flux or conersion rate of reaction. Equation (1) was separated into measured and unknown fluxes, S m * r m and S u *r u, respectiely, as follows: S u * r u = - S m * r m (2) The measured fluxes represent measured rates of uptake or release of extracellular metabolites and soling equation (2) gies estimates of intracellular fluxes. Howeer, there are still a number of questions that cannot be answered by the MFA framework since: a) It cannot proide a complete description of the inoled pathways since it relies on prepostulated information and a priori set of experimental results. b) Optimization of the enironmental parameters cannot be performed in a systematic and efficient way. c) Only a ery small set of possible parameter changes can be analyzed. To oercome some of these hindrances, the analysis proposed in this work utilizes optimization and mathematical programming ideas towards systematic parameter consideration for optimized culture systems.

3 2.2 Linear programming optimization Expressing the reaction rates as continuous ariables the following optimization formulation is proposed: target max N subect to : S i = b i, i = 1,..., M (3) = 1 where target min max is the targeted production rate (e.g. urea production); b i is the concentration of metabolite (i); M is the number of metabolites; S i is the stoichiometric coefficient of metabolite (i) in reaction (); N is the number of pathways. Model (3) expresses the maximization of the targeted flux whereas all stoichiometric constraints are satisfied and the flow rates of all inoled reactions are bounded. At this first stage, the obectie is to utilize the aailable experimental eidence through the preious studies (Chan et al. 2003a) by imposing the specific measured fluxes. 2.3 Multiobectie optimization The next step of the optimization-based analysis is to utilize the basic concepts of multiobectie optimization in order to determine the pareto optimal set of the different obecties of the hepatocyte metabolic network. max subect target2 N to : S i = b i, i = = 1 min max target1 ε 1,..., M (4) Figure 1: Pareto-optimal set of solutions

4 The solution of the optimization problem (4) for different alues of parameter ε results in the determination of the set of solutions where the two obecties are best compromised (Pareto optimal solutions). A graphical illustration of a pareto optimal set is gien in Figure 1. In moing from (point A) to another (point B) in the set, any improement in one of the obectie functions from its current alue would cause at least one of the other obectie functions to deteriorate from its current alue. Note that, based on this definition, point C is not Pareto. The Pareto optimal set yields an infinite set of solutions. In most cases, the Pareto optimal set is on the boundary of the feasible region. 3. Results and Discussion It has been shown that preconditioning rat hepatocyte cultures in low-insulin containing medium prior to plasma exposure decreased the storage of TG, whereas supplementing the media with amino acids restored albumin and urea synthesis. Based on this model, we deeloped a Linear Programming framework to optimize the system for specific hepatocyte function. The first question that we posed is whether additional substrate conditioning can boost the function of hepatocytes. This question is appropriate gien that although amino acid supplementation did increase urea and albumin synthesis rates, the leels obtained are still lower than hepatocytes cultured in high-insulin containing media. 3.1 Effect of ammonia and arginine uptake rates on urea synthesis rates Since arginine and ammonia are inoled in urea cycle fluxes, we chose these two fluxes as parameters to be aried to maximize hepatocyte function. GAMS/CPLEX was used to sole the gien problem. The optimization results are tabulated and compared with the published results in Table 1. Table 1: Optimizing ammonia and arginine fluxes for maximal urea synthesis: All metabolite rates are in µmol/million cells/day. Metabolites High-insulin medium Low insulin preconditioning Plasma + Amino Acids Urea synthesis 2.7± ± Arginine uptake 0.29± ± Ammonia uptake 0.22± ± Optimized alues using GAMS We hae not listed the remaining intracellular and extracellular fluxes since they all are within the aerage alues±standard deiation. Howeer, for maximum urea synthesis rates, the arginine uptake and ammonia clearance rates are significantly higher than the aerage±standard deiation alues.

5 3.2 Effect of amino acid supplementation on urea and albumin synthesis In the preious section, we showed how urea synthesis can be maximized based on ammonia and arginine supplementation. This, howeer, does not incorporate an increase in albumin synthesis in these cells. Marten et. al (1994) hae shown that amino acid limitation has an effect on albumin synthesis in hepatoma cells. Also, it has been shown that amino acid supplementation in plasma increases albumin synthesis (Washizu et. al, 2000). In order to search for the optimum amino acid leels to maximize both albumin and urea synthesis, we applied the LP optimization network with certain specific extracellular amino acid fluxes (listed in italics in first column of Table 2) as independent ariables. Table 2: Optimized amino acid alues for maximum urea and albumin synthesis rates: Metabolites High-insulin Low insulin Optimized alues medium preconditioning using GAMS Plasma + Amino Acids Urea synthesis 2.7± ± Arginine uptake 0.29± ± Ammonia uptake 0.22± ± Albumin ± ± synthesis Cysteine uptake 0.074± ± Tyrosine uptake 0.077± ± Threonine uptake 0.16± ± Lysine uptake 0.31± ± Phenylalanine 0.26± ± uptake Glutamine uptake 3.1± ± Histidine uptake 0.059± ± Methionine 0.16± ± uptake Valine uptake 0.055± ± Isoleucine uptake 0.078± ± Leucine uptake 0.11± ± (Numbers in bold indicate significantly different alues) From the aboe table, it is eident that the optimized alues for Arginine, Ammonia, Tyrosine, Threonine, Lysine, Phenylalanine, Histidine and Leucine are significantly different from measured alues for conditions reported by Chan C. et. al (2003a). Thus, based on these alues, we can add/ remoe specific amino acids to/from the media to condition the media for a desired output. Although the urea results seem appropriate, the approximately 10-fold increase in albumin is questionable and can be confirmed only by experimental results that are currently ongoing.

6 3.3 Multi-obectie optimization based on single parameter ariations Another point worth noting is that we may not need maximum synthesis rates of albumin and urea but a specific solution based on Pareto-optimal set of solutions that can be obtained using a multiobectie optimization framework. For the hepatocyte network, by permitting the arginine supplementation to ary outside the reported alues the Pareto optimal solutions that are shown in Figure 2 are obtained for the production of urea and albumin. Arginine is selected as the optimization parameter since it corresponds to extracellular flux and it participates in both urea cycle and albumin production Albumin Secretion (umol/millioncells/day) Urea secretion (umol/millioncells/day) Figure 2: Albumin s. urea secretion rates at different arginine concentrations. 4. Conclusions We hae deeloped a new computational framework that has been utilized for the analysis of the experimental results that are already aailable (Chan et al. 2002). Multiobectie optimization was also utilized to analyze the interactions between the desired metabolites leels and identify the most important extracellular fluxes that need to be altered. Finally the utilization of logic programming is under progress to identify important pathways that were not originally included in MFA studies. References Chan C., F. Berthiaume, K. Lee and M.L. Yarmush, 2003a, Biotech. Bioeng.81,1: Chan C., D. Hwang,G.N. Stephanopoulos,M.L. Yarmush,G. Stephanopoulos,2003b, Biotech.Prog.,19: Lee K, F Berthiaume,G.N. Stephanopoulos, M.L. Yarmush,1999,Tisue Eng.5: Lee K, F. Berthiaume, G.N. Stephanopoulos, D.M. Yarmush, M.L. Yarmush, Metab. Eng, 2: Marten N.W., E.J. Burke, J.M. Hayden, D.S. Straus, 1994, FASEB J,8: Washizu J, C. Chan, F. Berthiaume, R.G. Tompkins, M. Toner, M.L. Yarmush, 2000, Tissue Eng.6: