Analysis of complex reaction networks using mathematical programming - PowerPoint PPT Presentation

Analysis of complex reaction networks using mathematical programming approaches Marianthi Ierapetritou Department Chemical and Biochemical Engineering Piscataway, NJ 08854-8058

Complex Process Engineering Systems? PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

General Motivation Diverse complex systems spanning different scales � Liver metabolism (molecular level) � Combustion systems (process level) � Scheduling of multiproduct-multipurpose plants (plant level) PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Motivation -1: Liver Support Devices � Acute and chronic liver failure account for 30,000 deaths each year in the US � A large number of liver diseases: - Alagille Syndrome - Alpha 1 - Antitrypsin Deficiency - Autoimmune Hepatitis - Biliary Atresia - Chronic Hepatitis - Cancer of the Liver - Cirrhosis - Cystic Disease of the Liver - Fatty Liver - Galactosemia - Hepatitis A, B, C � Currently liver transplantation is primary therapeutic option. Scarcity of donor organs limits this treatment PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Solutions � Adjunct Internal Liver Support With Implantable Devices � Hepatocyte Transplantation � Implantable Devices � Encapsulated Hepatocytes � Extracorporeal Temporary Liver Support � Nonbiological devices: hemodialysis, hemofiltration, plasma exchange units � Hepatocyte- and liver cell–based extracorporeal devices PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Challenges a) How to maximize long-term functional stability of hepatocytes in inhospitable environments b) How to manufacture a liver functional unit that is scalable without creating transport limitations or excessive priming volume that must be filled by blood or plasma from the patient c) How to procure the large number of cells that is needed for a clinically effective device PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

… and the Reality � Problem complexity: System of large interconnectivity � Large number of adjustable variables � Uncertainty PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Motivation – 2 : Combustion Conversion of chemical energy to mechanical energy Fluid flows significantly affected by chemical reaction : Combustion, Aerospace propulsion Accuracy depends on : • Flow model • Kinetic model Require alternate representation of complex kinetic mechanism, without sacrificing accuracy PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Challenges: Combine Flow and Chemistry � How should these be combined ? Composition map Velocity map PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

…and the Reality Complex kinetics (LLNL Report, 2000) Uncertainty in kinetic parameters H2 mole fraction vs. time PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Motivation-3: Large-Scale Process Operations Goal: Address the optimization of large-scale short-term scheduling problem, specifically in the area of refinery operations Product Blending & Distribution Production Crude-oil Unloading and Blending Add $100s of million/year profit by optimizing crude-oil- marketing enterprise Crude Oil Storage Charging Component Crude Other Lifting/ Blend Finished Marine Tanks Tanks Stock Distillation Production Shipping Header Product Vessels Tanks Units Units Points Tanks Max Profit Subject to: Material Balance Constraints Allocation Constraints, Sequence Constraints Duration Constraints, Demand Constraints … PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Challenges: Parameter Fluctuations PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

…and the Reality Product 1 40% Int 60% 10% AB 40% Heating Reaction 2 Feed A Hot A 60% Imp E Separatio Int BC 80% n 90% 50% Reaction 1 Reaction 3 Feed B 20% Product 2 50% Feed C As time horizon of scheduling problem increases, the solution requires exponential computational time which makes the problem intractable. Ti im me e Nu um mb be er r o of f Ob bj je ec ct ti iv ve e CP PU U t ti im me e T N O C Ev E ve en nt t P Po oi in nt ts s fu f un nc ct ti io on n v va al lu ue e ( (s se ec c) ) 8 h ho ou ur rs s 5 14 49 98 8. .1 19 9 0. .4 47 7 8 5 1 0 16 6h ho ou ur rs s 9 37 73 37 7. .1 10 0 17 77 7. .9 93 3 1 9 3 1 24 2 4 h ho ou ur rs s 1 13 3 6 60 03 34 4. .9 92 2 9 92 23 36 67 7. .9 94 4 PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Systems Approaches � Mathematical programming Systematic consideration of variable dependences Continuous and discrete representation � Sensitivity – parametric analysis Identification of important features and parameters � Feasibility evaluation Conditions of acceptable operation � Optimization Multiobjective since we have more than one objective to optimize � Uncertainty Evaluation of solutions that are robust to highly fluctuating environment PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Presentation Outline � Complexity reduction using mathematical programming approaches � Optimization of hepatocyte functionality � Reduction of complex chemistry � Uncertainty analysis & feasibility evaluation � Analysis of alternative solutions PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Hepatic Metabolic Network Main Assumptions 1) Gluconeogenic and fatty acid oxidation enzymes are active in plasma 2) Energy-requiring pathways are negligible 3) Metabolic pools are at pseudo-steady state. Main Reactions Glucose Metabolism (v 1 -v 7 ) Lactate Metabolites & TCA Cycle(v 8 -v 14 ) Urea Cycle (v 15 -v 20 ) Amino acid uptake & metabolism (v 21 -v 68 , ,v 76 ) Lipid & Fatty Acid Metabolism (v 46 -v 50 ,v 71 -v 75 ) 45 internal metabolites 76 reactions: 33 irreversible + 43 reversible 34 measured (red) + 42 unknown Chan et al (2003) Biotechnol & Bioengineering PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Rationale for Metabolic Modeling � Interpretation and coupling to experimental data. � Gain insights into how cells adapt to environmental changes. � To identify key pathways for hepatocyte function. M etabolic F lux A nalysis ( MFA ) is developed to calculate unknown intracellular fluxes based on the extracellular measured fluxes. ⎡ ⎤ dA b 2 v ⎢ ⎥ dt 1 ⎢ ⎥ − 1 0 0 0 0 1 0 0 0 v dB dt 2 ⎢ ⎥ b 3 − − 1 1 1 0 0 0 0 0 0 v N ⎢ ⎥ 3 dC dt b 1 C ⎢ ⎥ − 0 1 0 0 0 0 1 0 0 v 4 v 1 ⎢ ⎥ = v 2 dD − − 0 0 1 1 1 0 0 0 0 ⎢ ⎥ v 5 A B E dt ⎢ ⎥ − 0 0 0 1 0 0 0 1 0 b dE dt ⎢ ⎥ 1 v 4 − 0 0 0 0 1 0 0 0 1 ⎢ ⎥ b 2 ⎢ ⎥ dF D − 0 1 0 0 2 0 0 0 0 b dt v 3 ⎢ ⎥ 3 ⎢ ⎥ dN b F ⎣ ⎦ 4 dt 2 N v 5 Pseudo-steady State Sv = 0 b 4 S v S v = − u u m m � Measure 2 fluxes: Uniquely-determined system � Measure 3 fluxes: Overdetermined System- Least Square method � Measure 1 flux: Underdetermined System- Linear Programming PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Optimization in Metabolic Networks Single-level Optimization: Optimize a single objective function � (e.g. maximization of a single metabolic flux). Eward & Palsson (2000) PNAS Schilling. et al., (2001) Biotechnol Bioeng Uygun et al., (2006) Ind. Eng. Chem. Res. Lee S. et al (2000) Computer & Chem. Eng. Multi-objective Optimization: Several objective functions are � simultaneously optimized (e.g. minimizing the toxicity and maximizing metabolic production). Nagrath D. et al. (2007) Annals of Biomedical Engineering Sharma N.P. et al., (2005) Biotechnol Bioeng Multi-level Optimization: Several objectives acting hierarchically to optimize � their own objective function (e.g. Minimize the difference of predicted fluxes from experimentally observed values to optimize the cellular objective function). Burgard & Maranas (2003) Biotechnol Bioeng Segre D. et al (2002) PNAS Nolan R.P et al (2005) Metabolic Engineering Uygun et al., (2007) Biotechnol Bioeng ≠ Multi-Objective Optimization Multi-level Optimization PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou

Single-level Optimization: Maximize Urea Secretion Aim: Identify the flux distributions for optimal urea production that can fulfill metabolites balances and flux constraints = : Max Z v urea N ∑ = ∀ ∈ : 0 Subject to S v i M ij j = 1 j ≤ ≤ ∀ ∈ min max v v v j K j j j Experimental Data* Optimal Value Increase HIP 0.23 ± 0.43 > 10 fold HPAA 1.32 ± 0.69 > 3 fold 6.81 LIP 0.17 ± 0.24 > 15 fold LPAA 2.35 ± 0.52 > 2 fold Unit: µmol/million cells/day *Chan & Yarmush et al (2003) Biotechnol Prog PASI: August 12-21, 2008, Mar del Plata, Argentina Marianthi Ierapetritou