Optimization Methods in Metabolic Networks.

Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1 MATHEMATICAL OPTIMIZATION FUNDAMENTALS -- 1.1 MATHEMATICAL OPTIMIZATION AND MODELING -- 1.2 BASIC CONCEPTS AND DEFINITIONS -- 1.2.1 Neighborhood of a Point -- 1.2.2 Interior of a Set -- 1.2.3 Open Set -- 1.2.4 Closure of a Set -- 1.2.5 Closed Set -- 1.2.6 Bounded Set -- 1.2.7 Compact Set -- 1.2.8 Continuous Functions -- 1.2.9 Global and Local Minima -- 1.2.10 Existence of an Optimal Solution -- 1.3 Convex Analysis -- 1.3.1 Convex Sets and Their Properties -- 1.3.2 Convex Functions and Their Properties -- 1.3.3 Convex Optimization Problems -- 1.3.4 Generalization of Convex Functions -- Exercises -- References -- Chapter 2 LP AND DUALITY THEORY -- 2.1 CANONICAL AND STANDARD FORMS OF AN LP PROBLEM -- 2.1.1 Canonical Form -- 2.1.2 Standard Form -- 2.2 GEOMETRIC INTERPRETATION OF AN LP PROBLEM -- 2.3 BASIC FEASIBLE SOLUTIONS -- 2.4 SIMPLEX METHOD -- 2.5 DUALITY IN LINEAR PROGRAMMING -- 2.5.1 Formulation of the Dual Problem -- 2.5.2 Primal-Dual Relations -- 2.5.3 The Karush-Kuhn-Tucker (KKT) Optimality Conditions -- 2.5.4 Economic Interpretation of the Dual Variables -- 2.6 NONLINEAR OPTIMIZATION PROBLEMS THAT CAN BE TRANSFORMED INTO LP PROBLEMS -- 2.6.1 Absolute Values in the Objective Function -- 2.6.2 Minmax Optimization Problems with Linear Constraints -- 2.6.3 Linear Fractional Programming -- Exercises -- References -- Chapter 3 FLUX BALANCE ANALYSIS AND LP PROBLEMS -- 3.1 MATHEMATICAL MODELING OF METABOLISM -- 3.1.1 Kinetic Modeling of Metabolism -- 3.1.2 Stoichiometric-Based Modeling of Metabolism -- 3.2 GENOME-SCALE STOICHIOMETRIC MODELS OF METABOLISM -- 3.2.1 Gene-Protein-Reaction Associations -- 3.2.2 The Biomass Reaction -- 3.2.3 Metabolite Compartments -- 3.2.4 Scope and Applications -- 3.3 FLUX BALANCE ANALYSIS (FBA).

3.3.1 Cellular Inputs, Outputs and Metabolic Sinks -- 3.3.2 Component Balances -- 3.3.3 Thermodynamic and Capacity Constraints -- 3.3.4 Objective Function -- 3.3.5 FBA Optimization Formulation -- 3.4 SIMULATING GENE KNOCKOUTS -- 3.5 MAXIMUM THEORETICAL YIELD -- 3.5.1 Maximum Theoretical Yield of Product Formation -- 3.5.2 Biomass vs. Product Trade-Off -- 3.6 FLUX VARIABILITY ANALYSIS (FVA) -- 3.7 Flux Coupling Analysis -- Exercises -- References -- Chapter 4 MODELING WITH BINARY VARIABLES AND MILP FUNDAMENTALS -- 4.1 Modeling with Binary Variables -- 4.1.1 Continuous Variable On/Off Switching -- 4.1.2 Condition-Dependent Variable Switching -- 4.1.3 Condition-Dependent Constraint Switching -- 4.1.4 Modeling AND Relations -- 4.1.5 Modeling OR Relations -- 4.1.6 Exact Linearization of the Product of a Continuous and a Binary Variable -- 4.1.7 Modeling Piecewise Linear Functions -- 4.2 SOLVING MILP PROBLEMS -- 4.2.1 Branch-and-Bound Procedure for Solving MILP Problems -- 4.2.2 Finding Alternative Optimal Integer Solutions -- 4.3 EFFICIENT FORMULATION STRATEGIES FOR MILP PROBLEMS -- 4.3.1 Using the Fewest Possible Binary Variables -- 4.3.2 Fix All Binary Variables that do not Affect the Optimal Solution -- 4.3.3 Group All Coupled Binary Variables -- 4.3.4 Segregate Binary Variables in Constraints Rather than in the Objective Function -- 4.3.5 Use Tight Bounds for All Continuous Variables -- 4.3.6 Introduce LP Relaxation Tightening Constraints -- 4.4 IDENTIFYING MINIMAL REACTION SETS SUPPORTING GROWTH -- Exercises -- References -- Chapter 5 THERMODYNAMIC ANALYSIS OF METABOLIC NETWORKS -- 5.1 THERMODYNAMIC ASSESSMENT OF REACTION DIRECTIONALITY -- 5.2 ELIMINATING THERMODYNAMICALLY INFEASIBLE CYCLES (TICs) -- 5.2.1 Cycles in Cellular Metabolism -- 5.2.2 Thermodynamically Infeasible Cycles -- 5.2.3 Identifying Reactions Participating in TICs.

5.2.4 Thermodynamics-Based Metabolic Flux Analysis -- 5.2.5 Elimination of the TICs by Applying the Loop Law -- 5.2.6 Elimination of the TICs by Modifying the Metabolic Model -- Exercises -- References -- Chapter 6 RESOLVING NETWORK GAPS AND GROWTH PREDICTION INCONSISTENCIES IN METABOLIC NETWORKS -- 6.1 FINDING AND FILLING NETWORK GAPS IN METABOLIC MODELS -- 6.1.1 Categorization of Gaps in a Metabolic Model -- 6.1.2 Gap Finding -- 6.1.3 Gap Filling -- 6.2 RESOLVING GROWTH PREDICTION INCONSISTENCIES -- 6.2.1 Quality Metrics for Quantifying the Accuracy of Metabolic Models -- 6.2.2 Automated Reconciliation of Growth Prediction Inconsistencies Using GrowMatch -- 6.2.3 Resolution of Higher-Order Gene Deletion Inconsistencies -- 6.3 VERIFICATION OF MODEL CORRECTION STRATEGIES -- Exercise -- References -- Chapter 7 IDENTIFICATION OF CONNECTED PATHS TO TARGET METABOLITES -- 7.1 USING MILP TO IDENTIFY SHORTEST PATHS IN METABOLIC GRAPHS -- 7.2 USING MILP TO IDENTIFY NON-NATIVE REACTIONS FOR THE PRODUCTION OF A TARGET METABOLITE -- 7.3 DESIGNING OVERALL STOICHIOMETRIC CONVERSIONS -- 7.3.1 Determining the Stoichiometry of Overall Conversion -- 7.3.2 Identifying Reactions Steps Conforming to the Identified Overall Stoichiometry -- Exercises -- References -- Chapter 8 COMPUTATIONAL STRAIN DESIGN -- 8.1 EARLY COMPUTATIONAL TREATMENT OF STRAIN DESIGN -- 8.2 OptKnock -- 8.2.1 Solution Procedure for OptKnock -- 8.2.2 Improving the Computational Efficiency of OptKnock -- 8.2.3 Connecting Reaction Eliminations with Gene Knockouts -- 8.2.4 Impact of Knockouts on the Biomass vs. Product Trade-Off -- 8.3 OptKnock MODIFICATIONS -- 8.3.1 RobustKnock -- 8.3.2 Tilting the Objective Function -- 8.4 OTHER STRAIN DESIGN ALGORITHMS -- Exercises -- References -- Chapter 9 NLP Fundamentals -- 9.1 UNCONSTRAINED NONLINEAR OPTIMIZATION.

9.1.1 Optimality Conditions for Unconstrained Optimization Problems -- 9.1.2 An Overview of the Solution Methods for Unconstrained Optimization Problems -- 9.1.3 Steepest Descent (Cauchy or Gradient) Method -- 9.1.4 Newton's Method -- 9.1.5 Quasi-Newton Methods -- 9.1.6 Conjugate Gradients (CG) Methods -- 9.2 CONSTRAINED NONLINEAR OPTIMIZATION -- 9.2.1 Equality-Constrained Nonlinear Problems -- 9.2.2 Nonlinear Problems with Equality and Inequality Constraints -- 9.2.3 Karush-Kuhn-Tucker Optimality Conditions -- 9.2.4 Sequential (Successive) Quadratic Programming -- 9.2.5 Generalized Reduced Gradient -- 9.3 LAGRANGIAN DUALITY THEORY -- 9.3.1 Relationships between the Primal and Dual Problems -- Exercises -- References -- Chapter 10 NLP APPLICATIONS IN METABOLIC NETWORKS -- 10.1 MINIMIZATION OF THE METABOLIC ADJUSTMENT -- 10.2 INCORPORATION OF KINETIC EXPRESSIONS IN STOICHIOMETRIC MODELS -- 10.3 METABOLIC FLUX ANALYSIS (MFA) -- 10.3.1 Definition of the Relevant Parameters and Variables -- 10.3.2 Isotopomer Mass Balance -- 10.3.3 Optimization Formulation for MFA -- Exercises -- References -- Chapter 11 MINLP FUNDAMENTALS AND APPLICATIONS -- 11.1 AN OVERVIEW OF THE MINLP SOLUTION PROCEDURES -- 11.2 GENERALIZED BENDERS DECOMPOSITION -- 11.2.1 The Primal Problem -- 11.2.2 The Master Problem -- 11.2.3 Steps of GBD Algorithm -- 11.3 OUTER APPROXIMATION -- 11.3.1 The Primal Problem -- 11.3.2 The Master Problem -- 11.3.3 Steps of the OA Algorithm -- 11.4 OUTER APPROXIMATION WITH EQUALITY RELAXATION -- 11.4.1 The Master Problem -- 11.5 KINETIC OPTKNOCK -- 11.5.1 k-OptKnock Formulation -- 11.5.2 Solution Procedure for k-OptKnock -- Exercises -- References -- Appendix A CODING OPTIMIZATION MODELS IN GAMS -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.