Provides a tutorial on the computational tools that use mathematical optimization concepts and representations for the curation, analysis and redesign of metabolic networks _ Organizes, for the first time, the fundamentals of mathematical optimization in the context of metabolic network analysis _ Reviews the fundamentals of different classes of optimization problems including LP, MILP, MLP and MINLP _ Explains the most efficient ways of formulating a biological problem using mathematical optimization _ Reviews a variety of relevant problems in metabolic network curation, analysis and redesign…mehr
Provides a tutorial on the computational tools that use mathematical optimization concepts and representations for the curation, analysis and redesign of metabolic networks _ Organizes, for the first time, the fundamentals of mathematical optimization in the context of metabolic network analysis _ Reviews the fundamentals of different classes of optimization problems including LP, MILP, MLP and MINLP _ Explains the most efficient ways of formulating a biological problem using mathematical optimization _ Reviews a variety of relevant problems in metabolic network curation, analysis and redesign with an emphasis on details of optimization formulations _ Provides a detailed treatment of bilevel optimization techniques for computational strain design and other relevant problemsHinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Costas D. Maranas is a Donald B. Broughton Professor in the Department of Chemical Engineering at Pennsylvania State University, USA. Dr. Maranas is a Fellow of the American Institute of Medical and Biological Engineering (AIMBE). In 2002 he was awarded by AIChE the Allan P. Colburn Award for Excellence in Publications by a Young Member of the Institute. Ali R. Zomorrodi obtained his PhD in Chemical Engineering at Pennsylvania State University and is currently a Postdoctoral Research Associate at Boston University, USA. Dr. Zomorrodi's areas of expertise include optimization-based modeling and model-driven analysis of biological networks.
Inhaltsangabe
Preface xiii
1 Mathematical Optimization Fundamentals 1
1.1 Mathematical Optimization and Modeling 1
1.2 Basic Concepts and Definitions 7
1.2.1 Neighborhood of a Point 7
1.2.2 Interior of a Set 7
1.2.3 Open Set 8
1.2.4 Closure of a Set 8
1.2.5 Closed Set 8
1.2.6 Bounded Set 8
1.2.7 Compact Set 8
1.2.8 Continuous Functions 9
1.2.9 Global and Local Minima 9
1.2.10 Existence of an Optimal Solution 9
1.3 Convex Analysis 10
1.3.1 Convex Sets and Their Properties 10
1.3.2 Convex Functions and Their Properties 13
1.3.3 Convex Optimization Problems 19
1.3.4 Generalization of Convex Functions 20
Exercises 20
References 22
2 LP and Duality Theory 23
2.1 Canonical and Standard Forms of an LP Problem 23
2.1.1 Canonical Form 24
2.1.2 Standard Form 24
2.2 Geometric Interpretation of an LP Problem 26
2.3 Basic Feasible Solutions 28
2.4 Simplex Method 30
2.5 Duality in Linear Programming 35
2.5.1 Formulation of the Dual Problem 35
2.5.2 Primal-Dual Relations 38
2.5.3 The Karush-Kuhn-Tucker (KKT) Optimality Conditions 39
2.5.4 Economic Interpretation of the Dual Variables 40
2.6 Nonlinear Optimization Problems that can be Transformed into LP Problems 45
2.6.1 Absolute Values in the Objective Function 45
2.6.2 Minmax Optimization Problems with Linear Constraints 46
2.6.3 Linear Fractional Programming 47
Exercises 49
References 50
3 Flux Balance Analysis and LP Problems 53
3.1 Mathematical Modeling of Metabolism 54
3.1.1 Kinetic Modeling of Metabolism 54
3.1.2 Stoichiometric-Based Modeling of Metabolism 54
3.2 Genome-Scale Stoichiometric Models of Metabolism 55
3.2.1 Gene-Protein-Reaction Associations 55
3.2.2 The Biomass Reaction 56
3.2.3 Metabolite Compartments 57
3.2.4 Scope and Applications 57
3.3 Flux Balance Analysis (FBA) 57
3.3.1 Cellular Inputs, Outputs and Metabolic Sinks 58
3.3.2 Component Balances 59
3.3.3 Thermodynamic and Capacity Constraints 60
3.3.4 Objective Function 61
3.3.5 FBA Optimization Formulation 62
3.4 Simulating Gene Knockouts 67
3.5 Maximum Theoretical Yield 68
3.5.1 Maximum Theoretical Yield of Product Formation 68
3.5.2 Biomass vs. Product Trade-Off 69
3.6 Flux Variability Analysis (Fva) 71
3.7 Flux Coupling Analysis 73
Exercises 77
References 78
4 Modeling with Binary Variables and MILP Fundamentals 81
4.1 Modeling with Binary Variables 83
4.1.1 Continuous Variable On/Off Switching 83
4.1.2 Condition-Dependent Variable Switching 83
4.1.3 Condition-Dependent Constraint Switching 84
4.1.4 Modeling AND Relations 84
4.1.5 Modeling OR Relations 86
4.1.6 Exact Linearization of the Product of a Continuous and a Binary Variable 86
4.1.7 Modeling Piecewise Linear Functions 87
4.2 Solving Milp Problems 89
4.2.1 Branch-and-Bound Procedure for Solving MILP Problems 90
4.2.2 Finding Alternative Optimal Integer Solutions 97
4.3 Efficient Formulation Strategies for Milp Problems 97
4.3.1 Using the Fewest Possible Binary Variables 97
4.3.2 Fix All Binary Variables that do not Affect the Optimal Solution 98
