Optimization Methods in Metabolic Networks

Costas D. Maranas, Ali R. Zomorrodi

• Publisher: Wiley
• Year: 2016
• Print ISBN: 9781119028499
• eBook ISBN: 9781119189015
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biotechnology
• Index: Biological Sciences

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 problems

1
MATHEMATICAL OPTIMIZATION FUNDAMENTALS

This chapter reviews the fundamentals of mathematical optimization and modeling. It starts with a biological network inference problem as a prototype example to highlight the basic steps of formulating an optimization problem. This is followed by a review of some basic mathematical concepts and definitions such as set and function properties and convexity analysis.

1.1 MATHEMATICAL OPTIMIZATION AND MODELING

Mathematical optimization (programming) systematically identifies the best solution out of a set of possible choices with respect to a pre-specified criterion. The general form of an optimization problem is as follows:

where

• x is a N-dimensional vector referred to as, the vector of variables.
• S is the set from which the elements of x assume values. For example, S can be the set of real, nonnegative real or nonnegative integers. In general, variables in an optimization problem can be continuous, discrete (integer) or combinations thereof. The former is used to capture the continuously varying properties of a system (e.g., concentrations), whereas the latter is used for discrete decision making (e.g., whether or not to eliminate a reaction).
• f(x) is referred to as the objective function and serves as a mathematical description of the desired property of the system that should be optimized (i.e., maximized or minimized).
• 
  and
  
  are constraints that must be satisfied as equalities or one-sided inequalities, respectively, and represent the feasible space of decision variables.

Any vector x that lies in S and satisfies h(x) and g(x) is called a feasible...

Table of contents

• COVER
• TITLE PAGE
• TABLE OF CONTENTS
• PREFACE
• 1 MATHEMATICAL OPTIMIZATION FUNDAMENTALS
• 2 LP AND DUALITY THEORY
• 3 FLUX BALANCE ANALYSIS AND LP PROBLEMS
• 4 MODELING WITH BINARY VARIABLES AND MILP FUNDAMENTALS
• 5 THERMODYNAMIC ANALYSIS OF METABOLIC NETWORKS
• 6 RESOLVING NETWORK GAPS AND GROWTH PREDICTIONINCONSISTENCIES IN METABOLIC NETWORKS
• 7 IDENTIFICATION OF CONNECTED PATHS TO TARGET METABOLITES
• 8 COMPUTATIONAL STRAIN DESIGN
• 9 NLP FUNDAMENTALS
• 10 NLP APPLICATIONS IN METABOLIC NETWORKS
• 11 MINLP FUNDAMENTALS AND APPLICATIONS
• APPENDIX A: CODING OPTIMIZATION MODELS IN GAMS
• INDEX
• END USER LICENSE AGREEMENT