The Compact Kernel of a Metabolic Flux Balance Solution Space. Concepts, Algorithms and Implementation

Description

Contents Dedication List of Tables List of Figures Chapter 1 Introduction 1.1 Constraint-Based Analysis of Steady States 1.2 Characterising Solution Spaces 1.3 FVA – Strengths and Weaknesses 1.4 A New Description of FBA Solution Spaces 1.5 Software Implementation References Chapter 2 Hop, Skip and Jump: Finding Fixed Fluxes 2.1 Different Approaches to Identify Fixed Flux Values 2.2 Orthogonal Flux Vectors: The SKIP Step 2.3 Downcasting Constraints by Projection 2.4 Sampling SS Points: The JUMP Step 2.5 Positive Confirmation of Frozen Fluxes — The HOP Step 2.6 Revisiting the Simplifying Assumptions 2.7 Computational Performance of the HSnJ Algorithm References Chapter 3 Centering and Redundancy 3.1 Recurring Reduction Steps 3.2 Centering Algorithms 3.2.1 The Constrained Linear Distance Algorithm 3.2.2 The Constrained Linear Ordered Differences Procedure 3.2.3 The Maximal Inscribed Hypersphere Centre 3.2.4 Iterative Centre Refinement 3.2.5 Illustrative Examples 3.3 Redundancy Elimination 3.3.1 Collinear Constraint Removal 3.3.2 Explicit Redundancy Testing by LP Chapter 4 Finding Rays 4.1 Ray Vectors, Ray Space and Convex Bases 4.2 The Reduced Solution Space: Linealities and Prismatic Rays 4.3 The Ray Matrix 4.4 Singleton Rays 4.5 Peripheral and Aligned Rays 4.6 Capping Rays and Closure Testing Reference Chapter 5 Classifying Polytope Facets 5.1 The Facet Hierarchy 5.2 Relationships and Facet Trees 5.2.1 The Structure of the Facet Tree 5.2.2 Polytopes and Facet Trees Have a Many-to-Many Association 5.3 Inheritance of Boundedness and Feasibility 5.4 FBF Base Level Facets 5.5 The Progenitor Facet 5.6 Feasibility and Boundedness Testing 5.6.1 Feasibility 5.6.2 Boundedness 5.6.3 Integrating Feasibility and Boundedness Testing Chapter 6 The Search for Base Level Feasible Bounded Facets 6.1 Systematic and Random Searches 6.2 A Scoring System for Constraint Hyperplanes 6.3 A Randomised Greedy Search Heuristic 6.4 Backtracking and Traceback 6.4.1 Backtracking 6.4.2 Traceback 6.4.3 Comparison Between Backtracking and Traceback 6.5 Traceback Determination of the Progenitor Hyperplane 6.6 Setting up the Facet Tree for Systematic Traversal 6.6.1 Structuring the Tree and the Traversal 6.6.2 Subtree Viability 6.7 A Tree Traversal Heuristic 6.8 Choosing Between Greedy Search and Tree Traversal Chapter 7 Constructing and Characterising the Solution Space Kernel 7.1 Tangent Capping of the Solution Space 7.2 Orthogonal Chords and Shape Characterisation 7.2.1 Chords and Aspect Ratios 7.2.2 Flattening Thin Directions 7.3 Calculating Maximal and Main Chords of a Polytope 7.3.1 Mixed Integer Linear Programming Determination of a Maximal Chord 7.3.2 Polytope Flipping — an Approximate LP Chord Calculation Method 7.3.3 Example Main Chord Calculations 7.3.4 Diameter-Based Main Chord Calculations 7.4 Graphical Representation of the SSK Geometry Chapter 8 Representative FBA Solutions Derived from the SSK 8.1 Validation of the SSK by Deconstruction 8.2 Discrete Sets of Representative Fluxes 8.3 A Representative Flux Region: The Peripheral Point Polytope 8.4 Estimation of the PPP Coverage 8.4.1 Coverage Estimation by Sampling 8.4.2 Coverage Estimation by Similar Envelopes 8.5 Comparing SSK Sizes of Different Models 8.5.1 Measures of SSK Hypervolume 8.5.2 Distance Measures of the SSK Size References Chapter 9 Case Studies of SSK Calculations for Realistic FBA Models 9.1 Solution Space Classifications 9.1.1 Compact Solution Spaces 9.1.2 Open Simple Cones 9.1.3 A Single Point SSK 9.1.4 The Facetted Cone SSK 9.2 Calculated SSKs for a Selection of Metabolic Models 9.2.1 Escherichia coli Core model, e_coli_core [3] 9.2.2 Homo sapiens Red Blood Cell, iAB_RBC_283 [4] 9.2.3 Helicobacter pylori, iIT341 [5] 9.2.4 Homo sapiens Blood Platelet, iAT_PLT_636 [6] 9.2.5 Methanosarcina barkeri, iAF692 [7] 9.2.6 Clostridium ljungdahlii, iHN637 [8] 9.2.7 Mycobacterium tuberculosis H37Rv, iNJ661 [9] and iEK1008 [10] 9.2.8 Salinispora: Core Model iCore_BMC, Arenicola iCCSA643_BMC and Pacifica iCCSP114_BMC [11] 9.2.9 Pseudomonas putida iJN746 [12] and iJN1463 [13] 9.2.10 Geobacter sulfurreducens [14–15] and Metallireducens iAF987 [16] 9.2.11 Escherichia coli K12, iML1515 [17] 9.2.12 Saccharomyces cerevisiae, iMM904 [18] 9.2.13 Rattus norvegicus liver cell, iRatLiver [19] 9.2.14 Homo sapiens, RECON1 [20] 9.3 Discussion and Future Perspectives References Index