The Compact Kernel of a Metabolic Flux Balance Solution Space

The Compact Kernel of a Metabolic Flux Balance Solution Space

Concepts, Algorithms and Implementation

Wynand S Verwoerd


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This monograph offers a fundamentally new approach to facilitate the study of metabolic networks in cells. It aims to overcome the limitations of either just a single FBA solution, or an overwhelming number of extreme pathways in a realistic network. Instead it focusses on the FBA solution space and describes it in a simplified way by extracting just a bounded subspace: the Solution Space Kernel or SSK. This reduces the relevant number of flux space dimensions by orders of magnitude, and allows its location, size and shape to be characterised. It is a multi-stage process, requiring many new concepts and algorithms for manipulating polytopes in high dimensional spaces.

The book introduces and develops these concepts in a pragmatic way that takes into account the difficulties of performing analyses in a flux space with dimensions counting in the hundreds or thousands. It emphasizes the details of implementation in computational code and applications to realistic models are demonstrated. For many cases, the number of constraints and flux variables that fully specify the SSK polytope is only a single or double-digit number. This allows the range of metabolic states accessible to a cell to be further interpreted geometrically in terms of a manageable set of orthogonal diameters and aspect ratios. In addition, explicit representative fluxes, giving the centre and periphery of the solution space kernel, become available for further exploration.


  • Introduction
  • Hop, Skip and Jump: Finding Fixed Fluxes
  • Centering and Redundancy
  • Finding Rays
  • Classifying Polytope Facets
  • The Search for Base Level Feasible Bounded Facets
  • Constructing and Characterising the Solution Space Kernel
  • Representative FBA Solutions Derived from the SSK
  • Case Studies of SSK Calculations for Realistic FBA Models

Readership: Students and Professionals in Bioinformatics/Biocomputing, Researchers in constraints based analysis of metabolic networks, or in bioengineering of cellullar metabolism.

Key Features:

  • Rather than piecemeal publication in journal articles, the book is a coherent and comprehensive presentation of a completely new research tool
  • It integrates the conceptual development with the algorithms needed in practice to perform the kernel space analysis
  • The presentation is in straightforward, mostly non-mathematical language and richly illustrated by examples