The FBA Solution Space Kernel – Introduction and Illustrative Examples

Abstract

AbstractMotivationThe solution space of an FBA-based model of cellular metabolism, can be characterized by extraction of a bounded, low dimensional kernel (the SSK) that facilitates perceiving it as a geometric object in multidimensional flux space. The aim is to produce an amenable description, intermediate between the single feasible extreme flux of FBA, and the intractable proliferation of extreme modes in conventional solution space descriptions. Fluxes that remain fixed are separated off while the focus of interest is put on the subset of variable fluxes that have a nonzero but finite range of values. For un-bounded fluxes, a finite subrange that geometrically corresponds to the variable flux range is determined, and is supplemented by a limited set of rays that encapsulates their unbounded aspects. In this way the kernel emphasizes the realistic range of flux variation allowed in the interconnected biochemical network by e.g. limited nutrient uptake, an optimized objective and other model constraints.ResultsIt is demonstrated how knowledge of the SSK and accompanying rays can be exploited to explore representative flux states of the metabolic network. A full presentation of the SSK approach was the subject of a research monograph (Verwoerd, 2022a). Moreover, since bioengineering interventions such as gene knockouts modify the solution space, new tools based on the SSK analysis are presented that predict the effects of such interventions on a target flux constructed to represent a desired metabolic output. A simple metabolic model is used first to demonstrate the special concepts and constructions needed to define and compute the SSK. The demonstration model is tweaked to produce typical behaviors of larger models, but with kernels in 1,2 or 3 dimensions that are explicitly displayed to visualize the concepts. General applicability to models where visualization is inaccessible, is illustrated by showing evaluation of potential bioengineering strategies for a genome scale model.