Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition.

MOTIVATION: Elementary flux mode analysis (EFMA) decomposes complex metabolic network models into tractable biochemical pathways, which have been used for rational design and analysis of metabolic and regulatory networks. However, application of EFMA has often been limited to targeted or simplified metabolic network representations due to computational demands of the method. RESULTS: Division of biological networks into subnetworks enables the complete enumeration of elementary flux modes (EFMs) for metabolic models of a broad range of complexities, including genome-scale. Here, subnetworks are defined using serial dichotomous suppression and enforcement of flux through model reactions. Rules for selecting appropriate reactions to generate subnetworks are proposed and tested; three test cases, including both prokaryotic and eukaryotic network models, verify the efficacy of these rules and demonstrate completeness and reproducibility of EFM enumeration. Division of models into subnetworks is demand-based and automated; computationally intractable subnetworks are further divided until the entire solution space is enumerated. To demonstrate the strategy's scalability, the splitting algorithm was implemented using an EFMA software package (EFMTool) and Windows PowerShell on a 50 node Microsoft high performance computing cluster. Enumeration of the EFMs in a genome-scale metabolic model of a diatom, Phaeodactylum tricornutum, identified ∼2 billion EFMs. The output represents an order of magnitude increase in EFMs computed compared with other published algorithms and demonstrates a scalable framework for EFMA of most systems.

Systems analysis of microbial adaptations to simultaneous stresses.

Microbes live in multi-factorial environments and have evolved under a variety of concurrent stresses including resource scarcity. Their metabolic organization is a reflection of their evolutionary histories and, in spite of decades of research, there is still a need for improved theoretical tools to explain fundamental aspects of microbial physiology. Using ecological and economic concepts, this chapter explores a resource-ratio based theory to elucidate microbial strategies for extracting and channeling mass and energy. The theory assumes cellular fitness is maximized by allocating scarce resources in appropriate proportions to multiple stress responses. Presented case studies deconstruct metabolic networks into a complete set of minimal biochemical pathways known as elementary flux modes. An economic analysis of the elementary flux modes tabulates enzyme atomic synthesis requirements from amino acid sequences and pathway operating costs from catabolic efficiencies, permitting characterization of inherent tradeoffs between resource investment and phenotype. A set of elementary flux modes with competitive tradeoffs properties can be mathematically projected onto experimental fluxomics datasets to decompose measured phenotypes into metabolic adaptations, interpreted as cellular responses proportional to the experienced culturing stresses. The resource-ratio based method describes the experimental phenotypes with greater accuracy than other contemporary approaches and further analysis suggests the results are both statistically and biologically significant. The insight into metabolic network design principles including tradeoffs associated with concurrent stress adaptation provides a foundation for interpreting physiology as well as for rational control and engineering of medically, environmentally, and industrially relevant microbes.

Molecular-level tradeoffs and metabolic adaptation to simultaneous stressors.

Life is a dynamic process driven by the complex interplay between physical constraints and selection pressures, ranging from nutrient limitation to inhibitory substances to predators. These stressors are not mutually exclusive; microbes have faced concurrent challenges for eons. Genome-enabled systems biology approaches are adapting economic and ecological concepts like tradeoff curves and strategic resource allocation theory to analyze metabolic adaptations to simultaneous stressors. These methodologies can accurately describe and predict metabolic adaptations to concurrent stresses by considering the tradeoff between investment of limiting resources into enzymatic machinery and the resulting cellular function. The approaches represent promising links between computational biology and well-established economic and ecological methodologies for analyzing the interplay between physical constraints and microbial fitness.