Advances in flux balance analysis by integrating machine learning and mechanism-based models.

The availability of multi-omics data sets and genome-scale metabolic models for various organisms provide a platform for modeling and analyzing genotype-to-phenotype relationships. Flux balance analysis is the main tool for predicting flux distributions in genome-scale metabolic models and various data-integrative approaches enable modeling context-specific network behavior. Due to its linear nature, this optimization framework is readily scalable to multi-tissue or -organ and even multi-organism models. However, both data and model size can hamper a straightforward biological interpretation of the estimated fluxes. Moreover, flux balance analysis simulates metabolism at steady-state and thus, in its most basic form, does not consider kinetics or regulatory events. The integration of flux balance analysis with complementary data analysis and modeling techniques offers the potential to overcome these challenges. In particular machine learning approaches have emerged as the tool of choice for data reduction and selection of most important variables in big data sets. Kinetic models and formal languages can be used to simulate dynamic behavior. This review article provides an overview of integrative studies that combine flux balance analysis with machine learning approaches, kinetic models, such as physiology-based pharmacokinetic models, and formal graphical modeling languages, such as Petri nets. We discuss the mathematical aspects and biological applications of these integrated approaches and outline challenges and future perspectives.

Evolution of C4 photosynthesis predicted by constraint-based modelling.

Constraint-based modelling (CBM) is a powerful tool for the analysis of evolutionary trajectories. Evolution, especially evolution in the distant past, is not easily accessible to laboratory experimentation. Modelling can provide a window into evolutionary processes by allowing the examination of selective pressures which lead to particular optimal solutions in the model. To study the evolution of C4 photosynthesis from a ground state of C3 photosynthesis, we initially construct a C3 model. After duplication into two cells to reflect typical C4 leaf architecture, we allow the model to predict the optimal metabolic solution under various conditions. The model thus identifies resource limitation in conjunction with high photorespiratory flux as a selective pressure relevant to the evolution of C4. It also predicts that light availability and distribution play a role in guiding the evolutionary choice of possible decarboxylation enzymes. The data shows evolutionary CBM in eukaryotes predicts molecular evolution with precision.

Virtually all plants use energy from sunlight to convert carbon dioxide and water into oxygen and sugars via a process called photosynthesis. This process has many steps that each rely on different enzymes to drive specific chemical reactions. Most plants use a pathway of enzymes that is referred to as C3 photosynthesis. Plants absorb carbon dioxide gas from the atmosphere. However, the levels of carbon dioxide in the atmosphere are very low, so this limits the amount of photosynthesis plants can perform. To overcome this problem, some plants have evolved a different type of photosynthesis ­ called C4 photosynthesis ­ with a mechanism that increases the levels of carbon dioxide in the cells. Today, plants that use C4 photosynthesis (so-called 'C4 plants') typically grow faster than other plants, especially in warmer climates. This gives C4 plants, such as corn, an advantage over their competitors and also helps them to colonize harsh environments that other plants struggle to thrive in. However, it remains unclear how C4 photosynthesis evolved in some plants living in wet habitats, or why other plants use forms of photosynthesis that are intermediate between C4 and C3 photosynthesis. C4 photosynthesis uses pathways containing enzymes that are found in all plants; therefore, C4 plants evolved by changing how they used enzymes they already had. To understand how these different enzyme pathways may have evolved, Blätke and Bräutigam used an approach known as constraint-based modelling. The researchers built a mathematical model of C3 photosynthesis and used it to predict the optimal enzyme pathways (for example, pathways involving the fewest enzymes or requiring the least energy) for photosynthesis under particular conditions. The model predicted that, in addition to shortages in carbon dioxide, shortages in an important plant nutrient known as nitrogen may have driven the evolution of C4 photosynthesis. Furthermore, enzyme pathways that were intermediate between C3 and C4 photosynthesis were predicted to be optimal solutions under particular conditions. Together, the findings of Blätke and Bräutigam may explain why different variations of C4 photosynthesis exist in plants. These findings could be used to breed crops that use the most efficient type of photosynthesis for the conditions they are grown in, leading to better yields.

BioModelKit - An Integrative Framework for Multi-Scale Biomodel-Engineering.

While high-throughput technology, advanced techniques in biochemistry and molecular biology have become increasingly powerful, the coherent interpretation of experimental results in an integrative context is still a challenge. BioModelKit (BMK) approaches this challenge by offering an integrative and versatile framework for biomodel-engineering based on a modular modelling concept with the purpose: (i) to represent knowledge about molecular mechanisms by consistent executable sub-models (modules) given as Petri nets equipped with defined interfaces facilitating their reuse and recombination; (ii) to compose complex and integrative models from an ad hoc chosen set of modules including different omic and abstraction levels with the option to integrate spatial aspects; (iii) to promote the construction of alternative models by either the exchange of competing module versions or the algorithmic mutation of the composed model; and (iv) to offer concepts for (omic) data integration and integration of existing resources, and thus facilitate their reuse. BMK is accessible through a public web interface (www.biomodelkit.org), where users can interact with the modules stored in a database, and make use of the model composition features. BMK facilitates and encourages multi-scale model-driven predictions and hypotheses supporting experimental research in a multilateral exchange.

Modelling and simulating reaction-diffusion systems using coloured Petri nets.

Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model.

JAK/STAT signalling--an executable model assembled from molecule-centred modules demonstrating a module-oriented database concept for systems and synthetic biology.

Mathematical models of molecular networks regulating biological processes in cells or organisms are most frequently designed as sets of ordinary differential equations. Various modularisation methods have been applied to reduce the complexity of models, to analyse their structural properties, to separate biological processes, or to reuse model parts. Taking the JAK/STAT signalling pathway with the extensive combinatorial cross-talk of its components as a case study, we make a natural approach to modularisation by creating one module for each biomolecule. Each module consists of a Petri net and associated metadata and is organised in a database publically accessible through a web interface (). The Petri net describes the reaction mechanism of a given biomolecule and its functional interactions with other components including relevant conformational states. The database is designed to support the curation, documentation, version control, and update of individual modules, and to assist the user in automatically composing complex models from modules. Biomolecule centred modules, associated metadata, and database support together allow the automatic creation of models by considering differential gene expression in given cell types or under certain physiological conditions or states of disease. Modularity also facilitates exploring the consequences of alternative molecular mechanisms by comparative simulation of automatically created models even for users without mathematical skills. Models may be selectively executed as an ODE system, stochastic, or qualitative models or hybrid and exported in the SBML format. The fully automated generation of models of redesigned networks by metadata-guided modification of modules representing biomolecules with mutated function or specificity is proposed.