Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models

in Metabolic Engineering (2022)

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of ... [more ▼]

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis. [less ▲]

The intertwined metabolism during symbiotic nitrogen fixation elucidated by metabolic modelling

in Scientific Reports (2018), 8

Genome-scale metabolic network models can be used for various analyses including the prediction of metabolic responses to changes in the environment. Legumes are well known for their rhizobial symbiosis ... [more ▼]

Genome-scale metabolic network models can be used for various analyses including the prediction of metabolic responses to changes in the environment. Legumes are well known for their rhizobial symbiosis that introduces nitrogen into the global nutrient cycle. Here, we describe a fully compartmentalised, mass and charge-balanced, genome-scale model of the clover Medicago truncatula, which has been adopted as a model organism for legumes. We employed flux balance analysis to demonstrate that the network is capable of producing biomass components in experimentally observed proportions, during day and night. By connecting the plant model to a model of its rhizobial symbiont, Sinorhizobium meliloti, we were able to investigate the effects of the symbiosis on metabolic fluxes and plant growth and could demonstrate how oxygen availability influences metabolic exchanges between plant and symbiont, thus elucidating potential benefits of inter organism amino acid cycling. We thus provide a modelling framework, in which the interlinked metabolism of plants and nodules can be studied from a theoretical perspective. [less ▲]

A systems-wide understanding of photosynthetic acclimation in algae and higher plants

in Journal of Experimental Botany (2017), 68(11), 26672681

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land ... [more ▼]

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology. [less ▲]

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels.

in Journal of Theoretical Biology (2014), 343

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical ... [more ▼]

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems. [less ▲]

Integration of proteomic and metabolomic profiling as well as metabolic modeling for the functional analysis of metabolic networks.

in Methods in Molecular Biology (2011), 694

The integrated analysis of different omics-level data sets is most naturally performed in the context of common process or pathway association. In this chapter, the two basic approaches for a metabolic ... [more ▼]

The integrated analysis of different omics-level data sets is most naturally performed in the context of common process or pathway association. In this chapter, the two basic approaches for a metabolic pathway-centric integration of proteomics and metabolomics data are described: the knowledge-based approach relying on existing metabolic pathway information, and a data-driven approach that aims to deduce functional (pathway) associations directly from the data. Relevant algorithmic approaches for the generation of metabolic networks of model organisms, their functional analysis, database resources, visualization and analysis tools will be described. The use of proteomics data in the process of metabolic network reconstruction will be discussed. [less ▲]

An integrative approach towards completing genome-scale metabolic networks.

in Molecular Biosystems (2009), 5(12), 1889-903

Genome-scale metabolic networks which have been automatically derived through sequence comparison techniques are necessarily incomplete. We propose a strategy that incorporates genomic sequence data and ... [more ▼]

Genome-scale metabolic networks which have been automatically derived through sequence comparison techniques are necessarily incomplete. We propose a strategy that incorporates genomic sequence data and metabolite profiles into modeling approaches to arrive at improved gene annotations and more complete genome-scale metabolic networks. The core of our strategy is an algorithm that computes minimal sets of reactions by which a draft network has to be extended in order to be consistent with experimental observations. A particular strength of our approach is that alternative possibilities are suggested and thus experimentally testable hypotheses are produced. We carefully evaluate our strategy on the well-studied metabolic network of Escherichia coli, demonstrating how the predictions can be improved by incorporating sequence data. Subsequently, we apply our method to the recently sequenced green alga Chlamydomonas reinhardtii. We suggest specific genes in the genome of Chlamydomonas which are the strongest candidates for coding the responsible enzymes. [less ▲]