Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities.

Engineering Bacteroides thetaiotaomicron to produce non-native butyrate based on a genome-scale metabolic model-guided design

Bacteroides thetaiotaomicron represents a major symbiont of the human gut microbiome that is increasingly viewed as a promising candidate strain for microbial therapeutics. Here, we engineer B. thetaiotaomicron for heterologous production of non-native butyrate as a proof-of-concept biochemical at therapeutically relevant concentrations. Since B. thetaiotaomicron is not a natural producer of butyrate, we heterologously expressed a butyrate biosynthetic pathway in the strain, which led to the production of butyrate at the final concentration of 12 mg/L in a rich medium. Further optimization of butyrate production was achieved by a round of metabolic engineering guided by an expanded genome-scale metabolic model (GEM) of B. thetaiotaomicron. The in silico knock-out simulation of the expanded model showed that pta and ldhD were the potent knock-out targets to enhance butyrate production. The maximum titer and specific productivity of butyrate in the pta-ldhD double knockout mutant increased by nearly 3.4 and 4.8 folds, respectively. To our knowledge, this is the first engineering attempt that enabled butyrate production from a non-butyrate producing commensal B. thetaiotaomicron. The study also highlights that B. thetaiotaomicron can serve as an effective strain for live microbial therapeutics in human.

Analyzing and Designing Cell Factories with OptFlux

OptFlux was launched in 2010 as the first open-source and user-friendly platform containing all the major methods for performing metabolic engineering tasks in silico. Main features included the possibility of performing microbial strain simulations with widely used methods such as Flux Balance Analysis and strain design using Evolutionary Algorithms. Since then, OptFlux suffered a major re-factoring to improve its efficiency and reliability, while many features were added in the form of novel plug-ins, such as the BioVisualizer and the over/under expression plug-ins. The current chapter described the main mathematical formulations of the major methods implemented within OptFlux, also providing a detailed guide on the usage of those functionalities.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering

BACKGROUND

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing.

RESULTS

We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli.

CONCLUSIONS

We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements.

Optimization of Multi-Omic Genome-Scale Models: Methodologies, Hands-on Tutorial, and Perspectives

Genome-scale metabolic models are valuable tools for assessing the metabolic potential of living organisms. Being downstream of gene expression, metabolism is increasingly being used as an indicator of the phenotypic outcome for drugs and therapies. We here present a review of the principal methods used for constraint-based modelling in systems biology, and explore how the integration of multi-omic data can be used to improve phenotypic predictions of genome-scale metabolic models. We believe that the large-scale comparison of the metabolic response of an organism to different environmental conditions will be an important challenge for genome-scale models. Therefore, within the context of multi-omic methods, we describe a tutorial for multi-objective optimization using the metabolic and transcriptomics adaptation estimator (METRADE), implemented in MATLAB. METRADE uses microarray and codon usage data to model bacterial metabolic response to environmental conditions (e.g., antibiotics, temperatures, heat shock). Finally, we discuss key considerations for the integration of multi-omic networks into metabolic models, towards automatically extracting knowledge from such models.

Selection Finder (SelFi): A computational metabolic engineering tool to enable directed evolution of enzymes

Directed evolution of enzymes consists of an iterative process of creating mutant libraries and choosing desired phenotypes through screening or selection until the enzymatic activity reaches a desired goal. The biggest challenge in directed enzyme evolution is identifying high-throughput screens or selections to isolate the variant(s) with the desired property. We present in this paper a computational metabolic engineering framework, Selection Finder (SelFi), to construct a selection pathway from a desired enzymatic product to a cellular host and to couple the pathway with cell survival. We applied SelFi to construct selection pathways for four enzymes and their desired enzymatic products xylitol, D-ribulose-1,5-bisphosphate, methanol, and aniline. Two of the selection pathways identified by SelFi were previously experimentally validated for engineering Xylose Reductase and RuBisCO. Importantly, SelFi advances directed evolution of enzymes as there is currently no known generalized strategies or computational techniques for identifying high-throughput selections for engineering enzymes.

A Markov chain model for N-linked protein glycosylation--towards a low-parameter tool for model-driven glycoengineering

Glycosylation is a critical quality attribute of most recombinant biotherapeutics. Consequently, drug development requires careful control of glycoforms to meet bioactivity and biosafety requirements. However, glycoengineering can be extraordinarily difficult given the complex reaction networks underlying glycosylation and the vast number of different glycans that can be synthesized in a host cell. Computational modeling offers an intriguing option to rationally guide glycoengineering, but the high parametric demands of current modeling approaches pose challenges to their application. Here we present a novel low-parameter approach to describe glycosylation using flux-balance and Markov chain modeling. The model recapitulates the biological complexity of glycosylation, but does not require user-provided kinetic information. We use this method to predict and experimentally validate glycoprofiles on EPO, IgG as well as the endogenous secretome following glycosyltransferase knock-out in different Chinese hamster ovary (CHO) cell lines. Our approach offers a flexible and user-friendly platform that can serve as a basis for powerful computational engineering efforts in mammalian cell factories for biopharmaceutical production.

Elucidating the adaptation and temporal coordination of metabolic pathways using in-silico evolution

Cellular metabolism, the interconversion of small molecules by chemical reactions, is a tightly coordinated process that requires integration of diverse environmental and intracellular cues. While for many organisms the topology of the network of metabolic reactions is increasingly known, the regulatory principles that shape the network's adaptation to diverse and changing environments remain largely elusive. To investigate the principles of metabolic adaptation and regulation in metabolic pathways, we propose a computational approach based on in-silico evolution. Rather than analyzing existing regulatory schemes, we let a population of minimal, prototypical metabolic cells evolve rate constants and appropriate regulatory schemes that allow for optimal growth in static and fluctuating environments. Applying our approach to a small, but already sufficiently complex, minimal system reveals intricate transitions between metabolic modes. These results have implications for trade-offs in resource allocation. Going from static to varying environments, we show that for fluctuating nutrient availability, active metabolic regulation results in a significantly increased overall rate of metabolism.