Constraint-Based Reconstruction and Analysis (COBRA) methods use biological knowledge and data to place constraints on intracellular fluxes, and in recent years have expanded to consider a wide range of recent omics techniques. Here we focus on extensions of COBRA methods that pertain to guiding strain designs from omics data, while a number of recent reviews have covered COBRA methods in greater depth (O’Brien et al., 2015; Campbell et al., 2017; Stalidzans et al., 2018). A central technique to COBRA methods is flux balance analysis (FBA), which assumes that metabolite concentrations in the cell reach a pseudo steady-state when compared to the time scales associated with substrate uptake and cell division (Orth et al., 2010). This assumption allows fluxes to be constrained by mass balance equations developed from databases of biochemical reaction stoichiometry. Mass balance constraints alone (in the absence of 13C isotope labeling or other product data) are often not sufficient to determine a unique vector of metabolic fluxes. By assuming a cellular objective such as maximizing biomass or ATP production, unique flux vectors can be predicted. The accuracy of these predicted flux values are dependent on the objective chosen, and some objective functions have shown good correlation with experimental omics data (Lewis et al., 2010). Since such models can be simulated quickly and rely primarily on well-curated databases of metabolic reactions, many genome-scale models (GEMs) of microbial metabolism have been created (Henry et al., 2010; King et al., 2015). While useful in understanding metabolic functionality and predicting the results of gene manipulation, these assumptions are not sufficient to fully incorporate the phenotypic observations resulting from omics analyses.

Extensions to the COBRA framework have therefore been proposed to impose additional constraints from experimental observations. One of the earliest such studies used transcriptomic data to block flux through reactions where gene expression for required enzymes was not observed (Åkesson et al., 2004). This method considered gene product expression through boolean logic, however, more recent studies have explicitly included gene product expression in the constraint-based framework (Becker and Palsson, 2008; Shlomi et al., 2008). Metabolism and gene-expression models (ME-models) explicitly model reactions involved in transcription and translations to build a quantitative model of enzyme production and usage (Lerman et al., 2012). These models therefore allow direct comparison of model predictions with transcriptomic and proteomic data (O’Brien et al., 2014, 2015). In a similar method, genome-scale models with protein structures (GEM-PROs) include structural information about each enzymatically catalyzed reaction (Chang et al., 2013). Such models allow the explicit simulation of the proteome fraction devoted to different cellular activities (Basan et al., 2015), and therefore might also be used to add additional constrains from proteomic analyses. The GECKO method combines literature knowledge of enzyme kinetics with proteomics data to constrain metabolic fluxes (Sánchez et al., 2017). However, while many enzymes have been kinetically characterized for well-studied species, these data are typically not available for non-model microbes (Nilsson et al., 2017).

Metabolomics data are typically incorporated in constraint-based models through the explicit consideration of reaction thermodynamics. If absolute metabolite concentrations are available, thermodynamic metabolic flux analysis can provide more condition-specific information on irreversible reactions (Henry et al., 2007). These principles have been successfully applied to select the most promising pathways for the synthesis of a variety of products (Averesch et al., 2017). Further extensions to the COBRA framework will likely include even more cellular functionality. Toward this goal, whole-cell models that integrate gene expression, protein production, and cell cycle have been constructed (Karr et al., 2012).

Constraint-Based Reconstruction and Analysis methods therefore represent an extensible and computationally efficient framework for connecting omics data of different types and have been used to successfully interpret omics data and improve strain designs in a number of studies (Wisselink et al., 2010; Brunk et al., 2016). An advantage of COBRA methods is their limited number of parameters that must be fit from experimental data, and therefore they are often able to suggest strain designs without substantial experimental support. In particular, these methods are especially efficient in determining metabolic changes that couple product production to cell growth (Long et al., 2015). The accuracy of constraint-based models in predicting de novo experimental results has not been rigorously evaluated and would serve a useful study in measuring the progress in our understanding of cellular behavior. However, even modest success rates from predictive tools are useful in guiding experimental efforts where the search space is vast. A limitation of constrained-based methods is that they are often less suitable for suggesting improvements to fine-tune the enzyme expression of an existing pathway. Such a task typically requires a kinetic description of the reactions in question, which we discuss in the next section.

The goal of kinetic metabolic models is to capture the dynamic behavior of individual enzymes and integrate these expressions into the behavior of the full metabolic network. These models allow the direct prediction steady-state flux distributions as a function of enzyme expression, which typically serve as the most reliable experimental data for validation. However, models that explicitly incorporate enzyme kinetics (if parameterized correctly) are capable of predicting finer details of pathway dynamics, including the effect of slight changes in enzyme activity on metabolic flux. In constraint-based models, metabolite pools are assumed to be in a pseudo steady-state, and thus the rate rules governing flux through each reaction can be ignored. While the steady-state assumption may be justified, the specific steady-state reached inside the cell is determined, among a multitude of factors, both by external metabolite conditions as well as the kinetics and expression levels of metabolic enzymes. Kinetic modeling frameworks therefore seek to estimate these reaction rate rules from observed metabolic phenotypes to predict how enzyme perturbation will affect steady-state concentrations and fluxes.

Small-scale kinetic models of core carbon metabolism can leverage enzyme kinetics in vitro and time-course metabolite concentration measurements in fitting parameter values (Chassagnole et al., 2002). However, transient cellular responses are difficult to measure at the genome-scale, and direct enzyme kinetic measurements are sparser for peripheral pathways. Large-scale dynamic metabolic simulations are therefore largely based on steady-state flux and concentration data (Vasilakou et al., 2016). Because of these limited data, quantifying parameter uncertainty is therefore a critical challenge in large-scale kinetic models (Tummler and Klipp, 2018). Metabolic ensemble modeling addresses this challenge directly by finding distributions in parameter values that all reproduce the observed experimental data (Tran et al., 2008). This approach has been used to suggest subsequent enzymes in a linear pathway for overexpression (Contador et al., 2009), and an ensemble-based kinetic model of Escherichia coli has demonstrated superior predictive ability of steady-state flux distributions (Khodayari et al., 2014).

Smaller-scale, hand-curated kinetic models can use rate rules for individual enzymes with experimentally validated functional forms. However, traditional rate rule expressions (such as Michaelis–Menten kinetics) become difficult to construct for reactions with many participating species. Accordingly, larger-scale kinetic models typically choose a generalizable framework for constructing rate rule expressions. These frameworks range in computational complexity and faithfulness to the underlying enzyme-substrate system, and we leave a detailed comparison of these approaches to a number of recently published reviews (Heijnen, 2005; Hadlich et al., 2009; Du et al., 2016; Saa and Nielsen, 2017). Software available for kinetic modeling has continued to improve, and typically allows the user to specify reaction stoichiometry and rate rules independently from the chosen simulation algorithm. Such software includes COPASI (Hoops et al., 2006), CellDesigner (Funahashi et al., 2008), and MATCONT (Dhooge et al., 2003).

Regardless of the framework chosen, a major hurdle in using kinetic models for interpretation of omics data is the computational effort required in parameter estimation. In metabolic ensemble modeling, parameters are sampled at random and retained in the final ensemble only if they match all the considered experimental data (Tran et al., 2008). As a result, as more data is added or the model expanded, the computational costs increase substantially. Methods for improving the computational speed of the approach have been developed (Greene et al., 2017), but calculating steady states of the dynamic model remains a computational bottleneck. Ensemble-based inference approaches are therefore typically applied to smaller, core-carbon metabolic networks (Khodayari et al., 2014). A recent genome-scale kinetic modeling study optimized only a single parameter set due to the added cost of ensemble-based parameter estimation (Khodayari and Maranas, 2016). However, this single parameter set demonstrated a superior ability to reproduce a wide range of experimental observations compared with constraint-based methods (Khodayari and Maranas, 2016). The ensemble modeling sampling approach has been recently formalized as a form of Bayesian inference (Saa and Nielsen, 2016), demonstrating that detailed posterior distributions in parameter estimates and model predictions could be found. Kinetic models therefore offer a promising future direction for incorporating vast quantities of omics data in metabolic reconstructions if computational bottlenecks can be circumvented (St. John et al., 2018). While difficult to fit, the added parameters from kinetic representations give these models more expressive power in fitting experimental data.

A factor complicating the analysis of experimental data with kinetic models is the stochasticity introduced by low cell volumes and small copy numbers of several key enzymes (Levine and Hwa, 2007; Kiviet et al., 2014). Cell to cell heterogeneity therefore imposes unique challenges in understanding microbial kinetics that might be resolved through the use of explicit stochastic simulation algorithms (Gillespie, 1977) as implemented in a variety of software packages (Hoops et al., 2006; Sanft et al., 2011; Abel et al., 2016) In the subsequent section we discuss machine learning approaches that add even more parameters to be fit, but may prove useful as high-throughput strain construction and characterization techniques improve.

Machine learning methods for interpreting omics data have taken a wide range of forms, largely due to the many varied biological questions that can be asked. In this section, we focus on methods that predict future targets for strain engineering. Integrative omics analyses attempt to draw connects between disparate omics data sources, either with or without prior biological knowledge (Berger et al., 2013; Bersanelli et al., 2016). These methods have been used to predict key regulatory genes correlated with metabolic productivity (Larsen et al., 2018), and inferred regulatory networks have also been incorporated into FBA models (Chandrasekaran and Price, 2010). Other studies have used machine learning to understand and predict metabolic performance from hyperparameters associated with cell growth. Wu et al. (2016) explored methods for machine learning in meta-analysis to predict likely pathway success as a function of the complexity of the engineered pathway and other factors. In Kim et al. (2016), machine learning methods are used both for data reconciliation between omics sources, as well as to directly map the genotype-phenotype relationship. Another interesting study used machine learning methods as a replacement for the traditional rate equation frameworks discussed in the previous section (Costello and Martin, 2018). In that study, rate equations were learned directly from time-series metabolomics and were successful in predicting medium-producing strains given high and low-producing varieties. Costello and Martin (2018) also quantified the amount of data required for accurate rate determination at approximately 10 strains. Given the rapid advancement of machine learning methods and biological data collection, these approaches may offer flexible and efficient ways of directly incorporate biological data in new strain designs.