(291b) Scalable and Efficient Bayesian Metabolic Modeling with Linear-Logarithmic Kinetics

Mathematical modeling of metabolic networks has shown significant promise in determining computational strain designs and improving bioprocess economics. Strain design methods based on flux balance analysis (FBA) quantify how metabolic networks can feasibly operate, and can determine optimal genetic interventions that seek to constrain organisms to a desirable metabolic state. These methods are most effective at predicting which reactions to knock out, since predicting the effects of enzyme overexpressions typically requires a kinetic description of the involved reactions. Metabolic ensemble modeling (1) has emerged in recent years as an effective tool for estimating confidence intervals in these kinetic descriptions from observable steady-state flux and concentration measurements. The method operates by sampling feasible kinetic parameters and filtering to sets of parameters that match experimental observations. There are therefore two computational bottlenecks that hinder an accurate determination of parameter identifiability given observed experimental results:

• Repeatedly solving the set of coupled ordinary differential equations for expected steady-state fluxes and concentrations following a change in enzyme expression, and
• the efficient sampling of parameter values that give rise to behavior consistent with experimental observations.

Recently, Saa & Nielsen (2) demonstrated that metabolic ensemble modeling could be understood through a Bayesian context, which allows Monte Carlo Markov chain samplers to reduce the number of parameter draws required to find those consistent with experimental observations. However, the slow integration of ODEs and lack of derivative information for the likelihood function continues to limit the scalability of the method to large data sets.

Here, we demonstrate how coupling linear-logarithmic kinetics for reaction flux to a metabolic ensemble modeling framework solves the two computational bottlenecks described above. The resulting method therefore represents a scalable, flexible framework for the integration of multiple ‘-omics’ datasets to predict flux control coefficients. Specifically, linear-logarithmic kinetics enable steady-state fluxes to be predicted linearly from kinetic parameters (3), removing the computational burden associated with solving for steady-state flux. Additionally, since linear solutions permit the easy determination of likelihood gradients, advanced Bayesian inference techniques such as Hamiltonian Monte Carlo and automatic differentiation variational inference can be applied to reliably estimate posterior parameter distributions even for high-dimensional models. We demonstrate the method through a number of case studies, including medium-sized metabolic models (with hundreds of metabolites and reactions) to simple in vitro reaction systems with novel experimental data.

1. L. M. Tran, M. L. Rizk, J. C. Liao, Biophysical Journal. 95, 5606–5617 (2008).
2. P. A. Saa, L. K. Nielsen, Sci. Rep., 1–13 (2016). (DOI: 10.1038/srep29635)
3. L. Wu, W. Wang, W. A. van Winden, W. M. van Gulik, J. J. Heijnen, European Journal of Biochemistry. 271, 3348–3359 (2004).