(568d) Extending a Scalable Bayesian Metabolic Modeling Framework with Thermodynamic Constraints and Support for Transcriptional Regulation

While the technology used by metabolic engineers to make genetic modifications is rapidly maturing, knowing which modifications to make in order to achieve a desired phenotype can be difficult due to the inherent complexity of biological systems. To deal with this complexity, mathematical models of metabolic networks are often used to predict how genetic manipulations affect desired phenotypes. For example, constraint-based modeling frameworks such as Flux Balance Analysis (FBA) are used to predict optimal flux distributions and the effects of enzyme knockouts. Constraint-based techniques have the advantage of being computationally inexpensive and can quickly inform metabolic engineering decisions. However, they lack kinetic details and typically use assumptions that metabolic regulation is used to achieve maximized objectives (e.g., growth) and do not describe apparent behavior in a number of biological systems. While kinetic models can incorporate more mechanistic detail, they also introduce a high-dimensional parameter space, which makes parameter estimation computationally expensive.

To overcome this limitation, Tran et al. have developed the Ensemble Modeling framework where instead of directly inferring parameter values, they generate an ensemble of parameter sets and keep those that, through the model, agree with multiple experimental observations (1). However, there are two relevant limitations: While this method works well for small and medium-scale models, it does not scale well to the genome-scale due to the need to integrate ordinary differential equations to attain the steady-state for every parameter set in the ensemble. Second, the approach employs rejection-sampling which does not give clear estimates of parameter uncertainties.

Here, we present an approximate kinetic framework where we use linear-logarithmic (lin-log) kinetics, allowing the steady-state fluxes to be solved for linearly, greatly reducing the computational time required (2). Because we can quickly solve for the steady-state, we are able to use advanced Bayesian inference methods such as Markov Chain Monte Carlo to estimate posterior distributions in model parameters. Importantly, these Bayesian techniques give us probability distributions for every parameter, which can be more informative than the single values typically generated by other non-Bayesian parameter estimation algorithms. We extend the modeling framework further based on ideas developed by Westerhoff and van Dam in order to incorporate thermodynamic constraints to improve model performance (3). Finally, we add effects of transcriptional regulation to the framework, which are typically difficult to include in kinetic models of metabolism due to the mechanistic complexity of the transcription and translation processes. We evaluate the performance of this framework by demonstrating the method on published small, medium, and genome-scale experimental datasets. We show that a genome-scale model with 25 experimental -omics data points can be run in 4 – 6 hours on a single modern CPU. Estimated posterior probability distributions were consistent with measured values. The framework we present here overcomes the computationally intensive and limited parameter estimation techniques put forth previously. We anticipate this modeling framework will be valuable to explicitly identify genetic modifications in metabolic networks that will improve desired phenotypes.

1. M. Tran, M. L. Rizk, J. C. Liao, Biophysical Journal. 95, 5606–5617 (2008).
2. Wu, W. Wang, W. A. van Winden, W. M. van Gulik, J. J. Heijnen, European Journal of Biochemistry. 271, 3348–3359 (2004).
3. Westerhoff, K. van Dam, “Thermodynamics and Control of Biological Free-Energy Transduction” (1987).