In this article, we present a protocol for generating a complete (genome-scale) metabolic resource allocation model, as well as a proposal for how to represent such models in the systems biology markup language (SBML). Such models are used to investigate enzyme levels and achievable growth rates in large-scale metabolic networks. Although the idea of metabolic resource allocation studies has been present in the field of systems biology for some years, no guidelines for generating such a model have been published up to now. This paper presents step-by-step instructions for building a (dynamic) resource allocation model, starting with prerequisites such as a genome-scale metabolic reconstruction, through building protein and noncatalytic biomass synthesis reactions and assigning turnover rates for each reaction. In addition, we explain how one can use SBML level 3 in combination with the flux balance constraints and our resource allocation modeling annotation to represent such models.

Constraint-based methods, such as the flux balance analysis (FBA), are widely used to model cellular growth processes without relying on knowledge of regulatory features. Regulation is instead substituted by an optimization problem to maximize a biological objective such as biomass accumulation. A recent extension to these methods is called dynamic enzyme-cost FBA (deFBA). This fully dynamic modeling method allows to predict optimal enzyme levels and reaction fluxes under changing environmental conditions. However, this method was designed for well-defined deterministic settings in which dynamics of the environment are exactly known. In this letter, we present a theoretical framework called the robust deFBA which extends the deFBA to handle uncertainty in nutrient availability. We achieve this by combining deFBA with multi-stage model predictive control which explicitly captures the evolution of uncertainty by a scenario tree. The resulting method is capable of predicting robust optimal gene expression levels for rapidly changing environments. We apply these algorithms to a model of the core metabolic process in bacteria under alternating oxygen availability.

Microorganisms have developed complex regulatory features controlling their reaction and internal adaptation to changing environments. When modeling these organisms we usually do not have full understanding of the regulation and rely on substituting it with an optimization problem using a biologically reasonable objective function. The resulting constraint-based methods like the Flux Balance Analysis (FBA) and Resource Balance Analysis (RBA) have proven to be powerful tools to predict growth rates, by-products, and pathway usage for fixed environments. In this work, we focus on the dynamic enzyme-cost Flux Balance Analysis (deFBA), which models the environment, biomass products, and their composition dynamically and contains reaction rate constraints based on enzyme capacity. We extend the original deFBA formalism to include storage molecules and biomass-related maintenance costs. Furthermore, we present a novel usage of the receding prediction horizon as used in Model Predictive Control (MPC) in the deFBA framework, which we call the short-term deFBA (sdeFBA). This way we eliminate some mathematical artifacts arising from the formulation as an optimization problem and gain access to new applications in MPC schemes. A major contribution of this paper is also a systematic approach for choosing the prediction horizon and identifying conditions to ensure solutions grow exponentially. We showcase the effects of using the sdeFBA with different horizons through a numerical example.