Optimality of extracellular enzyme production and activity in dynamic flux balance modeling

In microbial communities, many vital metabolic functions, including the degradation of cellulose, proteins and other complex macromolecules, are carried out by costly, extracellularly secreted enzymes. While significant effort has been dedicated to analyzing genome-scale metabolic networks for individual microbes and communities, little is known about the interplay between global allocation of metabolic resources in the cell and extracellular enzyme secretion and activity. Here we introduce a method for modeling the secretion and catalytic functions of extracellular enzymes using dynamic flux balance analysis. This new addition, implemented within COMETS (Computation Of Microbial Ecosystems in Time and Space), simulates the costly production and secretion of enzymes and their diffusion and activity throughout the environment, independent of the producing organism. After tuning our model based on data for a Saccharomyces cerevisiae strain engineered to produce exogenous cellulases, we explored the dynamics of the system at different cellulose concentrations and enzyme production rates. We found that there are distinct rates of constitutive enzyme secretion which maximize either growth rate or biomass yield. These optimal rates are strongly dependent on enzyme kinetic properties and environmental conditions, including the amount of cellulose substrate available. Our framework will facilitate the development of more realistic simulations of microbial community dynamics within environments rich in complex macromolecules, with applications in the study of soil and plant-associated ecosystems, and other natural and engineered microbiomes. Importance Many organisms - including soil, marine and human-associated bacteria and fungi - perform part of their metabolic functions outside of the boundary of the cell, through the secretion of extracellular enzymes that can diffuse and facilitate reactions independently of the organism that produced them. In order to better understand and predict microbial ecosystems, it would be helpful to create mathematical models incorporating these extracellular reactions within simulations of metabolism at the whole-cell level. In this paper we demonstrate the implementation of such a methodology and apply it to study a cellulase-secreting yeast. This work will be useful for a number of microbial ecology applications, including modeling of microbiome dynamics, engineering of bioproducts (e.g. biofuels) from plant biomass through synthetic communities or modified organisms, and testing of basic ecological hypotheses about the balance between cost and benefits of the production of common goods in microbial communities. ### Competing Interest Statement The authors have declared no competing interest.