Bridging substrate intake kinetics and bacterial growth phenotypes with flux balance analysis incorporating proteome allocation

Hong Zeng,Aidong Yang

doi:10.1038/s41598-020-61174-0

Abstract

Empirical kinetic models such as the Monod equation have been widely applied to relate the cell growth with substrate availability. The Monod equation shares a similar form with the mechanistically-based Michaelis-Menten kinetics for enzymatic processes, which has provoked long-standing and un-concluded conjectures on their relationship. In this work, we integrated proteome allocation principles into a Flux Balance Analysis (FBA) model of Escherichia coli, which quantitatively revealed potential mechanisms that underpin the phenomenological Monod parameters: the maximum specific growth rate could be dictated by the abundance of growth-controlling proteome and growth-pertinent proteome cost; more importantly, the Monod constant (Ks) was shown to relate to the Michaelis constant for substrate transport (Km,g), with the link being dependent on the cell’s metabolic strategy. Besides, the proposed model was able to predict glucose uptake rate at given external glucose concentration through the size of available proteome resource for substrate transport and its enzymatic cost, while growth rate and acetate overflow were accurately simulated for two E. coli strains. Bridging the enzymatic kinetics of substrate intake and overall growth phenotypes, this work offers a mechanistic interpretation to the empirical Monod law, and demonstrates the potential of coupling local and global cellular constrains in predictive modelling.

Highlights

Empirical kinetic models such as the Monod equation have been widely applied to relate the cell growth with substrate availability
Following the treatment in several recent studies on proteome allocation[14,19,25,26,27], we divide the overall cell proteome into four coarse-grained functional sectors: carbon-scavenging sector C that comprises enzymes for importing extracellular carbohydrate, energy biogenesis sector E that consists of enzymes used for respiration and fermentation, biomass synthesis sector BM that accounts for ribosomal proteins and enzymes carrying anabolic fluxes, and an offset sector Q that contains other proteins whose abundance do not vary with the fluxes in the above three sectors (Fig. 1a)
We modified the classic Flux Balance Analysis (FBA) model via embedding the coarse-grained proteome allocation constraints with an intention to reveal the potential mechanistic nature of the empirical growth kinetics proposed by Monod seventy years ago

Summary

Introduction

Empirical kinetic models such as the Monod equation have been widely applied to relate the cell growth with substrate availability. The proposed model was able to predict glucose uptake rate at given external glucose concentration through the size of available proteome resource for substrate transport and its enzymatic cost, while growth rate and acetate overflow were accurately simulated for two E. coli strains. We parameterized a correlation between the enzyme cost for carbon transport and the abundance of carbon source Applying these modelling concepts and parameterisation in FBA simulations, we were able to predict the glucose uptake rate, growth rate and the acetate overflow upon varying extracellular glucose level. We propose that a proper connection of local and global physiological constraints may be essential for improving the predictive power of FBA models

Methods

Results

Conclusion