Understanding FBA Solutions under Multiple Nutrient Limitations

On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis

In Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the 'Edinburgh pathway', the 'Amsterdam pathway', as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the 'catalytic control coefficients' of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a 'hard optimum' defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.

Multi-Objective Optimization of Microalgae Metabolism: An Evolutive Algorithm Based on FBA

Studies enabled by metabolic models of different species of microalgae have become significant since they allow us to understand changes in their metabolism and physiological stages. The most used method to study cell metabolism is FBA, which commonly focuses on optimizing a single objective function. However, recent studies have brought attention to the exploration of simultaneous optimization of multiple objectives. Such strategies have found application in optimizing biomass and several other bioproducts of interest; they usually use approaches such as multi-level models or enumerations schemes. This work proposes an alternative in silico multiobjective model based on an evolutionary algorithm that offers a broader approximation of the Pareto frontier, allowing a better angle for decision making in metabolic engineering. The proposed strategy is validated on a reduced metabolic network of the microalgae Chlamydomonas reinhardtii while optimizing for the production of protein, carbohydrates, and CO2 uptake. The results from the conducted experimental design show a favorable difference in the number of solutions achieved compared to a classic tool solving FBA.

The view of microbes as energy converters illustrates the trade-off between growth rate and yield

The application of thermodynamics to microbial growth has a long tradition that originated in the middle of the 20th century. This approach reflects the view that self-replication is a thermodynamic process that is not fundamentally different from mechanical thermodynamics. The key distinction is that a free energy gradient is not converted into mechanical (or any other form of) energy but rather into new biomass. As such, microbes can be viewed as energy converters that convert a part of the energy contained in environmental nutrients into chemical energy that drives self-replication. Before the advent of high-throughput sequencing technologies, only the most central metabolic pathways were known. However, precise measurement techniques allowed for the quantification of exchanged extracellular nutrients and heat of growing microbes with their environment. These data, together with the absence of knowledge of metabolic details, drove the development of so-called black-box models, which only consider the observable interactions of a cell with its environment and neglect all details of how exactly inputs are converted into outputs. Now, genome sequencing and genome-scale metabolic models (GEMs) provide us with unprecedented detail about metabolic processes inside the cell. However, mostly due to computational complexity issues, the derived modelling approaches make surprisingly little use of thermodynamic concepts. Here, we review classical black-box models and modern approaches that integrate thermodynamics into GEMs. We also illustrate how the description of microbial growth as an energy converter can help to understand and quantify the trade-off between microbial growth rate and yield.