The choice of the objective function in flux balance analysis is crucial for predicting replicative lifespans in yeast

Abstract

Flux balance analysis (FBA) is a powerful tool to study genome-scale models of the cellular metabolism, based on finding the optimal flux distributions over the network. While the objective function is crucial for the outcome, its choice, even though motivated by evolutionary arguments, has not been directly connected to related measures. Here, we used an available multi-scale mathematical model of yeast replicative ageing, integrating cellular metabolism, nutrient sensing and damage accumulation, to systematically test the effect of commonly used objective functions on features of replicative ageing in budding yeast, such as the number of cell divisions and the corresponding time between divisions. The simulations confirmed that assuming maximal growth is essential for reaching realistic lifespans. The usage of the parsimonious solution or the additional maximisation of a growth-independent energy cost can improve lifespan predictions, explained by either increased respiratory activity using resources otherwise allocated to cellular growth or by enhancing antioxidative activity, specifically in early life. Our work provides a new perspective on choosing the objective function in FBA by connecting it to replicative ageing.

Fig 1. Effect of objective functions on replicative lifespans and generation times.

Replicative lifespans (A) and generation times (B) for cells simulated with different objectives and flexibilities ϵ_1,2 using the non-parsimonious (left) and the parsimonious (right) solutions. (C) Counts of how many parameter combinations lead to replicative lifespans between 20 and 30 divisions, and generation times between 1.5 and 2.3h, denoted as wildtype cells.

Fig 2. Relative changes of normalised fluxes between the non-parsimonious and the parsimonious solution.

We limited the analysis to objectives that show a large increase in the replicative lifespans as a consequence of imposing parsimony. Included are 20 parameter combination with ϵ₁ ≥ 0.3 and ϵ₂ ≤ 0.2 per investigated objective (Fig 1). All fluxes are normalised by the glucose uptake rate and averaged over a metabolic phase (left: I, right: II). (A) Percentage of fluxes that are increased (white), unchanged (grey) or decreased (black) in all included pathways in the FBA model, when going from the non-parsimonious to the parsimonious solution. All objective functions are merged in this plot. (B) Relative changes of all fluxes in the respective pathways, when going from the non-parsimonious to the parsimonious solution. The grey bars indicate the interquartile ranges of the distributions.

Fig 3. Comparison between using the parsimonious solution or an additional optimisation of NGAM.

We compared only maximal growth, parsimonious maximal growth, and maximal growth plus maximal NGAM. Included are 20 parameter combination with ϵ₁ ≥ 0.3 and ϵ₂ ≤ 0.2 per investigated objective (Fig 1). All fluxes are normalised by the glucose uptake rate and averaged over a metabolic phase (left: I, right: II). (A) Relative changes of all fluxes in the respective pathways for parsimonious maximal growth and maximal growth plus maximal NGAM, both in relation to maximal growth only. (B) Average generation times for each included parameter set, sorted and coloured by the respective objective function. (C) Sum of all fluxes for each included parameter set, coloured by the respective objective function. (D) Sum of all enzyme usages, that were averaged over the respective metabolic phase, for each included parameter set, coloured by the respective objective function.

Fig 4. Comparison of overall properties of wildtype cells in the metabolic phases.

Number of divisions and time spent in each metabolic phase, and the damage at the end of each phase for all parameter combinations that lead to wildtype cells (replicative lifespans between 20 and 30 divisions, and generation times between 1.5 and 2.3h, see S1 Fig). The damage at the end of phase II corresponds to the fraction of damaged proteins when the cell dies. The cells are grouped by the respective combination of objective functions. Here, we only present the parsimonious cases.