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In silico evolution of diauxic growth.

Chu DF - BMC Evol. Biol. (2015)

Bottom Line: The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth.Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency.Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves.

View Article: PubMed Central - PubMed

Affiliation: School of Computing, University of Kent, Canterbury, CT2 7NF, UK. D.F.Chu@kent.ac.uk.

ABSTRACT

Background: The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture.

Methods: Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves.

Results: As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited.

Discussion: However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency.

Conclusions: Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression.

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a There is an optimal length for the lag-phase. Along the horizontal axis we vary the parameter dR that determines how fast the regulator is phosphorylated. The dependence of the fitness on this parameter shows two phases. For low values, corresponding to long lag-phases the fitness does not depend on the parameter. For higher values, there is an optimum dR for the competitor. The inset shows a detailed view of the optimum. In this particular example, the parameter dR evolved close to the otimal value. b The same data but time to take up N1 and the fitness plotted as a function of the switching delay. All data from in these plots was obtained by taking a single evolved solution and varying the parameter dR. All simulations here show an evolved solution and the incumbent against which this solution evolved
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Fig8: a There is an optimal length for the lag-phase. Along the horizontal axis we vary the parameter dR that determines how fast the regulator is phosphorylated. The dependence of the fitness on this parameter shows two phases. For low values, corresponding to long lag-phases the fitness does not depend on the parameter. For higher values, there is an optimum dR for the competitor. The inset shows a detailed view of the optimum. In this particular example, the parameter dR evolved close to the otimal value. b The same data but time to take up N1 and the fitness plotted as a function of the switching delay. All data from in these plots was obtained by taking a single evolved solution and varying the parameter dR. All simulations here show an evolved solution and the incumbent against which this solution evolved

Mentions: We have now established that regulated sequential uptake can only be realised when the parameters kb,kub and dR are in the right relationship. Yet, there are many ways to set these parameters so that they are compatible with regulation. The question is now whether or not some of these parameter configurations are better than others. To understand this we plotted the fitness as a function of the phosphorylation rate constant dR in Fig. 8a using a solution that had evolved to regulated sequential uptake. The figure indicates two different regimes. Firstly, for small values of dR (on the left side of the graph) the fitness of the competitor is very low but the fitness of the incumbent is high. Within this regime both are unaffected by further lowering the phosphorylation rate. This regime can be understood as follows: The lower the value of dR the longer it takes to switch on N2 uptake and metabolism, as shown above in Fig. 4a. The incumbent competes for the same N2 source and does so only a bit slower than the competitor. If the time required to switch goes above a certain value, then the incumbent will be able to take up all of N2 before the competitor can do so. The fitness of the competitor and incumbent cross where this happens. A further decrease of dR then remains inconsequential because switching has become irrelevant. Hence, the low competitor fitness in this regime indicates that it only takes up N1 but not N2.Fig. 8


In silico evolution of diauxic growth.

Chu DF - BMC Evol. Biol. (2015)

a There is an optimal length for the lag-phase. Along the horizontal axis we vary the parameter dR that determines how fast the regulator is phosphorylated. The dependence of the fitness on this parameter shows two phases. For low values, corresponding to long lag-phases the fitness does not depend on the parameter. For higher values, there is an optimum dR for the competitor. The inset shows a detailed view of the optimum. In this particular example, the parameter dR evolved close to the otimal value. b The same data but time to take up N1 and the fitness plotted as a function of the switching delay. All data from in these plots was obtained by taking a single evolved solution and varying the parameter dR. All simulations here show an evolved solution and the incumbent against which this solution evolved
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
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getmorefigures.php?uid=PMC4587919&req=5

Fig8: a There is an optimal length for the lag-phase. Along the horizontal axis we vary the parameter dR that determines how fast the regulator is phosphorylated. The dependence of the fitness on this parameter shows two phases. For low values, corresponding to long lag-phases the fitness does not depend on the parameter. For higher values, there is an optimum dR for the competitor. The inset shows a detailed view of the optimum. In this particular example, the parameter dR evolved close to the otimal value. b The same data but time to take up N1 and the fitness plotted as a function of the switching delay. All data from in these plots was obtained by taking a single evolved solution and varying the parameter dR. All simulations here show an evolved solution and the incumbent against which this solution evolved
Mentions: We have now established that regulated sequential uptake can only be realised when the parameters kb,kub and dR are in the right relationship. Yet, there are many ways to set these parameters so that they are compatible with regulation. The question is now whether or not some of these parameter configurations are better than others. To understand this we plotted the fitness as a function of the phosphorylation rate constant dR in Fig. 8a using a solution that had evolved to regulated sequential uptake. The figure indicates two different regimes. Firstly, for small values of dR (on the left side of the graph) the fitness of the competitor is very low but the fitness of the incumbent is high. Within this regime both are unaffected by further lowering the phosphorylation rate. This regime can be understood as follows: The lower the value of dR the longer it takes to switch on N2 uptake and metabolism, as shown above in Fig. 4a. The incumbent competes for the same N2 source and does so only a bit slower than the competitor. If the time required to switch goes above a certain value, then the incumbent will be able to take up all of N2 before the competitor can do so. The fitness of the competitor and incumbent cross where this happens. A further decrease of dR then remains inconsequential because switching has become irrelevant. Hence, the low competitor fitness in this regime indicates that it only takes up N1 but not N2.Fig. 8

Bottom Line: The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth.Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency.Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves.

View Article: PubMed Central - PubMed

Affiliation: School of Computing, University of Kent, Canterbury, CT2 7NF, UK. D.F.Chu@kent.ac.uk.

ABSTRACT

Background: The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture.

Methods: Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves.

Results: As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited.

Discussion: However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency.

Conclusions: Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression.

Show MeSH
Related in: MedlinePlus