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Evolution of taxis responses in virtual bacteria: non-adaptive dynamics.

Goldstein RA, Soyer OS - PLoS Comput. Biol. (2008)

Bottom Line: Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations.Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components.When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Biology, National Institute for Medical Research, London, United Kingdom. rgoldst@nimr.mrc.ac.uk

ABSTRACT
Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.

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Evolution of the taxis response in silico.The average fitness in an evolving population of virtual bacteria. The inset shows the time-averaged distribution of positions of the population at generation 0, 200 (corresponding to a fitness of approximately 2.0), and 5,000 (final generation) as a contour plot. Areas enclosed by darker lines indicate more time spent there. Note that in these simulations the entire population starts at grid location (30,30) while stimulus source is fixed at (50,50).
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pcbi-1000084-g001: Evolution of the taxis response in silico.The average fitness in an evolving population of virtual bacteria. The inset shows the time-averaged distribution of positions of the population at generation 0, 200 (corresponding to a fitness of approximately 2.0), and 5,000 (final generation) as a contour plot. Areas enclosed by darker lines indicate more time spent there. Note that in these simulations the entire population starts at grid location (30,30) while stimulus source is fixed at (50,50).

Mentions: Figure 1 shows the population average of fitness (encountered stimuli) during one evolutionary simulation for a signalling pathway consisting of four proteins. As shown, the fitness value rapidly improves over a few generations and reaches a plateau. Clearly, the pathway structure and dynamics in virtual bacteria are evolving in such a way to mediate taxis. This behaviour can be seen from the average time spent by the population at different parts of the environment (see insets of Figure 1). While un-evolved bacterial populations are distributed irrespective of stimulus source, final populations are able to quickly co-localise with it. This behaviour is mediated by a specific biochemical pathway dynamics; at steady state, in absence of any signal, the concentration of activated effector is at a low level and the bacterium mostly swims without tumbling (see Figure 2 for typical pathway structure and dynamics, kinetic parameters are shown in Dataset S1). When the bacterium encounters higher stimulus levels, the effector is rapidly activated and stays activated as long as the signal is present, resulting in increased bacterial tumbling. We find that the qualitative nature of this type of dynamics is independent of basal stimuli level (data not shown). This non-adaptive dynamics allow the bacteria to spend more time in regions of high stimulus and swim straight when the stimulus level decreases. In evolutionary simulations repeated five times for pathways of 2 to 5 proteins, this mechanism always evolved as the dominant one.


Evolution of taxis responses in virtual bacteria: non-adaptive dynamics.

Goldstein RA, Soyer OS - PLoS Comput. Biol. (2008)

Evolution of the taxis response in silico.The average fitness in an evolving population of virtual bacteria. The inset shows the time-averaged distribution of positions of the population at generation 0, 200 (corresponding to a fitness of approximately 2.0), and 5,000 (final generation) as a contour plot. Areas enclosed by darker lines indicate more time spent there. Note that in these simulations the entire population starts at grid location (30,30) while stimulus source is fixed at (50,50).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2386285&req=5

pcbi-1000084-g001: Evolution of the taxis response in silico.The average fitness in an evolving population of virtual bacteria. The inset shows the time-averaged distribution of positions of the population at generation 0, 200 (corresponding to a fitness of approximately 2.0), and 5,000 (final generation) as a contour plot. Areas enclosed by darker lines indicate more time spent there. Note that in these simulations the entire population starts at grid location (30,30) while stimulus source is fixed at (50,50).
Mentions: Figure 1 shows the population average of fitness (encountered stimuli) during one evolutionary simulation for a signalling pathway consisting of four proteins. As shown, the fitness value rapidly improves over a few generations and reaches a plateau. Clearly, the pathway structure and dynamics in virtual bacteria are evolving in such a way to mediate taxis. This behaviour can be seen from the average time spent by the population at different parts of the environment (see insets of Figure 1). While un-evolved bacterial populations are distributed irrespective of stimulus source, final populations are able to quickly co-localise with it. This behaviour is mediated by a specific biochemical pathway dynamics; at steady state, in absence of any signal, the concentration of activated effector is at a low level and the bacterium mostly swims without tumbling (see Figure 2 for typical pathway structure and dynamics, kinetic parameters are shown in Dataset S1). When the bacterium encounters higher stimulus levels, the effector is rapidly activated and stays activated as long as the signal is present, resulting in increased bacterial tumbling. We find that the qualitative nature of this type of dynamics is independent of basal stimuli level (data not shown). This non-adaptive dynamics allow the bacteria to spend more time in regions of high stimulus and swim straight when the stimulus level decreases. In evolutionary simulations repeated five times for pathways of 2 to 5 proteins, this mechanism always evolved as the dominant one.

Bottom Line: Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations.Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components.When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Biology, National Institute for Medical Research, London, United Kingdom. rgoldst@nimr.mrc.ac.uk

ABSTRACT
Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.

Show MeSH
Related in: MedlinePlus