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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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Diverse taxis mechanisms.Time course of active effector concentration for the most frequent and unique pathways obtained from selected evolutionary simulations that are run under different environmental conditions (see main text). Each panel displays dynamics for a specific pathway structure shown in the inset. The system is allowed to equilibrate for 1,000 timesteps at the background basal stimulus level. A stimulus of one is added at time 1,000 and removed at time 2,000. Pathway response to such stimuli given on top of a selected basal level is shown in different line types (basal level is 0, 1, and 2, respectively, for solid, dotted, and dashed). Pathways shown in the upper panels are from simulations with periodic boundary conditions and fluctuating stimulus source, while those shown in the lower panel are from simulations with non-periodic boundary conditions and fixed stimulus source. Kinetic parameters for these pathways are given in Dataset S1.
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pcbi-1000084-g003: Diverse taxis mechanisms.Time course of active effector concentration for the most frequent and unique pathways obtained from selected evolutionary simulations that are run under different environmental conditions (see main text). Each panel displays dynamics for a specific pathway structure shown in the inset. The system is allowed to equilibrate for 1,000 timesteps at the background basal stimulus level. A stimulus of one is added at time 1,000 and removed at time 2,000. Pathway response to such stimuli given on top of a selected basal level is shown in different line types (basal level is 0, 1, and 2, respectively, for solid, dotted, and dashed). Pathways shown in the upper panels are from simulations with periodic boundary conditions and fluctuating stimulus source, while those shown in the lower panel are from simulations with non-periodic boundary conditions and fixed stimulus source. Kinetic parameters for these pathways are given in Dataset S1.

Mentions: To explore the effect of environmental conditions on the evolution of chemotaxis, we ran two sets of simulations under (i) periodic-boundary conditions and fluctuating stimulus source and (ii) non-periodic boundary conditions and fixed stimulus source. The first set of conditions allow us to test the hypothesis that adaptive dynamics provide a means for bacteria to preserve robustness of the response to fluctuations in the external environment or internal parameters [23]. The latter conditions mimic an environment with scarce stimulus, where exploration is expected to be more important than exploitation. In five simulations run under each condition, we did not find pathways with dynamics that are adaptive over a wide range of stimuli as seen in E. coli. However, several simulations resulted in pathways that had dynamical behaviour similar to that of E. coli under some conditions. As shown in Figure 3, these pathways give a “normal” response (i.e. decreased tumbling probability with stimuli) and have limited adaptation to continuous stimuli. Interestingly, most pathways evolved under non-periodic boundary conditions show dynamics that are dependent on basal stimuli levels. This affects mostly the adaptation dynamics and we observe one pathway achieving perfect adaptation under a narrow range of basal stimuli levels (see Figure 3). Most simulations run under sparse stimulus conditions resulted in approximately same fitness levels as shown in Figure 1. However, simulations run under these conditions (ii) took much longer (usually more than 2000 generations) to reach these fitness levels. Taken together, these results indicate that realistic and complex environmental conditions lead to evolution of complex pathway dynamics that contain features of both adaptive and non-adaptive dynamics. Untangling the role of each type of dynamics in the efficiency of chemotaxis requires further detailed analyses.


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

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

Diverse taxis mechanisms.Time course of active effector concentration for the most frequent and unique pathways obtained from selected evolutionary simulations that are run under different environmental conditions (see main text). Each panel displays dynamics for a specific pathway structure shown in the inset. The system is allowed to equilibrate for 1,000 timesteps at the background basal stimulus level. A stimulus of one is added at time 1,000 and removed at time 2,000. Pathway response to such stimuli given on top of a selected basal level is shown in different line types (basal level is 0, 1, and 2, respectively, for solid, dotted, and dashed). Pathways shown in the upper panels are from simulations with periodic boundary conditions and fluctuating stimulus source, while those shown in the lower panel are from simulations with non-periodic boundary conditions and fixed stimulus source. Kinetic parameters for these pathways are given in Dataset S1.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000084-g003: Diverse taxis mechanisms.Time course of active effector concentration for the most frequent and unique pathways obtained from selected evolutionary simulations that are run under different environmental conditions (see main text). Each panel displays dynamics for a specific pathway structure shown in the inset. The system is allowed to equilibrate for 1,000 timesteps at the background basal stimulus level. A stimulus of one is added at time 1,000 and removed at time 2,000. Pathway response to such stimuli given on top of a selected basal level is shown in different line types (basal level is 0, 1, and 2, respectively, for solid, dotted, and dashed). Pathways shown in the upper panels are from simulations with periodic boundary conditions and fluctuating stimulus source, while those shown in the lower panel are from simulations with non-periodic boundary conditions and fixed stimulus source. Kinetic parameters for these pathways are given in Dataset S1.
Mentions: To explore the effect of environmental conditions on the evolution of chemotaxis, we ran two sets of simulations under (i) periodic-boundary conditions and fluctuating stimulus source and (ii) non-periodic boundary conditions and fixed stimulus source. The first set of conditions allow us to test the hypothesis that adaptive dynamics provide a means for bacteria to preserve robustness of the response to fluctuations in the external environment or internal parameters [23]. The latter conditions mimic an environment with scarce stimulus, where exploration is expected to be more important than exploitation. In five simulations run under each condition, we did not find pathways with dynamics that are adaptive over a wide range of stimuli as seen in E. coli. However, several simulations resulted in pathways that had dynamical behaviour similar to that of E. coli under some conditions. As shown in Figure 3, these pathways give a “normal” response (i.e. decreased tumbling probability with stimuli) and have limited adaptation to continuous stimuli. Interestingly, most pathways evolved under non-periodic boundary conditions show dynamics that are dependent on basal stimuli levels. This affects mostly the adaptation dynamics and we observe one pathway achieving perfect adaptation under a narrow range of basal stimuli levels (see Figure 3). Most simulations run under sparse stimulus conditions resulted in approximately same fitness levels as shown in Figure 1. However, simulations run under these conditions (ii) took much longer (usually more than 2000 generations) to reach these fitness levels. Taken together, these results indicate that realistic and complex environmental conditions lead to evolution of complex pathway dynamics that contain features of both adaptive and non-adaptive dynamics. Untangling the role of each type of dynamics in the efficiency of chemotaxis requires further detailed analyses.

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