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Noise regulation by quorum sensing in low mRNA copy number systems.

Weber M, Buceta J - BMC Syst Biol (2011)

Bottom Line: The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate.Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate.QS systems seems to avoid values of the diffusion that maximize the total noise.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computer Simulation and Modelling (Co.S.Mo.) Lab, Parc Científic de Barcelona, C/Baldiri Reixac 10-12, Barcelona 08028, Spain.

ABSTRACT

Background: Cells must face the ubiquitous presence of noise at the level of signaling molecules. The latter constitutes a major challenge for the regulation of cellular functions including communication processes. In the context of prokaryotic communication, the so-called quorum sensing (QS) mechanism relies on small diffusive molecules that are produced and detected by cells. This poses the intriguing question of how bacteria cope with the fluctuations for setting up a reliable information exchange.

Results: We present a stochastic model of gene expression that accounts for the main biochemical processes that describe the QS mechanism close to its activation threshold. Within that framework we study, both numerically and analytically, the role that diffusion plays in the regulation of the dynamics and the fluctuations of signaling molecules. In addition, we unveil the contribution of different sources of noise, intrinsic and transcriptional, in the QS mechanism.

Conclusions: The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate. Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate. QS systems seems to avoid values of the diffusion that maximize the total noise. These results point towards the direction that bacteria have adapted their communication mechanisms in order to improve the signal-to-noise ratio.

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Related in: MedlinePlus

Distributions and dynamics of the signaling molecule in a system with diffusion. Distributions (left column) and dynamics (center column) of cA at steady-state for different values of . The right most column stands for a density plot of the distribution of  as a function of  for discerning a putative increase in the molecular noise (see text). In all cases the parameters set (, ) is γ2 (see Figure 2B). The production rate  is modulated as a function of (, , ) in order to maintain constant the average 〈cA〉 = 25 nM. The histograms obtained in the stochastic simulations (blue bars, left column) are in qualitative agreement with the probability densities from the analytical calculations (blue line, left column). When increasing the diffusion coefficient, the system explores different dynamics as revealed by the trajectories shown in the center column. The grey-shaded background shown in the trajectories of cA indicates the presence of a mRNA molecule in the cell. The density plots (right column) reveals that the diffusion does not contribute to an increase of the intrinsic noise since the spreading of the distributions in a direction perpendicular to the diagonal does not grow.
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Figure 4: Distributions and dynamics of the signaling molecule in a system with diffusion. Distributions (left column) and dynamics (center column) of cA at steady-state for different values of . The right most column stands for a density plot of the distribution of as a function of for discerning a putative increase in the molecular noise (see text). In all cases the parameters set (, ) is γ2 (see Figure 2B). The production rate is modulated as a function of (, , ) in order to maintain constant the average 〈cA〉 = 25 nM. The histograms obtained in the stochastic simulations (blue bars, left column) are in qualitative agreement with the probability densities from the analytical calculations (blue line, left column). When increasing the diffusion coefficient, the system explores different dynamics as revealed by the trajectories shown in the center column. The grey-shaded background shown in the trajectories of cA indicates the presence of a mRNA molecule in the cell. The density plots (right column) reveals that the diffusion does not contribute to an increase of the intrinsic noise since the spreading of the distributions in a direction perpendicular to the diagonal does not grow.

Mentions: If > 0 we expect a more fruitful phenomenology since the transition lines between behaviors in the parameter space (, ) shift as a function of the diffusion (see Figure 2A). According to the analytical calculations we can anticipate that, for a given parameter set and as increases, the system explores different dynamical regimes. By taking as a reference the case γ2, that is (, ) = (15, 5), Figure 4 shows the effect of the diffusion on the distribution (left column) and dynamics (center column) of cA in a given cell. The system initially displays a single-peak distribution for = 1. By increasing the diffusion coefficient we observe transitions to the other phases (monotonically decreasing and double-peak distributions). The corresponding dynamics of cA (right panels) show how the diffusion, acting as an additional effective degradation on A, first increases the sharpness of the bursts of production. For = 10, the diffusion is large enough to remove signaling molecules between consecutive burst events, thus leading to a monotonically decreasing distribution. Increasing the diffusion rate to = 100 leads to the situation where both and becomes smaller than 1 + and a bistable dynamics develops. Under these circumstances the concentration of autoinducer alternates between two states that correspond to a low concentration, when there is no mRNA production, and a high concentration, following the mRNA synthesis. As the diffusion further increases, e.g. = 2 · 103, the autoinducer molecules diffusing from the external medium into the cell set a constitutive level of this species. The latter explains the presence of A molecules in the cell even if no mRNA is produced. Finally, at very large values of , e.g. = 5 · 104, the low constitutive concentration of the autoinducer increases due to the influx of molecules when no mRNA is present whereas the concentration of A that is internally produced decreases due to the efflux of molecules. In this case, the whole N-cells system can be considered as a single volume with no diffusive barriers between cells. Thus, the burst events average out and, as a consequence, a single effective peak appears.


Noise regulation by quorum sensing in low mRNA copy number systems.

Weber M, Buceta J - BMC Syst Biol (2011)

Distributions and dynamics of the signaling molecule in a system with diffusion. Distributions (left column) and dynamics (center column) of cA at steady-state for different values of . The right most column stands for a density plot of the distribution of  as a function of  for discerning a putative increase in the molecular noise (see text). In all cases the parameters set (, ) is γ2 (see Figure 2B). The production rate  is modulated as a function of (, , ) in order to maintain constant the average 〈cA〉 = 25 nM. The histograms obtained in the stochastic simulations (blue bars, left column) are in qualitative agreement with the probability densities from the analytical calculations (blue line, left column). When increasing the diffusion coefficient, the system explores different dynamics as revealed by the trajectories shown in the center column. The grey-shaded background shown in the trajectories of cA indicates the presence of a mRNA molecule in the cell. The density plots (right column) reveals that the diffusion does not contribute to an increase of the intrinsic noise since the spreading of the distributions in a direction perpendicular to the diagonal does not grow.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3037314&req=5

Figure 4: Distributions and dynamics of the signaling molecule in a system with diffusion. Distributions (left column) and dynamics (center column) of cA at steady-state for different values of . The right most column stands for a density plot of the distribution of as a function of for discerning a putative increase in the molecular noise (see text). In all cases the parameters set (, ) is γ2 (see Figure 2B). The production rate is modulated as a function of (, , ) in order to maintain constant the average 〈cA〉 = 25 nM. The histograms obtained in the stochastic simulations (blue bars, left column) are in qualitative agreement with the probability densities from the analytical calculations (blue line, left column). When increasing the diffusion coefficient, the system explores different dynamics as revealed by the trajectories shown in the center column. The grey-shaded background shown in the trajectories of cA indicates the presence of a mRNA molecule in the cell. The density plots (right column) reveals that the diffusion does not contribute to an increase of the intrinsic noise since the spreading of the distributions in a direction perpendicular to the diagonal does not grow.
Mentions: If > 0 we expect a more fruitful phenomenology since the transition lines between behaviors in the parameter space (, ) shift as a function of the diffusion (see Figure 2A). According to the analytical calculations we can anticipate that, for a given parameter set and as increases, the system explores different dynamical regimes. By taking as a reference the case γ2, that is (, ) = (15, 5), Figure 4 shows the effect of the diffusion on the distribution (left column) and dynamics (center column) of cA in a given cell. The system initially displays a single-peak distribution for = 1. By increasing the diffusion coefficient we observe transitions to the other phases (monotonically decreasing and double-peak distributions). The corresponding dynamics of cA (right panels) show how the diffusion, acting as an additional effective degradation on A, first increases the sharpness of the bursts of production. For = 10, the diffusion is large enough to remove signaling molecules between consecutive burst events, thus leading to a monotonically decreasing distribution. Increasing the diffusion rate to = 100 leads to the situation where both and becomes smaller than 1 + and a bistable dynamics develops. Under these circumstances the concentration of autoinducer alternates between two states that correspond to a low concentration, when there is no mRNA production, and a high concentration, following the mRNA synthesis. As the diffusion further increases, e.g. = 2 · 103, the autoinducer molecules diffusing from the external medium into the cell set a constitutive level of this species. The latter explains the presence of A molecules in the cell even if no mRNA is produced. Finally, at very large values of , e.g. = 5 · 104, the low constitutive concentration of the autoinducer increases due to the influx of molecules when no mRNA is present whereas the concentration of A that is internally produced decreases due to the efflux of molecules. In this case, the whole N-cells system can be considered as a single volume with no diffusive barriers between cells. Thus, the burst events average out and, as a consequence, a single effective peak appears.

Bottom Line: The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate.Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate.QS systems seems to avoid values of the diffusion that maximize the total noise.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computer Simulation and Modelling (Co.S.Mo.) Lab, Parc Científic de Barcelona, C/Baldiri Reixac 10-12, Barcelona 08028, Spain.

ABSTRACT

Background: Cells must face the ubiquitous presence of noise at the level of signaling molecules. The latter constitutes a major challenge for the regulation of cellular functions including communication processes. In the context of prokaryotic communication, the so-called quorum sensing (QS) mechanism relies on small diffusive molecules that are produced and detected by cells. This poses the intriguing question of how bacteria cope with the fluctuations for setting up a reliable information exchange.

Results: We present a stochastic model of gene expression that accounts for the main biochemical processes that describe the QS mechanism close to its activation threshold. Within that framework we study, both numerically and analytically, the role that diffusion plays in the regulation of the dynamics and the fluctuations of signaling molecules. In addition, we unveil the contribution of different sources of noise, intrinsic and transcriptional, in the QS mechanism.

Conclusions: The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate. Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate. QS systems seems to avoid values of the diffusion that maximize the total noise. These results point towards the direction that bacteria have adapted their communication mechanisms in order to improve the signal-to-noise ratio.

Show MeSH
Related in: MedlinePlus