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A general model for toxin-antitoxin module dynamics can explain persister cell formation in E. coli.

Gelens L, Hill L, Vandervelde A, Danckaert J, Loris R - PLoS Comput. Biol. (2013)

Bottom Line: Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced.The amplitude of these spikes determines the duration of the persister state.Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

View Article: PubMed Central - PubMed

Affiliation: Applied Physics Research Group APHY, Vrije Universiteit Brussel, Brussels, Belgium. lendert.gelens@vub.ac.be

ABSTRACT
Toxin-Antitoxin modules are small operons involved in stress response and persister cell formation that encode a "toxin" and its corresponding neutralizing "antitoxin". Regulation of these modules involves a complex mechanism known as conditional cooperativity, which is supposed to prevent unwanted toxin activation. Here we develop mathematical models for their regulation, based on published molecular and structural data, and parameterized using experimental data for F-plasmid ccdAB, bacteriophage P1 phd/doc and E. coli relBE. We show that the level of free toxin in the cell is mainly controlled through toxin sequestration in toxin-antitoxin complexes of various stoichiometry rather than by gene regulation. If the toxin translation rate exceeds twice the antitoxin translation rate, toxins accumulate in all cells. Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced. Combining conditional cooperativity and bridging of antitoxins by toxins when bound to their operator sites allows creation of persister cells through rare, extreme stochastic spikes in the free toxin level. The amplitude of these spikes determines the duration of the persister state. Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

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If the toxin translation rate exceeds twice the antitoxin translation rate, free toxin accumulates.Parameter scans for  versus  show the level of the free antitoxin A and the free toxin in the case of independent binding sites on the operator. The response of 200 cells has been averaged after simulating for 500 minutes. In the region [K], indicated in gray, the free toxin level grows continuously to large numbers, corresponding to a non-culturable cell population. The lower panels show the effect of a change in , keeping  at its normal value (see table 1), on the ∶ ratio and total protein number (+). No toxic feedback effects are included: .
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pcbi-1003190-g005: If the toxin translation rate exceeds twice the antitoxin translation rate, free toxin accumulates.Parameter scans for versus show the level of the free antitoxin A and the free toxin in the case of independent binding sites on the operator. The response of 200 cells has been averaged after simulating for 500 minutes. In the region [K], indicated in gray, the free toxin level grows continuously to large numbers, corresponding to a non-culturable cell population. The lower panels show the effect of a change in , keeping at its normal value (see table 1), on the ∶ ratio and total protein number (+). No toxic feedback effects are included: .

Mentions: The translation rates for the antitoxin and the toxin, and , are hard to determine experimentally but are important parameters for the behavior of the toxin-antitoxin module. The translation rates in this article are based on the average translation rate in E. coli, on the lengths of the proteins, on the fact if monomers or dimers are formed in solution (immediate dimerization is assumed and therefore the translation rate is halved in the case of dimers) and on the translational coupling, ensuring that toxins are produced at a lower rate than antitoxins. In order to show the influence of variations in both translation rates, Figure 5 shows the free antitoxin and the free toxin level in the parameter plane (, ), using the model for independent binding sites on the operator. Two regions are clearly visible in this parameter space: One in which the free antitoxin level is high and the free toxin level is controlled (on average less than one free toxin per cell is present) and one in which the free toxin level is very high with negligible amounts of free antitoxin present, corresponding to a non-culturable cell population. The latter region is indicated as [K] in Figure 5. There is a clear threshold between these two cell populations, which is crossed when the toxin translation rate exceeds twice the antitoxin translation rate. In all currently investigated TA modules, the synthesis rate for the antitoxin was higher than the one for the toxin [17]. Therefore, these modules can be safely maintained in a cell population.


A general model for toxin-antitoxin module dynamics can explain persister cell formation in E. coli.

Gelens L, Hill L, Vandervelde A, Danckaert J, Loris R - PLoS Comput. Biol. (2013)

If the toxin translation rate exceeds twice the antitoxin translation rate, free toxin accumulates.Parameter scans for  versus  show the level of the free antitoxin A and the free toxin in the case of independent binding sites on the operator. The response of 200 cells has been averaged after simulating for 500 minutes. In the region [K], indicated in gray, the free toxin level grows continuously to large numbers, corresponding to a non-culturable cell population. The lower panels show the effect of a change in , keeping  at its normal value (see table 1), on the ∶ ratio and total protein number (+). No toxic feedback effects are included: .
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3757116&req=5

pcbi-1003190-g005: If the toxin translation rate exceeds twice the antitoxin translation rate, free toxin accumulates.Parameter scans for versus show the level of the free antitoxin A and the free toxin in the case of independent binding sites on the operator. The response of 200 cells has been averaged after simulating for 500 minutes. In the region [K], indicated in gray, the free toxin level grows continuously to large numbers, corresponding to a non-culturable cell population. The lower panels show the effect of a change in , keeping at its normal value (see table 1), on the ∶ ratio and total protein number (+). No toxic feedback effects are included: .
Mentions: The translation rates for the antitoxin and the toxin, and , are hard to determine experimentally but are important parameters for the behavior of the toxin-antitoxin module. The translation rates in this article are based on the average translation rate in E. coli, on the lengths of the proteins, on the fact if monomers or dimers are formed in solution (immediate dimerization is assumed and therefore the translation rate is halved in the case of dimers) and on the translational coupling, ensuring that toxins are produced at a lower rate than antitoxins. In order to show the influence of variations in both translation rates, Figure 5 shows the free antitoxin and the free toxin level in the parameter plane (, ), using the model for independent binding sites on the operator. Two regions are clearly visible in this parameter space: One in which the free antitoxin level is high and the free toxin level is controlled (on average less than one free toxin per cell is present) and one in which the free toxin level is very high with negligible amounts of free antitoxin present, corresponding to a non-culturable cell population. The latter region is indicated as [K] in Figure 5. There is a clear threshold between these two cell populations, which is crossed when the toxin translation rate exceeds twice the antitoxin translation rate. In all currently investigated TA modules, the synthesis rate for the antitoxin was higher than the one for the toxin [17]. Therefore, these modules can be safely maintained in a cell population.

Bottom Line: Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced.The amplitude of these spikes determines the duration of the persister state.Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

View Article: PubMed Central - PubMed

Affiliation: Applied Physics Research Group APHY, Vrije Universiteit Brussel, Brussels, Belgium. lendert.gelens@vub.ac.be

ABSTRACT
Toxin-Antitoxin modules are small operons involved in stress response and persister cell formation that encode a "toxin" and its corresponding neutralizing "antitoxin". Regulation of these modules involves a complex mechanism known as conditional cooperativity, which is supposed to prevent unwanted toxin activation. Here we develop mathematical models for their regulation, based on published molecular and structural data, and parameterized using experimental data for F-plasmid ccdAB, bacteriophage P1 phd/doc and E. coli relBE. We show that the level of free toxin in the cell is mainly controlled through toxin sequestration in toxin-antitoxin complexes of various stoichiometry rather than by gene regulation. If the toxin translation rate exceeds twice the antitoxin translation rate, toxins accumulate in all cells. Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced. Combining conditional cooperativity and bridging of antitoxins by toxins when bound to their operator sites allows creation of persister cells through rare, extreme stochastic spikes in the free toxin level. The amplitude of these spikes determines the duration of the persister state. Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

Show MeSH
Related in: MedlinePlus