Conditional cooperativity in toxin-antitoxin regulation prevents random toxin activation and promotes fast translational recovery

Abstract

Many toxin-antitoxin (TA) loci are known to strongly repress their own transcription. This auto-inhibition is often called 'conditional cooperativity' as it relies on cooperative binding of TA complexes to operator DNA that occurs only when toxins are in a proper stoichiometric relationship with antitoxins. There has recently been an explosion of interest in TA systems due to their role in bacterial persistence, however the role of conditional cooperativity is still unclear. We reveal the biological function of conditional cooperativity by constructing a mathematical model of the well studied TA system, relBE of Escherichia coli. We show that the model with the in vivo and in vitro established parameters reproduces experimentally observed response to nutritional stress. We further demonstrate that conditional cooperativity stabilizes the level of antitoxin in rapidly growing cells such that random induction of relBE is minimized. At the same time it enables quick removal of free toxin when the starvation is terminated.

Figure 1.

(A) Model description: antitoxin RelB (B) and toxin RelE (E) are encoded on the same mRNA (m), with only 1/100 of the ribosome that translate relB continues to translate relE. RelE cleaves mRNAs when it is free. RelB forms dimer RelB₂ when it is free, and RelB₂ and RelE can form two kinds of complexes: RelB₂RelE and RelB₂RelE₂. For simplicity, we use RelB₂ as a unit for RelB and do not consider RelB monomers explicitly. Translation rates for RelB₂ is trans_B = 15/min, and for RelE is trans_E = 0.3/min. In our simulation there will be 44 nM RelE and 200 nM of RelB₂ in total in the non-starved condition. A list of parameters and references used are given in the ‘Materials and Methods’ section. (B) Visualization of conditional cooperativity due to the formation of RelB₂RelE₂, that does not repress the promoter.

Figure 2.

Response to amino acid starvation and later recovery. The system is starved for amino acids from 200 min to 500 min. (A) Probability distribution P([E_f], t) of a cell having a certain concentration [E_f] nM of free RelE at a given moment t. (B) Time courses averaged over 1000 cells, for free RelE, free RelB and relBE mRNA, illustrating how the system switches between a state of high antitoxin to a state of high free toxin. (C) The dynamics at entrance to the starvation at the single cell level. Three examples are shown, and the total amount of free RelE is plotted as function of time, from time 180 to time 300.

Figure 3.

Role of conditional cooperativity. (A) The time evolution of free RelE level for the system with (red) and without (blue) conditional cooperativity. The system is starved for amino acid from 200 to 500 min. (B) Probability distribution of free RelE in the non-starved state without conditional cooperativity (blue) and with conditional cooperativity (red). Free RelE takes higher value without conditional cooperativity.

Figure 4.

Summary of the model behavior against parameter changes. For each parameters (horizontal axis), fold change of the values from our reference values are tried one by one. The color gradients indicate how the model deviates from the reference behavior: yellow indicates too many free toxins in the healthy states, green indicates too slow rise of free RelE at amino acid starvation and red indicates too slow drop of toxins after the removal of amino acid starvation. In the first entry, K_dB2E = K_dB2E2, the ratio of the dissociation constants K_dB₂E and K_dB2E2 are kept to be one, but the value itself is changed. In the second entry, the ratio K_dB₂E/K_dB2E2 is changed, while keeping smaller dissociation constant to be the reference value 0.3 nM. For the entry trans, the translation rates for RelB and RelE are changed by the given folds, while trans_B/trans_E and trans_B/trans_B(AS) [trans_B(AS) is the translation rate of RelB during the amino acid starvation] are kept to the reference values. For the entry trans_B/trans_E and trans_B/trans_B(AS) the given ratio is changed with keeping the value of the translation for RelB trans_B to be 15/min. For the entry τ_B (τ_C), the lifetime of the RelB₂ (RelB's in the complexes) are changed with keeping the 1/8-fold reduction of the lifetime during the amino acid starvation. For the entry k_c (the 12th entry), the value of the cleavage rate is changed, while for the entry k_c(k_c × F = 16) (the last entry), the value of k_c and the fold-change of the RelB degradation rate F are changed, so that k_c × F is kept to the reference value 16.