Distinctive topologies of partner-switching signaling networks correlate with their physiological roles

Abstract

Regulatory networks controlling bacterial gene expression often evolve from common origins and share homologous proteins and similar network motifs. However, when functioning in different physiological contexts, these motifs may be re-arranged with different topologies that significantly affect network performance. Here we analyze two related signaling networks in the bacterium Bacillus subtilis in order to assess the consequences of their different topologies, with the aim of formulating design principles applicable to other systems. These two networks control the activities of the general stress response factor sigma(B) and the first sporulation-specific factor sigma(F). Both networks have at their core a "partner-switching" mechanism, in which an anti-sigma factor forms alternate complexes either with the sigma factor, holding it inactive, or with an anti-anti-sigma factor, thereby freeing sigma. However, clear differences in network structure are apparent: the anti-sigma factor for sigma(F) forms a long-lived, "dead-end" complex with its anti-anti-sigma factor and ADP, whereas the genes encoding sigma(B) and its network partners lie in a sigma(B)-controlled operon, resulting in positive and negative feedback loops. We constructed mathematical models of both networks and examined which features were critical for the performance of each design. The sigma(F) model predicts that the self-enhancing formation of the dead-end complex transforms the network into a largely irreversible hysteretic switch; the simulations reported here also demonstrate that hysteresis and slow turn off kinetics are the only two system properties associated with this complex formation. By contrast, the sigma(B) model predicts that the positive and negative feedback loops produce graded, reversible behavior with high regulatory capacity and fast response time. Our models demonstrate how alterations in network design result in different system properties that correlate with regulatory demands. These design principles agree with the known or suspected roles of similar networks in diverse bacteria.

Fig. 1

Conceptual (a, b) and kinetic (c, d) models of the partner-switching networks regulating σ^F and σ^B. For simplicity, only one subunit of the anti-sigma factor dimer is shown, and binding of sigma to RNA polymerase core is omitted as it does not affect the partner-switching equilibrium (see Modeling Procedures). (a) Level of free σ^F is determined by the level of unphosphorylated SpoIIAA anti-anti-sigma (AA), where P indicates serine phosphate (see text). Activity of the SpoIIE phosphatase in the forespore increases upon formation of the asymmetric sporulation septum, turning the system ON. (b) Level of free σ^B is determined by the level of unphosphorylated RsbV anti-anti-sigma (V). Activity of either the RsbU environmental phosphatase or the RsbP energy phosphatase increases when a stress is perceived, turning the system ON. (c) Formation of a long-lived, dead-end complex in the σ^F network. The SpoIIAB anti-sigma factor (AB) with ATP in its catalytic site can phosphorylate and release the AA anti-anti-sigma factor, leaving AB associated with ADP in a non-catalytic complex. The binding of another AA molecule locks AB in this state. (d) Feedback loops in the σ^B network. Genes encoding σ^B, its anti-sigma RsbW (W) and anti-anti-sigma V lie in the σ^B-controlled sigB operon. The resulting feedback loops are shown by dashed lines. An additional feedback loop through the RsbX phosphatase, which acts indirectly via the environmental-stress branch of the network, is shown by the dotted line. Each of the nodes containing W and its complexes are assumed to be in equilibrium, with a mixed population of ATP, ADP and nucleotide-free forms, so no explicit nucleotide exchange is shown.

Fig. 2

Comparison of σ^F networks with (dashed or solid lines) and without (dotted line) dead-end complex formation using parameter values that allow hysteresis ([AA]=1.5[AB]=9μM; [σ^F]=2μM) (a) Steady-state concentration of free sigma factor as a function of dephosphorylation rate. Under these conditions, when [AA] is in 50% excess to [AB], the network with the dead-end complex possesses two stable steady states, depending on system history. For comparison, only one steady state is possible for the network without the complex (see text). (b) Dynamic response of free sigma factor to a step increase in rate of dephosphorylation. (c) Dynamic response of free sigma factor to a step decrease in the rate of dephosphorylation. Note that the time axes in kinetic plots (b and c) are represented with a logarithmic scale.

Fig. 3

Comparison of σ^F networks with (solid line) and without (dotted line) dead-end complex formation using values that preclude hysteresis ([AA]=[AB]=6μM; [σ^F]=2μM). (a) Steady-state concentration of free sigma factor as a function of dephosphorylation rate. Under these conditions when [AA] is equal to [AB], the network with the dead-end complex possesses only one stable steady-state; the network without the complex performs similarly. (b) Dynamic response of free sigma factor to a step decrease in the rate of dephosphorylation (compare to Fig 2c).

Fig. 4

Comparison of σ^B networks with and without feedback resulting from σ^B-dependent transcription of the operon encoding σ^B and its network partners. These simulations were done under energy stress conditions to focus on the contribution of the V-W-σ^B feedback loop. (Fig. 5 separately addresses the contribution of the RsbX feedback loop in the environmental signaling branch.) The solid line corresponds to the reference (wild type) system with feedback present. The dashed line corresponds to an alternative system without feedback in which the rate of protein synthesis is set to match the level of free sigma at high dephosphorylation rates. The dotted line corresponds to an alternative system without feedback in which the rate of protein synthesis is set to match the level of free sigma at low dephosphorylation rates. (a) Steady-state concentration of free sigma as a function of the dephosphorylation rate. The insert shows the same curve plotted with log-log scales. (b) Dynamic response of free sigma following a step increase in the rate of dephosphorylation.

Fig. 5

Comparison of σ^B networks with and without negative feedback involving RsbX. These simulations were done under environmental stress conditions. The dynamic behavior of the concentration of free sigma factor in the reference (wild type) system with negative feedback (solid line); in the alternative system without feedback and the RsbX concentration kept constant at the pre-stress level of the reference system (dashed line); and in the alternative system without feedback and the RsbX concentration kept constant at the maximum-stress level of the reference system (dotted line).

Fig. 6

Removal of either positive autocatalytic loop affects steady state performance of the σ^B network. (a) Elimination of σ^B control of V expression leads to reduced regulatory capacity. The reference (wild-type) steady state response is shown by a solid line. Dashed and dotted lines correspond to maximum- and pre-stress levels of V expression, respectively. (b) Elimination of σ^B control of σ^B expression also leads to reduced regulatory capacity. Line designations are as in panel a, but here dashed and dotted lines correspond to maximum- and pre-stress levels of σ^B expression.

Fig. 7

Elimination of σ^B control of W expression results in ALL or NONE bistability in the σ^B network. Stable steady state solutions are shown by dashed (OFF) and dash-dotted (ON) lines whereas an unstable steady state between the two stable states is shown by the dotted line. The OFF state corresponds to a low level of σ^B, as would result from expression of its structural gene when the σ^B–dependent promoter of the sigB operon is not activated. The ON state corresponds to a high level of σ^B, as would result when the σ^B–dependent promoter of the sigB operon is fully activated by stress. (a) For low W expression (1.2×10⁻⁴ μMs⁻¹) the network displays two stable steady states only at low dephosphorylation rates; at high rates only the ON state exists. An irreversible transition from OFF to ON can be induced by an increasing dephosphorylation rate, as indicated by the up arrow. (b) For intermediate W expression (5×10⁻⁴μMs⁻¹) the network displays two stable steady states over the entire range of dephosphorylation rates. (c) For high W expression (3×10⁻³μMs⁻¹) the network displays two stable steady states only at high dephosphorylation rates; at low rates only the OFF state exists. An irreversible transition from ON to OFF can be induced by a decreasing dephosphorylation rate, as indicated by the down arrow. See text for details.