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Phosphate sink containing two-component signaling systems as tunable threshold devices.

Amin M, Kothamachu VB, Feliu E, Scharf BE, Porter SL, Soyer OS - PLoS Comput. Biol. (2014)

Bottom Line: Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling.We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve.We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7).

View Article: PubMed Central - PubMed

Affiliation: Biosciences, College of Life and Environmental Sciences, University of Exeter, Exeter, United Kingdom; Systems Biology Program, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.

ABSTRACT
Synthetic biology aims to design de novo biological systems and reengineer existing ones. These efforts have mostly focused on transcriptional circuits, with reengineering of signaling circuits hampered by limited understanding of their systems dynamics and experimental challenges. Bacterial two-component signaling systems offer a rich diversity of sensory systems that are built around a core phosphotransfer reaction between histidine kinases and their output response regulator proteins, and thus are a good target for reengineering through synthetic biology. Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling. In this motif, a single histidine kinase (HK) phosphotransfers reversibly to two separate output response regulator (RR) proteins. We show that, under the experimentally observed parameters from bacteria and yeast, this motif not only allows rapid signal termination, whereby one of the RRs acts as a phosphate sink towards the other RR (i.e. the output RR), but also implements a sigmoidal signal-response relationship. We identify two mathematical conditions on system parameters that are necessary for sigmoidal signal-response relationships and define key parameters that control threshold levels and sensitivity of the signal-response curve. We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve. We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7). These findings show that the one HK-two RR motif allows bacteria and yeast to implement tunable switch-like signal processing and provides an ideal basis for developing threshold devices for synthetic biology applications.

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The effect of parameter changes on the “sigmoidality” of the signal-response curve.The level of sigmoidality, Hill coefficient, is shown as a heat map on each panel. (A) Effect of varying the forward and reverse phosphotransfer rates for the sink RR (CheY1; x-axis; kS and y-axis; krS). (B) Effect of varying the total concentration of the output RR (CheY2; y-axis) and sink RR (CheY1; x-axis). (C) Effect of changing the phosphotransfer rate (ks) from CheA to the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated by the coloured spots on the heatmap shown in panel (A). (D) Effect of changing the concentration of the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated the coloured spots on the heatmap shown in panel (B).
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pcbi-1003890-g002: The effect of parameter changes on the “sigmoidality” of the signal-response curve.The level of sigmoidality, Hill coefficient, is shown as a heat map on each panel. (A) Effect of varying the forward and reverse phosphotransfer rates for the sink RR (CheY1; x-axis; kS and y-axis; krS). (B) Effect of varying the total concentration of the output RR (CheY2; y-axis) and sink RR (CheY1; x-axis). (C) Effect of changing the phosphotransfer rate (ks) from CheA to the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated by the coloured spots on the heatmap shown in panel (A). (D) Effect of changing the concentration of the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated the coloured spots on the heatmap shown in panel (B).

Mentions: To better understand whether the sensitivity and threshold levels in the sigmoidal signal-response curve can be controlled, and by which parameters, we performed a sensitivity analysis around experimentally measured kinetic rates from S. meliloti and yeast (Figures 2, S4, S5 and S2). This revealed several kinetic features for ensuring a sigmoidal signal-response relationship (see below for exact necessary conditions). For example, we found that a key kinetic feature is for phosphotransfer to the sink-RR (parameter kS) to be faster than reverse phosphotransfer from the sink-RR back to the HK (parameter krS). Under this condition, the steady state phosphorylation level of output-RR remains low until the sink-RR is almost fully phosphorylated (Figure S3), resulting in a high level of sigmoidality in the signal-response curve (Figures 2A and S2A). We also found that both the sharpness of the sigmoidal signal-response relationship and the threshold signal level can be controlled through changes in parameters and the ratio of the concentration of HK to the two RRs (Figures S4 and S5). In particular, the phosphotransfer rate constant between the HK and sink-RR (Figures 2A and S2A), and the autodephosphorylation rate constant of the sink-RR (Figures S4 and S2) can affect the sharpness of the signal-response curve, while the threshold signal level is determined by the amount of sink present (Figures 2B and S2B). The effect of the autodephosphorylation rate of the sink-RR can be intuitively understood as increasing this rate directly increases the level of signal required to “fill” the sink-RR. The effect of the forward phosphotransfer rate (between the HK and sink-RR) can be understood when considering the dynamics of the system. When the phosphotransfer from the HK to the two RRs occurs at comparable rates, the increase in the phosphorylation of both RRs occurs in linear fashion. In other words, any increase in the signal levels trickles down the system to affect both RRs. However, what is required from an ultrasensitive signal-response relationship is that one of the RRs remains largely unaffected by increasing signals until a threshold signal is reached. To create such dynamics, having a higher phosphotransfer rate to the other RR is essential, such that any small increases in signal predominantly result in alterations of only this RR.


Phosphate sink containing two-component signaling systems as tunable threshold devices.

Amin M, Kothamachu VB, Feliu E, Scharf BE, Porter SL, Soyer OS - PLoS Comput. Biol. (2014)

The effect of parameter changes on the “sigmoidality” of the signal-response curve.The level of sigmoidality, Hill coefficient, is shown as a heat map on each panel. (A) Effect of varying the forward and reverse phosphotransfer rates for the sink RR (CheY1; x-axis; kS and y-axis; krS). (B) Effect of varying the total concentration of the output RR (CheY2; y-axis) and sink RR (CheY1; x-axis). (C) Effect of changing the phosphotransfer rate (ks) from CheA to the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated by the coloured spots on the heatmap shown in panel (A). (D) Effect of changing the concentration of the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated the coloured spots on the heatmap shown in panel (B).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214558&req=5

pcbi-1003890-g002: The effect of parameter changes on the “sigmoidality” of the signal-response curve.The level of sigmoidality, Hill coefficient, is shown as a heat map on each panel. (A) Effect of varying the forward and reverse phosphotransfer rates for the sink RR (CheY1; x-axis; kS and y-axis; krS). (B) Effect of varying the total concentration of the output RR (CheY2; y-axis) and sink RR (CheY1; x-axis). (C) Effect of changing the phosphotransfer rate (ks) from CheA to the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated by the coloured spots on the heatmap shown in panel (A). (D) Effect of changing the concentration of the sink protein (CheY1) on the signal response curve. Each curve is coloured to match the parameter values indicated the coloured spots on the heatmap shown in panel (B).
Mentions: To better understand whether the sensitivity and threshold levels in the sigmoidal signal-response curve can be controlled, and by which parameters, we performed a sensitivity analysis around experimentally measured kinetic rates from S. meliloti and yeast (Figures 2, S4, S5 and S2). This revealed several kinetic features for ensuring a sigmoidal signal-response relationship (see below for exact necessary conditions). For example, we found that a key kinetic feature is for phosphotransfer to the sink-RR (parameter kS) to be faster than reverse phosphotransfer from the sink-RR back to the HK (parameter krS). Under this condition, the steady state phosphorylation level of output-RR remains low until the sink-RR is almost fully phosphorylated (Figure S3), resulting in a high level of sigmoidality in the signal-response curve (Figures 2A and S2A). We also found that both the sharpness of the sigmoidal signal-response relationship and the threshold signal level can be controlled through changes in parameters and the ratio of the concentration of HK to the two RRs (Figures S4 and S5). In particular, the phosphotransfer rate constant between the HK and sink-RR (Figures 2A and S2A), and the autodephosphorylation rate constant of the sink-RR (Figures S4 and S2) can affect the sharpness of the signal-response curve, while the threshold signal level is determined by the amount of sink present (Figures 2B and S2B). The effect of the autodephosphorylation rate of the sink-RR can be intuitively understood as increasing this rate directly increases the level of signal required to “fill” the sink-RR. The effect of the forward phosphotransfer rate (between the HK and sink-RR) can be understood when considering the dynamics of the system. When the phosphotransfer from the HK to the two RRs occurs at comparable rates, the increase in the phosphorylation of both RRs occurs in linear fashion. In other words, any increase in the signal levels trickles down the system to affect both RRs. However, what is required from an ultrasensitive signal-response relationship is that one of the RRs remains largely unaffected by increasing signals until a threshold signal is reached. To create such dynamics, having a higher phosphotransfer rate to the other RR is essential, such that any small increases in signal predominantly result in alterations of only this RR.

Bottom Line: Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling.We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve.We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7).

View Article: PubMed Central - PubMed

Affiliation: Biosciences, College of Life and Environmental Sciences, University of Exeter, Exeter, United Kingdom; Systems Biology Program, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.

ABSTRACT
Synthetic biology aims to design de novo biological systems and reengineer existing ones. These efforts have mostly focused on transcriptional circuits, with reengineering of signaling circuits hampered by limited understanding of their systems dynamics and experimental challenges. Bacterial two-component signaling systems offer a rich diversity of sensory systems that are built around a core phosphotransfer reaction between histidine kinases and their output response regulator proteins, and thus are a good target for reengineering through synthetic biology. Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling. In this motif, a single histidine kinase (HK) phosphotransfers reversibly to two separate output response regulator (RR) proteins. We show that, under the experimentally observed parameters from bacteria and yeast, this motif not only allows rapid signal termination, whereby one of the RRs acts as a phosphate sink towards the other RR (i.e. the output RR), but also implements a sigmoidal signal-response relationship. We identify two mathematical conditions on system parameters that are necessary for sigmoidal signal-response relationships and define key parameters that control threshold levels and sensitivity of the signal-response curve. We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve. We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7). These findings show that the one HK-two RR motif allows bacteria and yeast to implement tunable switch-like signal processing and provides an ideal basis for developing threshold devices for synthetic biology applications.

Show MeSH
Related in: MedlinePlus