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Unlimited multistability and Boolean logic in microbial signalling.

Kothamachu VB, Feliu E, Cardelli L, Soyer OS - J R Soc Interface (2015)

Bottom Line: We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals.Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them.These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Program, College of Engineering, Computing and Mathematics, University of Exeter, Exeter, UK.

ABSTRACT
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

No MeSH data available.


(a) Cartoon representation of the yeast two-component system involved in osmosensing. This system contains a hybrid HK (Sln1), that transfers a phosphate group to an Hpt (Ypd), which subsequently transfers a phosphate group to two RRs (Ssk1 and Skn7). (b,c) Bifurcation plots for the system shown in (a), for a specific set of parameters combining the experimentally measured rates in [30] with biologically feasible parameter values (see the electronic supplementary material, table S2 for parameters and electronic supplementary material, SI-2 for the computer-executable full model of this system). The bifurcation plot shows the fraction of phosphorylated Ssk1 at steady state for a given input level. The change in input level shown on the x-axis is simulated by varying the auto-phosphorylation rate constants of Sln1, k1 and k3, while keeping the ratio k3/k1 fixed. (b) Shows the effect of increasing the total concentration of Ypd (from 1, to 2, to 3), while (c) shows the effect of increasing the total concentration of Skn7 (from 0.5, to 1.5, to 2.5) on the bifurcation plot. In each plot, the solid and dashed lines correspond to stable versus unstable steady states.
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RSIF20150234F5: (a) Cartoon representation of the yeast two-component system involved in osmosensing. This system contains a hybrid HK (Sln1), that transfers a phosphate group to an Hpt (Ypd), which subsequently transfers a phosphate group to two RRs (Ssk1 and Skn7). (b,c) Bifurcation plots for the system shown in (a), for a specific set of parameters combining the experimentally measured rates in [30] with biologically feasible parameter values (see the electronic supplementary material, table S2 for parameters and electronic supplementary material, SI-2 for the computer-executable full model of this system). The bifurcation plot shows the fraction of phosphorylated Ssk1 at steady state for a given input level. The change in input level shown on the x-axis is simulated by varying the auto-phosphorylation rate constants of Sln1, k1 and k3, while keeping the ratio k3/k1 fixed. (b) Shows the effect of increasing the total concentration of Ypd (from 1, to 2, to 3), while (c) shows the effect of increasing the total concentration of Skn7 (from 0.5, to 1.5, to 2.5) on the bifurcation plot. In each plot, the solid and dashed lines correspond to stable versus unstable steady states.

Mentions: Despite the high prevalence of hybrid and unorthodox HKs, detailed experimental studies of these systems are rare. The most well-studied cases are those involved in the quorum sensing system of Vibrio harveyi [36] and the osmosensing system of yeast [30]. The former system implements three hybrid HKs that share the same Hpt, and, as such, closely resembles one of the systems considered in this work. Experiments with a modified version of this quorum sensing system involving just two HKs have shown that the ability to perform a summation as shown in figure 4 is possible in a natural system [36]. In the yeast osmosensing system, a hybrid HK transfers a phosphate group to two downstream RRs as schematically shown in figure 5a. While we do not have experimental data on response dynamics of this system, in vitro phosphotransfer experiments provide kinetic rate measurements for some of the phosphotransfer reactions [30]. We have developed a model of this system, which is provided as an executable model in the electronic supplementary material, SI-2. In this model, we considered the experimentally measured kinetic rates and set the remaining parameters in a biologically feasible regime (see the electronic supplementary material, table S2). The analysis of this model shows that this system exhibits bistability. Furthermore, we observe a significant level of hysteresis, that is, the threshold point for switching between the two stable steady states depends highly on whether the signal is being increased or decreased (figure 5b).FigureĀ 5.


Unlimited multistability and Boolean logic in microbial signalling.

Kothamachu VB, Feliu E, Cardelli L, Soyer OS - J R Soc Interface (2015)

(a) Cartoon representation of the yeast two-component system involved in osmosensing. This system contains a hybrid HK (Sln1), that transfers a phosphate group to an Hpt (Ypd), which subsequently transfers a phosphate group to two RRs (Ssk1 and Skn7). (b,c) Bifurcation plots for the system shown in (a), for a specific set of parameters combining the experimentally measured rates in [30] with biologically feasible parameter values (see the electronic supplementary material, table S2 for parameters and electronic supplementary material, SI-2 for the computer-executable full model of this system). The bifurcation plot shows the fraction of phosphorylated Ssk1 at steady state for a given input level. The change in input level shown on the x-axis is simulated by varying the auto-phosphorylation rate constants of Sln1, k1 and k3, while keeping the ratio k3/k1 fixed. (b) Shows the effect of increasing the total concentration of Ypd (from 1, to 2, to 3), while (c) shows the effect of increasing the total concentration of Skn7 (from 0.5, to 1.5, to 2.5) on the bifurcation plot. In each plot, the solid and dashed lines correspond to stable versus unstable steady states.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4528588&req=5

RSIF20150234F5: (a) Cartoon representation of the yeast two-component system involved in osmosensing. This system contains a hybrid HK (Sln1), that transfers a phosphate group to an Hpt (Ypd), which subsequently transfers a phosphate group to two RRs (Ssk1 and Skn7). (b,c) Bifurcation plots for the system shown in (a), for a specific set of parameters combining the experimentally measured rates in [30] with biologically feasible parameter values (see the electronic supplementary material, table S2 for parameters and electronic supplementary material, SI-2 for the computer-executable full model of this system). The bifurcation plot shows the fraction of phosphorylated Ssk1 at steady state for a given input level. The change in input level shown on the x-axis is simulated by varying the auto-phosphorylation rate constants of Sln1, k1 and k3, while keeping the ratio k3/k1 fixed. (b) Shows the effect of increasing the total concentration of Ypd (from 1, to 2, to 3), while (c) shows the effect of increasing the total concentration of Skn7 (from 0.5, to 1.5, to 2.5) on the bifurcation plot. In each plot, the solid and dashed lines correspond to stable versus unstable steady states.
Mentions: Despite the high prevalence of hybrid and unorthodox HKs, detailed experimental studies of these systems are rare. The most well-studied cases are those involved in the quorum sensing system of Vibrio harveyi [36] and the osmosensing system of yeast [30]. The former system implements three hybrid HKs that share the same Hpt, and, as such, closely resembles one of the systems considered in this work. Experiments with a modified version of this quorum sensing system involving just two HKs have shown that the ability to perform a summation as shown in figure 4 is possible in a natural system [36]. In the yeast osmosensing system, a hybrid HK transfers a phosphate group to two downstream RRs as schematically shown in figure 5a. While we do not have experimental data on response dynamics of this system, in vitro phosphotransfer experiments provide kinetic rate measurements for some of the phosphotransfer reactions [30]. We have developed a model of this system, which is provided as an executable model in the electronic supplementary material, SI-2. In this model, we considered the experimentally measured kinetic rates and set the remaining parameters in a biologically feasible regime (see the electronic supplementary material, table S2). The analysis of this model shows that this system exhibits bistability. Furthermore, we observe a significant level of hysteresis, that is, the threshold point for switching between the two stable steady states depends highly on whether the signal is being increased or decreased (figure 5b).FigureĀ 5.

Bottom Line: We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals.Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them.These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Program, College of Engineering, Computing and Mathematics, University of Exeter, Exeter, UK.

ABSTRACT
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

No MeSH data available.