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Operating regimes of signaling cycles: statics, dynamics, and noise filtering.

Gomez-Uribe C, Verghese GC, Mirny LA - PLoS Comput. Biol. (2007)

Bottom Line: These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions.Numerical simulations show that our analytical results hold well even for noise of large amplitude.We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

View Article: PubMed Central - PubMed

Affiliation: Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.

ABSTRACT
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act--in all four regimes--as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

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Steady-State Behavior of the Four Cycle Regimes(A) When both enzymes are unsaturated, the steady-state response is hyperbolic. The parameters used for this cycle are 							, a1 = 1, K1 = 10,000, a2 = 1,							, K2 = 10,000, k1 = 1, and k2 = 1, where all reaction rates are in units of 1/s, concentrations and Michaelis constants are in nanomoles, and second-order reaction rates (a1 and a2) are in 1/nM/s.						(B) When the kinase is saturated and the phosphatase unsaturated, a linear response results. The parameters here are 							, a1 = 100, K1 = 10, a2 = 1, 							, K2 = 10,000, k1 = 500, and k2 = 10,000.						(C) When the kinase is unsaturated and the phosphatase saturated, a threshold-hyperbolic response results. The parameters for this cycle are 							, a1 = 100, K1 = 10,000, a2 = 100, 							, K2 = 1, k1 = 25, and k2 = 1.						(D) When both enzymes are saturated, an ultrasensitive response results. The parameters used for this cycle are 							, a1 = 100, K1 = 10, a2 = 100, 							, K2 = 10, k1 = 1, and k2 = 1. The parameters for the four cycles were chosen to be comparable in magnitude to values found in the literature (see [11,62], for example).
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pcbi-0030246-g002: Steady-State Behavior of the Four Cycle Regimes(A) When both enzymes are unsaturated, the steady-state response is hyperbolic. The parameters used for this cycle are , a1 = 1, K1 = 10,000, a2 = 1, , K2 = 10,000, k1 = 1, and k2 = 1, where all reaction rates are in units of 1/s, concentrations and Michaelis constants are in nanomoles, and second-order reaction rates (a1 and a2) are in 1/nM/s. (B) When the kinase is saturated and the phosphatase unsaturated, a linear response results. The parameters here are , a1 = 100, K1 = 10, a2 = 1, , K2 = 10,000, k1 = 500, and k2 = 10,000. (C) When the kinase is unsaturated and the phosphatase saturated, a threshold-hyperbolic response results. The parameters for this cycle are , a1 = 100, K1 = 10,000, a2 = 100, , K2 = 1, k1 = 25, and k2 = 1. (D) When both enzymes are saturated, an ultrasensitive response results. The parameters used for this cycle are , a1 = 100, K1 = 10, a2 = 100, , K2 = 10, k1 = 1, and k2 = 1. The parameters for the four cycles were chosen to be comparable in magnitude to values found in the literature (see [11,62], for example).

Mentions: Since the signaling cycle is built of two enzymatic reactions, it can exhibit four regimes of signaling (see Figure 2), corresponding to the two regimes of each reaction. The conditions for each of the four regimes are summarized in Table 1. The steady-state behavior of two of the four regimes (when the kinase and the phosphatase are either both saturated or both unsaturated, referred to as ultrasensitive and hyperbolic, respectively) has been characterized earlier by Goldbeter and Koshland [28]. Using tQSSA, we are able to refine the range of parameter values for which these behaviors hold. The other two regimes have not been identified before, to the best of our knowledge.


Operating regimes of signaling cycles: statics, dynamics, and noise filtering.

Gomez-Uribe C, Verghese GC, Mirny LA - PLoS Comput. Biol. (2007)

Steady-State Behavior of the Four Cycle Regimes(A) When both enzymes are unsaturated, the steady-state response is hyperbolic. The parameters used for this cycle are 							, a1 = 1, K1 = 10,000, a2 = 1,							, K2 = 10,000, k1 = 1, and k2 = 1, where all reaction rates are in units of 1/s, concentrations and Michaelis constants are in nanomoles, and second-order reaction rates (a1 and a2) are in 1/nM/s.						(B) When the kinase is saturated and the phosphatase unsaturated, a linear response results. The parameters here are 							, a1 = 100, K1 = 10, a2 = 1, 							, K2 = 10,000, k1 = 500, and k2 = 10,000.						(C) When the kinase is unsaturated and the phosphatase saturated, a threshold-hyperbolic response results. The parameters for this cycle are 							, a1 = 100, K1 = 10,000, a2 = 100, 							, K2 = 1, k1 = 25, and k2 = 1.						(D) When both enzymes are saturated, an ultrasensitive response results. The parameters used for this cycle are 							, a1 = 100, K1 = 10, a2 = 100, 							, K2 = 10, k1 = 1, and k2 = 1. The parameters for the four cycles were chosen to be comparable in magnitude to values found in the literature (see [11,62], for example).
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pcbi-0030246-g002: Steady-State Behavior of the Four Cycle Regimes(A) When both enzymes are unsaturated, the steady-state response is hyperbolic. The parameters used for this cycle are , a1 = 1, K1 = 10,000, a2 = 1, , K2 = 10,000, k1 = 1, and k2 = 1, where all reaction rates are in units of 1/s, concentrations and Michaelis constants are in nanomoles, and second-order reaction rates (a1 and a2) are in 1/nM/s. (B) When the kinase is saturated and the phosphatase unsaturated, a linear response results. The parameters here are , a1 = 100, K1 = 10, a2 = 1, , K2 = 10,000, k1 = 500, and k2 = 10,000. (C) When the kinase is unsaturated and the phosphatase saturated, a threshold-hyperbolic response results. The parameters for this cycle are , a1 = 100, K1 = 10,000, a2 = 100, , K2 = 1, k1 = 25, and k2 = 1. (D) When both enzymes are saturated, an ultrasensitive response results. The parameters used for this cycle are , a1 = 100, K1 = 10, a2 = 100, , K2 = 10, k1 = 1, and k2 = 1. The parameters for the four cycles were chosen to be comparable in magnitude to values found in the literature (see [11,62], for example).
Mentions: Since the signaling cycle is built of two enzymatic reactions, it can exhibit four regimes of signaling (see Figure 2), corresponding to the two regimes of each reaction. The conditions for each of the four regimes are summarized in Table 1. The steady-state behavior of two of the four regimes (when the kinase and the phosphatase are either both saturated or both unsaturated, referred to as ultrasensitive and hyperbolic, respectively) has been characterized earlier by Goldbeter and Koshland [28]. Using tQSSA, we are able to refine the range of parameter values for which these behaviors hold. The other two regimes have not been identified before, to the best of our knowledge.

Bottom Line: These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions.Numerical simulations show that our analytical results hold well even for noise of large amplitude.We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

View Article: PubMed Central - PubMed

Affiliation: Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.

ABSTRACT
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act--in all four regimes--as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

Show MeSH
Related in: MedlinePlus