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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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Related in: MedlinePlus

Magnitude of the Response of the Cycle O (Normalized by the Steady-State Saturation Value) versus the Input Frequency ω, for Three Different Input Amplitudes aThe traces in (A), (B), (C), and (D) show the response of the hyperbolic, signal-transducing, threshold-hyperbolic, and ultrasensitive switches, respectively, as shown in Figure 2. The solid lines are the analytical approximation (Equation 4). The dotted lines are obtained from numerical simulation of the full system.
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pcbi-0030246-g004: Magnitude of the Response of the Cycle O (Normalized by the Steady-State Saturation Value) versus the Input Frequency ω, for Three Different Input Amplitudes aThe traces in (A), (B), (C), and (D) show the response of the hyperbolic, signal-transducing, threshold-hyperbolic, and ultrasensitive switches, respectively, as shown in Figure 2. The solid lines are the analytical approximation (Equation 4). The dotted lines are obtained from numerical simulation of the full system.

Mentions: Figure 4 shows the amplitude O of the variations in the output (normalized by the steady-state saturation value of the cycle), obtained by numerical simulation for three values of a, and as a function of input frequency ω. Invariably, the response is flat and high at low frequencies, but starts to decrease after a particular frequency is reached. These results are very well-described in the case of the smallest a (corresponding to 11% deviations) by the expression obtained analytically using small-signal approximations (see Text S4): where E0 is the background kinase level, and where the gain g and the cutoff frequency ωc are functions of the cycle parameters that are different for the four regimes (see Table 3). The analytical approximation continues to hold quite well even for larger values of a, the deviation amplitude (up to 91% of the baseline for the results in Figure 4). For frequencies much smaller than the cutoff, the amplitude of the output variations is constant and proportional to the ratio of gain to cutoff frequency. For frequencies above the cutoff, the output variations have an amplitude that decays as 1/ω. Figure S1 presents more detailed results on the variation of O as a function of both a and ω, again obtained by numerical simulations (see Text S6 for a description of Figure S1).


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

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

Magnitude of the Response of the Cycle O (Normalized by the Steady-State Saturation Value) versus the Input Frequency ω, for Three Different Input Amplitudes aThe traces in (A), (B), (C), and (D) show the response of the hyperbolic, signal-transducing, threshold-hyperbolic, and ultrasensitive switches, respectively, as shown in Figure 2. The solid lines are the analytical approximation (Equation 4). The dotted lines are obtained from numerical simulation of the full system.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2230677&req=5

pcbi-0030246-g004: Magnitude of the Response of the Cycle O (Normalized by the Steady-State Saturation Value) versus the Input Frequency ω, for Three Different Input Amplitudes aThe traces in (A), (B), (C), and (D) show the response of the hyperbolic, signal-transducing, threshold-hyperbolic, and ultrasensitive switches, respectively, as shown in Figure 2. The solid lines are the analytical approximation (Equation 4). The dotted lines are obtained from numerical simulation of the full system.
Mentions: Figure 4 shows the amplitude O of the variations in the output (normalized by the steady-state saturation value of the cycle), obtained by numerical simulation for three values of a, and as a function of input frequency ω. Invariably, the response is flat and high at low frequencies, but starts to decrease after a particular frequency is reached. These results are very well-described in the case of the smallest a (corresponding to 11% deviations) by the expression obtained analytically using small-signal approximations (see Text S4): where E0 is the background kinase level, and where the gain g and the cutoff frequency ωc are functions of the cycle parameters that are different for the four regimes (see Table 3). The analytical approximation continues to hold quite well even for larger values of a, the deviation amplitude (up to 91% of the baseline for the results in Figure 4). For frequencies much smaller than the cutoff, the amplitude of the output variations is constant and proportional to the ratio of gain to cutoff frequency. For frequencies above the cutoff, the output variations have an amplitude that decays as 1/ω. Figure S1 presents more detailed results on the variation of O as a function of both a and ω, again obtained by numerical simulations (see Text S6 for a description of Figure S1).

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