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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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Dynamic Response of the Cycles to Fast and Slow InputsThe cycle has a characteristic response time τc that is a function of its parameters (see “Dynamic Response” in Results), and which is different for all four regimes. This plot shows the response of all four regimes to (1) a slow input that has a period equal to twice the characteristic response time of the cycle, followed by (2) a fast input with a period equal to one-fifth of the cycle's response time. For clarity, time was normalized by dividing by the characteristic time of each cycle. The signal in red represents the input kinase levels (for the threshold-hyperbolic switch, the input used is actually twice the red signal), whereas the blue 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.
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pcbi-0030246-g005: Dynamic Response of the Cycles to Fast and Slow InputsThe cycle has a characteristic response time τc that is a function of its parameters (see “Dynamic Response” in Results), and which is different for all four regimes. This plot shows the response of all four regimes to (1) a slow input that has a period equal to twice the characteristic response time of the cycle, followed by (2) a fast input with a period equal to one-fifth of the cycle's response time. For clarity, time was normalized by dividing by the characteristic time of each cycle. The signal in red represents the input kinase levels (for the threshold-hyperbolic switch, the input used is actually twice the red signal), whereas the blue 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.

Mentions: It is easy to understand the origin of the low-pass filtering behavior. First, consider a cycle subjected to a slowly varying input (Figure 5): if the input changes so slowly that the cycle has enough time to reach its steady-state level before the kinase level changes by a significant amount, the cycle simply tracks the kinase level as a function of time through its steady-state response curve, characteristic for its operational regime. Now consider a rapidly changing input. Since the kinase level changes faster, the cycle has less time to adjust to its steady state corresponding to the new value of the input before the kinase level changes again. Thus the output will not be able to reach its full amplitude before the kinase levels change again in the opposite direction, and the amplitude of the output is thus decreased (see Figure 5). As the signal changes faster and faster, the amplitude of the output will decrease, until the kinase levels vary so fast that the cycle simply does not respond.


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

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

Dynamic Response of the Cycles to Fast and Slow InputsThe cycle has a characteristic response time τc that is a function of its parameters (see “Dynamic Response” in Results), and which is different for all four regimes. This plot shows the response of all four regimes to (1) a slow input that has a period equal to twice the characteristic response time of the cycle, followed by (2) a fast input with a period equal to one-fifth of the cycle's response time. For clarity, time was normalized by dividing by the characteristic time of each cycle. The signal in red represents the input kinase levels (for the threshold-hyperbolic switch, the input used is actually twice the red signal), whereas the blue 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.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0030246-g005: Dynamic Response of the Cycles to Fast and Slow InputsThe cycle has a characteristic response time τc that is a function of its parameters (see “Dynamic Response” in Results), and which is different for all four regimes. This plot shows the response of all four regimes to (1) a slow input that has a period equal to twice the characteristic response time of the cycle, followed by (2) a fast input with a period equal to one-fifth of the cycle's response time. For clarity, time was normalized by dividing by the characteristic time of each cycle. The signal in red represents the input kinase levels (for the threshold-hyperbolic switch, the input used is actually twice the red signal), whereas the blue 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.
Mentions: It is easy to understand the origin of the low-pass filtering behavior. First, consider a cycle subjected to a slowly varying input (Figure 5): if the input changes so slowly that the cycle has enough time to reach its steady-state level before the kinase level changes by a significant amount, the cycle simply tracks the kinase level as a function of time through its steady-state response curve, characteristic for its operational regime. Now consider a rapidly changing input. Since the kinase level changes faster, the cycle has less time to adjust to its steady state corresponding to the new value of the input before the kinase level changes again. Thus the output will not be able to reach its full amplitude before the kinase levels change again in the opposite direction, and the amplitude of the output is thus decreased (see Figure 5). As the signal changes faster and faster, the amplitude of the output will decrease, until the kinase levels vary so fast that the cycle simply does not respond.

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