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Structural discrimination of robustness in transcriptional feedforward loops for pattern formation.

Rodrigo G, Elena SF - PLoS ONE (2011)

Bottom Line: We found four different solutions for precision, corresponding to the four incoherent architectures, but remarkably only one mode for adaptiveness, the incoherent type 4 (I4-FFL).Strikingly, we showed a strong correlation between the input (environment-related) and the intrinsic (mutation-related) susceptibilities.Finally, we discussed the evolution of incoherent regulations in terms of multifunctionality and robustness.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Biología Molecular y Celular de Plantas, Consejo Superior de Investigaciones Científicas-Universidad Politécnica de Valencia, Valencia, Spain. guirodta@ibmcp.upv.es

ABSTRACT
Signaling pathways are interconnected to regulatory circuits for sensing the environment and expressing the appropriate genetic profile. In particular, gradients of diffusing molecules (morphogens) determine cell fate at a given position, dictating development and spatial organization. The feedforward loop (FFL) circuit is among the simplest genetic architectures able to generate one-stripe patterns by operating as an amplitude detection device, where high output levels are achieved at intermediate input ones. Here, using a heuristic optimization-based approach, we dissected the design space containing all possible topologies and parameter values of the FFL circuits. We explored the ability of being sensitive or adaptive to variations in the critical morphogen level where cell fate is switched. We found four different solutions for precision, corresponding to the four incoherent architectures, but remarkably only one mode for adaptiveness, the incoherent type 4 (I4-FFL). We further carried out a theoretical study to unveil the design principle for such structural discrimination, finding that the synergistic action and cooperative binding on the downstream promoter are instrumental to achieve absolute adaptive responses. Subsequently, we analyzed the robustness of these optimal circuits against perturbations in the kinetic parameters and molecular noise, which has allowed us to depict a scenario where adaptiveness, parameter sensitivity and noise tolerance are different, correlated facets of the robustness of the I4-FFL circuit. Strikingly, we showed a strong correlation between the input (environment-related) and the intrinsic (mutation-related) susceptibilities. Finally, we discussed the evolution of incoherent regulations in terms of multifunctionality and robustness.

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Noise tolerance for optimal designs.Noise in output expression () for different FFL circuits due to intrinsic effects and several noise levels at the input; v represents the corresponding Fano factor (see Materials and Methods).
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pone-0016904-g004: Noise tolerance for optimal designs.Noise in output expression () for different FFL circuits due to intrinsic effects and several noise levels at the input; v represents the corresponding Fano factor (see Materials and Methods).

Mentions: In addition to the susceptibility calculations, we carried out a stochastic analysis to study the robustness of the circuits against molecular noise [28]–[31]. We considered an intrinsic source of noise due to the low number of molecules together with a noisy input signal (see Materials and Methods). We performed numerical simulations to calculate the noise level in the output gene at the state ON (Fig. 4) for different noise amplitudes in the input for the optimal circuits (I1-FFL-P, I2-FFL-P, I3-FFL-P, I4-FFL-P, and I4-FFL-A). Essentially, noise in gene expression can be decomposed into three terms, one intrinsic that is Poissonian for genes without self-regulation, another due to propagation effects, and a third extrinsic one accounting for sources common to all species [30]. In our case, we did not consider extrinsic noise, and the propagation term accounts for noise directly resulting from the input (Nu) and noise coming indirectly via the intermediary element (Ny). These terms are proportional to their susceptibilities (, ). Then we can write the expression for noise in the output. Circuits with similar transfer functions have similar susceptibilities, however noise tolerance is structure-dependent. Indeed, at the state ON, the concentration of the intermediary element is low for circuits I1-FFL-P and I2-FFL-P because this gene represses the output, whereas it is high for circuits I3-FFL-P and I4-FFL-P as in these cases it activates the output. This fact entails that the term Ny is higher for circuits I1-FFL-P and I2-FFL-P than for circuits I3-FFL-P and I4-FFL-P, since noise is inversely proportional to concentration. As we can observe, noise increases in circuits optimized for precision with randomly fluctuating input signals, whereas circuit I4-FFL-A is highly insensitive to such stochastic events, maintaining a constant Poissonian noise level (). This can be rationalized knowing that for this circuit. For high input fluctuations (), we have thereby precise circuits show similar noise levels.


Structural discrimination of robustness in transcriptional feedforward loops for pattern formation.

Rodrigo G, Elena SF - PLoS ONE (2011)

Noise tolerance for optimal designs.Noise in output expression () for different FFL circuits due to intrinsic effects and several noise levels at the input; v represents the corresponding Fano factor (see Materials and Methods).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3038866&req=5

pone-0016904-g004: Noise tolerance for optimal designs.Noise in output expression () for different FFL circuits due to intrinsic effects and several noise levels at the input; v represents the corresponding Fano factor (see Materials and Methods).
Mentions: In addition to the susceptibility calculations, we carried out a stochastic analysis to study the robustness of the circuits against molecular noise [28]–[31]. We considered an intrinsic source of noise due to the low number of molecules together with a noisy input signal (see Materials and Methods). We performed numerical simulations to calculate the noise level in the output gene at the state ON (Fig. 4) for different noise amplitudes in the input for the optimal circuits (I1-FFL-P, I2-FFL-P, I3-FFL-P, I4-FFL-P, and I4-FFL-A). Essentially, noise in gene expression can be decomposed into three terms, one intrinsic that is Poissonian for genes without self-regulation, another due to propagation effects, and a third extrinsic one accounting for sources common to all species [30]. In our case, we did not consider extrinsic noise, and the propagation term accounts for noise directly resulting from the input (Nu) and noise coming indirectly via the intermediary element (Ny). These terms are proportional to their susceptibilities (, ). Then we can write the expression for noise in the output. Circuits with similar transfer functions have similar susceptibilities, however noise tolerance is structure-dependent. Indeed, at the state ON, the concentration of the intermediary element is low for circuits I1-FFL-P and I2-FFL-P because this gene represses the output, whereas it is high for circuits I3-FFL-P and I4-FFL-P as in these cases it activates the output. This fact entails that the term Ny is higher for circuits I1-FFL-P and I2-FFL-P than for circuits I3-FFL-P and I4-FFL-P, since noise is inversely proportional to concentration. As we can observe, noise increases in circuits optimized for precision with randomly fluctuating input signals, whereas circuit I4-FFL-A is highly insensitive to such stochastic events, maintaining a constant Poissonian noise level (). This can be rationalized knowing that for this circuit. For high input fluctuations (), we have thereby precise circuits show similar noise levels.

Bottom Line: We found four different solutions for precision, corresponding to the four incoherent architectures, but remarkably only one mode for adaptiveness, the incoherent type 4 (I4-FFL).Strikingly, we showed a strong correlation between the input (environment-related) and the intrinsic (mutation-related) susceptibilities.Finally, we discussed the evolution of incoherent regulations in terms of multifunctionality and robustness.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Biología Molecular y Celular de Plantas, Consejo Superior de Investigaciones Científicas-Universidad Politécnica de Valencia, Valencia, Spain. guirodta@ibmcp.upv.es

ABSTRACT
Signaling pathways are interconnected to regulatory circuits for sensing the environment and expressing the appropriate genetic profile. In particular, gradients of diffusing molecules (morphogens) determine cell fate at a given position, dictating development and spatial organization. The feedforward loop (FFL) circuit is among the simplest genetic architectures able to generate one-stripe patterns by operating as an amplitude detection device, where high output levels are achieved at intermediate input ones. Here, using a heuristic optimization-based approach, we dissected the design space containing all possible topologies and parameter values of the FFL circuits. We explored the ability of being sensitive or adaptive to variations in the critical morphogen level where cell fate is switched. We found four different solutions for precision, corresponding to the four incoherent architectures, but remarkably only one mode for adaptiveness, the incoherent type 4 (I4-FFL). We further carried out a theoretical study to unveil the design principle for such structural discrimination, finding that the synergistic action and cooperative binding on the downstream promoter are instrumental to achieve absolute adaptive responses. Subsequently, we analyzed the robustness of these optimal circuits against perturbations in the kinetic parameters and molecular noise, which has allowed us to depict a scenario where adaptiveness, parameter sensitivity and noise tolerance are different, correlated facets of the robustness of the I4-FFL circuit. Strikingly, we showed a strong correlation between the input (environment-related) and the intrinsic (mutation-related) susceptibilities. Finally, we discussed the evolution of incoherent regulations in terms of multifunctionality and robustness.

Show MeSH
Related in: MedlinePlus