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Cooperativity to increase Turing pattern space for synthetic biology.

Diambra L, Senthivel VR, Menendez DB, Isalan M - ACS Synth Biol (2014)

Bottom Line: We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning.Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor.These results demonstrate some of the limitations of linear scenarios for reaction-diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

View Article: PubMed Central - PubMed

Affiliation: Centro Regional de Estudios Geńomicos, Universidad Nacional de La Plata , Blvd. 120 No. 1461, 1900 La Plata, Argentine.

ABSTRACT
It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction-diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells.1 The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose-response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction-diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

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Speed of pattern appearance versus pattern size. Behaviorof ω+ as a function of k for n = 2, D = 0.01, ra = 2.5, rh = 7.0,and three different values of μ: 3.75 (green), 4.5 (red), and6.5 (blue). ω+ presents only one maximum in kmax, whose particular value depends on the parameterset (D, μ, ra, and rh). Forthis particular set of parameter values, we can see that speed ofpattern appearance, ωmax, increases with the typicalsize of the pattern.
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fig5: Speed of pattern appearance versus pattern size. Behaviorof ω+ as a function of k for n = 2, D = 0.01, ra = 2.5, rh = 7.0,and three different values of μ: 3.75 (green), 4.5 (red), and6.5 (blue). ω+ presents only one maximum in kmax, whose particular value depends on the parameterset (D, μ, ra, and rh). Forthis particular set of parameter values, we can see that speed ofpattern appearance, ωmax, increases with the typicalsize of the pattern.

Mentions: In Figure 5, we can see the growth rateω+ as a function of the k for differentvalues of μ. The position of local maximum kmax changes with μ (the ratio of the degradationrates of inhibitor relative to the activator). From Figure 5, the maximum growth rate of patterns, denoted byωmax = ω+(kmax), seems to increase with μ for this particular setof values. In general, the maximum growth rate of patterns dependson the parameter set D, μ, ra, and rh. Figure 6A,B depicts howωmax depends on these parameters for cross-sectionsof the same volume represented in Figure 3 for D = 0.01. These plots show that smaller patterns grow moreslowly. This prediction is in agreement with the simulation shownin Figure 6C, which depicts the temporal evolutionof the concentration of a at the position x = 25.


Cooperativity to increase Turing pattern space for synthetic biology.

Diambra L, Senthivel VR, Menendez DB, Isalan M - ACS Synth Biol (2014)

Speed of pattern appearance versus pattern size. Behaviorof ω+ as a function of k for n = 2, D = 0.01, ra = 2.5, rh = 7.0,and three different values of μ: 3.75 (green), 4.5 (red), and6.5 (blue). ω+ presents only one maximum in kmax, whose particular value depends on the parameterset (D, μ, ra, and rh). Forthis particular set of parameter values, we can see that speed ofpattern appearance, ωmax, increases with the typicalsize of the pattern.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4384830&req=5

fig5: Speed of pattern appearance versus pattern size. Behaviorof ω+ as a function of k for n = 2, D = 0.01, ra = 2.5, rh = 7.0,and three different values of μ: 3.75 (green), 4.5 (red), and6.5 (blue). ω+ presents only one maximum in kmax, whose particular value depends on the parameterset (D, μ, ra, and rh). Forthis particular set of parameter values, we can see that speed ofpattern appearance, ωmax, increases with the typicalsize of the pattern.
Mentions: In Figure 5, we can see the growth rateω+ as a function of the k for differentvalues of μ. The position of local maximum kmax changes with μ (the ratio of the degradationrates of inhibitor relative to the activator). From Figure 5, the maximum growth rate of patterns, denoted byωmax = ω+(kmax), seems to increase with μ for this particular setof values. In general, the maximum growth rate of patterns dependson the parameter set D, μ, ra, and rh. Figure 6A,B depicts howωmax depends on these parameters for cross-sectionsof the same volume represented in Figure 3 for D = 0.01. These plots show that smaller patterns grow moreslowly. This prediction is in agreement with the simulation shownin Figure 6C, which depicts the temporal evolutionof the concentration of a at the position x = 25.

Bottom Line: We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning.Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor.These results demonstrate some of the limitations of linear scenarios for reaction-diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

View Article: PubMed Central - PubMed

Affiliation: Centro Regional de Estudios Geńomicos, Universidad Nacional de La Plata , Blvd. 120 No. 1461, 1900 La Plata, Argentine.

ABSTRACT
It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction-diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells.1 The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose-response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction-diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

Show MeSH