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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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Growth rates of patterning. (Top) Similar to that in Figure 3, we see the intersection of the volume of Figure 2A, with plane rh = 0.5 (A) and with the plane ra = 5 (B), but now the color scale depicts ωmax values instead of kmax. ωmax quantifies the speed of pattern appearance; for highervalues, one expects faster-forming patterns. (C) Pattern formationdynamics for the concentration of a at x = 25. Parameter values correspond to the white dots in panel B (D= 0.01, nH = 2, ra = 5, rh = 5, and with three different values of μ: 0.45 (greenline), 1.0 (red line), and 1.5 (blue line)).
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fig6: Growth rates of patterning. (Top) Similar to that in Figure 3, we see the intersection of the volume of Figure 2A, with plane rh = 0.5 (A) and with the plane ra = 5 (B), but now the color scale depicts ωmax values instead of kmax. ωmax quantifies the speed of pattern appearance; for highervalues, one expects faster-forming patterns. (C) Pattern formationdynamics for the concentration of a at x = 25. Parameter values correspond to the white dots in panel B (D= 0.01, nH = 2, ra = 5, rh = 5, and with three different values of μ: 0.45 (greenline), 1.0 (red line), and 1.5 (blue line)).

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)

Growth rates of patterning. (Top) Similar to that in Figure 3, we see the intersection of the volume of Figure 2A, with plane rh = 0.5 (A) and with the plane ra = 5 (B), but now the color scale depicts ωmax values instead of kmax. ωmax quantifies the speed of pattern appearance; for highervalues, one expects faster-forming patterns. (C) Pattern formationdynamics for the concentration of a at x = 25. Parameter values correspond to the white dots in panel B (D= 0.01, nH = 2, ra = 5, rh = 5, and with three different values of μ: 0.45 (greenline), 1.0 (red line), and 1.5 (blue line)).
© Copyright Policy
Related In: Results  -  Collection

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

fig6: Growth rates of patterning. (Top) Similar to that in Figure 3, we see the intersection of the volume of Figure 2A, with plane rh = 0.5 (A) and with the plane ra = 5 (B), but now the color scale depicts ωmax values instead of kmax. ωmax quantifies the speed of pattern appearance; for highervalues, one expects faster-forming patterns. (C) Pattern formationdynamics for the concentration of a at x = 25. Parameter values correspond to the white dots in panel B (D= 0.01, nH = 2, ra = 5, rh = 5, and with three different values of μ: 0.45 (greenline), 1.0 (red line), and 1.5 (blue line)).
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