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Design Space Toolbox V2: Automated Software Enabling a Novel Phenotype-Centric Modeling Strategy for Natural and Synthetic Biological Systems.

Lomnitz JG, Savageau MA - Front Genet (2016)

Bottom Line: We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy.The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach.In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, University of California, Davis Davis, CA, USA.

ABSTRACT
Mathematical models of biochemical systems provide a means to elucidate the link between the genotype, environment, and phenotype. A subclass of mathematical models, known as mechanistic models, quantitatively describe the complex non-linear mechanisms that capture the intricate interactions between biochemical components. However, the study of mechanistic models is challenging because most are analytically intractable and involve large numbers of system parameters. Conventional methods to analyze them rely on local analyses about a nominal parameter set and they do not reveal the vast majority of potential phenotypes possible for a given system design. We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy. Instead, this approach relies on architectural features of the model to identify the phenotypic repertoire and then predict values for the parameters that yield specific instances of the system that realize desired phenotypic characteristics. Here, we present a collection of software tools, the Design Space Toolbox V2 based on the System Design Space method, that automates (1) enumeration of the repertoire of model phenotypes, (2) prediction of values for the parameters for any model phenotype, and (3) analysis of model phenotypes through analytical and numerical methods. The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach. We illustrate the power of these new tools by applying them to a synthetic gene circuit that can exhibit multi-stability. We then predict values for the system parameters such that the design exhibits 2, 3, and 4 stable steady states. In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count. This example shows the power of these new automated methods to rapidly identify behaviors of interest and efficiently predict parameter values for their realization. These tools may be applied to understand complex natural circuitry and to aid in the rational design of synthetic circuits.

No MeSH data available.


Visualization of the system design space and a phenotypic trait for the simple synthetic gene circuit in Figure 1. (A,B) The x-axis represents the concentration of the complimentary protein, X2. The y-axis represents the rate constant for X1 loss from either dilution or active degradation. (A) System design space showing the qualitatively-distinct phenotypes by color on the z-axis. Regions of overlap, represented by regions with multiple qualitatively-distinct phenotypes as shown in the colorbar, correspond to regions with multiple fixed points. (B) Stability plot showing the number of eigenvalues with positive real part on the z-axis. Blue corresponds to monostability; Red corresponds to bistability. Note that the regions of bistability in (B) correspond to the regions of overlap in (A).
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Figure 3: Visualization of the system design space and a phenotypic trait for the simple synthetic gene circuit in Figure 1. (A,B) The x-axis represents the concentration of the complimentary protein, X2. The y-axis represents the rate constant for X1 loss from either dilution or active degradation. (A) System design space showing the qualitatively-distinct phenotypes by color on the z-axis. Regions of overlap, represented by regions with multiple qualitatively-distinct phenotypes as shown in the colorbar, correspond to regions with multiple fixed points. (B) Stability plot showing the number of eigenvalues with positive real part on the z-axis. Blue corresponds to monostability; Red corresponds to bistability. Note that the regions of bistability in (B) correspond to the regions of overlap in (A).

Mentions: as shown in Figure 3A. The first argument is a matplotlib axis object for a plot canvas; the second argument is an instance of the VariablePool class with the values for the parameters; the third is the name of the x-axis; the fourth argument is the name of the y-axis; the fifth argument is the range of the x-axis in Cartesian coordinates; the sixth argument is the range of the y-axis in Cartesian coordinates; the seventh argument indicates the number of intersections of cases to be drawn, where [1, 3] indicates it will display regions associated with individual phenotypes and with three phenotypes consistent with bi-stability (i.e., 2 stable and 1 unstable).


Design Space Toolbox V2: Automated Software Enabling a Novel Phenotype-Centric Modeling Strategy for Natural and Synthetic Biological Systems.

Lomnitz JG, Savageau MA - Front Genet (2016)

Visualization of the system design space and a phenotypic trait for the simple synthetic gene circuit in Figure 1. (A,B) The x-axis represents the concentration of the complimentary protein, X2. The y-axis represents the rate constant for X1 loss from either dilution or active degradation. (A) System design space showing the qualitatively-distinct phenotypes by color on the z-axis. Regions of overlap, represented by regions with multiple qualitatively-distinct phenotypes as shown in the colorbar, correspond to regions with multiple fixed points. (B) Stability plot showing the number of eigenvalues with positive real part on the z-axis. Blue corresponds to monostability; Red corresponds to bistability. Note that the regions of bistability in (B) correspond to the regions of overlap in (A).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4940394&req=5

Figure 3: Visualization of the system design space and a phenotypic trait for the simple synthetic gene circuit in Figure 1. (A,B) The x-axis represents the concentration of the complimentary protein, X2. The y-axis represents the rate constant for X1 loss from either dilution or active degradation. (A) System design space showing the qualitatively-distinct phenotypes by color on the z-axis. Regions of overlap, represented by regions with multiple qualitatively-distinct phenotypes as shown in the colorbar, correspond to regions with multiple fixed points. (B) Stability plot showing the number of eigenvalues with positive real part on the z-axis. Blue corresponds to monostability; Red corresponds to bistability. Note that the regions of bistability in (B) correspond to the regions of overlap in (A).
Mentions: as shown in Figure 3A. The first argument is a matplotlib axis object for a plot canvas; the second argument is an instance of the VariablePool class with the values for the parameters; the third is the name of the x-axis; the fourth argument is the name of the y-axis; the fifth argument is the range of the x-axis in Cartesian coordinates; the sixth argument is the range of the y-axis in Cartesian coordinates; the seventh argument indicates the number of intersections of cases to be drawn, where [1, 3] indicates it will display regions associated with individual phenotypes and with three phenotypes consistent with bi-stability (i.e., 2 stable and 1 unstable).

Bottom Line: We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy.The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach.In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, University of California, Davis Davis, CA, USA.

ABSTRACT
Mathematical models of biochemical systems provide a means to elucidate the link between the genotype, environment, and phenotype. A subclass of mathematical models, known as mechanistic models, quantitatively describe the complex non-linear mechanisms that capture the intricate interactions between biochemical components. However, the study of mechanistic models is challenging because most are analytically intractable and involve large numbers of system parameters. Conventional methods to analyze them rely on local analyses about a nominal parameter set and they do not reveal the vast majority of potential phenotypes possible for a given system design. We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy. Instead, this approach relies on architectural features of the model to identify the phenotypic repertoire and then predict values for the parameters that yield specific instances of the system that realize desired phenotypic characteristics. Here, we present a collection of software tools, the Design Space Toolbox V2 based on the System Design Space method, that automates (1) enumeration of the repertoire of model phenotypes, (2) prediction of values for the parameters for any model phenotype, and (3) analysis of model phenotypes through analytical and numerical methods. The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach. We illustrate the power of these new tools by applying them to a synthetic gene circuit that can exhibit multi-stability. We then predict values for the system parameters such that the design exhibits 2, 3, and 4 stable steady states. In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count. This example shows the power of these new automated methods to rapidly identify behaviors of interest and efficiently predict parameter values for their realization. These tools may be applied to understand complex natural circuitry and to aid in the rational design of synthetic circuits.

No MeSH data available.