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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.


Dynamic behavior of a quadrastable instance of the synthetic gene circuit. (A,B) The x-axis represents the logarithm of the concentration of the first activator, X1; the y-axis represents the logarithm of the concentration of the second activator, X2. (A) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. The steady states of the system are represented by black circles (stable) and white circles (unstable). The colors of the different regions correspond to regions with different qualitatively-distinct trajectories as described in the caption of Figure 5. (B) The basin of attraction, represented by the colored regions, represent the domains of state space that are attracted to a particular stable steady state (black circles). The boundaries between the basins of attraction are obtained by refinement using the original equations.
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Figure 6: Dynamic behavior of a quadrastable instance of the synthetic gene circuit. (A,B) The x-axis represents the logarithm of the concentration of the first activator, X1; the y-axis represents the logarithm of the concentration of the second activator, X2. (A) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. The steady states of the system are represented by black circles (stable) and white circles (unstable). The colors of the different regions correspond to regions with different qualitatively-distinct trajectories as described in the caption of Figure 5. (B) The basin of attraction, represented by the colored regions, represent the domains of state space that are attracted to a particular stable steady state (black circles). The boundaries between the basins of attraction are obtained by refinement using the original equations.

Mentions: One arrangement of particular interest has one steady-state attractor that occupies each of the quadrants—consistent with four binary boolean states, represented by (−, −), (−, +), (+, −), and (+, +). We find that all of the ensembles identified in Section Predicting Parameter Sets for Realization of Multi-Stability are able to yield this particular arrangement of steady-state attractors, an example of which is shown in Figure 6, where Xr,1 = 1 and Xr,2 = 1.


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)

Dynamic behavior of a quadrastable instance of the synthetic gene circuit. (A,B) The x-axis represents the logarithm of the concentration of the first activator, X1; the y-axis represents the logarithm of the concentration of the second activator, X2. (A) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. The steady states of the system are represented by black circles (stable) and white circles (unstable). The colors of the different regions correspond to regions with different qualitatively-distinct trajectories as described in the caption of Figure 5. (B) The basin of attraction, represented by the colored regions, represent the domains of state space that are attracted to a particular stable steady state (black circles). The boundaries between the basins of attraction are obtained by refinement using the original equations.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4940394&req=5

Figure 6: Dynamic behavior of a quadrastable instance of the synthetic gene circuit. (A,B) The x-axis represents the logarithm of the concentration of the first activator, X1; the y-axis represents the logarithm of the concentration of the second activator, X2. (A) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. The steady states of the system are represented by black circles (stable) and white circles (unstable). The colors of the different regions correspond to regions with different qualitatively-distinct trajectories as described in the caption of Figure 5. (B) The basin of attraction, represented by the colored regions, represent the domains of state space that are attracted to a particular stable steady state (black circles). The boundaries between the basins of attraction are obtained by refinement using the original equations.
Mentions: One arrangement of particular interest has one steady-state attractor that occupies each of the quadrants—consistent with four binary boolean states, represented by (−, −), (−, +), (+, −), and (+, +). We find that all of the ensembles identified in Section Predicting Parameter Sets for Realization of Multi-Stability are able to yield this particular arrangement of steady-state attractors, an example of which is shown in Figure 6, where Xr,1 = 1 and Xr,2 = 1.

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.