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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.


Related in: MedlinePlus

Dynamic behavior for the bistable, tristable, and quadrastable instances of the synthetic gene circuit in Figure 4. (A–C) 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. The axes are normalized with respect to the mean of the values for X1 and X2 for each of the stable steady states in a given instance, respectively. The dynamic behaviors and basins of attraction for each of the stable states for instances of the system exhibiting (A) bistability, (B) tristability, and (C) quadrastability. The steady states of the system are represented by black circles (stable) and white circles (unstable). (Left panels) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. Different colored regions represent areas where the dynamics of the system follow a particular trajectory: southwest (purple); southeast (green); northwest (orange); and northeast (blue). (Right Panels) Different colored regions represent values for the activators that are attracted to a unique steady-state (•). The boundaries between the basins of attraction are obtained by refinement using the original equations.
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Figure 5: Dynamic behavior for the bistable, tristable, and quadrastable instances of the synthetic gene circuit in Figure 4. (A–C) 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. The axes are normalized with respect to the mean of the values for X1 and X2 for each of the stable steady states in a given instance, respectively. The dynamic behaviors and basins of attraction for each of the stable states for instances of the system exhibiting (A) bistability, (B) tristability, and (C) quadrastability. The steady states of the system are represented by black circles (stable) and white circles (unstable). (Left panels) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. Different colored regions represent areas where the dynamics of the system follow a particular trajectory: southwest (purple); southeast (green); northwest (orange); and northeast (blue). (Right Panels) Different colored regions represent values for the activators that are attracted to a unique steady-state (•). The boundaries between the basins of attraction are obtained by refinement using the original equations.

Mentions: The System Design Space method we have described can be applied for a deconstruction of dynamic behaviors in state space. This deconstruction, which is still in the early phases of its development, partitions state space into regions that exhibit qualitatively-distinct trajectories that provide valuable information regarding the system's basins of attraction and response to transient perturbations. The dominance conditions define (n + m)-dimensional polytopes, where n is the number of dependent variables and m is the number of independent variables/parameters. For each equation in the Dominant S-System, we can identify regions where the positive term is greater than the negative term and thus a region with a qualitatively-defined trajectory. The particular arrangement of steady states and the trajectories around these steady states can be represented visually, as shown in the left panels of Figure 5, and can be compared with the basins of attraction for the original system of equations, as shown in the right panels of Figure 5. In each of these examples, our automated tools provide rich information for rapid identification of interesting properties for the system. The results can then be refined by applying conventional methods to the full system.


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 for the bistable, tristable, and quadrastable instances of the synthetic gene circuit in Figure 4. (A–C) 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. The axes are normalized with respect to the mean of the values for X1 and X2 for each of the stable steady states in a given instance, respectively. The dynamic behaviors and basins of attraction for each of the stable states for instances of the system exhibiting (A) bistability, (B) tristability, and (C) quadrastability. The steady states of the system are represented by black circles (stable) and white circles (unstable). (Left panels) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. Different colored regions represent areas where the dynamics of the system follow a particular trajectory: southwest (purple); southeast (green); northwest (orange); and northeast (blue). (Right Panels) Different colored regions represent values for the activators that are attracted to a unique steady-state (•). The boundaries between the basins of attraction are obtained by refinement using the original equations.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 5: Dynamic behavior for the bistable, tristable, and quadrastable instances of the synthetic gene circuit in Figure 4. (A–C) 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. The axes are normalized with respect to the mean of the values for X1 and X2 for each of the stable steady states in a given instance, respectively. The dynamic behaviors and basins of attraction for each of the stable states for instances of the system exhibiting (A) bistability, (B) tristability, and (C) quadrastability. The steady states of the system are represented by black circles (stable) and white circles (unstable). (Left panels) State-space deconstruction of the gene circuit by system design space showing qualitatively-distinct trajectories. Different colored regions represent areas where the dynamics of the system follow a particular trajectory: southwest (purple); southeast (green); northwest (orange); and northeast (blue). (Right Panels) Different colored regions represent values for the activators that are attracted to a unique steady-state (•). The boundaries between the basins of attraction are obtained by refinement using the original equations.
Mentions: The System Design Space method we have described can be applied for a deconstruction of dynamic behaviors in state space. This deconstruction, which is still in the early phases of its development, partitions state space into regions that exhibit qualitatively-distinct trajectories that provide valuable information regarding the system's basins of attraction and response to transient perturbations. The dominance conditions define (n + m)-dimensional polytopes, where n is the number of dependent variables and m is the number of independent variables/parameters. For each equation in the Dominant S-System, we can identify regions where the positive term is greater than the negative term and thus a region with a qualitatively-defined trajectory. The particular arrangement of steady states and the trajectories around these steady states can be represented visually, as shown in the left panels of Figure 5, and can be compared with the basins of attraction for the original system of equations, as shown in the right panels of Figure 5. In each of these examples, our automated tools provide rich information for rapid identification of interesting properties for the system. The results can then be refined by applying conventional methods to the full system.

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.


Related in: MedlinePlus