Limits...
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.


Basins of attraction for a 4-state genetic counter. 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. Different colored regions represent values for the activators that converge to a unique steady-state attractor. Transitions from an initial steady state (white circle) to a new steady state (black circle) following an equal size bolus (275 μM) in one of the two activators. The top panels show transient simulations following a bolus of X1 (green arrows). The bottom panels show transient simulations following a bolus of X2 (red arrows). Left and right sub-panels show the transitions from different initial steady-state attractors.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4940394&req=5

Figure 7: Basins of attraction for a 4-state genetic counter. 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. Different colored regions represent values for the activators that converge to a unique steady-state attractor. Transitions from an initial steady state (white circle) to a new steady state (black circle) following an equal size bolus (275 μM) in one of the two activators. The top panels show transient simulations following a bolus of X1 (green arrows). The bottom panels show transient simulations following a bolus of X2 (red arrows). Left and right sub-panels show the transitions from different initial steady-state attractors.

Mentions: This is reflected in the teardrop-shaped basin of attraction for the steady-state attractor in the (+, +) quadrant: when the system is at the (+, +) attractor and there is a transient increase in the concentration of either X1 or X2, the dynamics of the system are such that it leaves the basin of attraction for the (+, +) attractor and enters the basin of attraction for the (+, −) or (−, +) attractor, respectively. A visual representation of the transitions between the steady-state attractors following transient stimulation is shown in Figure 7.


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)

Basins of attraction for a 4-state genetic counter. 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. Different colored regions represent values for the activators that converge to a unique steady-state attractor. Transitions from an initial steady state (white circle) to a new steady state (black circle) following an equal size bolus (275 μM) in one of the two activators. The top panels show transient simulations following a bolus of X1 (green arrows). The bottom panels show transient simulations following a bolus of X2 (red arrows). Left and right sub-panels show the transitions from different initial steady-state attractors.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 7: Basins of attraction for a 4-state genetic counter. 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. Different colored regions represent values for the activators that converge to a unique steady-state attractor. Transitions from an initial steady state (white circle) to a new steady state (black circle) following an equal size bolus (275 μM) in one of the two activators. The top panels show transient simulations following a bolus of X1 (green arrows). The bottom panels show transient simulations following a bolus of X2 (red arrows). Left and right sub-panels show the transitions from different initial steady-state attractors.
Mentions: This is reflected in the teardrop-shaped basin of attraction for the steady-state attractor in the (+, +) quadrant: when the system is at the (+, +) attractor and there is a transient increase in the concentration of either X1 or X2, the dynamics of the system are such that it leaves the basin of attraction for the (+, +) attractor and enters the basin of attraction for the (+, −) or (−, +) attractor, respectively. A visual representation of the transitions between the steady-state attractors following transient stimulation is shown in Figure 7.

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.