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From Boolean Network Model to Continuous Model Helps in Design of Functional Circuits.

Shao B, Liu X, Zhang D, Wu J, Ouyang Q - PLoS ONE (2015)

Bottom Line: In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model.Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions.Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, China; The Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China.

ABSTRACT
Computational circuit design with desired functions in a living cell is a challenging task in synthetic biology. To achieve this task, numerous methods that either focus on small scale networks or use evolutionary algorithms have been developed. Here, we propose a two-step approach to facilitate the design of functional circuits. In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model. In the second step, continuous simulation is applied to evaluate the performance of these topologies. We demonstrate the usefulness of this method by designing an example biological function: the SOS response of E. coli. Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions. Possible circuits are ranked according to their robustness against perturbations in parameter and gene expressions. The biological network is among the candidate networks, yet novel designs can be generated. Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks.

No MeSH data available.


Workflow of continuous simulation.For networks selected by Boolean network model, 1000 random parameter sets and 32 initial conditions are used to quantitatively assess their robustness. The ordinary differential equations describing these transcriptional networks are solved numerically to generate the dynamics of each network component. The proportion of parameter sets and number of initial conditions that can achieve a successful response is termed as the Q value and basin size, respectively, for the corresponding network.
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pone.0128630.g002: Workflow of continuous simulation.For networks selected by Boolean network model, 1000 random parameter sets and 32 initial conditions are used to quantitatively assess their robustness. The ordinary differential equations describing these transcriptional networks are solved numerically to generate the dynamics of each network component. The proportion of parameter sets and number of initial conditions that can achieve a successful response is termed as the Q value and basin size, respectively, for the corresponding network.

Mentions: The evaluation process of circuit performance is presented in Fig 2, in which two scores that can reflect robustness of networks are employed. The first score is Q value that estimates the volume of the functional parameter space [9]. For each network, we randomly choose 1000 sets of parameters using Latin hypercube sampling. Starting from the same initial state, the network dynamics with each parameter set is obtained by solving the ODEs. Time series of all nodes are then checked to see if they present a successful response, i.e., if they meet three criteria above. For a particular network structure, the proportion of parameter sets that can achieve our desired function is defined as the Q value of that structure. A larger Q value implies that the network can generate successful response to DNA damage over a wide range of parameters and, hence, is less sensitive to parameter variation. The second score is relevant to robustness in state space. For the Boolean network model, the state of the system is updated using Eq 1 until it reaches a fixed point, which can also be called an attractor. The number of initial states that will flow into an attractor is defined as the basin size of that attractor. It is proposed that a biological state should have a large basin size in order to generate stability [17]. We held similar assumption in our design procedure that normal state with node3 activated should be a big attractor and stable against fluctuations in gene expression. In the Boolean network model, all possible initial conditions (2N for network with N nodes) are enumerated to calculate the basin size, which is not practical in continuous simulation. To sample the space of initial states in the ODE model, we employ a similar approach in which the state of the nodes is treated as a continuous variable instead of a Boolean variable, e.g., the initial state (1.0, 0.1, 1.0, 0.1, 0.1, 1.0) is used instead of (1, 0, 1, 0, 0, 1). Criteria (i) and (ii) are used to see if the state of system flows into the normal state. Criteria (iii) is abandoned, as changing of the initial state may affect the dynamic patterns of the nodes. ssDNA is set to be 1.0, leaving 32 initial states in total.


From Boolean Network Model to Continuous Model Helps in Design of Functional Circuits.

Shao B, Liu X, Zhang D, Wu J, Ouyang Q - PLoS ONE (2015)

Workflow of continuous simulation.For networks selected by Boolean network model, 1000 random parameter sets and 32 initial conditions are used to quantitatively assess their robustness. The ordinary differential equations describing these transcriptional networks are solved numerically to generate the dynamics of each network component. The proportion of parameter sets and number of initial conditions that can achieve a successful response is termed as the Q value and basin size, respectively, for the corresponding network.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4464762&req=5

pone.0128630.g002: Workflow of continuous simulation.For networks selected by Boolean network model, 1000 random parameter sets and 32 initial conditions are used to quantitatively assess their robustness. The ordinary differential equations describing these transcriptional networks are solved numerically to generate the dynamics of each network component. The proportion of parameter sets and number of initial conditions that can achieve a successful response is termed as the Q value and basin size, respectively, for the corresponding network.
Mentions: The evaluation process of circuit performance is presented in Fig 2, in which two scores that can reflect robustness of networks are employed. The first score is Q value that estimates the volume of the functional parameter space [9]. For each network, we randomly choose 1000 sets of parameters using Latin hypercube sampling. Starting from the same initial state, the network dynamics with each parameter set is obtained by solving the ODEs. Time series of all nodes are then checked to see if they present a successful response, i.e., if they meet three criteria above. For a particular network structure, the proportion of parameter sets that can achieve our desired function is defined as the Q value of that structure. A larger Q value implies that the network can generate successful response to DNA damage over a wide range of parameters and, hence, is less sensitive to parameter variation. The second score is relevant to robustness in state space. For the Boolean network model, the state of the system is updated using Eq 1 until it reaches a fixed point, which can also be called an attractor. The number of initial states that will flow into an attractor is defined as the basin size of that attractor. It is proposed that a biological state should have a large basin size in order to generate stability [17]. We held similar assumption in our design procedure that normal state with node3 activated should be a big attractor and stable against fluctuations in gene expression. In the Boolean network model, all possible initial conditions (2N for network with N nodes) are enumerated to calculate the basin size, which is not practical in continuous simulation. To sample the space of initial states in the ODE model, we employ a similar approach in which the state of the nodes is treated as a continuous variable instead of a Boolean variable, e.g., the initial state (1.0, 0.1, 1.0, 0.1, 0.1, 1.0) is used instead of (1, 0, 1, 0, 0, 1). Criteria (i) and (ii) are used to see if the state of system flows into the normal state. Criteria (iii) is abandoned, as changing of the initial state may affect the dynamic patterns of the nodes. ssDNA is set to be 1.0, leaving 32 initial states in total.

Bottom Line: In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model.Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions.Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, China; The Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China.

ABSTRACT
Computational circuit design with desired functions in a living cell is a challenging task in synthetic biology. To achieve this task, numerous methods that either focus on small scale networks or use evolutionary algorithms have been developed. Here, we propose a two-step approach to facilitate the design of functional circuits. In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model. In the second step, continuous simulation is applied to evaluate the performance of these topologies. We demonstrate the usefulness of this method by designing an example biological function: the SOS response of E. coli. Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions. Possible circuits are ranked according to their robustness against perturbations in parameter and gene expressions. The biological network is among the candidate networks, yet novel designs can be generated. Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks.

No MeSH data available.