Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case

Abstract

Background: Model based design plays a fundamental role in synthetic biology. Exploiting modularity, i.e. using biological parts and interconnecting them to build new and more complex biological circuits is one of the key issues. In this context, mathematical models have been used to generate predictions of the behavior of the designed device. Designers not only want the ability to predict the circuit behavior once all its components have been determined, but also to help on the design and selection of its biological parts, i.e. to provide guidelines for the experimental implementation. This is tantamount to obtaining proper values of the model parameters, for the circuit behavior results from the interplay between model structure and parameters tuning. However, determining crisp values for parameters of the involved parts is not a realistic approach. Uncertainty is ubiquitous to biology, and the characterization of biological parts is not exempt from it. Moreover, the desired dynamical behavior for the designed circuit usually results from a trade-off among several goals to be optimized.

Results: We propose the use of a multi-objective optimization tuning framework to get a model-based set of guidelines for the selection of the kinetic parameters required to build a biological device with desired behavior. The design criteria are encoded in the formulation of the objectives and optimization problem itself. As a result, on the one hand the designer obtains qualitative regions/intervals of values of the circuit parameters giving rise to the predefined circuit behavior; on the other hand, he obtains useful information for its guidance in the implementation process. These parameters are chosen so that they can effectively be tuned at the wet-lab, i.e. they are effective biological tuning knobs. To show the proposed approach, the methodology is applied to the design of a well known biological circuit: a genetic incoherent feed-forward circuit showing adaptive behavior.

Conclusion: The proposed multi-objective optimization design framework is able to provide effective guidelines to tune biological parameters so as to achieve a desired circuit behavior. Moreover, it is easy to analyze the impact of the context on the synthetic device to be designed. That is, one can analyze how the presence of a downstream load influences the performance of the designed circuit, and take it into account.

Keywords: Biological circuits; Biological tuning knobs; Dynamic behavior; Kinetic parameters; Multi-objective optimization.

Fig. 1

Steps for the multi-objective optimization design procedure

Fig. 2

Input-output adaptive behavior. Adaptation is an important property of biological systems, related to homeostasis. After an input stimulus the output signal responds by first quickly reaching a peak value, after which it returns to its previous value even if the stimulus persists

Fig. 3

Three-node incoherent type 1 feedforward loop. a Gene gA produces the protein A, which forms a dimer with the inducer I. The dimer activates both genes gC and gB. In turn, the product of gB represses gC. b Representation of a cell incorporating an incoherent feedforward loop synthetic circuit

Fig. 4

Pareto Front comparison. Pareto Front representation for J ₁ and J ₂ obtained with the spMODE algorithm for the MOO (blue line). Monte-Carlo random sampling results are colored in red and the dominant solutions are in green. The time response of the C protein concentration for three representative points are shown

Fig. 5

Pareto front representation in the cluster-modified LD tool. a Value of the objectives J ₁ and J ₂ for each solution where each cluster is identified by a different color. Clusters range from high sensitivity-low precision (red) to low sensitivity-high precision ones (blue). b Time courses of protein C concentration for the different solution in the clusters

Fig. 6

Representation of the Pareto set. Cluster-modified LD representation for decision variables (kinetic parameters) in the High Sensitivity Strategy (cluster 1, red dots) and in the High Precision Strategy (cluster 2, blue dots)

Fig. 7

Application scenario I Pareto Front in blue line connected dots. A. Dots with reddish color are obtained when using the RBS strength of gene C as a trade-off tuning knob and represented by modifying k p _C∈ [ 5 0.05] starting at the extreme solution. Notice, that decreasing only k p _C it is possible to increase the sensitivity, almost without losing optimality (without getting away from the Pareto front). Inset shows the time course of protein C. As expected, sensitivity of the solution is increased, i.e. the peak of protein concentration after stimulus is higher. B. Dots with blueish color are obtained when using the promoter strength and plasmid copy number gene B by modifying K m _B C g B∈ [ 200 1]

Fig. 8

Application scenario II Depiction of the incorporation of information on the context. Connecting our module to a load

Fig. 9

Application scenario II Pareto front of the functional module without load (blue circles) and with load (red diamonds). Inset: temporal responses of the solutions 1, 2 and 3 with (red line) and without load (blue line)