Computational design of synthetic regulatory networks from a genetic library to characterize the designability of dynamical behaviors

Abstract

The engineering of synthetic gene networks has mostly relied on the assembly of few characterized regulatory elements using rational design principles. It is of outmost importance to analyze the scalability and limits of such a design workflow. To analyze the design capabilities of libraries of regulatory elements, we have developed the first automated design approach that combines such elements to search the genotype space associated to a given phenotypic behavior. Herein, we calculated the designability of dynamical functions obtained from circuits assembled with a given genetic library. By designing circuits working as amplitude filters, pulse counters and oscillators, we could infer new mechanisms for such behaviors. We also highlighted the hierarchical design and the optimization of the interface between devices. We dissected the functional diversity of a constrained library and we found that even such libraries can provide a rich variety of behaviors. We also found that intrinsic noise slightly reduces the designability of digital circuits, but it increases the designability of oscillators. Finally, we analyzed the robust design as a strategy to counteract the evolvability and noise in gene expression of the engineered circuits within a cellular background, obtaining mechanisms for robustness through non-linear negative feedback loops.

Figure 1.

Scheme of the design platform adopted by harnessing a library of models of composable regulatory elements. We explore the functional networks that can be engineered either by exhaustive combinatorial assembly or by heuristic optimization.

Figure 2.

Schemes of several FFL-based gene circuits optimized to operate as amplitude filters (also called band detectors). The mathematical model for each circuit is provided in SBML format in the Supplementary File sbml.zip.

Figure 3.

Schemes of two two-gene circuits designed to reach tristability, showing the corresponding phase diagrams. Filled and open circles represent stable and unstable states respectively. The mathematical model for each circuit is provided in SBML format in the Supplementary File sbml.zip.

Figure 4.

(A) Scheme of a complex regulatory system comprising a frequency-tunable oscillator and a state detector, designed by using the tristable device as an element of the library. Moreover, we show the transfer functions of the different devices that form the system. (B) Dynamics of the output genes of the complex system. Pulses in the input (I) of 20 min and 1000-fold of amplitude were applied at t = 1000 and 2000 min.

Figure 5.

(A) Graphical representation of the exhaustive design strategy. Starting from a library of composable genetic regulatory elements (mathematical models provided in SBML format in the Supplementary File sbml.zip), we constructed all possible circuits up to three genes for simulation. (B) Dynamical spectrum of the library by exhaustive exploration (functional diversity). We represent the percentage of circuits that behave as oscillators, amplitude filters, memories and logic gates (designability). To differentiate between two states of a circuit, we imposed at least one order of magnitude in concentration.

Figure 6.

Sensitivity analysis of the dynamical spectrum. We release one regulatory element of the library (in particular, one gene) to analyze its contribution to the dynamical spectrum (we represent the remaining number of functional circuits relative to the total).

Figure 7.

(A) Scheme of a genetic circuit optimized to operate as a robust amplitude filter. U and Z are the input and output, respectively. (B) Fitness function versus the robustness weight for the robust circuit shown above (red) and the same circuit optimized with (blue), illustrating the cost of robustness.