### abstract ###
De novo computational design of synthetic gene circuits that achieve well-defined target functions is a hard task.
Existing, brute-force approaches run optimization algorithms on the structure and on the kinetic parameter values of the network.
However, more direct rational methods for automatic circuit design are lacking.
Focusing on digital synthetic gene circuits, we developed a methodology and a corresponding tool for in silico automatic design.
For a given truth table that specifies a circuit's input output relations, our algorithm generates and ranks several possible circuit schemes without the need for any optimization.
Logic behavior is reproduced by the action of regulatory factors and chemicals on the promoters and on the ribosome binding sites of biological Boolean gates.
Simulations of circuits with up to four inputs show a faithful and unequivocal truth table representation, even under parametric perturbations and stochastic noise.
A comparison with already implemented circuits, in addition, reveals the potential for simpler designs with the same function.
Therefore, we expect the method to help both in devising new circuits and in simplifying existing solutions.
### introduction ###
A central concept of Synthetic Biology CITATION is the rational design of synthetic gene circuits by means of modularized, standard parts, which are DNA traits with well-defined functions.
The field aims at adapting methods and ideas such as part composability and abstraction hierarchy from engineering to biology.
Several computational tools embracing these concepts have been developed.
Moreover, some tools permit to realize circuits in a drag and drop way as it is typical in electronics CITATION CITATION.
Nevertheless, de novo design of circuits able to reproduce a target function is not an easy task and its automation represents a major challenge in Synthetic Biology.
Previously, Fran ois and Hakim CITATION showed that small networks characterized by a desired behavior can be obtained by evolutionary optimization of a set of independent circuits.
Similar optimization-based tools like Genetdes CITATION and OptCircuit CITATION use simulated annealing and mixed integer dynamic optimization, respectively.
These approaches yielded interesting circuit designs, but they have several inherent limitations.
Computational complexity requires very simplified models that do not represent basic parts but lump functionalities of entire genes.
Similarly, brute-force optimization can only cope with rather small networks, and it requires dual optimization of circuit structure and of kinetic parameter values.
Hence, more direct, rational design methods are desired.
Here, instead of looking for a general solution to the automatic design challenge, we focus on digital circuits.
These circuits employ Boolean logic where input and output signals can take only two values: 0 and 1.
In the simplest case, a Boolean gate uses two input signals to compute a single logical output.
More complex digital circuits convert FORMULA inputs into a single output.
In both cases, the input-output relation is represented by a truth table where each entry specifies one of the possible FORMULA combinations of input signal values and the corresponding binary output.
In biology, digital circuits are important for several reasons.
First, logical gates such as those determined by the action of two different activators on a promoter are abundant in natural systems.
They are often found in association with feed-forward loop motifs and provide more complicated functionalities such as sign sensitive delays CITATION, CITATION and pulse generation CITATION.
More complex networks of several FFLs interacting with basic Boolean gates control sporulation in B. subtilis CITATION as well as the neuronal system of C. elegans CITATION.
An analysis of possible implementations of logical gates could, thus, help further our understanding of natural biological networks.
In synthetic biology, secondly, complex digital circuits are required for the construction of biosensors and molecular computers.
Biosensors should respond to well-defined external cues that may be specified with a truth table.
The more inputs can be sensed, the better is the ability of the biosensor to discriminate between similar environmental conditions.
Such biosensors could be integrated, for instance, into bioreactors for the production of biofuels CITATION.
Furthermore, they could play an important role in disease treatment Anderson et al. CITATION implemented a biosensor that mimics a logical gate to control bacterial invasion of tumor cells in response to signals from the tumor environment.
Even more complex biosensors could work as molecular computers that perform a diagnosis on the basis of the sensed substances and release drugs if necessary CITATION .
Motivated by these two aspects, several synthetic gene circuits that implement Boolean logic have been realized experimentally in the past years.
Most of these circuits rely on transcriptional control schemes.
In fact, it is well known that bacterial promoters can display logic behavior when controlled by two transcription factors CITATION CITATION.
More complex Boolean promoters have been engineered, for instance, in mammalian cells CITATION.
However, the number of repressors and activators generally used in synthetic biology is low and the rational engineering of transcription factors can be a complex process CITATION .
Alternatively, Boolean gates are achieved in nature by mechanisms of translation control like base-pairing between antisense small-RNAs and the mRNA, or structural mRNA modifications due to the binding of chemical effectors to riboswitches and ribozymes CITATION, CITATION.
These are complex RNA structures made of two modules: an aptamer, where a chemical binds, and an actuator that either undergoes structural modifications in a riboswitch or gets spliced in a ribozyme as a consequence of the chemical binding.
Both riboswitches and ribozymes can either repress or activate translation CITATION.
Furthermore, a tandem riboswitch, where a single actuator is under the control of two aptamers, has been observed in B. clausii CITATION.
With two distinct inputs, it represents a natural Boolean gate located on the mRNA.
Taking these structures as models, similar synthetic RNA constructs have been engineered recently CITATION.
In particular, Win and Smolke CITATION have built complex ribozymes that establish the most common two-input Boolean gates.
Importantly, the design of small RNAs is easy compared to the design of transcription factors.
Despite these individual successes, synthetic biology fundamentally lacks tools and concepts for automatic computational design.
Logical circuits are suitable starting points for automatic design because the target function can be defined easily by a truth table.
Here, we combine approaches from electrical circuit design with our previous model for circuit design with composable parts CITATION, CITATION to develop a method for the automatic design of digital synthetic gene circuits.
It is implemented as an add-on for the process modeling tool ProMoT CITATION, CITATION.
The circuits use a set of standard biological parts and Boolean gates whose kinetic parameters take appropriate default values without invoking any optimization algorithms.
In addition to previously developed building blocks such as two-operator-containing promoters, we consider externally controllable ribosome binding sites.
The method requires only a truth table to directly produce several possible circuit designs that process up to four different inputs to yield a unique, pre-defined output signal.
Design alternatives are ranked according to a complexity score that reflects the efforts for practical implementation.
Simulations on single gates and on networks of different complexity confirm the validity of our approach by highlighting accurate representation of the truth table and robustness of the designed circuits.
