Success in synthetic biology depends on the efficient construction of robust genetic circuitry. However, even the direct engineering of the simplest genetic elements (switches, logic gates) is a challenge and involves intense lab work. As the complexity of biological circuits grows, it becomes more complicated and less fruitful to rely on the rational design paradigm, because it demands many time-consuming trial-and-error cycles. One of the reasons is the context-dependent behavior of small assembly parts (like BioBricks), which in a complex environment often interact in an unpredictable way. Therefore, the idea of evolutionary engineering (artificial directed in vivo evolution) based on screening and selection of randomized combinatorial genetic circuit libraries became popular. In this article we build on the so-called dual selection technique. We propose a plasmid-based framework using toxin-antitoxin pairs together with the relaxase conjugative protein, enabling an efficient autonomous in vivo evolutionary selection of simple Boolean circuits in bacteria (E. coli was chosen for demonstration). Unlike previously reported protocols, both on and off selection steps can run simultaneously in various cells in the same environment without human intervention; and good circuits not only survive the selection process but are also horizontally transferred by conjugation to the neighbor cells to accelerate the convergence rate of the selection process. Our directed evolution strategy combines a new dual selection method with fluorescence-based screening to increase the robustness of the technique against mutations. As there are more orthogonal toxin-antitoxin pairs in E. coli, the approach is likely to be scalable to more complex functions. In silico experiments based on empirical data confirm the high search and selection capability of the protocol.
The technological and knowledge progress in the past fifty years has allowed us not only to observe natural evolution and to study its laws, but also to gradually control and harness it, up to the point where it is seen as a tool of genome-scale engineering . Microbes and even simpler organisms such as viruses (bacteriophages) are a natural choice for directed evolution experiments, due to their rapid life cycle, exponential growth, large populations, and easy horizontal gene transfer between host cells; see, for example,  for an overview. Why might this directed evolution paradigm be useful in genetic circuit engineering? Because genetic networks with a precise behavior are difficult to engineer in vivo. As the complexity of biological circuits grows, it becomes more complicated and less efficient to rely only on rational design. Mathematical models to guide their design contain many parameters that we understand poorly and that limit its predictive power. But biological systems have a unique and versatile design property: They can evolve and adapt to natural or artificial environments. In fact, evolution is the mechanism that has designed all natural biological hardware: Evolution is Nature's optimization algorithm . So, directed evolution (evolution in the laboratory) is a natural strategy to follow when building new biological devices , reengineering pathways [37, 17], or even assembling whole new genomes .
But directed evolution has also three main limitations : (1) the size of the genetic circuits' libraries that can be prepared is limited, (2) the rate of screening or selection is also limited, and (3) every cycle of library generation and screening and selection usually requires time-intensive human labor.
The dual selection protocol presented in this article tries to alleviate those limitations by minimizing human intervention (library search and cycles of selection are done autonomously by plasmids and bacteria) and combining screening with in vivo selection strategies to allow the fast search of big libraries of genetic circuits. The new multicellular dual selection protocol is applied to the directed evolution of a yes gate (a positively regulated promoter) and a not gate (a negatively regulated promoter), showing (from in silico experiments) a high search and selection potential and able to quickly discard from the initial library bad leaky or lazy promoters without a “digital” behavior.
The article describes in the next section basic principles of directed evolution of genetic circuits. Section 2 describes details of our selection protocol. A description of materials and methods is given in Section 3. In Section 4, we report the results of in silico experiments. A short overview of the achievements concludes the article.
2 Directed Evolution
Directed evolution (evolution in the laboratory) was started in the mid twentieth century in , using chemical mutagens as a means to introduce mutations in the bacterium Aerobacter aerogenes to study and replicate natural evolutionary processes. Work in the Spiegelman Lab  on evolving RNA molecules in vitro was also pioneering in the field. In the 1980s, phage display , using libraries of peptides fused to the coat of phages, expanded the field of directed selection to protein engineering. In the 1990s, new techniques to introduce random variations in DNA sequences, such as error-prone polymerase chain reactions  and DNA shuffling , allowed the successful directed evolution of proteins. More recently, directed evolution has been applied at the level of pathway or even genome engineering, as in multiplex automated genome engineering (MAGE) from Church's lab .
In vitro directed evolution was applied for the first time to engineer and fine-tune a genetic circuit in . In vivo directed evolution with dual selection protocols was introduced in  and is described below. Phage-assisted continuous evolution (PACE)  is also a promising new technique for in vivo selection of biomolecules.
In silico directed evolution started with  and followed with  and with work in Jaramillo's lab [25, 26]. This group has developed algorithms, based on transcriptional regulation, that search the space of artificial genetic networks to find optimal circuits with a targeted behavior as logic gates and switches. Their most recent work applies an in silico evolutionary strategy (a Monte Carlo simulated annealing optimization protocol) to evolve RNA circuits  and transcriptional regulatory networks .
Leibler's group  described a combinatorial procedure based on repressors and promoters to construct, in vivo, genetic networks that could implement logic gates such as nand, nor, or not. Based on the library of five promoters and three repressors, 125 different circuits were generated. Combinatorial signal integration at the level of transcriptional control has also been studied , showing that complex and-or and or-and genetic circuits could be programmed by just engineering the promoter region of bacterial transcription factor genes. But this rational design of Boolean genetic circuits often fails to get the desired function and usually involves a long and tedious process of debugging, based mainly on trial and error. Directed evolution  can rapidly tune these nonfunctional circuits or even engineer novel logic functions, because directed evolution is a powerful algorithmic procedure for the engineering of synthetic gene circuits with prescribed behavior.
A directed evolutionary strategy for genetic circuit engineering is an iterative process that consists basically of two steps: (1) generation of a library of variants of the circuit and (2) screening and selection for the best ones. To identify the best genetic circuit variants with the desired properties, screening and competitive selection are the two main types of protocols—see the excellent recent review :
Screening. A genetic circuit with two states (on and off) must be tested for correctness for all the different states and all the different combinations of inputs. For example, to select for a good and gate of two inputs, the genetic circuit should survive four screening steps for every pair of inputs: one positive screen (with output on when both inputs are 1) and three negative screens (with output off when one or both inputs are 0). Circuits that do not survive these four sequential screens should be discarded. In general, the screening is nothing more than a selection process that discards circuits obeying any row of the complementary truth table of the desired Boolean logic function.
Selection. Good circuits can increase the chances of survival of their hosts. Bad circuits are discarded due to dead activation of their hosts. Thus, selection of genetic circuits can be done by coupling the (correct) output with the survival of the host cells. The basic strategies rely mainly on linking a rescue gene to the operation of good circuits and a killer gene to that of bad circuits [38, 7]. On positive selections (on state), good circuits produce the rescue gene, and on negative selections (off state), only good circuits that don't express the killer gene survive. However, the use of two independent selector genes is not very robust, especially against false positives. This can be improved on by using the same selector marker (one gene) for both positive and negative selection, as in  or .
With regard to the selection strategy (which is considered also in this article), dual selection protocols have become the usual tool for exploring Boolean genetic circuits. On one hand, the authors of  use this term to couple both on and off selection states with cell survival by controlling two potentially lethal genes. On the other hand, the term dual selector in  denotes a protocol using the same gene for both on and off selection. In this article we use the term in the first sense. In on selection, only cells with output 1 (on state) survive. In off selection, only cells with output 0 (off state) survive. In the next section, we will describe details of a dual selection protocol using two pairs of toxin-antitoxin genes and a relaxase gene (a conjugative protein able to mobilize a plasmid by conjugation). Unlike the protocols reported in the above-mentioned articles, which require a change of the bacterial colony environment to switch between on and off selection rounds, our protocol is switched by the presence or absence of a special input plasmid in each single cell. Using donor cells conjugating the input plasmids leads to autonomous changes of each computing cell between off and on selection states. The input signal in donor cells is carried in conjugative plasmids that propagate through the bacterial population. There are asynchronous and parallel off-on cycles of selection running independently in each bacterium.
We now describe the selection protocol.
There exist four possible Boolean circuits with one input and one output, with different input-output mappings: yes, not, tautology, and contradiction. (See Figure 1). The goal of our directed selection protocol is to select, from a library with different circuits in different bacteria (E. coli), only those plasmids carrying a required circuit (yes or not transcriptional logic gate) in the form of a promoter that is inducible or repressible by a certain transition factor (TF). The selection is based on the interplay of two orthogonal toxin-antitoxin pairs together with a relaxase protein Rel in a population of intensively conjugating bacteria. We describe two experiments, one for the selection of yes gates, another for not gates. The two experimental protocols are similar; the only difference is in the construction of the computing plasmid. The protocol seems to be scalable to more complex circuits as well, as there are several orthogonal toxin-antitoxin pairs acting in E. coli.
For the selection process we assume an initial combinatorial library of promoters and a fixed transcription factor TF (an activator for the yes gate, and a repressor for the not gate). The main components of the experimental setup can be summarized as follows:
Goal: Select from a library of different promoters (circuits or logic gates) the best promoter PYES (or PNOT) implementing a yes (or not) gate. The dual selection protocol will remove from the library the promoters (leaky or lazy) with bad behavior; good PYES (or PNOT) promoters will survive and will be propagated by conjugation through the bacterial population.
Input of the circuit: A transcription factor TF in a self-conjugative input plasmid. Tfa: an activator used for yes-gate selection. Tfr: a repressor used for not-gate selection. These input plasmids will be spread on the bacterial population through conjugation, infecting bacteria with the different computing plasmids.
Circuit: An inducible (or repressible) promoter PYES (or PNOT) regulated by the input TF (an activator or a repressor respectively). There is a library of different promoters to be evaluated and selected. Every computing plasmid contains a variant of the logic gate to be selected, encoded as a different promoter sequence. The input of the logic gate can be 0 (if the input plasmid is not present) or 1 (if the input plasmid is present).
Output of the circuit: The activation level (on or off) of the promoter (PYES or PNOT). If the output is 0, the promoter is inactive and the genes under its control in the computing plasmid are not expressed. The output 1 means an active promoter and expression of genes in the computing plasmid. For instance, the combination (input 0, output 1) in the yes gate denotes a malfunctioning circuit with leaky promoter PYES, which is active even without the presence of Tfa. Such circuits are eliminated during the selection process; see Figures 2 and 3.
There are two plasmids that carry the different genes needed to implement the selection protocol: the input plasmid and the computing plasmid.
Input plasmid: A self-conjugative plasmid with genes for an antitoxin A1 and a toxin T2. Furthermore, every input plasmid carries the same transcription factor TF. See the input plasmids in Figures 2 and 4. The promoter of the input plasmid should be repressed in donor bacteria (bacteria initially transmitting input plasmids toward bacteria harboring computing plasmids). As an additional safety mechanism, donor bacteria could contain a2 gene activated.
Computing plasmid: A mobilizable plasmid with a variant of the promoter (the genetic circuit) we want to select for, that is, the promoter PYES or PNOT. Each different promoter of the library to be searched is encoded in a computing plasmid. A computing plasmid is transmissible by conjugation only when the relaxase gene is expressed. For a description of the computing plasmids used in the selection of yes- and not-gate circuits see Figures 2 and 4, respectively. Computing plasmids also contain a toxin gene t1 (whose corresponding neutralizing antitoxin is a1), an antitoxin gene a2 (whose associated toxin gene is t2), and a relaxase gene rel (a conjugative gene whose activation makes computing plasmid conjugative and transmissible). gfp (green fluorescent protein) and rfp (red fluorescent protein) are genes used to screen and debug the selection process. The lambda phage cI/Pλ repressor-promoter pair is also present in the computing plasmid used for selecting not-gate circuits (inverter promoters).
Our simulations are based on experimental parameters of two pairs of toxin-antitoxin genes, t1-a1 and t2-a2: the well-known toxin-antitoxin pairs ccdB-ccdA and hok-sok . Additional information on the toxin-antitoxin pairs is given in Section 3.
Setup: A bacterial population with some bacteria harboring computing plasmid, the rest of the bacteria uninfected. After a few hours of cultivation and selection without input plasmid (input 0), bacteria with input plasmid carrying the transcription factor TF are added to the population to start the selection with input 1. After the addition of input plasmids, both selections happen in parallel: Some bacteria are selecting circuits with input 0, and others with input 1.
Selection: At each moment every single bacterium carrying a computing plasmid is executing a different selection step (positive or negative), depending on whether the input plasmid is inside the same bacterial host (input 1) or not (input 0). Only good circuits in the computing plasmid (yes or not gates, respectively) will survive these different selection steps and will be transmitted by conjugation to the neighboring bacteria, increasing gradually its relative frequency in the bacterial population. Bacteria carrying computing plasmids with malfunctioning circuits will be killed by a toxin.
Autonomous continuous selection: Good circuits that survive a selection and are transmitted by conjugation to new bacteria are again subject to new selection processes with input 1 or 0 (depending on whether recipient bacteria harbor the input plasmid or not). These on-off selections run in parallel, autonomously and asynchronously, in different cells, depending on whether an input plasmid is present or not. This is in contrast with classical on-off rounds of dual selection protocols that must be executed sequentially, iterated, and manually controlled by the bioengineer. At the end of the selection process, good circuits will be present at higher frequency than bad ones in the bacterial population.
Detection: Our protocol combines dual genetic selection with fluorescence-based screening. Muranaka et al.  also use a gfp gene fused to a dual selection marker gene tetA. By adding the gfp and rfp reporter genes to the computing plasmid, flow cytometry allows us to finally separate bacteria containing computing plasmids that pass the selection process. Using fluorescence-activated cell sorting (FACS), we can separate cells expressing gfp and/or rfp. In that way, we can select and screen bacteria with required yes (or not) gate circuits and reduce the potential errors (false positives) due to mutations in the toxin genes. See the details of the screening process and how it allows increasing the robustness of the selection protocol in Section 2.3.
2.1 Dual Selection Protocol—yes Gate
The plasmids used for the selection of a promoter PYES implementing a yes gate are shown in Figure 2. In this experiment we want to select computing plasmids encoding yes gates, while the plasmids encoding not, taut, or cont gates should be eliminated from the population. There are four different input-output combinations, as shown in Figure 3:
OFF selection. When the input is 0, only bacteria with output 0 (off state) should be selected and survive. Two cases:
0-0 column: Input plasmid is not present; then neither the antitoxin A1 nor the toxin T2 is produced. The promoter PYES in the computing plasmid is inactive; then neither the toxin T1 nor the antitoxin A2 is produced. Relaxase is not produced; the computing plasmid is not conjugated. Bacteria survive; computing plasmid is spread by vertical transfer only.
0-1 column: Input plasmid is not present; neither the antitoxin A1 nor the toxin T2 is produced. The promoter PYES in the computing plasmid is active; both T1 and A2 are produced. The relaxase is produced, too, but the bacteria are killed by T1 before it can significantly conjugate the computing plasmid.
ON selection: When the input is 1, only bacteria with output 1 (on state) should be selected and survive. Two cases:
1-0 column: Input plasmid is present; both A1 and T2 are produced. The promoter PYES in the computing plasmid is inactive; neither T1 nor A2 is produced. Also, relaxase is not produced; the computing plasmid is not conjugated. Bacteria are eventually killed by T2 (A2 is not produced).
1-1 column: Input plasmid is present; both A1 and T2 are produced. The promoter in the computing plasmid is active; both T1 and A2 are produced. Both toxins are neutralized by antitoxins. The relaxase is produced, too, and the computing plasmid is intensively conjugated.
2.2 Dual Selection Protocol—not Gate
The plasmids used for the selection of a promoter PNOT implementing a not gate are shown in Figure 4.
This experiment differs from the previous one only by the presence of an intermediate repressor (CI protein) and the associated repressible promoter Pλ in the computing plasmid. We want to select computing plasmids encoding not gates, while the plasmids encoding yes, taut, or cont gates should be eliminated from the population. The possible input-output combinations are as follows (see Figure 5):
ON selection: When the input is 0, only bacteria with output 1 (on state) should be selected and survive. Two cases:
0-0 column: Input plasmid is not present; neither A1 nor T2 is produced. The promoter PNOT in the computing plasmid is inactive; CI is not produced. The production of A2 and T1 is not repressed. Also, relaxase is produced; the computing plasmid can be conjugated, but the bacteria are quickly killed by T1.
0-1 column: Input plasmid is not present; neither A1 nor T2 is produced. The promoter PNOT in the computing plasmid is active, CI is produced. The production of both T1 and A2 is blocked. Relaxase is not produced; computing plasmid is not conjugated. Bacteria survive; computing plasmid is spread by vertical transfer only.
OFF selection: When the input is 1, only bacteria with output 0 (off state) should be selected and survive. Two cases:
1-0 column: Input plasmid is present; both A1 and T2 are produced. The promoter PNOT in the computing plasmid is inactive; CI is not produced. The production of A2 and T1 is not repressed. All the toxins are blocked by the antitoxins. The relaxase is produced, too, and the computing plasmid is conjugated.
1-1 column: Input plasmid is present; both A1 and T2 are produced. The promoter PNOT in the computing plasmid is active; CI is produced. The production of both A2 and T1 is blocked. Relaxase is not produced; the computing plasmid is not conjugated. Bacteria are eventually killed by T2.
2.3 The Effect of Mutations and the Screening Process
As confirmed by many authors, false positives are observed with almost all genetic selection and screening methods, due to mutations in selection circuits . Up to 0.1% of the total transformed cells are usually reported to be false positives, the exact amount depending on experimental methods. Specifically, in the case of dual selection, several mutations of the selection circuit produce false negatives, which are self-eliminating (the bacteria with mutated plasmid are killed by a toxin or the plasmid is unable to spread in the population), but any mutation disabling the function of the killer gene results in false positives . Due to the use of two orthogonal toxin-antitoxin pairs and the final screening step, our selection circuit is more robust with respect to possible mutations than some others reported previously . We analyze the effect of mutations in various parts of the selection circuit for the yes gate:
Mutations in the antitoxin genes lead to death of the cell in various phases of the selection process whenever the corresponding toxin is produced. For example, when the a1 gene is mutated, then whenever the output is 1 (the promoter PYES in the computing plasmid is activated by the transcription factor TF), T1 is produced and the bacterium dies. The same happens if gene a2 is mutated and T2 is produced: The bacterium dies. These are cases of false negatives that can reduce the convergence rate of the selection process.
Mutations disabling the TF gene (the activator tfa) turn the whole circuit into the cont variant, as the output is always zero. These circuits are eliminated as described in Section 2.1.
Mutations in the rel gene prevent conjugation of the mutated plasmid, so that it does not spread in the population.
Mutations in toxin genes may disable the lethal effect of the toxin and produce false positives. In the case of mutated t2 gene, circuits with input = 1 and output = 0 will survive. In the case of mutations in the t1 gene, circuits with input = 0 and output = 1 survive.
As reported in , in such a case it is suggested to plate out cells on Petri dishes (instead of liquid media) during selections, to prevent the false positives from rapidly outgrowing the rare positive library members. In our experiments, we already use Petri dishes and bacteria on agar.
Moreover, we use fluorescence-based screening to detect false positives. For example, in the selection of a yes gate we can avoid false positives (e.g., circuits with input = 0 and output = 1) by selecting non-glowing bacteria from the off selection (if we see green light during the off selection, that means toxin T1 is not killing actively bad circuits), and selecting green-lighting bacteria from the on selection (in that way, we avoid selecting false positive circuits with input = 1 and output = 0 due to mutations in toxin T2). So, the screening process is an extra step that increases the robustness of our protocol against potential mutations in killer genes.
Also, the probability of mutation in the ccdB gene (our chosen T1 gene) suppressing its lethal activity is rather low, as the mutation rate of E. coli is about 10−2 per organism per division. The length of the ccdB gene is only about 300 bp, and furthermore its toxic effects are located in the region coding for the last three C-terminal residues .
In the case of not-gate selection, the results of mutations are analogous. Furthermore, there is a possibility of mutation in the cI gene leading to false negatives. This mutation would eventually produce an inactive variant of CI, resulting in the production of the toxin T1 and relaxase. The bacteria will be killed by T1 during the on selection phase when the input plasmid with the gene producing antitoxin A1 is not present.
The fluorescence screening of a not-gate selection also allows the detection of false positives and potential mutations in toxin genes. Cells that should be selected in the screening process are: green cells in the off selection (when the input is 1 and the output must be 0) and red cells in the on selection (when the input is 0 and the correct output is 1).
3 Materials and Methods
E. coli is one of the most popular microorganisms used in both in vivo and in vitro evolutionary experiments. An extensive database of its gene function and regulation is available, its genome is well annotated, and there is a broad experience with its manipulation. We chose E. coli due to its largely documented functions, but our evolution framework does not rely on its specific properties. The experimental data underlying bacterial conjugation dynamics in E. coli were obtained from . A conjugative plasmid pSU2007 (a derivative of the plasmid R388) and a mobilizable plasmid based on the RP4 plasmid from Fernando de la Cruz's Lab served as models for the input and the computing plasmid, respectively, and their specific parameters reported in the literature were used in simulations. They are reported to be low-copy-number plasmids , and their copy number was set to 5 in the experiments. However, the copy number proved to be almost irrelevant to the experimental results.
Conjugation dynamics, dependence on nutrient concentration (Monod forms), and endpoint conjugation rates were set according to . The simulation, however, does not follow the continuous Monod forms, but their discrete approximation. Among important parameters we mention the growth rate ψ under high nutrient concentration (h−1), which was set to (43 min−1) (1.40 h−1) for donor and recipient bacteria, and (46 min−1) (1.30 h−1) for transconjugant bacteria (private communication from Fernando de la Cruz's lab). The transconjugants were not sterile, that is, were able to conjugate further the plasmids they received. The conjugation rate was tested for several values in the interval from 0.5 to 2 conjugative events per donor cell cycle. The selection speed (the progress in the ratio of correct and incorrect circuits) was found to depend positively on the conjugation rate. The selection principle itself, however, proved robust against conjugation rate change. The experimental results in Section 4 assume the rate of 1.25 transmitted plasmids per reproduction cycle.
Two orthogonal toxin-antitoxin pairs were used in the simulations. The first was Hok/Sok, a type I toxin-antitoxin system that relies on the base-pairing of complementary antitoxin RNA with the toxin's mRNA. The half-life of Hok is 20 min, while the half-life of Sok is about 0.5 min . The second pair was CcdB/CcdA, which is a type II toxin-antitoxin system, with direct interaction between protein toxin and antitoxin. The half-life of CcdB is around 1 h; the half-life of CcdA is around 30 min .
The toxin killing rate generally depends on the expression platform (plasmid + promoter), and there are not many exact data available. For instance,  uses CcdB in his predator-prey model in E. coli and reports the cell death rate is about 1 h−1 and the cell growth rate around 0.7 h−1, which corresponds to a killing/growth ratio of 1.4. Similar results are reported in . For our experiments that ratio is important. The results in Section 4 are based on equal killing and growth rates. The selection was highly efficient when the killing rate of toxins was similar to or higher than the growth rate. The selection process still worked with the ratio 1/3, but the quality of the selection (the ratio of correct to incorrect gates) was lower by an order of magnitude.
3.1 The Simulator Engine
The in silico experiments were carried out with the use of the bacterial simulator Bactosim II with the emphasis on conjugation in spatially structured microbial populations. Basic simulated entities are bacteria and plasmids. Bactosim II keeps track of every single entity, which puts it in the field of individual-based modeling (IBM). We have chosen the IBM approach to be able to observe emergent properties of a colony (such as the plasmid spread rate) based on simple description of individuals' behavior. The maximum size of the simulation grid is 1000 × 1000 × 100 bacterium sites, corresponding to a 3D distribution of bacteria in a Petri dish. However, the third dimension was not used in the experiments described here, as the initial tests showed that its influence is minimal. Hence, all the experiments were carried out only in 2D, using the 1000 × 1000 × 1 grid.
The basic discrete entities in the simulator are bacteria and plasmids. The most important numerical parameters of bacteria include the growth rate, and the amount of nutrient needed to produce a new cell. If there is no space at the grid, the dividing bacterium pushes its neighbors out to a certain distance to make space for the new cell. Concerning plasmids, several independent types can coexist. Each plasmid can be mobile (true or false), and transconjugants can be sterile (true or false). Numerical parameters of a plasmid include the conjugation rate, loss rate, metabolic burden, and copy number. The initial setup and validation of these conjugation parameters was performed with the data from  (with other plasmids than those used here).
Bactosim II uses a parallel selection mechanism for the interaction rules between agents. All bacteria are selected at once, and rules are evaluated in parallel. Instead of changing the environment instantly, bacterial events are stored in an event buffer. Before the environment is changed, the event buffer must be scanned for conflicting actions. Conflicts such as two bacteria that want to move to the same location must be resolved. This selection mechanism seems to be closer to reality than the sequential selection mechanism used in  or the random selection mechanism in . All the processes, such as bacterial growth, conjugation events, nutrient uptake, movement of bacteria due to their growth and division, toxin and antitoxin effects, and protein production, are simulated in discrete time steps. One step of the simulation corresponds to 4 min of real time, and it includes the integrated effect of all these types of processes.
The nutrient consumption effects limit the time scale of experiments on the dish. The solution is to remove bacteria from the dish, mix them up, take a small sample, and replate it to a new dish with fresh nutrients. This method is implemented in Bactosim II to keep the conjugation rate high and also to switch between the on and off selection phases.
4 In Silico Experimental Results
In this section we provide results of two experiments, selecting the not gate. This setup is a bit more complex than for the yes gate, because an intermediate regulation via cI repressor and lambda promoter is used. Therefore, the selection of yes gates is more robust and provides similar or better results than the selection of not gates (data for yes not shown). All the charts displaying experimental data in this section were obtained as an average of five experiments.
4.1 Experiment 1—Obtaining a Pure Culture with not Gates
The first experiment started with equal amounts of each possible type of logic gates encoded in the computing plasmid: yes, not, taut, and cont (1000 bacteria of each type). The purpose of the experiment was to check the minimum time the selection process needs to eliminate from the population almost all plasmids encoding an incorrect logic gate. The selection consisted of two phases that can be run in parallel but that we describe separately for clarity. This involved a manual replating of the bacteria (allowing also for a longer selection time until the nutrient was spent). Actually, however, both phases ran in parallel on the dish: The bacteria without the input plasmid were in phase 1, while those that have already got the input plasmid by conjugation were in phase 2.
In the first phase only computing plasmids were present (then the input for all cells was 0), resulting in the on selection: Only cells with output 1 should survive. The bacteria containing plasmids with yes and cont circuits were eliminated thanks to the toxin T1, since the antitoxin A1 was not produced by these two types of gates (also, the production of relaxase Rel was repressed). The plasmids with the other two types of gates (not and taut) were spread during this phase. The cultivation was ended after 4 h, the content of the dish was mixed, and about 10% of the bacteria were conserved. Charts showing concentrations (numbers) of the four types of plasmids in the population in the first 4 h are shown in Figure 6.
In the second phase, donor bacteria with Input plasmid were mixed with the sample of bacteria with computing plasmid from the first phase in 1 : 1 ratio, and the mixture was replated on a fresh dish. After an initial period, the conjugation started and the off selection applied to the bacteria with input and computing plasmids. The taut gates were subsequently eliminated by the toxin T2. After 8 h of cultivation the dish contained more than 99.99% bacteria with the required not circuit. The results are displayed in Figure 7.
4.2 Experiment 2—the Minimum Selectable Concentration
The second in silico experiment was designed to find the minimum concentration of the not gates in the population that is still detectable by the selection process. As the first selection phase in the previous experiment worked efficiently, eliminating practically all yes and cont circuits, we focused on the second phase. A sequence of experiments with decreasing initial ratio of not : taut gates was run, until the not gates were not able to grow stably and outperform the amount of taut in the population. The limiting concentration was found at about 1 : 400; experiments with 1 : 500 concentration did not guarantee convergent growth of the not gates. Results of experiments with initial 1 : 400 ratio are shown in Figure 8. The charts show that the concentrations of the not and taut gates were equal after 6.5 h of cultivation, corresponding to a 400-fold enrichment factor. After 13 more hours the ratio not : taut was about 2000 : 90, corresponding to an 8900-fold enrichment factor.
The genetic search and selection capability of populations of E. coli containing engineered bio-circuits was investigated, using plasmids as mobile genetic elements. The best Boolean circuits (yes and not gates) were autonomously selected from a library of different promoter sequences. Our new dual selection protocol allows the combination of on and off selection simultaneously in the same population, without the necessity of manual change of external conditions.
As a novelty, our protocol uses conjugation to distribute the input plasmids towards the bacteria with the computing plasmids (those containing the variants of the genetic circuit to be selected). The selection method (apart from killing bacteria harboring bad circuits with toxins and allowing bacteria with good circuits to survive) uses a new and additional amplification step of the good circuits: Only plasmids encoding good circuits are horizontally transferred by conjugation. This mechanism allows increasing the convergence rate and the relative frequency of good circuits in the bacterial population. Another advantage of our protocol is that it does not require a change of cultivation environment to switch between on and off selection states; both of them can act simultaneously in different cells, depending on the presence of a specific input plasmid.
To verify the strength of this theoretically designed protocol, we developed an in silico bacterial conjugation simulator BactoSIM II based on the individual-based model (IBM) of bacteria. The simulator is discrete in space and time, keeping track of individual entities such as plasmids and bacteria, while other variables such as protein expression levels and concentrations of toxin and antitoxin, are expressed by numbers. Parameters of the simulator were previously tuned and verified against published experimental results from several experimental articles such as  and additional experimental data personally communicated by Fernando de la Cruz.
Two in silico experiments focusing on artificial selection of yes and not gates were conducted and described in the previous section. The first experiment started from a population of bacteria with equally mixed four possible types of one-to-one gates implemented in a specific plasmid. The desired not circuit was cultivated under selection pressure so that after several hours it formed more than 99.99% of the plasmid population. The second experiment studied the search capability of the selection protocol. The desired circuit was initially contained in the population in 1 : 400 ratio. After 20 h of selection it formed again the vast majority of the plasmid population, corresponding to a 8900-fold enrichment factor.
The achieved results are compatible with those reported in the review article . Furthermore, a possible influence of mutations during the selection process and the use of fluorescence-based screening as a debugging final step were discussed in Section 2.3. Our protocol is likely to be scalable to more complex logic gates and bio-circuits, as several orthogonal toxin-antitoxin pairs are known to exist in E. coli and similar families of bacteria. However, their number is unclear yet; the review article  cites different opinions and results about possible crosstalk between various toxin-antitoxin pairs. Future work will include wet lab implementation of the dual selection of a yes and a not gate and the application of the selection protocol described here to the evolution of more complex genetic two-input logic gates.
This work was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), by the FP7–ICT-FET EU research project 610730 (EVOPROG), the FP7–ICT-FET EU research project 612146 (PLASWIRES), by the Silesian University in Opava under the Student Funding Scheme, project SGS/6/2014, and by Spanish project TIN2012-36992.
Research Institute of the IT4 Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic.
Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, Boadilla del Monte, 28660 Madrid, Spain. E-mail: firstname.lastname@example.org (A.R.-P.)