Abstract
The multicellular incoherent feedforward loop (mIFFL) is an extension of the traditional intracellular IFFL gene motif where the interacting nodes no longer need to be genes inside the same cell but can be spatially distributed in different cells. We studied for the first time the spatial computing abilities of these mIFFL through in silico simulations done with individual-based models (run in Morpheus and GRO software). We observed that: 1) a genetic circuit working as a mIFFL can behaves as an edge detector of the border of an infection, and 2) a mIFFL can be the inner mechanism generating the complex 7 stripe pattern of eve in D. melanogaster embryogenesis. So, in this work, we show that multicellular IFFL architectures can produce spatial patterns and are a promising spatial computing motif that deserves to be incorporated into the toolbox of pattern generation and multicellular coordination mechanisms. This study opens several future lines of research: multi-agent IFFL applied in ecology as a tool to predict spatial position of interacting animals or in distributed robotics.
INTRODUCTION
Patterning in Systems and Synthetic Biology
Patterning is a common area of study in Synthetic and Systems biology. At its most basic level, patterning can be defined as the process that leads to the features of an organism being arranged into a structured and ordered configuration. Such patterns can be spatial, temporal or both and may arise from many diverse underlying mechanisms [Kondo, 2011], such as the implementation of biological circuits based on recurrent architectures, better known as motifs [Alon, 2007; Schaerli, 2014]. These motifs exhibit well-known interactions that drive the dynamical behavior of the circuit. A combination of motifs with morphogen gradients has been used for spatiotemporal pattern formation [Basu, 2005; Tabor, 2009].
As the research trend has recently changed into multicellular environments [Amos, 2014; Kolar, 2015; Solé, 2016], in this work, we propose adaptions of network motives for their implementation in multicellular configurations. The use of spatially distributed motives [Macía, 2016] reduces the metabolic burden of the carrier and ease the implementation of the circuit, since each cell only runs a specific part of the circuit. Besides, the disposition of the different elements along the circuit, interconnected by diverse communication systems, will lead to a richer spectrum of patterns.
Incoherent Feedforward Loops
The feedforward loops (FFL) are a type of motif where a factor, Z, is regulated under two different paths. On the one hand, there is a direct regulation from X to Z that defines the X-Z pathway. On the other hand, there is an indirect pathway (X-Y-Z) where a factor X regulates Z through a third element, Y. Whenever these two regulation paths are consistent, meaning that both activate or repress, then the FFL is coherent, when opposite, it is incoherent.
Depending on the combination of interactions, there is a classification of types of FFL architectures [Alon, 2007], represented in Fig. 1A. Additionally, feedforward motifs exhibit a dynamical behavior highly dependent on the architecture, on the strength of the interactions and on the time response of each component [Mangan, 2003]. They are widely present in nature in many biological regulatory networks. A good example of how a network, with an asymmetrical response as mentioned before, can become a reliable regulator is the Gal-system in E. coli, explained as a feedforward regulatory network in [Kaplan, 2008].
In this study, we will focus on the incoherent feedforward loops (IFFLs). It has been shown how these kind of incoherent networks form nonlinear behaviors like temporal pulses [Hart, 2013; Schaerli, 2014] and low/high pass filters [Sohka, 2009].
In some configurations of a traditional FFL, the components X, Y, Z are intracellular and interactions between them produce a temporal pulse of Z expression (Schaerli, 2014). The hypothesis of our work is that by using some intercellular interactions instead of their intracellular counterparts (bacterial conjugation or diffusible signals, for instance), then, the expected output will be a stripe-shaped spatial pattern. In the intracellular version of the circuit, different response times for each of the two regulatory paths are required for the stripe to appear. In the multicellular IFFL, this condition translates into intercellular interactions of different ranges. Further details about this novel design are addressed in Fig 1b.
In this work we have chosen an in silico approach, so the methods are the simulation software used, specifically, two individual based models (IBM). An IBM is a class of computational model that explicitly simulate the actions and interactions of autonomous agents. The IBMs have been used in many fields, like ecology. However, its use in Systems and Synthetic biology has begun recently. The IBMs are often composed of numerous agents, which represent each of the individuals. In our case, those agents are the cells of a synthetic bacterial colony and of a Drosophila embryo. The IBM is also composed of a decision-making heuristic, which characterizes the response of each individual of the system. For our model these decision rules will be, for instance, the probability of conjugation to a neighbor, in the case of E. coli, or the level of production of a certain morphogen by the cell, in response to certain concentrations of other morphogen, in the case of D. melanogaster.
We used the gro IBM [Jang, 2012; Gutierrez, 2017] for the simulation and evaluation of the E. coli synthetic circuit presented in this work. In gro, each cell contains proteins and plasmids. The plasmids determine which proteins are produced and those proteins, depending on its presence or absence, determine the behavior of the cell, including intercellular interactions. The behavior of the population then emerges from these interactions. Additionally, each agent can execute actions under certain conditions. An example of these actions is the light emission of the agent by a fluorescent protein expression, cell death, bacterial conjugation or environmental signal emission and absorption. This system can simulate a large amount of cells (in the order of 105 bacteria) in less than 10 minutes. As gro also implements several forms of intercellular communication, it is ideal for prototyping and testing multicellular IFFL circuits on a large scale. We will focus mainly on two intercellular communication actions: conjugation and diffusible molecular signals.
The triggering of conjugation in gro is based on a frequency rate, where each cell carrying a conjugative plasmid is checked for the appropriate protein condition. If this condition is met, then, based on the conjugation rate, a probability is calculated for transferring the plasmid. Also, a recipient neighbor is chosen randomly. Conjugation is used as a programmable local communication mechanism and is a key participant in the designs presented in this paper.
On the other hand, the simulation of diffusible signals is based on bacterial quorum sensing. Sender bacteria emit a molecule to the environment and receiver bacteria are able to detect and absorb it. This way, one bacterium can change the genetic state of a far neighbor.
Morpheus
Morpheus is the IBM selected for the in silico approach of Drosophila melanogaster embryogenesis. Morpheus is a modeling and simulation environment for the study of multiscale and multicellular systems developed at the University of Dresden [Starruss, 2014].
Morpheus allows defining models with different groups of cells and designing genetic networks that link them. Our model includes relations between different morphogenes and the activities of them within each cell. This is a suitable IBM because it allows for both intercellular and intracellular modeling. Another characteristic of Morpheus is that it is capable to solve partial differential equations, so it is able to estimate the concentrations of morphogenes at each point of the embryo. This capability is essential because the activations/inhibitions of the genes are driven by these concentrations.
Finally, both simulators have a graphical interface that allows the visualization of the results in a simple and comprehensible way by representing each cell individually.
RESULTS
In this section we explain the mechanisms driving the proposed genetic circuits in this work and we show the results from the simulations. In the first place, we present a bacterial edge detection system, with the simulator gro. In the second place, we reproduce the stripped pattern of eve gene in D.melanogaster with the Morpheus simulator.
A synthetic edge detection system
We present an edge detection circuit able to remark the border of an infective self-conjugative plasmid (Px) spreading area. The edge (i.e. the spatial pattern) arises from the interaction of this input plasmid with a conditionally mobilizable sensor plasmid, henceforth called infection and sentinel plasmids, respectively. By adding bacteria carrying a sentinel plasmid (Ps) to a colony where the infective plasmid proliferating radially outwards from a spot source, then the expected behavior of the system is to dynamically report the outer border of the area where bacteria with the infective plasmid are located.
In this document, the modularization of IFFL gene regulatory networks into different plasmids distributed along the colony is proposed for the dynamical generation of patterns. It is in this spirit that conditional conjugation is presented as a control mechanism over the horizontal spread of plasmids. Conditional conjugation is the process by which the transcription of the conjugative machinery of a plasmid is regulated. In this case, the plasmid will only be conjugative when the inducer/repressor of its expression is present/absent. In Fig.S1, we show a simple circuit where the conjugation of a plasmid is regulated by the presence of an autoinducer (AHL). In the presented edge detection system, the conjugation of Px into a cell carrying Ps induces its mobilization. Thus, conditional conjugation is crucial for our goal to be achieved, because we do not want the conjugation of Ps to occur randomly, but to be selectively guided within the colony.
Along with the conditional conjugation outcome, plasmids may also initiate intercellular communication actions with other parts of the distributed circuit through the emission of diffusible molecules. Small molecules and horizontal gene transfer are thus the two mechanisms used in the presented circuits for communication between different plasmids and forming the distributed motifs. The difference between both mechanisms makes the combination stronger, because plasmids spread by local contact between bacteria. Nevertheless, diffusible signals exhibit a higher diffusive rate and the capability of accumulation in case of excess of emitters [Ortiz, 2012; Goñi-Moreno, 2013].
In our edge detector, there is an initial colony with cells both empty and carrying the infective plasmid and. The sentinel plasmids (able to sense and report the infection) are inserted in new bacteria added to the colony. The reporting consists of the expression of the luminescence protein GFP. Initially, there is an intrinsic repression of this protein in the cell by means of an extra non-conjugative plasmid ps0. Otherwise, sentinels would report the edge everywhere. Here is where the previously explained concept of conditional conjugation becomes crucial.
When Px is spreading and arrives to a sentinel cell, then the conjugative machinery of Ps switches to an active state. After, the conjugation of Ps to a plasmid-free cell enables gfp to be expressed since there is no intrinsic repression of the gene. Whenever Px arrives to this same cell, it represses the gfp expression again, since this bacterium is no longer located in the outer border but instead belongs to the infected region. This happens due to the underlying incoherent regulation of gfp by Px. The indirect side of the motif induces its expression by mobilizing Ps, but then when Px reaches this point by conjugation, it represses the promoter regulating gfp. A visual explanation of the logic can be consulted in Fig2.
In summary, there are two spatially-separated pathways for the regulation of gfp: either Ps senses the proximity of the infection and it can conjugate and express gfp, or the infection finally arrives to a reporter cell and represses it. Therefore, the system can be considered a distributed multicellular type-3 IFFL that dynamically generates a spatial pattern consisting of the perimeter of the spreading area of Px (see figure Fig. 3B).
In our simulations, we found some issues in the design. These issues are independent of the plasmids logic, but momentous for the performance. One of them is the requirement for Ps to conjugate faster than Px. This is necessary for the spatial stripe to be generated because he indirect pathway of the mIFFL must be the fastest. As we want to determine the outer border of a region, it is necessary that the activator of the reporter arrives before the inhibitor.
The strategies to overcome it are based on the current knowledge about the origin of transfer (oriT) of plasmids [Del Campo, 2012]. By using a RP4-based plasmids as sensors and a R388 class as infection plasmids, we will get a noticeable difference in conjugation rates, since RP4 has a higher frequency of conjugation. This can be improved by including both the oriT of RP4 and the R388 one into the sequence of the sentinels. In case of coinfection, there will be a competition for the same conjugative machinery and it will reduce the velocity of spreading of Px.
Another critical issue is the use of quorum sensing as an intercellular channel. The version of this circuit that relies only on conjugation for communication showed poor results. Hence, an extra intercellular mechanism was included for Ps to notice when Px is nearby. In this case, the mobilization of the plasmid is regulated by a dual promoter, inducible by both an intracellular element of Px and a quorum sensing signal emitted by far infected cells. The infective plasmid is supposed to emit an autoinducer that allows Ps to sense its closeness in advance. This new feature leads the system to a much better performance.
Both features together with the initial logic of plasmids make the edge detection system very efficient. The SBOL diagram of the plasmids used in the high-performance edge detector are introduced in Fig. 3A
The final issue we identified is related to the distribution of sensing and empty bacteria used to detect the edge. Since the reporting module needs to be hosted by initially empty bacteria, if the amount of sentinels surrounding the infection is large, then the conjugation of the plasmid will be blocked due to the entry exclusion mechanism [Smillie, 2010], leaving no possibility for reporting. Further details of the importance of these phenomena are shown in SI2 and a sensitivity analysis about the ratios between the different types of plasmids and the effect on the pattern obtained can be found in SI2.
The edge detector simulation shown in Fig2c results from the inclusion of the totality of features enumerated above and the use of optimal parameters. As it can be seen, the final outcome is definitely successful in relation to the expected pattern.
Another interesting variant of the edge detection system has also been tested. It is based on an infection plasmid that can be arrested by the sensor in case of coinfection. In this case, the multicellular IFFL incorporates an extra inhibition path, so it can be considered as an even more extended version of the concept of mIFFL (more info at Fig. SI3).
In order to prove the versatility, scalability and robustness of the mIFFL as a pattern generator in bacterial colonies we tested two extra circuits, which are considerably different in behavior to the edge detector. At first, we present a spatial XOR system, different from previous designs that only focused on computation [Tamsir, 2011; Ji, 2013; Goñi, 2013]. This is an extended design of the edge detector (using two self-conjugative plasmids as input signals) able to detect the different regions of the space where these inputs are present: the 1-1 (both inputs present), the 1-0 or 0-1 (only one of them is present) and 0-0 (both are absent). The initial setup consists of two spot sources of the plasmids, that grow radially outwards. A more complex sentinel plasmid is added and the expected behavior is to report the edges of the regions mentioned above. Further details of the system and the results of a simulation are shown in Fig. SI4a.
Finally, we designed a band detection system able to report the area between two thresholds of an external inducer (IPTG). The pattern that arises is a centered ring that reports the area between two thresholds of IPTG concentration. If the concentration profile of IPTG remains constant, the shape of the ring will be constant. Nevertheless, the system can become dynamic if the IPTG concentration changes in time, thus changing the shape of the ring. As a big difference from the previous design of [Basu, 2005], in this case there two different type of plasmids with a part of the circuit. Cells are able to communicate with each other, runs the same circuit, thus reducing their metabolic burden. A detailed explanation of the plasmids and the results from a simulation are shown in Fig. SI4b.
In conclusion, the synthetic genetic circuits introduced in this paper show how the mIFFL is a versatile mechanism for the generation of functional multicellular biocircuits. We introduced an edge detection system, we extended it to two different inputs and finally we designed a spatially distributed version of a band detector. These circuits can also be seen as pattern generators in bacterial colonies as they form ordered structures over space. By adding new features to improve the results of the first version we obtained better performance in function and higher quality in the spatial arrangement.
7-stripe Eve pattern formation during Drosophila melanogaster embryogenesis
The embryogenesis of the fruit fly (Drosophila melanogaster) consists of the group of processes that control the transformation of a single cell into a mature individual of Drosophila melanogaster. During the early stages of embryogenesis two axes are defined, the dorso-ventral and the anterior-posterior [Kimelman, 2011]. For the definition of these axes, it is essential the action of the morphogenes, mobile molecules whose non-uniform distribution drives the formation of differentiated structures.
These genes are sequentially expressed and drive the embryo to the differentiation of three regions (head, thorax and abdomen) [Gilbert, 2001]. The effects of the morphogenes in the formation of the dorsoventral axis has been previously studied [Hart, 2013]. Besides, they induce the segmentation of these zones.
One of the genes involved in this process is even-skipped (eve). Eve belongs to a gene group called pair-rule genes and plays a crucial role in the formation of the 14 segments of D. melanogaster. However, for the expression of this gene, it is necessary the presence of other groups of genes such as the maternal-effect genes and the gap genes. Both groups are expressed before the pair-rule genes.
The maternal-effect genes have a non-homogeneous distribution prior to the formation of the embryo [Macdonald, 1996]. This non-homogeneous distribution has its origins in the oocyte and it is caused by the differential affinity of the maternal-effect genes over the microtubules of the oocyte [Cha, 2001]. The most relevant representative of this group is bicoid (bcd). These morphogenes do not only have a direct effect over the pair-rule genes (including eve), usually acting as transcriptional activators, but also regulate the expression of the gap genes [Driever, 1990].
The expression of the gap genes marks the beginning of the embryo segmentation process, which starts during the cell cycle number 13. The interactions between these genes are quite complex and some are not clear yet. Nevertheless, the most relevant interactions are well understood [Jaeger, 2011]. The outcome of this network is the formation of a characteristic pattern of expression for every morphogen [Struhl, 1992] that will be the basis for the next group of genes to begin their expression, the pair-rule genes.
There also exists another group of genes that regulates the expression of the gap and pair-rule genes, the terminal genes. This group is only expressed in the anterior and posterior ends of the embryo. The terminal genes play a major role in the formation of structures such as the head or the tail and they normally repress other genes in these zones [Janssens, 2013]. The most relevant gene of this group is tailless (tll) that is expressed both in the anterior and posterior ends.
The pair-rule genes begin to express once the patterns of the gap genes are stablished towards the end of the cell cycle 13. There is a total of 8 pair-rule gene [Schroeder, 2011] and they give rise to very characteristic patterns of expression, consisting on thick stripes arranged perpendicularly to the anterior-posterior axis.
Even-skipped is one of the most studied pair-rule gene as it is the first of this group that is expressed and have influence in the rest pair-rule genes [Clark, 2017]. Eve originates a pattern of expression composed of 7 bands, perpendicularly arranged to the anterior-posterior axis. The current explanation by a series of independent enhancers, each of them activating a cluster of bands [Hare, 2008; Harding, 2018]. The mechanism of some enhancers has been widely studied, such as the one giving rise to the second stripe of Eve (Eve2) [Small, 1992; Goltsev, 2004; Bothma, 2014]. Other enhancers are not so well understood and even there are some stripes whose enhancers are still unknown. Even if the enhancer is known, it is extremely difficult to determine which morphogen activates or represses it. The combination of all these factors made extremely difficult the development of a global model that give rise to this pattern.
In order to stablish a global mechanism that explains the formation of all the eve bands, we develop an in silico model of an embryo of D. melanogaster in the beginning of the anterior-posterior segmentation, when the embryo is in the blastoderm stage between cell cycles 13 and 14. All the data related to the length, size, shape and number of cells of the embryo refer to this stage of development and can be found in SI5a. Moreover, we simulate the expression of the maternal-effect genes as an input and the gap-gene spatial pattern is dynamically generated from them, according to the interaction network shown in Fig.4A. Finally, the eve bands are obtained by means of an autoregulatory mIFFL. The spatial distribution of its expression will be very susceptible to both the concentrations of the maternal-effect genes used as input and the gap-genes obtained.
It is necessary to consider that at this stage of development of the embryo some genes have been already expressed so, at the beginning of the simulation, some morphogenes from the maternal-effect and gap-gene groups will be initially located. For these inputs, we used interpolation polynomials based on experimental data from [Perkins, 2006], that can be consulted at SI5b.
In order to define the dynamical concentration of morphogenes we use an SDD (Synthesis, Diffusion, Degradation) model [Ellis, 2009]. The diffusion and degradation parameters are defined as constants and their values, extracted from the literature. To define the synthesis of every morphogen, we make use of the Unc-logic model from [Perkins, 2006], based on logical rules.
In the first place, we simulate the formation of the pattern of the gap genes. With this simulation, we have obtained 2D images, and then we compare them to experimental images of D. melanogaster embryo. Simulations of the gap-genes expression are very similar to the in vivo results, as can be seen in Fig.4b.
Once the gap genes are fully expressed, the expression of pair-rule genes and, therefore, eve begins. Eve is expressed in 7 bands perpendicularly arranged to the anterior-posterior axis of the embryo.
In order to obtain this pattern in our model, we propose an mIFFL motif. In this motif Eve activates and represses itself by two independent and incoherent pathways. First, we introduce constitutive repressor that inhibits the expression of Eve along the embryo. We also propose that cells expressing Eve can emit two intercellular signals: a fast and short-range self-inhibitory signal and another slow, long-range signal that inactivates the constitutive repressor and, consequently, induces the expression of Eve. By means of this incoherent regulation and together with an adequate choice of parameters, we ensure that the new eve stripes appear in the desired position. The newly formed stripes have the same behavior, so they keep stablishing the pattern. Finally, to explain the absence of Eve stripes in the anterior part of the embryo, we take Bcd as a concentration-dependent repressor to prevent the expression of Eve in the anterior border.
Nevertheless, this system needs a trigger (see Fig 5A-B) to start because otherwise the constitutive repressor of Eve will never be silenced, and eve genes will never be expressed. So, there must exist an external mechanism that inhibits the constitutive repressor and switches the mIFFL on. As it has been previously discussed there are numerous enhancers of Eve stripes, but some of them are not yet well understood so we take as a trigger the best documented one, the one that activates the expression of Eve 2 and Eve 7. We have chosen this enhancer because it is clear which morphogenes activate and inhibit it, but there could be more starting points apart from this. We also obtain promising results with the simulations of the mutants for some of the morphogenes, this fact sets a positive evidence of taking the enhancer of the stripes 2 and 7 as a trigger to this mechanism (SI7).
The simulations of Eve expression are very similar to the in vivo results. We obtain the same number of stripes and also these stripes have a similar wide and space between them compared to the experimental observations (see Fig 5C).
The result of this simulation supports our hypothesis that with an mIFFL it is possible to generate the eve pattern in D. melanogaster.
CONCLUSIONS
Traditional 3-gene IFFLs motifs were developed to model intracellular genetic networks. In this work we have extended the IFFL motif to multicellular environments. In a multicellular IFFL the interacting nodes are no longer genes inside the same cell. The nodes can be spatially distributed over space and not necessarily in the same cell. The interaction between nodes is done by intercellular communication.
With the in silico simulations done with IBMs (Morpheus and GRO) we have shown that: 1) a mIFFL can work as an edge detector of the border of an infection, and 2) a mIFFL can generate the 7 stripe pattern of even-skipped in D. melanogaster embryogenesis. So, in this study, we have probed that type-2 and type-3 multicellular IFFL architectures are able to produce spatial patterns. Why are these precise IFFL motifs able to process spatial information? The main reason is that the indirect arms of the motif are supposed to be longer ranged than the direct ones, so there is a spatial delay in the mobilization of elements that drives to dynamical spatial patterns.
This study, that introduces the mIFFL motif for spatial computing, opens several promising future lines of research:
It is an open problem for future research whether other types of multicellular incoherent (or coherent) feedforward loops are also robust strategies for spatial information processing.
mIFFLs could be applied to model other processes of cellular differentiation in embryogenesis and developmental biology, as for example, the somitogenesis in vertebrates [Hester, 2011].
The study of other variants of mIFFLs and mCFFLs that can also be interesting, not only for spatial patterning, but also as a tool to model higher-order interaction motifs, present in complex microbiomas, like human microbiota or for programming complex multicell consortia.
The possible extension of mIFFLs to multi-agent IFFL in ecology, where the nodes would be the different species interacting in an ecosystem, would allow to predict the spatial distributions of the animals (analogously as done with “rock-paper-scissor” ecology models).
In distributed robotics, multi-agent IFFL motifs could be used to program interactions between robots to generate complex spatial robot distributions.
S3. VARIANT OF EDGE DETECTOR
Furthermore, it shows an even more complex extension of mIFFLs, with feedback between nodes. This complex architectures yield very rich spatial behaviors.
S5. MATHEMATICAL MODEL OF DROSOPHILA EMBRYO
1 Geometry
The space where the simulations were carried out is a mask of a real embryo of Drosophila Melanogaster. The embryo is in the stage 6 of gastrulation (Interactive Fly), the number of cells at this stage is around 6000 (Zalokar, 1976). We only simulate 2200 because we are only representing the external surface of one lateral face of the embryo.
The size of the embryo at this stage is approximately 0.5mm long (Drocco, 2011)
2 PDE + Unc-Logic Model
The production and decay rates have units min−1, and the diffusion rates have units (1% embryo length)2 min−1
The dynamic model of the genes is modeled by the synthesis, diffusion and degradation (SDD) equation (Grimm, 2010)
Where C(x,y,t) represents the concentration of a morphogen at time t and position x,y. D is the diffusion coefficient, α the degradation rate and j(x,t) describes the morphogen production.
3 Inputs
These are the polynomials of interpolation used as input for the gap gene simulation.
S7. MUTANTS
In general, our model does not correctly reproduce the mutants patterns of expression of Eve. However, in some cases it partially reproduces some patterns of expression as it can be seen in the fig S7.
We will need to further analysis to refine the parameters.
ACKNOWLEDGMENT
This work was supported by the European Union project PLASWIRES (612146/FP7-ICT-FET-Proactive), by Spanish MINECO projects TIN2016-81079-R and by the grant S2017/BMD-3691 InGEMICS-CM, funded by Comunidad de Madrid (Spain) and European Structural and Investment Funds.