Expanding the Landscape of Biological Computation with Synthetic Multicellular Consortia

Ricard V. Solé Javier Macia

SFI WORKING PAPER: 2013-05-020

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SANTA FE INSTITUTE

Expanding the landscape of biological computation with synthetic multicellular consortia

Ricard V. Sol´e∗1, 2, 3 and Javier Macia1, 2 1ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 88, 08003 Barcelona, Spain 2Institut de Biologia Evolutiva, UPF-CSIC, Psg Barceloneta 37, 08003 Barcelona, Spain 3Santa Fe Institute, 1399 Hyde Park Road, Santa Fe NM 87501, USA

Computation is an intrinsic attribute of biological entities. All of them gather and process information and respond in predictable ways to an uncertain external environment. Are these computations similar to those performed by artificial systems? Can a living computer be constructed following standard engineering practices? Despite the similarities between molecular networks associated with information processing and the wiring diagrams used to represent electronic circuits, major differences arise. Such differences are especially relevant while engineering molecular circuits in order to build novel functionalities. Among others, wiring molecular components within a cell becomes a great challenge as soon as the complexity of the circuit becomes larger than simple gates. An alternative approach has been recently introduced based on a non-standard approach to cellular computation. By breaking some standard assumptions of engineering design, it allows the synthesis of multicellular engineered circuits able to perform complex functions and open a novel form of computation. Here we review previous studies dealing with both natural and synthetic forms of computation. We compare different systems spanning many spatial and temporal scales and outline a possible space of biological forms of computation. We suggest that a novel approach to building synthetic devices using multicellular consortia allows us to expand this space in new directions.

Keywords: Synthetic biology, cell computing, circuit design, evolution, robustness

I. INTRODUCTION unreliable components within crowded cell interiors, self- renewing tissues, neuronal loss as well as uncertain environments. A global view of how is this repertoire of Living systems are characterized by their potential solutions is related and how to define a space of possible for performing computations (Hopfield 1994; Bray 1995; forms of computation requires defining a proper theo- Arbib 1995; Amos 2004; Soléet al 2007; Nurse 2008; retical framework and a systematic comparison between Brenner 2012). Early evolution of life was marked by existing systems (Bray 1995). Understanding the simi- a plethora of events involving efficient energy use and larities as well as the differences between man-made com- an adequate exploitation of available matter to power puting artifacts and their natural counterparts has been their metabolic pathways and build and maintain their a central issue in the study of natural computing. We internal organization. But the real trick involved de- know from comparative biology that common solutions veloping mechanisms to gather, store, process and react are often found as a result of independent evolutionary to information in complex, adaptive ways. As it occurs paths (Conway Morris 2004). with computers, biological systems are information pro- cessors, and as complexity grows with evolution, more Information-processing systems provide a neat exam- complex computational tasks emerge. However, it has ple of the power of such convergent designs. Some of been well known since the beginnings of computation these systems, such as cortical networks processing visual that crucial differences exist in the way computations information, display an architecture that is no different are actually performed by living entities compared with from the solutions found by engineers designing paral- man-made artifacts. This was early identified as a ma- lel computers performing visual recognition tasks (Nel- jor issue when computers and brains were compared (von son and Bower 1990). Such convergence in evolved ver- Neumann 1956, 1958). The rise of molecular biology pro- sus planned designs is remarkable, since engineers were vided additional evidence for an unexpected robustness not getting any inspiration from cortical circuits. Simi- of cellular information processing suggesting that a whole lar scenarios have been found associated to wiring very range of biological systems exhibit such reliable compu- large scale integrated (VLSI) circuits under strong pack- tation capacity out from unreliable, noisy components ing constraints (Moses et al 2008) which are also followed (Kitano 2004, 2007). by brains (Bassett et al 2010; Soléet al., 2013). Biological systems have found through evolution dif- If such similarities were powerful enough, it could be ferent mechanisms to deal with molecular fluctuations, argued that a technology-inspired evolutionary theory of biological computation should be taken as a good starting point. If true, it would be possible to establish a mapping between man-made computational devices of increasing ∗corresponding author complexity and the repertoire of computationally mean- 2

a b

c d

e f

FIG. 1 Electronic circuits (a) are the iconic representations of standard computing machines. In biology, computations are often distributed among individuals having a limited information about their neighbors but are able to generate stable large-scale structures which allow collective decisions to take place. In (b) we illustrate this with the choice performed by Physarum colonies, which are able to decide among different food sources (picture by Audrey Dussutour, see http://dussutou.free.fr/). Parallel computation is widespread in several important biological examples, where a fluid neural-like structure is involved, as it occurs with the immune system (c) where some particular cells, such as dendritic cells (c, from http://en.wikipedia.org/wiki/Dendritic cell) or ant colonies while solving computational problems, such as finding the shortest path among two alternatives (d, image courtesy of Guy Theraulaz). In systems where single-cell behavior is the dominant form of behavior, as it occurs for example with yeast cells (e) intracellular decision making networks exist. At the molecular scale (f) complex nanomachines, such as the DNA polymerase ”read” DNA as a tape (picture generated using Pymol software). All these systems perform computations of some type, and their special characteristics make them inhabit different locations in the abstract landscape of biocomputation. 3 ingful living structures (see Sauro and Khodolenko 2004; based on a parallel exploration of a spatial domain un- Istrail et al 2007; Hogeweg 2002). A standard approach der a pattern-formation process (Adamatzky 2007; see to this is given by so called theoretical morphospaces, also Dussutour et al 2010). The role played by space an abstract way of geometrically characterize the pos- is particularly important when dealing with communi- sible spectrum of biological structures of a given class cation taking place among different individuals, wether (McGhee 2006). By defining a small number of axes (usu- cells or ants. Due to the constraints associated to spatial ally related to geometrical or physiological properties) it interactions, parallelism is a necessary condition for reli- is possible to see what part of the space is occupied, what able computation. Space provides a well-defined dimen- part is empty and look for an interpretation of such dis- sion for our morphospace. It allows multiple segregated tribution. The recent developments within the emergent components to interact locally with others, provides a field of synthetic biology (Bennett 1982; Tan et al 2007; natural source of modularization and it also defines a Benenson 2009) have created a new scenario where the deep connection between pattern formation and pattern manipulation of cellular systems provides a new oppor- recognition (Haken 2004, 1979). Back again to synthetic tunity of expanding the space of biological computations biology, engineering cell-cell communications in a spatial (Weiss et al 2003; Brenner 2012). Since such novel de- context allows to explore the formation of multicellular signs are not the result of evolutionary paths nor need systems (Kinkhabwala and Bastiaens 2010). to be restricted to standard forms of engineering, they Similarly, phenotypic diversity among cells involved in offer the potential for creating new classes of computa- a given process of pattern recognition, as it is done by tion living devices. In this paper we explore this idea by the immune system (figure 1c) where detecting a poten- comparing different known biological computing systems tial universe of invaders while properly recognizing the and novel ways of building them using synthetic biology. self requires an enormous plasticity. This system, in some ways similar to the behavior of ant colonies (d) which also display self versus non-self recognition while make deci- II. TOWARDS A NATURAL COMPUTATION SPACE sions about how to exploit their environments (Camazine et al., 2003) behaves as a fluid neural network, exhibiting Let us first summarize some key aspects of biological memory and learning (Soléet al 1993; Soléand Delgado computation that might provide the natural dimensions 1996). Agent diversity provides a second axis for our of a computation morphospace. In this section we will space of computational living designs. A diverse range examine several aspects of the problem by means of ex- of agents able to perform different operations is another amples and their implications. We also consider synthetic way of exploiting modularity and division of labor. Such biological devices as a particular case. potential has been crucial through evolution and not sur- Let us start with the most common link: living and prisingly also to the evolution of computation in the nat- man-made circuits. We could place small standard cir- ural world. Within synthetic biology, the engineering of cuits, sequential and made of some standard class of logic multiple types of cells is at the core of achieving complex gate, at one corner of our morphospace. Here we could computational tasks (see below). In this context, despite also place small circuits defining specific network motifs many well known model organisms such as yeast cells or the simplest engineered genetic circuits implementing (figure 1e) are unicellular, they often display more com- logic gates. The similarities between cellular and elec- plex features associated to multicellular responses. This tronic circuits are certainly appealing, but are cellular can actually be artificially evolved (Ratcliff et al 2012). networks really similar to the wiring diagrams of elec- Under stress, these and other species of unicellular life tronic circuits (figure 1a)? These technological systems forms can behave collectively as information-processing define one of the standards to be considered here. Biolo- swarms. gist Yuri Lazebnik suggested that the response to muta- A final example to be mentioned is connected to the tions in a cellular network can be understood in similar lowest scale defined by molecular machines and interac- terms as the effects of removing or damaging electronic tions (Reed and Tour 2000) . Computational metaphors components. In this way we could think in a radio as are also good descriptions of many relevant molecular a proper metaphor of cell complexity (Lazebnik, 2002). processes, such as DNA-protein interactions (f). Many Failure in some components will have a small effect, while known and synthetic molecular processes ca be easily others are too important and make the whole system fail. mapped into logical functions. Such mapping was also Parallel distribution of computational tasks offers a pow- early recognized by early researchers in the field of com- erful solution to this problem and is one dimension of our plex systems (Kauffman 1993). More recently, it has been morphospace. suggested that computational processes of high complex- Despite its frequent use, the engineering metaphor falls ity can take place in chromatin strands (Bryant 2012). short in describing some types of computation, particu- The previous examples provide a good repertoire of larly those where pattern formation is an intrinsic part possible forms of computation in natural systems, span- of information processing, such as resource allocation ning multiple scales and a diverse array of forms of inter- and exploitation in Physarum (figure 1b) or in army action and processing. Somewhat, they could be located ant colonies (Deneubourg et al. 1989; Soléet al. 2000) within an abstract space with appropriate axes introduc- 4

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FIG. 2 Single cells (a) from the bacterium E. coli can be engineered in order to perform given computations (photograph adapted from http : //en.wikipedia.org/wiki/Escherichia − coli). One possible way of modifying them is to construct living logic gates. As an illustration, consider the NAND gate (b) which can be obtained by trivial combinatorial logic, linking in series a AND gate with a NOT gate. This particular gate can be easily constructed using a cell as container by engineering a small gene regulatory network (c) where two external signals (here indicated as α and β) can act as repressors on two promoters (PA and PB , respectively) associated to two genes whose protein products, if both present, form a heterodimer which then acts on a third gene expressing a fluorescent protein (GFP). This cell-based circuit design can be considered one particular module that could be connected to others as logic gates within chips (d). Although this seems to be in principle a reasonable approach to achieve complex computations, the strategy fails to work when translated to real biological circuits. ing key traits, such as system size, degree of parallelism et al 2009: Ausslander 2012). Here we present some of or modularity, to cite just a few possibilities. Are they these results and suggest a potential framework to define a complete representation of what is possible? As will a space of computational designs that includes existing be discussed here, it is important to consider novel forms natural and artificial systems as well as engineered, ar- of computing based on new principles that depart from tificial ones. By introducing the concept of multicellular both biology and standard engineering. This counter- distributed computation (Macia et al 2012) we suggest intuitive scenarios are fairly well illustrated by evolved that such space can be expanded in new directions that natural and artificial computing networks. Such analysis somewhat escape from both biological and technological suggests that we might need to identify other organiza- schemes. tion principles, such as degeneracy (Tononi et al 1999, Macia and Sole 2009) as main players in natural designs. Roughly speaking, degeneracy is defined as the capacity III. DISTRIBUTED MULTICELLULAR CIRCUITS of elements of a given system that are structurally different to perform the same function or yield the same One way of creating synthetic biological circuits per- output. Instead of the redundant solution chosen by an forming predefined logic operations is based on engineer- engineer, evolved circuits seem to display some sort of ing genetic regulatory systems (Weiss et al. 2003; Kramer nested distributed robustness. et al 2004; Kobayashi et al 2004; Soléet al 2007; Pur- How can we go beyond the limits imposed by real sys- nick and Weiss 2009; Benenson 2009; Tamsir et al., 2010; tems, which are the result of evolution and might be diffi- Silva-Rocha and de Lorenzo, 2011; Auslander et al 2012). cult to fully characterize? Similarly, how can we test ex- In figure (2) we show some examples of logic gates that isting theories and try novel ones if they are sometimes can be implemented by using available genetic compo- difficult to compare with their real counterparts? The nents and their interactions. Such circuits are obtained field of synthetic biology seems to provide the best sce- by means of standard genetic engineering techniques and nario for designing novel computational systems in vivo the components can actually come from different, com- whereas non-standard forms of computation are used as pletely unrelated species, which can mix together genes alternatives to engineering-inspired metaphors (Tan et al from viruses, bacteria or mammals. Using the well known 2007; Smaldon et al 2010, Friedland et al 2009; Perkins bacterium E coli (figure 2a) as model organism, a given and Swain 2009; Marchisio and Stelling 2009; Fernando logic gate, such as the NAND gate (fig 1b) can be eas- 5

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FIG. 3 Recipe for multicellular distributed computation. The problem with standard combinatorial circuit design when translated into single-cell living circuits. We illustrate this here using a well known example from electronics: the multiplexer (MUX) circuit, a three-input, one-output circuit defined by the table shown in (a). A possible implementation of this is provided in (b) and in (c) we show the MUX in its standard symbolic representation and how to build it from a set of elementary gates. Instead of building the synthetic cell with all the circuitry inside only one cell (d) a distributed circuit can be build using several cells, each one carrying part of the circuit but all potentially able to generate the output signal. In (e-f) we show how the MUX circuit can be build using a disconnected cellular consortium where each cell is able to express the GFP reporter signal. ily implemented using a small set of interacting genes tiple NAND gates. In principle, every circuits could be (c). In our example the NAND gate is obtained by us- designed in this way. However, a major difficulty emerges ing a molecular complex formed by two different proteins here: in electronics, every wire is defined in terms of a which repress the expression of a so called reporter gene conducting piece of material, which is always the same. (here GFP=green fluorescent protein) which generates, When dealing with cellular engineered systems, where when activated, a fluorescent signal. molecules share the same medium where they are mixed, These examples illustrate the standard approach of identity becomes a problem (Kwok 2010). In a cell, every electronic design based on combinatorial logic and a liv- wire needs to be a different molecule to properly connect ing chip (figure 2d) would be designed by combining mul- different elements or cells. Because the liquid nature of 6 the medium where computations need to occur, the spa- cells belonging to different kingdoms are involved (We- tial insulation of wires that is assumed in electronics is ber and Fussenegger 2007) . Once again, however, the no longer satisfied. As a consequence, each wire needs resulting synthetic cells are hard to reuse to obtain other to be implemented by using a different molecular carrier types of computations. An alternative approach requires and the chemical diversity of constructs rapidly grows. breaking some predefined rules. Somehow, we get in- This is illustrated in figure 3 by the so called multiplexor spiration in physics when crisis appeared and classical (MUX) widely used in electronic designs. This is a 3- models failed to explain some key phenomena. Here we input, one-output system where a given signal ”selects” too will make a leap by removing from the basic design one of the two inputs. In principle a synthetic genetic principles some essential rules of combinatorial circuit network implementing a MUX circuit can be designed design. (an example shown in figure 3b) using a single cell im- In any standard circuit design, the truth table defines plementation. Although such circuit can be constructed the input-output relation between incoming sets of sig- (Moon et al 2010) it is a hard task, with no hope of being nals and the resulting outputs. The outputs are placed in re-used as part of a larger system (as it occurs in elec- given locations of the circuit and it makes sense that this tronics). Moreover, beyond this complexity threshold as- is the case. Let us limit ourselves here to a single-output sociated to complex decision making circuits dealing with system. That means that there is an output unit where three inputs and one output, things become much more the final result of the information processing is released. difficult and practically unlikely to be constructed. What happens if we free ourselves from such (rather rea- To sum up, the combinatorial approach can lead to sonable) assumption? The view of a computational de- a nightmare when dealing with an experimental design, vice as being implemented by a circuit that clearly dif- since the properties of each carrier and how it interacts ferentiates between input, processing and output units with other can be very different and difficult to predict. seems too obvious to replace it by some other paradigm. Additionally, one goal of the field is to have engineered But there is actually one solution that emerges from not systems capable of extensive reuse of available parts in forcing that assumption to be true. Instead, more than a such a way that a LEGO-like system is at work. Both cell type is able to respond as output element. The result premises are basic requirements for reaching the compu- of this radical approach is illustrated in figure 2d, where tational complexity for achieving autonomous machines we provide an example of how a multicellular MUX cir- able to make decisions in a biological context. Only re- cuit can be build. The circuit is formed by two cells, cently a general approach, based on engineering several each responding to only two of the inputs and without cell types, has been successfully obtained. cell-cell communication. Using this consortium, it can be easily shown that the MUX table is implemented. The system requires minimal engineering, is uncoupled and IV. CELLULAR CONSORTIA: DIVISION OF LABOR the output is distributed over the two cells.

One way of dealing with the wiring problem is considering alternative ways of avoiding the mixing of molecular V. DISTRIBUTED COMPUTATION carriers that seems inevitable within the single-cell scenario. Spatial segregation of the basic components pro- Here we introduce our general approach to synthetic vides one easy way of dealing with computation avoid- multicellular computation. We will use a Boolean ap- ing molecular mixing. This segregation can be achieved proximation, thus confining our approximation to the by using cellular consortia, namely a population of cells digital domain. Our state space will be described by a having different types of engineering designs. In such set Σ = {0, 1}. Although this is in principle a limitation, scenario, a library of different cell types, each one having many relevant cellular computations seem to take place a different subset of genetic components, is build out of by means of genetic switches. Such switches effectively a collection of molecular components and the required define binary states with low and high levels of gene ex- computations are separated within different ”modules” pression. A given functionality will be described as an defined each by a different type of engineered cell (Basu input string I ∈ Σ, namely an element of et al 2005; Brenner et al 2008; Wintermute and Silver N 2010; Goni-Moreno and Amos 2012; Macia et al 2012; Σ = {0, 1} × ... × {0, 1} (1) | {z } Chuang 2012). n This type of multicellular consortium has been used in many different contexts. In particular, using It will indicate, in our framework, a string of absent (0) two cell types it was possible to artificially create or present (1) chemical signals. population-control systems, pattern forming band de- The functional trait to be implemented is formally de- tectors, predator-prey systems, mutualistic ensembles or fined as a Boolean function φi with N input signals and parasitic organizations (You et al. 2004; Basu et al 2005; a single output. Formaly, this reads: Shou et al. 2006; Brenner et al 2007). Extensions of these N include multispecies ecosystems where different groups of φi :Σ −→ Σ (2) 7

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Review Trends in Biotechnology June 2012, Vol. 30, No. 6 Distributed multicellular

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(f)250 (g) 250 d e 200 200

150 150

100 100

Number of functions 50 Number of functions 50

0 0

1 2 3 4 5 1 2 3 4 5 Number of cells Number of wires

TRENDS in Biotechnology

FIG. 4 Standard combinatorial design versus distributed multicellular computation. We schematically show the diﬀerences

Figure 5. A non-standard alternative to synthetic design of cellular devices involves the use of a library of engineered cells (a) where several cell types can produce the output

between both approaches in terms of how the components are combined among them. Here in (a-c) four diﬀerent examples of

signal, here indicated as R or r. The different engineered cell types are indicated by different colors, a indicates a diffusible communicating signal used as our wire. These cells

can haveMDCreceptors implementationsfor external signals areas well displayed,as for cell–cell all ofcommunication them obtainedwires. byThe combiningkey difference AND,here is that NOTthe output and N-IMPis distributed gates.over different Each functionalengineered cells. systemThis

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logic functionswith two(N implies smalland gatesNOR) (NORbut also andcomplex N-IMPLIES)ones, as is the wecase alsofor the displaymultiplexer the(MUX) MUXor a andcomparator comparator(COMP) where (COMP).two reporters The(R laterand r) isare aused circuitto indicate that

which decidesentry is larger whichthan ofthe theother. twoThis enteringapproach bitswas issuccessfully larger thanimplemented the other.using Manyyeast strains other[70] circuits. The potential can alsoof this beapproach constructedcompared usingto standard this librarydesigns oris

illustrated in (f) and (g). Here, we have computed, for different numbers of cells (f) and wires (g), the number of possible computational devices (functions) that can be

implementedsmall using extensionsdistributed ofcomputation it. These consortia(blue bars) and areNOR-based to be comparedsystems (yellow withbars) thewhere expectedonly NOR circuitsgates have implementedbeen used according from standardwith standard combinatorialdesign rules. As

we candesignsee, in the (lowerdistributed group).scenario, Thea small rapidnumber increaseof cell intypes theor numberwires allow ofconstruction potentialof functionsa large number associatedof functional todevices. our method, compared with the expected from NOR-based standard circuits is illustrated by ﬁgures d and e. Blue and yellow bars are associated to the standard

and non-standard methods.

distributed approach, versus the number of cells required to Discussion

implement each function. In the same ﬁgure, we display the Increasing complexity has been a trademark of circuit

number of functions that can be obtained combining only design [63]. Simple circuits dealing with oscillators,

NOR-gates according with standard design rules. Similarly, switches and sensors have slowly been replaced by more

in Figure 5g, we display the number of different functions complex molecular constructs inside engineered cells able

versus the number of wires required for their implementa- to detect and respond to external inputs in sophisticated

tion, either using the distributed approach or the standard ways. Moreover, much more sophisticated designs have

NOR-based designs. In both cases, the distributed method been developed in order to respond in complex ways to

allows us to build a large number of functional constructs, chemical cues (such as toxins), such as in response to clean

rapidly approaching the maximum limit. Using just three fuel [75] or in recognizing tumors [76]. The enormous

cell types is already enough to construct most of the reper- potential of mixing together molecular components belong-

toire of potential circuits. Additional wires (Figure 5g) fur- ing to completely unrelated organisms puts SB on the same

ther increase the combinatorial power of the system. path as microelectronics. Is the current trend of growth in

347 8

Two particularly relevant subsets of Boolean func- a tions are the one input-one output gates, i. e. the set b G(1,1) = {NOT, Id} (the negation and identity functions, respectively) and the 24 two-input logic gates deﬁning the (2,1) set G = {gj} where gj is a maping

2 gj :Σ −→ Σ (3) (represented by a simple table). Standard functions include OR, AND and their “inverse”, i. e. NOR and c d NAND. Both the NOR and the NAND gates allow to build any possible type of logic circuits under the right set of combinatorial rules (Enderton 2001) In figure 4 we show some examples of circuits build out of simple gates. Our approach to a general design of complex computational circuits (Regot et al 2011; Macia et al 2012; Macia and Sole 2013) is based on two general assumptions, to be translated into a basic circuit design (fig 4, upper part). First, we limit ourselves to a feed-forward network where each node is one type of engineered cell from the library. Each link means the existence of a molecular connection, i. e. a diffusible wire molecule. Secondly, several cell types can incorporate the gene responsible for the output FIG. 5 Multiplexers are an essential element in a vast num- molecule (GFP). Once a given Boolean table is chosen, ber of electronic circuits. A multiplexer is a device that se- an evolutionary algorithm is applied to the basic wiring lects one of several input signals and forwards the selected structure, which explores the landscape of potential net- input into a single output. A multiplexer of 2n inputs has works implementing the desired function. The algorithm n select lines, which allow for select which input line will be searches over the space of basic functions, wiring con- sent to the output. In (a) the minimal multiplexer involv- figurations and other constraints. Once a given network ing two inputs (MUX2to1) I0 and I1 is shown. The chan- is found, standard rules of circuit minimization are ap- nel selector is C0. In (b) the standard implementation of a plied in order to obtain the minimal circuit solving the MUX2to1using NOT and NAND gates. Construction of big- problem by means of distributed computation. ger circuits involving more inputs and channel selector lines What are the results of this method? Along with this are easy achieved connecting multiplexers i n cascades. In (c) a multiplexer MUX4to1 is obtained as a cascade of MUX2to1 evolutionary algorithm, the theoretical analysis demon- multiplexers. Similarly, 8-inputs multiplexers (MUX8to1) can strates that it is possible to minimize the number of re- be build connecting MUX2to1 in cascade (d). quired cells and wires using the distributed output assumption combined with a small library of cells implementing only the AND and the inverted Implies gates (N-IMPLIES). Despite this combination of gates are not usually used in circuit designs they define a functional to the enormous capacity for tinkering and combination. complete set, i.e. any arbitrary Boolean function can be Here, we have computed, for different numbers of cells implemented only combining this two gates. In some em- (figure 4f) and wires (figure 4g), the number of possi- bodiments, these gates can be simplified and replaced by ble computational devices (functions) that can be imple- the IDENTITY and the NOT gates respectively allow- mented using distributed computation (blue bars) and ing for a circuit simplification. Furthermore, the wiring NOR-based systems (yellow bars) where only NOR gates pattern of connections is restricted, i.e. different circuits have been used according with standard design rules. As can involve different number of cells and wires but all cells we can see, in the distributed scenario, a small number of only respond to an external input and to single diffusible cell types or wires allow construction of a large number molecule acting as a wire according with the specific logic of functional devices, whereas the expected number of function implemented, i.e. AND or N-IMPLIES, inde- circuits arising from standard combinations grows much pendently on the circuit complexity. more slowly. The potential power of distributed computation as de- A major goal of synthetic biology is to develop com- scribed above is illustrated by noticing that even a small plex, decision-making circuits able to solve non-trivial number of engineered cell types makes possible to create tasks and respond to a diverse array of external and in- hundreds of synthetic circuits (Regot et al 2011, Macia ternal signals. This means that the method used to im- et al 2012) and thus a huge potential array of functions. plement the circuits requires to be scalable. The scalabil- Adding wires makes the combinatorial power of the sys- ity of our method is illustrated by considering much more tem to rapidly increase in orders of magnitude the num- complex circuits. Take for example the multiplexer. The ber of potential circuits, which are easily achieved thanks simpler, two-input MUX circuit is used in electronics as 9

FIG. 6 Multiplexers can be easily implemented using synthetic distributed cell consortia, as illustrated here. In (a) the standard implementation is shown connecting NOT and NAND gates. Dashed lines represent internal wires (ωi). The same circuit can be obtained using cellular consortia implementing the AND and the non-standard N-IMPLIES gates, combined with the distributed output production (b). Here, dashed lines represent the number of required wires. As figures show, the alternative implementation using cellular consortia have a significant reduction of the wires required and hence the resulting circuits are feasible for experimental implementation ensuring their scalability. a building block for designing more complex multiplexers to properly address some of the key problems in the field, (figure 5). Such scalability is easy to achieve from com- namely wiring constraints and real combinatorial design. binatorial design, but it rapidly becomes too difficult in Our recent work shows that by removing the assumption terms of molecular wiring. Take for example the circuit of specified output units and by allowing the output to be shown in figure 6a. Here a four-input system is consid- distributed over multiple cell types, low-wiring, complex ered. Internally, it would involve eleven wires (indicated combinatorial circuits can be obtained. with dashed lines). The corresponding DMC circuit is The previous results are encouraging in two different displayed in figure 6b. The minimal consortium solving ways. On the one hand, given the truly combinatorial this involves six different cells with minimal engineering potential of the method, hundreds of possible synthetic and only two different wires. designs can now be constructed (Macia et al 2012). The method allows to predict possible ways of building minimal circuits and thus adapt the required result to ex- VI. DISCUSSION perimental constraints. But it also opens an interesting framework to approach more general questions. Our Synthetic biology has been rapidly gaining relevance method shows that an unexpected way of solving com- and potential as novel techniques are getting incorpo- putational problems can be obtained. rated to the field and new applications start to emerge The class of networks constructed from our method (Chang 2005; Ruder et al 2011; Weber and Fussenegger depart from previously known computational devices or 2012, Ausslander et al 2012). Our view approach allows cellular circuits. The resulting solutions are counterintu- 10

Cellular automata! Distributed computing Connection machine

NAND,NOR! FPGAs chips

Polymorphic ant ! colonies neural systems

Monomorphic ! Spatial ant colonies Synthetic! NOR circuits Physarum! computing Distributed ! Mixed consortia Recurrent ! DNA computing NN IS SPATIAL EMBEDDING

parallel HC LV Mixed sequential

PARALLELISM Standard! Single type Consortia SynBio CELL (AGENT) DIVERSITY

FIG. 7 An idealized landscape of computations is represented here as a three-dimensional space, where the three axes include the presence of spatial segregation, degree of multicellularity (agent diversity) and to what extent the computation is sequential or parallel. Several well known examples are located at roughly representative locations. Several scales re involved, from molecular systems (such as DNA computing) to ant colonies, or neural networks. The diversity of ”agents” (cells, ants, nucleotide sequences, neurons or logic gates) is an important dimension here and similar systems can exhibit different degrees of individual diversity. Ant colonies for example can be monomorphic or polymorphic. In the first cases all individuals look physically similar and tasks are distributed among them in a flexible way. In the second case, several fixed casts (physically differentiated individuals) tend to perform preferentially some tasks. Here LV= Lotka-Volterra synthetic ecosystem, HC=mutualistic synthetic system, NAND, NOR chips: small chips constituted by only NAND and NOR gates, widely used as basic building blocks in many electronic designs; FPGAs: field programmable arrays.

itive and reveal an alternative form of actually achieving derstanding the differences, the intrinsic robustness of the right computation through cellular consortia that can DMC and its potential application to both living and be disconnected into several pieces. Where are our sys- technological systems is becoming a very active area. tems located in the potential universe of computational The synthetic biology approach presented here can be structures? In figure 7 we provide an idealized picture of extended in multiple directions, potentially capable of the space of computations using three basic axes involv- filling the empty voids of the computation morphospace ing the degree of relevance of space, agent (cell) diversity and perhaps allowing us to understand the origins of and how distributed the system is (this was inspired in a their emptiness. These include using spatially extended previous work by Sipper, 1999). The size of the spheres constructs, cellular movement, memory modules or cell- is intended to reflect the abundance of known systems in computer interfaces. Moreover, by using non-standard each class. Distributed computation occupies the domain approaches we might also be able to create novel types highlighted on the right face of the cube using thick edges. of cells and tissues unreachable by Darwinian evolution. Close to neural networks, combinatorial molecular computing but also (and specially) to diverse cellular systems able to adapt and compute, such as the immune system (IS in the picture) our distributed multicellular comput- VII. ACKNOWLEDGEMENTS ing approach shares some properties with several known systems but also differs in other, fundamental ways. Un- We would like to thank the members of the Complex Systems Lab as well as to F. Posas, L. de Nadal and JF 11

Sebastian for interesting discussions on biocomputation. consortium. Proc. Natl. Acad. Sci. USA 104, This work has been supported by a European Research 17300-17304. Council (ERC) Advanced Grant, and grants from the MINECO FIS2009-12365, the Botin Foundation and by 14. Brenner, K. et al. 2008. Engineering microbial con- the Santa Fe Institute. sortia: a new frontier in synthetic biology. Trends Biotech. 28, 483-489

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