Computing with biological switches and clocks

Computing with biological switches and clocks The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch- like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing. Keywords DNA computing  Systems biology  Synthetic biology  Distributed computing  Oscillation Bistability  Feedback loop  Network 1 History of understanding biological clocks, respectively (Tyson et al. 2008). We have under- computation stood much about the behaviour of these basic units of biological computation (Ferrell 2002; Nova ´k and Tyson In the last 50 years, biology has inspired computing in 2008; Tyson et al. 2003) and simple switches and clocks several ways (Navlakha and Bar-Joseph 2011; Cardelli have been synthesized in single cells more than 15 years et al. 2017). During this time, computational thinking has ago (Becskei and Serrano 2000; Gardner et al. 2000; also improved our understanding of biological systems Elowitz and Leibler 2000). Nevertheless, we still lack a (Bray 1995; Goldbeter 2002; Nurse 2008). Using principles comprehensive understanding of how these computational from chemistry, physics and mathematics, we have modules have emerged, and which features and molecular understood that the highly complex behaviour of biological interactions are responsible for their efficient and robust systems is caused by a multitude of coupled feedback and behaviour (Cardelli et al. 2017). Ideas from computing feed-forward loops in the underlying molecular regulatory might help us to take this last step, which might enable networks (Alon 2007; Tyson and Nova ´k 2010). In partic- biological switches and clocks to be influential in the ular, we have learned that positive and negative feedback development of future computing technologies. The simi- loops are responsible for driving biological switches and larity between the biological switch controlling mitotic entry and the approximate majority algorithm of distributed computing (Angluin et al. 2008; Cardelli and Csika ´sz- Neil Dalchau, Gregory Szep, and Rosa Hernansaiz- Nagy 2012) suggests that computing and molecular biology Ballesteros have contributed equally. could further influence each other in the future. With the & Attila Csika ´sz-Nagy emergence of the fields of systems and synthetic biology, csikasznagy@gmail.com there has been increased interaction between computer 1 science and biology, but there are a few steps needed Microsoft Research, Cambridge, UK before we can realise a biology-inspired soft-matter com- King’s College London, London, UK putational revolution. In this paper we review some of the University College London, London, UK key advances we have seen as a result of the interplay University of Oxford, Oxford, UK between computing and biology and speculate on the ´ ´ ´ Pazmany Peter Catholic University, Budapest, Hungary 123 762 N. Dalchau et al. directions that a possible joint field could take in the near much of cellular function. Oscillations can also be future. observed in systems consisting of just 1 to 3 proteins, as in the case of the KaiC circadian oscillator (Nakajima et al. 1.1 Computation 2005), although those proteins have a very sophisticated structure. Theoretically, many chemical oscillators con- The basic components of computational devices, including sisting of 2 to 3 simple species have been studied modern electronic circuits and earlier mechanical equiva- (Bayramov 2005). lents, consist mainly of Boolean and arithmetic functional Although similar basic components (switches, oscilla- units (Boolean control logic, integer and floating point tors, and functional units) are found both in biology and in units, analog to digital converters, etc.), of registers to hold computer engineering, it does not necessarily mean that intermediate results of iterative algorithms, and of coordi- these systems compute ‘‘in the same way’’. In particular, nation components that orchestrate the flow of information coordination is achieved in fundamentally different ways in across registers and functional units. Coordination is most biological systems than in the von Neumann architecture. often achieved by clocks: at each tick data is frozen into In biology, oscillators coordinate events only at the registers, and between ticks data flows between registers coarsest level of granularity, while fine-grained coordina- through the functional units. This is the so called von tion is achieved by direct interaction between molecular Neumann architecture that, despite dramatic technology components. In the central processing unit of computers, improvements and architectural refinements, has remained oscillators instead coordinate events at the finest grain, and largely unchanged since the first electronic computers. do so at great cost. As a result, low-power devices tend to Functional units compute Boolean and mathematical employ clock-free coordination strategies to save power. functions by combinational logic (that is, without requiring At the level of computer networks, though, coordination is memory or timing coordination). We can easily find ana- achieved by message passing, because individual clocks logues of these in biology, like the function computed by can get out of step and network latency may vary. Many the regulatory region of a single gene (Arnone and non-von Neumann models of computation have been Davidson 1997). Synthetic biology has demonstrated how studied in the area of distributed computing: these models many such functions, typically Boolean gates, can be resemble, and sometimes even technically coincide, with engineered in vivo by a variety of genetic and protein- biochemical models (Angluin et al. 2006; Chen et al. based mechanisms (Siuti et al. 2013). More theoretically, it 2014). has been shown how chemical reaction networks can The general architecture of computation in biochemical compute complex functions (Buisman et al. 2009). systems is still a matter of investigation, and so is the functioning of many subsystems that appear to process Although much of this work has mimicked digital com- ponents, there is a sentiment that functional units in biol- information. For the moment we can focus on how nature ogy work mostly in the analog domain, and that synthetic achieves the functionality of the basic components, biology could benefit from this approach (Sauro and Kim switches, oscillators and functional units, while using 2013). material and constraints that are very different from those In this review we focus mainly on the other two classes that come from engineering. of components: memory and coordination. A switch is a memory unit capable of storing a single bit: at the core 1.2 How do natural systems compute? there is a bistable dynamical systems coupled with a mechanism to force the system from one stable state to the The complex dynamics of natural systems drew research other. Switching behaviour is pervasive in biology: it is interest a long time ago. The theory of dynamical systems achieved by a range of mechanisms, from individual and chaos was born at the turn of the twentieth century, molecular components like phosphorylation sites and with a focus on understanding the weather and the many- riboswitches, to whole complex biochemical networks that body problem (Strogatz 2000). Pioneers of mathematical switch from one configuration to another, such as in the modelling of biological systems came from the field of cell cycle switch. Synthetic genetic switches have also chemical physics and used their experience learned from been demonstrated (Gardner et al. 2000). non-equilibrium chemical systems to investigate biological The intricate feedback loops of biochemical networks switches and clocks (Goldbeter 2017). Ideas on the tend to produce oscillations in abundance, both stable and chemical basis of biological behaviour were also used by transient, many of which are poorly understood. The most the computer scientist Alan Turing to explain develop- prominent oscillators in biology, found also in the most mental pattern formation (Turing 1952). Yet still comput- primitive organisms, are those involved in the cell cycle ing had far less influence on our thinking about biological and in circadian clocks, whose cyclic activities coordinate systems than chemistry, physics or mathematics. Indeed, 123 Computing with biological switches and clocks 763 biological behaviour is controlled by (bio)chemical reac- contain only interactions of activation, while double-neg- tions and the underlying reaction kinetics can be under- ative PFBLs, or antagonistic interactions, contain an even stood by looking at the microscopic physical behaviour of number of inhibitions (plus any number of activations). molecules, but to turn these into a comprehensive form, (Fig. 1). mathematical expertise is required. Since the 1990s, Feedback loops (FBLs) constitute a basic relationship advances in computing have enabled us to solve highly between molecular species to construct complex beha- complex equations describing the physical interactions of viours and consequently are abundant in protein regulatory the chemical reactions driving biological behaviour, but it networks. FBLs can produce various dynamical beha- was the appearance of systems biology (Kitano 2002a) that viours, such as efficient switching and oscillations (Thomas led to the understanding that we need more computing to et al. 1995; Thomas 1981; Tyson et al. 2003; Tyson and truly understand biological systems (Kitano 2002b). Data- Nova ´k 2010; Hernansaiz-Ballesteros et al. 2016; Cardelli rich biological experiments at the molecular level have et al. 2017). Switch-like dynamics requires PFBLs, pro- identified the ubiquity of switches and clocks (Goldbeter ducing two (or more) stable states of the system (usually 2002) as core components of complex biological regulatory on/off states), when a given species is either fully active or networks. inactive. This feature of PFBLs is known to be key for developmental and decision-making processes (Ferrell 1.2.1 Feedback loops 2002). In contrast, oscillations require the presence of NFBLs. While direct negative feedback can stabilize a Already by the 1960’s it was known that feedback loops system, the introduction of a delay arising from regulation are the key determinants of the dynamics of biological via an intermediate, or simply through a slow accumula- systems (Griffith 1968a, b). Positive feedback loops are key tion, can very easily lead to oscillations. If a system con- to the appearance of switching behaviour, while negative tains at least three different molecular species and a strong feedback loops are needed for oscillations (Ferrell 2002; non-linearity, a damped or sustained oscillator may arise Goldbeter 2002). The complex dynamics of biological (Griffith 1968b). Systems with only two molecular species systems is determined by the combination of multiple of and without explicit time delays can also oscillate, but they such feedback loops (Tyson et al. 2003). Here we present require the presence of a PFBL, creating a switch that the main features of feedback loops that enables them to drives the oscillation. In contrast, the combination of pos- drive key biological processes. itive feedbacks with the depletion of one of the species Feedback loops (FBLs) arise when at least two molec- creates systems that can oscillate without an explicit neg- ular species regulate each other’s activity (Fig. 1). There ative feedback loop. These so-called relaxation oscillators are two types of FBLs, negative or positive. Negative FBLs produce characteristic fast switching in one direction, with (NFBLs) appear when the production or activation of a slow switching in the other direction, producing triangular- species is either directly or indirectly repressed when this like waveforms (Sel’Kov 1968). Finally, several natural same species is active (autoregulation) (Thomas and D’Ari oscillations are known to integrate positive and negative 1990; Thomas et al. 1995). Negative feedback loops con- feedback loops, which is thought to enhance the oscillator tain an odd number of inhibitions. In Fig. 1, a system of network robustness to intrinsic or extrinsic fluctuations only two components is shown, where one of the molecular (Thomas 1981; Thomas et al. 1995; Nova ´k and Tyson species (X) exhibits inhibitory activity over the other (Y), 2008; Ferrell et al. 2011). while this other molecule Y is activating the first molecule X. 1.2.2 Systems biology of switches and clocks Positive FBLs (PFBLs) auto-enhance the production of the species involved in the loop. There are two subtypes of The importance of switches and clocks as basic modules of PFBL, pure positive or double-negative. Pure PFBLs biological networks was highlighted at the birth of systems biology (Hartwell et al. 1999). Two contrasting approaches of systems biology modelling are (1) a top-down approach, where large-scale datasets are used to infer an underlying molecular regulatory network and (2) a bottom-up approach, where an abstract model of a regulatory system is derived from existing experimental data, and the model is subsequently tested against additional experimental data Fig. 1 Examples of Feedback loops. Left, a negative feedback loop (Bruggeman and Westerhoff 2007). The bottom-up composed of two molecules. Right, a pure positive feedback loop is approach often involves models that combine feedback formed by only positive interactions, while a double-negative loops to explain complex dynamical behaviour, which feedback loop contains an even number of negative interactions 123 764 N. Dalchau et al. often include a combination of switches and clocks (Tyson 2010) and double positive autoregulatory loops, resulting et al. 2003). Indeed, some of the earliest examples of in a quadrastable switch (Wu et al. 2017). The genetic cycles of model refinement and testing (Chen et al. toggle switch has also been coupled with quorum sensing 2000, 2004; Cross et al. 2002) came from the analysis of systems to create a population-based switch, which swit- the cell cycle regulatory network, which combines two ched states dependent on the local cell density (Kobayashi switches to control the major cell cycle transitions and an et al. 2004). In bacterial cells, the cellular context is of oscillator that is responsible for the periodicity of the increasing interest and this can affect genetic switch per- process (Nova ´k and Tyson 2008). Oscillators and switches formance in a number of ways including changes in sta- were also shown to be important in the context of spatio- bility at low molecule numbers (Ma et al. 2012), plus temporal control of cell signalling (Kholodenko 2006). dependence on host growth rate (Tan et al. 2009), sequence Furthermore, the effect of the coupling between positive orientation (Yeung et al. 2017) and copy number (Lee and negative feedback loops was also shown to be et al. 2016). This suggests that natural systems have likely important for the robust periodicity of oscillators (Tsai evolved mechanisms that are robust to some of these fac- et al. 2008). These and several other landmark papers have tors. However, gene regulatory networks are only one way led to legitimate claims of understanding the functioning of to create switch-like behaviours. Alternatives include the these network motifs (Shoval and Alon 2010) and initial use of recombinases, which allow the DNA itself to flip thinking about what could be the algorithms underlying orientation (Friedland et al. 2009; Bonnet et al. 2012; cellular computation (Lim et al. 2013). In recent years, Courbet et al. 2015; Fernandez-Rodriguez et al. 2015), and major steps have been taken to understand biological the use of transcriptional (RNA) systems (Kim et al. 2006). algorithms by synthesizing biological regulatory networks Accompanying theoretical and computational work has de novo, which aim to compute specific functions. been equally diverse, with insights into possible network topologies (Angeli et al. 2004; Otero-Muras et al. 2012), 1.3 Chemical reaction network design stochasticity (Tian and Burrage 2006; Munsky and and synthetic biology Khammash 2010; Jaruszewicz and Lipniacki 2013; Leon et al. 2016), robustness (Kim and Wang 2007; Barnes et al. The advent of ever more precise genetic engineering 2011), time dependent transient behaviour (Verd et al. requires an understanding of information processing in 2014), and emergent properties of populations of switches reaction-diffusion networks and harnessing the emergence linked by quorum sensing (Kuznetsov et al. 2004; Wang of self-organising properties of such systems. Systems with et al. 2007; Nikolaev and Sontag 2016). Following the switch-like and oscillatory behaviours have been a focus of pioneering work in bacteria, there has now been an synthetic biology for almost two decades. In a now classic explosion of engineered switches for mammalian systems Nature edition from 2000, the genetic toggle switch and the (see Kis et al. 2015 for a comprehensive review), which repressilator systems were described, which opened up a use components from diverse backgrounds (prokaryotic, new field of biological engineering (Gardner et al. 2000; eukaryotic and synthetic), and target a variety of Elowitz and Leibler 2000). These systems not only serve as applications. models for the engineering of complex emergent beha- viours, but also allow us to test our hypotheses on how 1.3.2 Engineered biological oscillators biological systems use feedback mechanisms within com- plex networks to function and perform computations. In the Synthetic genetic oscillators have undergone a number of past few years, genetic switches and oscillators have also significant developments. The original repressilator was been used in a number of applications. constructed from three transcriptional repressor proteins arranged in a negative feedback cycle (Elowitz and Leibler 1.3.1 Synthetic switching systems 2000). Another topology that combined positive and neg- ative feedback was first studied theoretically (Barkai and The classic genetic toggle switch used two mutually Leibler 2000) and then constructed in E. coli (Atkinson repressing transcription factors, which gives rise to bis- et al. 2003). An extension of this negative feedback tablity and hysteresis (Gardner et al. 2000; Litcofsky et al. oscillator, combining a further negative autoregulatory 2012). Subsequently, genetic switches were also con- feedback loop, showed increased tunability and robustness structed using positive autoregulatory feedback loops (Hasty et al. 2002; Stricker et al. 2008). In a series of (Isaacs et al. 2003; Atkinson et al. 2003). More recently, landmark papers, this network topology was coupled with circuits combining mutual repression with positive quorum sensing to create populations of synchronised autoregulatory feedback have been built, including the oscillators at different scales (Danino et al. 2010; Mon- addition of a single positive feedback loop (Lou et al. drago ´ n-Palomino et al. 2011; Prindle et al. 2012). This 123 Computing with biological switches and clocks 765 population-based circuit was eventually used for the et al. 2010), including a Pavlovian-like conditioning treatment of tumours in mice, the oscillatory dynamics genetic circuit (Zhang et al. 2014). Most recently, work has causing bacterial cells to lyse and release a chemothera- shown that ribocomputing devices based on RNA opera- peutic agent directly into metastatic sites (Din et al. 2016). tions can be used to create complex logic functions in More recently, in an interesting development, the original living cells (Green et al. 2017). Notable examples of the negative feedback topology of the repressilator was revis- translation of these approaches include cancer cell type ited and re-engineered using detailed stochastic modelling discrimination (Xie et al. 2011) and immunotherapy (Nis- to vastly improve its robustness, so much so that the sim et al. 2017), both of which use Boolean logic com- oscillations remained synchronised without any need for putations on intracellular mRNA signals within quorum system interactions (Potvin-Trottier et al. 2016). mammalian cells. Oscillators have also been implemented at the RNA level The synthetic switches and oscillators described above (Kim and Winfree 2011), metabolic network level (Fung have been used in a small number of non-Boolean com- et al. 2005), and in mammalian cells (Tigges et al. puting applications inside living cells. For example, genetic 2009, 2010). The theoretical properties of genetic oscilla- switches have been used in signal processing applications tors have been studied extensively, including design prin- including detecting small molecule signals in the mam- ciples (Guantes and Poyatos 2006; Novak and Tyson malian gut (Kotula et al. 2014; Riglar et al. 2017) and 2008), robustness (Wagner 2005; Ghaemi et al. 2009; Tsai glucose sensing (Chen and Jiang 2017). In another land- et al. 2008; Woods et al. 2016; Otero-Muras and Banga mark study, coordination of genetic oscillators was 2016) and stochasticity (Vilar et al. 2002; Turcotte et al. achieved through coupling of post-translational processing 2008). of proteins (Prindle et al. 2014). External input signals in The engineering of biological systems in all organisms the form of chemical inducers and flow rate were encoded faces similar implementation challenges. Perhaps the main into frequency modulated oscillations. By exploiting the challenge is context dependence, which can occur at mul- inherent queuing structure of protein degradation, both tiple levels (sequence, parts, evolutionary and environ- oscillators become coupled and the corresponding input mental) (Cardinale and Arkin 2012; Arkin 2013). These signals combined into a single multispectral timeseries include predictability of transcription and translation encoding both signals (Prindle et al. 2014). The theoretical (Mutalik et al. 2013a, b); development of orthogonal part study of multifunctionality in fixed network topologies has libraries (Wang et al. 2011; Nielsen et al. 2013; Chen et al. become of great interest recently (Jime ´nez et al. 2017) and 2013b; Stanton et al. 2014); resource demand (burden, see work has shown that a genetic circuit comprising of both a later discussion); and impedance matching or retroactivity toggle switch and a repressilator, known as the AC–DC (balancing input sensitivity and output strengths) (Vecchio circuit, has emergent properties such as coherent oscilla- et al. 2008; Jayanthi et al. 2013). Eukaryotic systems offer tions, excitability and spatial signal processing (Perez- additional challenges over prokaryotes due to their multi- Carrasco et al. 2018). These examples show that biological cellularity, more complex genomes and higher levels of systems can be engineered to exploit feedback structures regulation (Ceroni and Ellis 2018). These challenges are for analog and digital signal processing and that complex increasingly being met with an interdisciplinary approach computations are possible at different scales. A computer incorporating mathematical modelling, biochemistry, science viewpoint of how biological systems process ‘omics’ approaches and ultimately a deeper understanding information and perform computation could help synthetic of the biology. biology construct more complex systems, further eluci- dating how natural biological systems function. 1.3.3 Synthetic biology and computation Perhaps the most developed area of non-Boolean com- puting within synthetic biology is molecular programming, Within the field of synthetic biology, a large body of work which uses nucleic acids (DNA, RNA) as the computa- on computation has focussed on genetic Boolean gates tional substrate. The use of DNA for computation was first (Moon et al. 2012). In this arena the state-of-the-art in introduced by Adelman to solve an instance of the transcription circuitry is the CELLO algorithm, which uses Hamiltonian path problem (Adleman 1994). It worked by a characterised library of repressor proteins to design mapping DNA oligomers to edges between nodes in a functional genetic implementations for any three-input small network and exploiting the huge parallelism of Boolean circuit (Nielsen et al. 2016). Recombinases (Siuti  10 molecules to compute all possible paths using et al. 2013) and the CRISPR/Cas system (Nielsen and repeated use of polymerase chain reaction (PCR). Finally, Voigt 2014) can also be used to construct Boolean gates, oligomers of the correct length and containing the correct and genetic Boolean circuits have also been combined with start and end sequences were extracted, in principle the toggle switch to create sequential logic operations (Lou 123 766 N. Dalchau et al. providing solutions to this NP-complete problem. Fur- (number of agents). Moreover, the steady states are robust thermore, the number of oligomers required is linear in the to large perturbations, and they are reached quickly even size of the network. Since then, molecular programming when starting from ambiguous configurations (Angluin has progressed significantly and two modern approaches et al. 2008). A third (undecided) state is critical for the will be discussed in detail in Sect. 3. functionality of the algorithm. Mapping this protocol to a biochemical reaction network produces a system described by 3 species (one per belief state) and 4 reactions (Fig. 2a). 2 Dynamical correspondence Initialised with n total molecules, this reaction network between biological and computing enjoys the same Oðlog nÞ convergence. While this basic networks network exhibits only the bistability aspect of a switch, external controls can be added to flip the system from one The primary mathematical feature of a switch is bistability, state to the other. which necessitates the existence of positive feedback loops. In the biological literature, the exact interaction pattern The simplest (bimolecular) chemical reaction network that of AM can be found in epigenetic switches, where DNA realizes a robust bistable switch is the Approximate histones can be in one of three states: (M)ethylated, Majority (AM) network, a system based on competing U(nmodified), or (A)cetylated (Dodd et al. 2007). A con- autocatalytic feedback loops (Fig. 2a). tiguous stretch of DNA consists of a population of histones The name Approximate Majority comes from its origin that should be uniformly methylated or acetylated. This is in distributed computing, where the algorithm is used by a achieved by the M and A states activating two proteins population of agents to reach consensus over one of two each that catalyse transitions between M–U–A states beliefs (states) that each agent can independently adopt through the whole population. The known properties of (Angluin et al. 2008). At steady state, the whole population AM imply robust uniform settling of the whole histone reaches the belief state that was initially in majority, but population into either M or A states, which is also the only approximately, since the algorithm is inherently interpretation suggested in Ref. Dodd et al. (2007). stochastic. Nevertheless, it has been shown that this algo- Many other biological switching systems employ sys- rithm asymptotically optimally convergences to one of two tems that can be related to the AM algorithm. Usually these stable steady states in Oðlog nÞ time with high probability appear in a less direct way, with multiple species involved (Angluin et al. 2008), where n is the population size in the feedback loops. Even though these more complicated A B Fig. 2 Structural morphism and emulation of AM by GW. a, b Wiring same dynamics and that the individual species in GW (X, R, Y, S) can diagrams of Approximate Majority (AM) network and a system be mapped to the different forms of AM. Active forms of X and R (x containing four species embedded in multiple feedback loops (GW). a and r ) and inactive forms of Y and S (y and s ) collapse into x from 0 2 2 0 The AM network shows the reactions involving the three forms of a AM. Inactive forms of X and R (x and r ) and active forms of Y and 2 2 single molecular species X (empty, ball ended arrows mean catalysis S(y and s ) collapse into x from AM. All intermediary forms ( ) 0 0 2 1 of a given reaction). b The GW network shows the interactions collapse with the intermediary form of AM. The similarity between between four species. Arrows indicate the interactions between them the networks of panel A and B represent a structural morphism and (filled, ball-end means activation and dash-end means inhibition). c, d the similarity of their dynamics mean network emulation exists Simulation traces of AM and GW show that they follow exactly the between these two systems 123 Computing with biological switches and clocks 767 systems may look quite different, it is possible to apply a the energy source decreases the system will switch to the model reduction technique that maps them down to the unmodified state OO. basic AM network (Cardelli 2014). Similar reductions can The TI system maintains its toggle-switch behaviour be shown for various models of the cell cycle switch even if some of the reaction paths are blocked (Hernansaiz- (Cardelli and Csikasz-Nagy 2012), and can be summarized Ballesteros et al. 2018). The switching behaviour is lost as follows. only when at least two reactions are removed, which then A trajectory is a time-course evolution of the concen- results in oscillatory behaviour. The Spontaneous Oscilla- tration of a single species. A complex network emulates a tor (SO) network (Fig. 3b) is the simplest oscillatory sys- simpler network if it can reproduce all the possible tra- tem that can be reached from TI by removal of reaction jectories of the simpler network, species by species, in the paths (Hernansaiz-Ballesteros et al. 2018). The oscillations following sense: for any initial conditions of the simple of SO autonomously follow the path OO ! OP ! PP ! network, there are initial conditions of the complex net- PO ! OO (Fig. 3b). Curiously, the SO network is work such that the set of trajectories of the complex net- remarkably similar to a well-known biological oscillator, work is (with replications) exactly the same as the set of the network driving the circadian clock of cyanobacteria trajectories of the simple network (Fig. 2c,d). In short, (Fig. 3c). Here, the autocatalytic molecule KaiC, with the emulation holds if the complex network can always mimic help of KaiA and KaiB, drives 24 h oscillations of phos- the simple network. Moreover, this emulation condition on phorylation cycles (Nakajima et al. 2005). It has been trajectories, which is predicated on all possible initial found that amongst the three components, KaiC is the most states, can be shown to hold just by examining the structure conserved, and sometimes appears in organisms without its of the networks (including rates and stoichiometry, but two partners (Loza-Correa et al. 2010). Thus it was pro- without considering initial conditions). In such a fashion it posed that KaiC-like molecules in primitive organisms can be shown that various idealized cell cycle switches could have adopted a topology similar to either the TI or emulate AM (Cardelli and Csikasz-Nagy 2012; Cardelli the SO systems, thus they could be working there either as 2014). For instance, the Greatwall network (GW) (Cardelli switches or oscillators respectively (Hernansaiz-Ballesteros and Csikasz-Nagy 2012) summarizes the interactions of the et al. 2018). cell cycle regulators Cdk, Wee1, Cdc25 and PP2a, corre- There is a critical interest in finding minimal networks sponding to species X, S, R and Y respectively (Fig. 2b). that can serve crucial biological functions. AM was already This network can emulate the behaviour of the AM net- shown to serve as a minimal switch (Cardelli and Csika ´sz- work (Fig. 2c,d). Nagy 2012), and we can now see that SO could serve as a minimal clock (Hernansaiz-Ballesteros et al. 2018). As the 2.1 From switch-like behaviours to oscillatory two can be converted to one another through reaction dynamics duplications and reaction removals, there is some sugges- tion of an evolutionary link between these architectures. Switch-like dynamics are widely exploited to control bio- This gives us a hope that these and other related systems logical systems requiring memory and decision making could be implemented in synthetic networks that can be (Tyson and Novak 2010). The AM system can efficiently used for complex biological or computing tasks. function as a bistable switch and its dynamics can be emu- lated by a large class of complex biological networks (Car- delli 2014). AM works with a single undecided state, but in a 3 Molecular programming real molecular system, the two modifications that lead to the two active forms of AM might not affect the same site. This Molecular Programming involves ‘‘the specification of led us to consider a Two Intermediates (TI) system with two structures, circuits, and behaviours both within living and intermediates (OP and PO) between the autocatalytic forms non-living systems–systems in which computing and deci- (OO and PP) (Fig. 3a). OO and PP can convert these species sion-making are carried out by chemical processes them- between the various forms producing a specific pattern of selves’’ (molecular-programming.org). Nucleic acids are modification: OO !OP !PP !PO !OO. From a currently the molecules of choice for molecular program- dynamical systems point of view, the TI system produces ming, due to their high degree of programmability via switch-like behaviour and emulates AM. In a biological Watson-Crick complementarity and their ability to directly context, this system has been proposed to function as a interface with biological components, with potential primitive sensor of the source of energy (Hernansaiz- applications in sensing, diagnosis and treatment of disease. Ballesteros et al. 2018). When energy level is above a critical A number of approaches have been proposed for imple- threshold TI will be in the fully modified state PP, while as menting computation in nucleic acids. Here we will sum- marise two of the main ones—DNA Strand Displacement 123 768 N. Dalchau et al. Fig. 3 A simple switch turned into an oscillator. a The Two cyanobacteria circadian clock (Loza-Correa et al. 2010), where KaiC Intermediates (TI) system, that is behaving like a switch and hexamers are helped to convert themselves between forms that are emulating the behaviour of AM. b The Spontaneous Oscillator (SO) phosphorylated an unphosphorylated at two critical sites (labelled T system is derived from TI and functions as robust oscillator. Solid and S). KaiA (blue triangle) facilitates the phosphorylation reactions, arrows represent catalytic transitions with ball end arrows showing while KaiB (yellow rod) helps the dephosphorylation reactions. the activator of transitions, grey empty arrows represent first order (Color figure online) conversions. c Representation of the KaiABC system of the and PEN DNA Toolbox—and describe how they have been DNA Strand Displacement scheme was proposed (Cardelli used to implement switches and clocks. 2013), which enabled gates to be manufactured using plasmid DNA grown in cell culture. Since the DNA 3.1 DNA strand displacement replication machinery of cells is substantially more accu- rate than existing DNA synthesis technology, particularly Pioneering theoretical work (Soloveichik et al. 2010) for long sequences, a large number of copies of the same showed how DNA could be used to implement a broad double-stranded DNA sequence can be clonally replicated range of computation, including any computation that can in cell culture. The culture is sequenced to check that no be expressed as a chemical reaction network. The mecha- errors have been introduced and, since the population is nism proposed was that of toehold-mediated DNA strand clonal, if the sample sequence is correct then all copies of displacement (Zhang and Seelig 2011), whose systematic the sequence are also highly likely to be correct. The use was pioneered by Yurke et al. (2000). During this 2-domain scheme was used to implement the computa- process, an invading single strand of DNA displaces an tional core of a switching network (Chen et al. 2013a) incumbent strand hybridized to a template (Fig. 4a). The (Fig. 6). Overall, one of the main advantages of using DNA process is mediated by a short exposed single-stranded region of DNA, referred to as a toehold. Various types of strand displacement for the design and implementation of computation have been implemented experimentally using molecular-scale computation is its high degree of pro- this approach, including elementary Boolean logic (Seelig grammability, since all interactions are precisely encoded et al. 2006), square root computation (Qian and Winfree by the choice of DNA sequence. Moreover, system 2011), neural network computation (Qian et al. 2011), dynamics can be accurately predicted from computational distributed consensus capable of switching (Chen et al. models of their components (Chen et al. 2013a; Srinivas 2013a), and oscillations (Srinivas et al. 2017). et al. 2017). Another important advantage is that the entire The general approach proposed by Soloveichik et al. computation can be implemented solely in terms of DNA, (2010) for implementing an arbitrary chemical reaction without requiring additional enzymes. This simplifies sys- network in DNA is based on a 4-domain scheme (Fig. 4). tem production, and also allows systems to be used in a This approach was subsequently used by Srinivas et al. broad range of biological contexts, with limited disruption. (2017) to implement an oscillator consisting solely of DNA One of the main challenges is the need to replenish DNA (Fig. 5). strands and complexes in cases where dynamic behaviour One of the potential drawbacks of the 4-domain needs to sustained for extended periods. To address this, scheme is that it requires synthetic DNA strands to be complexes and fuel strands could be replenished periodi- annealed. These synthetic strands can contain synthesis cally, or a system of buffered gates (Lakin et al. 2012) errors, which increase with strand length. A 2-domain could be used. Another challenge is that unintended 123 Computing with biological switches and clocks 769 12 23 (1) (2) (3) 1 23 12 3 1* 2* 3* 1* 2* 3* 23 12 single-reaction model 1* 2* 3* 1* 2* 3* species identifier q 27 3 14 0 11 ?1 2 3 * 2* 3* 2* 3* 1q q i i O G waste species species 6 9 identifier identifier 5 8 37 14 0 11 2 3 14 0 11 7 14 0 11 10 4 5 6 11 7 8 9 1* 0* 4 11*7* 3* 1* 0*4*1* 1 7 3* O X X 2 3 waste Fig. 4 A 4-domain scheme for implementing chemical reaction the formal unimolecular reaction X ! X þ X , with reaction index 1 2 3 networks in DNA, reproduced from Soloveichik et al. (2010). a An i. The species of this formal reaction are represented as DNA strands elementary DNA strand displacement interaction, modelled by the and highlighted by boxes, with X represented as \ ?1 23[, X as 1 2 chemical reaction X þ G ! Y þ H. Chemical species X denotes a \10 4 5 6[ and X as\11 7 8 9[. Black domains are assumed to be single DNA strand consisting of domains 1 and 2, where each domain unique to each reaction i, while green, red and blue domains are corresponds to a DNA sequence. The strand X is written \12[, associated to species X , X and X , respectively. The formal reaction 1 2 3 where the 3’ end of the strand is assumed to be on the right, X ! X þ X is implemented by two DNA complexes, which are 1 2 3 represented graphically by an arrowhead. The species G denotes a assumed to be present in excess and are consumed over time. The first complex consisting of strand\23[ hybridized to the strand\3* 2* complex G binds the species X and produces the intermediate O , 1 1 i 1*[, where the star (*) denotes Watson-Crick complementarity. The while the second complex T binds the intermediate O and produces i i reaction takes place in three steps: (1) The domain 1 binds to its the two species X and X . The additional intermediate step is needed 2 3 complement 1*. The reaction is reversible, since the domain 1 is to ensure that the reactant species X does not contain any assumed to be short enough to spontaneously unbind. These short overlapping domains with the product species X and X . Note that 2 3 domains are referred to as toeholds; (2) The domain 2 of strand\12[ the sequence of toehold domain 1 can also be adjusted to be only displaces the domain 2 of strand \23[ by a random walk process, partially complementary to domain 1, in order to tune the reaction rate referred to as branch migration; (3) The toehold domain 3 sponta- q . (Color figure online) neously unbinds from its complement 3*. b A 4-domain encoding of interactions between strands can lead to a decrease in feedback controller systems, and a comparison with alter- system performance, for instance due to blunt-end strand native nucleic acid implementation strategies. displacement interactions that occur in the absence of a toehold, also known as leaks. One strategy for mitigating 3.2 The polymerase-exonuclease-nickase these leaks involves the use of toehold clamps (Qian and dynamic network assembly (PEN-DNA) Winfree 2011), which can be used effectively in a sys- toolbox tematic way (Wang et al. 2017). Another approach for reducing unwanted interference between DNA molecules An alternative to DNA strand displacement for performing more generally is to localise the molecules to DNA origami molecular computation uses enzymes to manipulate DNA (Dalchau et al. 2015; Chatterjee et al. 2017), such that signals. The PEN-DNA (Polymerase—Exonuclease— strands which are meant to interact are placed close to each Nickase Dynamic Network Assembly) toolbox is a set of other. This increases the local concentration of interacting modules that can be composed to implement molecular strands, allowing fast computation, while reducing inter- programs (Fig. 7a) and, as we shall describe in this section, ference. See Yordanov et al. (2014) for a more in-depth has successfully been used to implement switches and discussion on the advantages and challenges of using DNA oscillators. strand displacement in the context of implementing 123 770 N. Dalchau et al. Fig. 5 Implementation of an oscillator using a 4-domain DNA strand similar to the one described in Fig. 4. Each molecular species is displacement scheme, reproduced from Srinivas et al. (2017). a The implemented as single DNA strand, and each reaction is implemented desired oscillatory dynamics are implemented by a molecular as a pair of DNA complexes together with an additional fuel strand. program, which is specified as a chemical reaction network. The For example, the reaction Aþ C ! 2A is implemented as a complex network consists of three species (A, B, C) and three autocatalytic that consumes the A and C strands to produce an intermediate strand, reactions, in which B converts A to itself, C converts B to itself, and and a complex that consumes the intermediate to produce two A A converts C to itself. This corresponds to the so-called rock-paper- strands, with the help of a fuel strand. The complexes and fuel strands scissors oscillator (Lachmann and Sella 1995). b The chemical are assumed to be present in excess and are consumed over time in a reaction network is then translated to a 4-domain DNA architecture, closed system, resulting in progressively slower oscillations Fig. 6 Implementation of a switch using a 2-domain DNA strand described in Fig. 5, the behaviour of the systems is specified as a displacement encoding, reproduced from Chen et al. (2013a). The chemical reaction network consisting of three reactions, in which X system takes as input two populations of signals, encoded as DNA and Y cancel each other out to produce two intermediates B, species strands, and uses a distributed consensus network to determine which X converts B to itself, and species Y converts B to itself. This is population is in the majority. The output of the system is a equivalent to the Approximate Majority network (Angluin et al. homogeneous population of strands, in which all of the minority 2008) described in Fig. 2 strands have been converted to the majority. As with the oscillator An activation module enables a short single-stranded b domain, producing a full duplex. The sequences of a and DNA (ssDNA) signal a to stimulate production of another b are chosen to enable a Nickase enzyme to bind and ssDNA signal b. This is achieved by a longer template convert the duplex into a nicked double-stranded molecule. strand a to b composed of two consecutive domains, one This separates the upper domains, such that their affinity complementary to a and the other complementary to b. for the template is reduced and they can more easily When a binds to the 3’ side of the atob template, Poly- unbind, leading to the release of the pre-existing a and de merase is recruited, and elongates the input strand over the novo synthesized b ssDNA signals. As such, a catalyses 123 Computing with biological switches and clocks 771 Fig. 7 The PEN-DNA toolbox. a Summary of the PEN-DNA toolbox state, red symbols represent the low a-high b state, and green/orange modules (reproduced from Meijer et al. 2017), with Polymerase (Pol), symbols are the external inputs. Measurements correspond to treating Exonuclease (Exo) and Nickase (Nick) enzymes. b The switchable with 2.5 nM or 5 nM of dtob, as indicated. All graphics are memory circuit from Padirac et al. (2012). In the network diagram, reproduced from Padirac et al. (2012). c The negative feedback loop blue symbols represent components associated with the high a-low b oscillator from Montagne et al. (2011). (Color figure online) the production of b, analogous to the reaction a ! aþ b. 3.2.1 Switches as memory devices A deactivation module implements the reaction a ! a , where a is notionally inactive. This is achieved by a A bistable switch was one of the first circuits constructed using the PEN-DNA toolbox (Padirac et al. 2012) pseudo-template pTa that extends a with a short oligonu- cleotide tail, preventing a from participating in activation (Fig. 7b). The circuit design combined self-activation with mutual inhibition, resembling the MI network described reactions. Finally, a 5’-3’ Exonuclease destroys all ssDNA signals, representing a non-specific degradation module. above. The inner mutual inhibition module was achieved using four template strands: two templates implemented self-activation for a (a to a) and b (b to b), while a further two templates implemented inhibition with the production 123 772 N. Dalchau et al. of inactive signals ia and ib, which block a and b templates Compared to oscillators constructed from purely DNA respectively. An additional two templates were then used to systems, the PEN-DNA systems exhibit temporal dynamics mediate inputs c and d that could switch the device that can be sustained for substantially longer time periods. between the a and b states. The authors demonstrated that a A feature of PEN-DNA that is likely to contribute to this is high concentration of external input could switch the the ability to synthesize new copies of the signal strands. device in approximately 200 minutes, but with lower This is not possible with a purely strand displacement concentrations leading only to a transient excursion and system, which produce new signal strands by releasing then return to the pre-existing stable state. While the them from previously constructed gate species, supplied as demonstration of the robustness of the switch is impressive, fuel. Accordingly, the gate species are consumed over time such a long switching time could prohibit its usage in some and oscillator amplitudes drop. The PEN-DNA systems applications/ Nevertheless, by this circuit being both also exhibit changes in dynamics over time as the supply of bistable and switchable, it can be used for long term nucleotides and other reagents is depleted, though this memory storage. A push-push memory device was also occurs on a longer time scale relative to the system constructed, which enabled switching back and forth in dynamics. response to the same input signal. Switches are fundamental building blocks for many computational devices, but their utilisation requires sensing 4 Future of biological computing of inputs and actuation. Recently, it was demonstrated how the PEN-DNA memory switch of Padirac et al. (2012) can 4.1 Molecular programming in cells be connected to downstream enzymatic actuators, enabling the connection of DNA-based memory devices to triggered Despite the limitations discussed above, there are consid- downstream signalling (Meijer et al. 2017). To achieve erable advantages to using DNA circuits to implement this, a translator module was developed that dynamically computation in cells. DNA offers a natural interface to the perceives the short single-stranded DNA molecules of the cellular machinery and is inherently biocompatible. After bistable switchable memory device described above, then several years of exploring the computational potential of produces longer DNA strands that can be used to control nucleic acid circuits in vitro, there are now efforts to the activation of two enzymes, NanoLuc and TEM1 b- deliver DNA circuits into live cells. In Groves et al. (2015), lactamase. Importantly, the translator was designed to a variety of methods were compared for delivering nucleic minimize retroactivity back to the memory switch, which acid circuits to mammalian (CHO and HeLa) cells, and it was demonstrated with a detailed experimental and theo- was shown that multi-input computation in live cells could retical characterization. Finally, the activation/inactivation be detected using flow cytometry. In the same study, of the enzymes relies on interactions with conjugated chemical modifications to DNA and RNA strands were oligonucleotides, which are modulated by the output of the shown to improve binding kinetics, most likely a result of translator module. This appears to be the first time memory reduced nuclease activity against the modified strands. This devices and actuators have been connected in a synthetic has stimulated more detailed characterization studies of molecular circuit, and is an important step towards realis- nuclease activity against nucleic acid circuits (Fern and ing more general molecular computers. Schulman 2017). Another fruitful strategy for delivering DNA circuits to live cells has been the use of DNA ori- 3.2.2 Limit cycle oscillators as clocks gami, which provides both a localizing and protective effect on circuit components, leading to faster circuit The first attempt to produce an oscillator using the PEN operation (Dalchau et al. 2015; Chatterjee et al. 2017), but toolbox approach was based on recapitulating a network also successful operation in a live animal (Amir et al. topology that is known to robustly produce oscillatory 2014). behaviours (Montagne et al. 2011). Subsequently, another Introducing molecular circuits based on the PEN-DNA network architecture based on a predator-prey interaction toolbox into cells is made challenging by the need to was developed (Fujii and Rondelez 2013). Using both express the PEN enzymes in the target cells. Enzymes strategies, the Rondelez group were able to sustain oscil- impose several design constraints on the selection of DNA lations for more than 10 cycles, with only a small ampli- sequences. Nicking enzymes have specific recognition tude loss. By taking advantage of molecular diffusion, and sites, which imposes a limit on the diversity of signal visualizing the solution between two glass slides, a follow- strands that can be used in a PEN-DNA circuit. In contrast, up work illustrated how these DNA-based oscillators can polymerase and exonuclease are non-specific, meaning that also produce travelling wave phenomena (Padirac et al. the activation and degradation reaction rates are difficult to 2013). control. While differential activation rates could be 123 Computing with biological switches and clocks 773 achieved by controlling activation template concentrations, Whitley and Sutton 2012; Yang 2014). Such advances will dynamic behaviours that require differential degradation continue, driven by the desire for scalability and robustness would be harder to engineer. as the complexity of solid state technology approaches that Nucleic acid circuits have the added benefit of requiring of biological systems. a reduced regulatory approval process compared with As precision in designing chemical systems increases, genetically modified organisms, for applications such as we look towards chemical computational units with which disease diagnosis and treatment. There have already been we may construct complex behaviours systematically. We several attempts to use nucleic acids circuits, combined have seen how computational DNA circuits and related with transcriptional machinery, for biosensing and diag- technologies can be used as flexible molecular mechanisms nosis (Pardee et al. 2016). Non-transcriptional nucleic acid to engineer switches, oscillators, and other computational circuits are in principle easier to program than transcrip- components in vitro, with efforts being made also in vivo. tional networks based on promoter regulation by proteins. Moreover, such computational units can be coupled with In part, this is due to transcriptional control requiring the molecular sensors, actuators, and scaffolding to provide pairing of a protein surface with a DNA binding motif, an complete nanoscale devices. Many such devices and interaction that is challenging to engineer synthetically. components can be individually designed and engineered However, new approaches based on CRISPR/dCas9 could using the DNA, RNA, and enzyme tricks of the biochem- lead to a more targeted way of engineering networks with ical trade. precise topologies. Finally, nucleic acid circuits are a convenient test framework for programmed genetic cir- 4.3 From single-cells to computational cuits. They force the engineer to consider energy/substrate communities economy and the physical limitations of molecular binding, which, for example, is analogous to ribosomal usage and Building on the fascinating advances in our ability to transcriptional and translational efficiency of synthetic program cell-autonomous behaviours, there are now sev- gene circuits. Much of what we have learned in the design, eral examples of establishing behaviours that rely on characterization and analysis of nucleic acid circuits can be multicellularity. Switches within individual cells can be applied to the engineering of computational circuits based linked via inter-cellular communication (see Hennig et al. on other biomolecular frameworks. 2015 for a thorough review), including natural quorum sensing molecules (Camilli and Bassler 2006) and artificial 4.2 From molecular networks to algorithms DNA messengers (Ortiz and Endy 2012; Gon ˜ i-Moreno et al. 2013). As such, it is possible to achieve behaviours of As we have seen above, algorithms that mimic the beha- distributed computing algorithms with cells. Based on viour of biological switches and clocks can be imple- temporal logic, it was shown how cell populations could be mented using DNA circuits, and the same dynamics can used for timing and recording chemical events (Hsiao et al. also be achieved using synthetic gene regulatory networks. 2016). It remains to be seen how more complex gene regulatory In additional to temporal control, intercellular commu- networks could implement more advanced algorithms, nication also enables spatial control, and therefore pro- enabled by advanced genome editing techniques (Cong grammed pattern formation. Already, this has enabled et al. 2013). More complex engineered networks of circuits that can detect spatial boundaries between an switches and clocks could also be combined with electronic environmental signal (light) (Tabor et al. 2009) and circuits (Cao et al. 2017) to serve as biosensors. These establish stripe patterns in expanding colonies (Liu et al. applications could have a major influence on disease 2011). More exploratory work with communicating bac- detection and treatment. However, to reach this stage terial populations has begun to shed light on how devel- requires a better understanding and control of elementary opmental patterns can be scale invariant (Cao et al. 2016), computing units. Thus, algorithmic thinking might be but also suggest a new platform for testing ecological leveraged to detect and ultimately treat complex disease theory, via synthetic ecosystems (Song et al. 2009). Fur- states, by combining switches and clocks with the existing thermore, techniques such as live cell lithography can logic circuit toolbox. create regular structures of communicating microbes at Historically, the analysis of biological mechanisms and resolutions of 5 lm (Mirsaidov et al. 2008). There is also collective behaviour from an algorithmic perspective led to work in controlling spatial distributions of DNA molecules simplified models, which aided understanding of informa- directly (Dalchau et al. 2014; calise and Schulman 2014), tion processing in natural systems. This laid the ground- which could be used to pre-pattern cellular systems. work for future breakthroughs across disciplines Put together, there is now real promise for designing cell (Marblestone et al. 2016; Navlakha and Bar-Joseph 2011; colonies that control their own temporal dynamics and 123 774 N. Dalchau et al. spatial positioning. This could be highly relevant to bio- understand the capability of synthetic multicellular logics production in bioreactors, where spatial hetero- platforms. geneity in resources and cell density could lead to inefficiencies. The advantages of automatic control can be 4.4 Learning from biological computing readily seen in more traditional control engineering appli- cations, and consequently, there is now rising interest of As we increasingly rely on computing to process large implementing control algorithms in biological circuits (Del datasets for everyday tasks at home and at work, power Vecchio et al. 2016). Earlier strategies were based on consumption will become a future limiting factor (Council transcriptional negative autoregulation (Becskei and Ser- 2011; Kamil et al. 2008). In fact the effects of thermody- rano 2000; Rosenfeld et al. 2002), but more recently, a namics—that is removing heat efficiently from semicon- more advanced integral control via negative feedback has ductor devices—has already driven the shift to multicore been demonstrated in metabolic circuits (Briat and chips and parallel computing, which can improve on the Khammash 2018), but also using optogenetics via in silico performance scaling of single processors, but will funda- controllers (Milias-Argeitis et al. 2016; Lugagne et al. mentally change how we develop programs (Council 2017). Automatic control will bring robust operation and 2011). Biological systems perform computations at much self-adaptation to biological circuits, which will help to lower levels of power consumption: estimates report 4 make biotechnology more efficient and ultimately more orders of magnitude for molecular machines (Nicolau et al. competitive in the marketplace (Del Vecchio et al. 2016). 2016) and up to 12 orders of magnitude for DNA com- Despite the promise of synthetic biology, significant puting (Adleman 1994). In addition, these computations challenges remain for regulating biological behaviours are carried out in a robust manner, embedded within fluc- with the insertion of designed networks of transcriptional tuating environments, and often utilising components that components. One challenge relates to timescale: tran- are unreliable and noisy (Sarpeshkar 2010). This incredible scriptional control is slow, though is the dominant mode of performance is achieved through multi-scale hybrid analog regulation in synthetic biology applications to date. Control and digital information processing. Biological computers algorithms are sometimes inefficient in the face of delays, have the additional advantage that they can interface and so their success might depend on establishing faster directly with living systems and therefore open up new modes of biological regulation. Here, molecular program- applications in biosensing with industrial and clinical rel- ming might provide a solution, as DNA-based circuits can evance. For example, signal processing in the ear has be localized, speeding up their operation (Chatterjee et al. already inspired electronics for low power cochlear 2017). Another challenge of using transcriptional regula- implants (Mandal et al. 2009) and pattern recognition by tion is that each additional component introduces a burden neurons led to a novel analog-to-digital converter (Yang on the host cell, which can lead to poor growth of the and Sarpeshkar 2006). These properties, combined with the colony, thus altering the performance of existing compo- high information storage density of DNA (Church et al. nents and/or reduce yields (Scott et al. 2010; Borkowski 2012; Goldman et al. 2013; Erlich and Zielinski 2017), et al. 2016; Wu et al. 2016). For example, inserting a provide exciting future directions for further research. component that leads to high levels of protein translation In this review we have highlighted how complex will impose a burden on the ribosome pool (Scott et al. biomolecular networks make use of switches and oscilla- 2010; Shachrai et al. 2010), high levels of transcription tors to perform computation. The continued understanding will impose a burden on RNA polymerase (Gyorgy et al. of how this information processing is achieved at such high 2015), and high levels of protein degradation will impose a levels of robustness and low power requirements will burden on proteases (Cookson et al. 2011). While some of require the concerted efforts of systems and synthetic these can be mitigated with quantification of the burden biology in addition to leveraging tools from engineering and careful design (Nielsen et al. 2016), establishing cel- and computer science. While it is unlikely that biological lular control with components that do not consume/occupy systems will ever replace silicon as our dominant com- shared cellular resources could be a major advantage. puting platform, learning how they compute could have a However, it remains unclear as to whether DNA circuits significant impact on future computing architectures. can operate reliably enough inside cells to rival existing Open Access This article is distributed under the terms of the Creative approaches to cellular control. Commons Attribution 4.0 International License (http://creative The extent to which spatiotemporal control can improve commons.org/licenses/by/4.0/), which permits unrestricted use, dis- biotechnology applications is relatively unexplored. tribution, and reproduction in any medium, provided you give Therefore, more theoretical work is needed to establish the appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were performance that can be achieved by algorithms based on made. chemistry and cellular communication, and therefore to 123 Computing with biological switches and clocks 775 Cardelli L (2014) Morphisms of reaction networks that couple References structure to function. BMC Syst Biol 8(1):84 Cardelli L, Csikasz-Nagy A (2012) The cell cycle switch computes Adleman LM (1994) Molecular computation of solutions to combi- approximate majority. Sci Rep 2(1):656 natorial problems. 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Abstract

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch- like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing. Keywords DNA computing  Systems biology  Synthetic biology  Distributed computing  Oscillation Bistability  Feedback loop  Network 1 History of understanding biological clocks, respectively (Tyson et al. 2008). We have under- computation stood much about the behaviour of these basic units of biological computation (Ferrell 2002; Nova ´k and Tyson In the last 50 years, biology has inspired computing in 2008; Tyson et al. 2003) and simple switches and clocks several ways (Navlakha and Bar-Joseph 2011; Cardelli have been synthesized in single cells more than 15 years et al. 2017). During this time, computational thinking has ago (Becskei and Serrano 2000; Gardner et al. 2000; also improved our understanding of biological systems Elowitz and Leibler 2000). Nevertheless, we still lack a (Bray 1995; Goldbeter 2002; Nurse 2008). Using principles comprehensive understanding of how these computational from chemistry, physics and mathematics, we have modules have emerged, and which features and molecular understood that the highly complex behaviour of biological interactions are responsible for their efficient and robust systems is caused by a multitude of coupled feedback and behaviour (Cardelli et al. 2017). Ideas from computing feed-forward loops in the underlying molecular regulatory might help us to take this last step, which might enable networks (Alon 2007; Tyson and Nova ´k 2010). In partic- biological switches and clocks to be influential in the ular, we have learned that positive and negative feedback development of future computing technologies. The simi- loops are responsible for driving biological switches and larity between the biological switch controlling mitotic entry and the approximate majority algorithm of distributed computing (Angluin et al. 2008; Cardelli and Csika ´sz- Neil Dalchau, Gregory Szep, and Rosa Hernansaiz- Nagy 2012) suggests that computing and molecular biology Ballesteros have contributed equally. could further influence each other in the future. With the & Attila Csika ´sz-Nagy emergence of the fields of systems and synthetic biology, csikasznagy@gmail.com there has been increased interaction between computer 1 science and biology, but there are a few steps needed Microsoft Research, Cambridge, UK before we can realise a biology-inspired soft-matter com- King’s College London, London, UK putational revolution. In this paper we review some of the University College London, London, UK key advances we have seen as a result of the interplay University of Oxford, Oxford, UK between computing and biology and speculate on the ´ ´ ´ Pazmany Peter Catholic University, Budapest, Hungary 123 762 N. Dalchau et al. directions that a possible joint field could take in the near much of cellular function. Oscillations can also be future. observed in systems consisting of just 1 to 3 proteins, as in the case of the KaiC circadian oscillator (Nakajima et al. 1.1 Computation 2005), although those proteins have a very sophisticated structure. Theoretically, many chemical oscillators con- The basic components of computational devices, including sisting of 2 to 3 simple species have been studied modern electronic circuits and earlier mechanical equiva- (Bayramov 2005). lents, consist mainly of Boolean and arithmetic functional Although similar basic components (switches, oscilla- units (Boolean control logic, integer and floating point tors, and functional units) are found both in biology and in units, analog to digital converters, etc.), of registers to hold computer engineering, it does not necessarily mean that intermediate results of iterative algorithms, and of coordi- these systems compute ‘‘in the same way’’. In particular, nation components that orchestrate the flow of information coordination is achieved in fundamentally different ways in across registers and functional units. Coordination is most biological systems than in the von Neumann architecture. often achieved by clocks: at each tick data is frozen into In biology, oscillators coordinate events only at the registers, and between ticks data flows between registers coarsest level of granularity, while fine-grained coordina- through the functional units. This is the so called von tion is achieved by direct interaction between molecular Neumann architecture that, despite dramatic technology components. In the central processing unit of computers, improvements and architectural refinements, has remained oscillators instead coordinate events at the finest grain, and largely unchanged since the first electronic computers. do so at great cost. As a result, low-power devices tend to Functional units compute Boolean and mathematical employ clock-free coordination strategies to save power. functions by combinational logic (that is, without requiring At the level of computer networks, though, coordination is memory or timing coordination). We can easily find ana- achieved by message passing, because individual clocks logues of these in biology, like the function computed by can get out of step and network latency may vary. Many the regulatory region of a single gene (Arnone and non-von Neumann models of computation have been Davidson 1997). Synthetic biology has demonstrated how studied in the area of distributed computing: these models many such functions, typically Boolean gates, can be resemble, and sometimes even technically coincide, with engineered in vivo by a variety of genetic and protein- biochemical models (Angluin et al. 2006; Chen et al. based mechanisms (Siuti et al. 2013). More theoretically, it 2014). has been shown how chemical reaction networks can The general architecture of computation in biochemical compute complex functions (Buisman et al. 2009). systems is still a matter of investigation, and so is the functioning of many subsystems that appear to process Although much of this work has mimicked digital com- ponents, there is a sentiment that functional units in biol- information. For the moment we can focus on how nature ogy work mostly in the analog domain, and that synthetic achieves the functionality of the basic components, biology could benefit from this approach (Sauro and Kim switches, oscillators and functional units, while using 2013). material and constraints that are very different from those In this review we focus mainly on the other two classes that come from engineering. of components: memory and coordination. A switch is a memory unit capable of storing a single bit: at the core 1.2 How do natural systems compute? there is a bistable dynamical systems coupled with a mechanism to force the system from one stable state to the The complex dynamics of natural systems drew research other. Switching behaviour is pervasive in biology: it is interest a long time ago. The theory of dynamical systems achieved by a range of mechanisms, from individual and chaos was born at the turn of the twentieth century, molecular components like phosphorylation sites and with a focus on understanding the weather and the many- riboswitches, to whole complex biochemical networks that body problem (Strogatz 2000). Pioneers of mathematical switch from one configuration to another, such as in the modelling of biological systems came from the field of cell cycle switch. Synthetic genetic switches have also chemical physics and used their experience learned from been demonstrated (Gardner et al. 2000). non-equilibrium chemical systems to investigate biological The intricate feedback loops of biochemical networks switches and clocks (Goldbeter 2017). Ideas on the tend to produce oscillations in abundance, both stable and chemical basis of biological behaviour were also used by transient, many of which are poorly understood. The most the computer scientist Alan Turing to explain develop- prominent oscillators in biology, found also in the most mental pattern formation (Turing 1952). Yet still comput- primitive organisms, are those involved in the cell cycle ing had far less influence on our thinking about biological and in circadian clocks, whose cyclic activities coordinate systems than chemistry, physics or mathematics. Indeed, 123 Computing with biological switches and clocks 763 biological behaviour is controlled by (bio)chemical reac- contain only interactions of activation, while double-neg- tions and the underlying reaction kinetics can be under- ative PFBLs, or antagonistic interactions, contain an even stood by looking at the microscopic physical behaviour of number of inhibitions (plus any number of activations). molecules, but to turn these into a comprehensive form, (Fig. 1). mathematical expertise is required. Since the 1990s, Feedback loops (FBLs) constitute a basic relationship advances in computing have enabled us to solve highly between molecular species to construct complex beha- complex equations describing the physical interactions of viours and consequently are abundant in protein regulatory the chemical reactions driving biological behaviour, but it networks. FBLs can produce various dynamical beha- was the appearance of systems biology (Kitano 2002a) that viours, such as efficient switching and oscillations (Thomas led to the understanding that we need more computing to et al. 1995; Thomas 1981; Tyson et al. 2003; Tyson and truly understand biological systems (Kitano 2002b). Data- Nova ´k 2010; Hernansaiz-Ballesteros et al. 2016; Cardelli rich biological experiments at the molecular level have et al. 2017). Switch-like dynamics requires PFBLs, pro- identified the ubiquity of switches and clocks (Goldbeter ducing two (or more) stable states of the system (usually 2002) as core components of complex biological regulatory on/off states), when a given species is either fully active or networks. inactive. This feature of PFBLs is known to be key for developmental and decision-making processes (Ferrell 1.2.1 Feedback loops 2002). In contrast, oscillations require the presence of NFBLs. While direct negative feedback can stabilize a Already by the 1960’s it was known that feedback loops system, the introduction of a delay arising from regulation are the key determinants of the dynamics of biological via an intermediate, or simply through a slow accumula- systems (Griffith 1968a, b). Positive feedback loops are key tion, can very easily lead to oscillations. If a system con- to the appearance of switching behaviour, while negative tains at least three different molecular species and a strong feedback loops are needed for oscillations (Ferrell 2002; non-linearity, a damped or sustained oscillator may arise Goldbeter 2002). The complex dynamics of biological (Griffith 1968b). Systems with only two molecular species systems is determined by the combination of multiple of and without explicit time delays can also oscillate, but they such feedback loops (Tyson et al. 2003). Here we present require the presence of a PFBL, creating a switch that the main features of feedback loops that enables them to drives the oscillation. In contrast, the combination of pos- drive key biological processes. itive feedbacks with the depletion of one of the species Feedback loops (FBLs) arise when at least two molec- creates systems that can oscillate without an explicit neg- ular species regulate each other’s activity (Fig. 1). There ative feedback loop. These so-called relaxation oscillators are two types of FBLs, negative or positive. Negative FBLs produce characteristic fast switching in one direction, with (NFBLs) appear when the production or activation of a slow switching in the other direction, producing triangular- species is either directly or indirectly repressed when this like waveforms (Sel’Kov 1968). Finally, several natural same species is active (autoregulation) (Thomas and D’Ari oscillations are known to integrate positive and negative 1990; Thomas et al. 1995). Negative feedback loops con- feedback loops, which is thought to enhance the oscillator tain an odd number of inhibitions. In Fig. 1, a system of network robustness to intrinsic or extrinsic fluctuations only two components is shown, where one of the molecular (Thomas 1981; Thomas et al. 1995; Nova ´k and Tyson species (X) exhibits inhibitory activity over the other (Y), 2008; Ferrell et al. 2011). while this other molecule Y is activating the first molecule X. 1.2.2 Systems biology of switches and clocks Positive FBLs (PFBLs) auto-enhance the production of the species involved in the loop. There are two subtypes of The importance of switches and clocks as basic modules of PFBL, pure positive or double-negative. Pure PFBLs biological networks was highlighted at the birth of systems biology (Hartwell et al. 1999). Two contrasting approaches of systems biology modelling are (1) a top-down approach, where large-scale datasets are used to infer an underlying molecular regulatory network and (2) a bottom-up approach, where an abstract model of a regulatory system is derived from existing experimental data, and the model is subsequently tested against additional experimental data Fig. 1 Examples of Feedback loops. Left, a negative feedback loop (Bruggeman and Westerhoff 2007). The bottom-up composed of two molecules. Right, a pure positive feedback loop is approach often involves models that combine feedback formed by only positive interactions, while a double-negative loops to explain complex dynamical behaviour, which feedback loop contains an even number of negative interactions 123 764 N. Dalchau et al. often include a combination of switches and clocks (Tyson 2010) and double positive autoregulatory loops, resulting et al. 2003). Indeed, some of the earliest examples of in a quadrastable switch (Wu et al. 2017). The genetic cycles of model refinement and testing (Chen et al. toggle switch has also been coupled with quorum sensing 2000, 2004; Cross et al. 2002) came from the analysis of systems to create a population-based switch, which swit- the cell cycle regulatory network, which combines two ched states dependent on the local cell density (Kobayashi switches to control the major cell cycle transitions and an et al. 2004). In bacterial cells, the cellular context is of oscillator that is responsible for the periodicity of the increasing interest and this can affect genetic switch per- process (Nova ´k and Tyson 2008). Oscillators and switches formance in a number of ways including changes in sta- were also shown to be important in the context of spatio- bility at low molecule numbers (Ma et al. 2012), plus temporal control of cell signalling (Kholodenko 2006). dependence on host growth rate (Tan et al. 2009), sequence Furthermore, the effect of the coupling between positive orientation (Yeung et al. 2017) and copy number (Lee and negative feedback loops was also shown to be et al. 2016). This suggests that natural systems have likely important for the robust periodicity of oscillators (Tsai evolved mechanisms that are robust to some of these fac- et al. 2008). These and several other landmark papers have tors. However, gene regulatory networks are only one way led to legitimate claims of understanding the functioning of to create switch-like behaviours. Alternatives include the these network motifs (Shoval and Alon 2010) and initial use of recombinases, which allow the DNA itself to flip thinking about what could be the algorithms underlying orientation (Friedland et al. 2009; Bonnet et al. 2012; cellular computation (Lim et al. 2013). In recent years, Courbet et al. 2015; Fernandez-Rodriguez et al. 2015), and major steps have been taken to understand biological the use of transcriptional (RNA) systems (Kim et al. 2006). algorithms by synthesizing biological regulatory networks Accompanying theoretical and computational work has de novo, which aim to compute specific functions. been equally diverse, with insights into possible network topologies (Angeli et al. 2004; Otero-Muras et al. 2012), 1.3 Chemical reaction network design stochasticity (Tian and Burrage 2006; Munsky and and synthetic biology Khammash 2010; Jaruszewicz and Lipniacki 2013; Leon et al. 2016), robustness (Kim and Wang 2007; Barnes et al. The advent of ever more precise genetic engineering 2011), time dependent transient behaviour (Verd et al. requires an understanding of information processing in 2014), and emergent properties of populations of switches reaction-diffusion networks and harnessing the emergence linked by quorum sensing (Kuznetsov et al. 2004; Wang of self-organising properties of such systems. Systems with et al. 2007; Nikolaev and Sontag 2016). Following the switch-like and oscillatory behaviours have been a focus of pioneering work in bacteria, there has now been an synthetic biology for almost two decades. In a now classic explosion of engineered switches for mammalian systems Nature edition from 2000, the genetic toggle switch and the (see Kis et al. 2015 for a comprehensive review), which repressilator systems were described, which opened up a use components from diverse backgrounds (prokaryotic, new field of biological engineering (Gardner et al. 2000; eukaryotic and synthetic), and target a variety of Elowitz and Leibler 2000). These systems not only serve as applications. models for the engineering of complex emergent beha- viours, but also allow us to test our hypotheses on how 1.3.2 Engineered biological oscillators biological systems use feedback mechanisms within com- plex networks to function and perform computations. In the Synthetic genetic oscillators have undergone a number of past few years, genetic switches and oscillators have also significant developments. The original repressilator was been used in a number of applications. constructed from three transcriptional repressor proteins arranged in a negative feedback cycle (Elowitz and Leibler 1.3.1 Synthetic switching systems 2000). Another topology that combined positive and neg- ative feedback was first studied theoretically (Barkai and The classic genetic toggle switch used two mutually Leibler 2000) and then constructed in E. coli (Atkinson repressing transcription factors, which gives rise to bis- et al. 2003). An extension of this negative feedback tablity and hysteresis (Gardner et al. 2000; Litcofsky et al. oscillator, combining a further negative autoregulatory 2012). Subsequently, genetic switches were also con- feedback loop, showed increased tunability and robustness structed using positive autoregulatory feedback loops (Hasty et al. 2002; Stricker et al. 2008). In a series of (Isaacs et al. 2003; Atkinson et al. 2003). More recently, landmark papers, this network topology was coupled with circuits combining mutual repression with positive quorum sensing to create populations of synchronised autoregulatory feedback have been built, including the oscillators at different scales (Danino et al. 2010; Mon- addition of a single positive feedback loop (Lou et al. drago ´ n-Palomino et al. 2011; Prindle et al. 2012). This 123 Computing with biological switches and clocks 765 population-based circuit was eventually used for the et al. 2010), including a Pavlovian-like conditioning treatment of tumours in mice, the oscillatory dynamics genetic circuit (Zhang et al. 2014). Most recently, work has causing bacterial cells to lyse and release a chemothera- shown that ribocomputing devices based on RNA opera- peutic agent directly into metastatic sites (Din et al. 2016). tions can be used to create complex logic functions in More recently, in an interesting development, the original living cells (Green et al. 2017). Notable examples of the negative feedback topology of the repressilator was revis- translation of these approaches include cancer cell type ited and re-engineered using detailed stochastic modelling discrimination (Xie et al. 2011) and immunotherapy (Nis- to vastly improve its robustness, so much so that the sim et al. 2017), both of which use Boolean logic com- oscillations remained synchronised without any need for putations on intracellular mRNA signals within quorum system interactions (Potvin-Trottier et al. 2016). mammalian cells. Oscillators have also been implemented at the RNA level The synthetic switches and oscillators described above (Kim and Winfree 2011), metabolic network level (Fung have been used in a small number of non-Boolean com- et al. 2005), and in mammalian cells (Tigges et al. puting applications inside living cells. For example, genetic 2009, 2010). The theoretical properties of genetic oscilla- switches have been used in signal processing applications tors have been studied extensively, including design prin- including detecting small molecule signals in the mam- ciples (Guantes and Poyatos 2006; Novak and Tyson malian gut (Kotula et al. 2014; Riglar et al. 2017) and 2008), robustness (Wagner 2005; Ghaemi et al. 2009; Tsai glucose sensing (Chen and Jiang 2017). In another land- et al. 2008; Woods et al. 2016; Otero-Muras and Banga mark study, coordination of genetic oscillators was 2016) and stochasticity (Vilar et al. 2002; Turcotte et al. achieved through coupling of post-translational processing 2008). of proteins (Prindle et al. 2014). External input signals in The engineering of biological systems in all organisms the form of chemical inducers and flow rate were encoded faces similar implementation challenges. Perhaps the main into frequency modulated oscillations. By exploiting the challenge is context dependence, which can occur at mul- inherent queuing structure of protein degradation, both tiple levels (sequence, parts, evolutionary and environ- oscillators become coupled and the corresponding input mental) (Cardinale and Arkin 2012; Arkin 2013). These signals combined into a single multispectral timeseries include predictability of transcription and translation encoding both signals (Prindle et al. 2014). The theoretical (Mutalik et al. 2013a, b); development of orthogonal part study of multifunctionality in fixed network topologies has libraries (Wang et al. 2011; Nielsen et al. 2013; Chen et al. become of great interest recently (Jime ´nez et al. 2017) and 2013b; Stanton et al. 2014); resource demand (burden, see work has shown that a genetic circuit comprising of both a later discussion); and impedance matching or retroactivity toggle switch and a repressilator, known as the AC–DC (balancing input sensitivity and output strengths) (Vecchio circuit, has emergent properties such as coherent oscilla- et al. 2008; Jayanthi et al. 2013). Eukaryotic systems offer tions, excitability and spatial signal processing (Perez- additional challenges over prokaryotes due to their multi- Carrasco et al. 2018). These examples show that biological cellularity, more complex genomes and higher levels of systems can be engineered to exploit feedback structures regulation (Ceroni and Ellis 2018). These challenges are for analog and digital signal processing and that complex increasingly being met with an interdisciplinary approach computations are possible at different scales. A computer incorporating mathematical modelling, biochemistry, science viewpoint of how biological systems process ‘omics’ approaches and ultimately a deeper understanding information and perform computation could help synthetic of the biology. biology construct more complex systems, further eluci- dating how natural biological systems function. 1.3.3 Synthetic biology and computation Perhaps the most developed area of non-Boolean com- puting within synthetic biology is molecular programming, Within the field of synthetic biology, a large body of work which uses nucleic acids (DNA, RNA) as the computa- on computation has focussed on genetic Boolean gates tional substrate. The use of DNA for computation was first (Moon et al. 2012). In this arena the state-of-the-art in introduced by Adelman to solve an instance of the transcription circuitry is the CELLO algorithm, which uses Hamiltonian path problem (Adleman 1994). It worked by a characterised library of repressor proteins to design mapping DNA oligomers to edges between nodes in a functional genetic implementations for any three-input small network and exploiting the huge parallelism of Boolean circuit (Nielsen et al. 2016). Recombinases (Siuti  10 molecules to compute all possible paths using et al. 2013) and the CRISPR/Cas system (Nielsen and repeated use of polymerase chain reaction (PCR). Finally, Voigt 2014) can also be used to construct Boolean gates, oligomers of the correct length and containing the correct and genetic Boolean circuits have also been combined with start and end sequences were extracted, in principle the toggle switch to create sequential logic operations (Lou 123 766 N. Dalchau et al. providing solutions to this NP-complete problem. Fur- (number of agents). Moreover, the steady states are robust thermore, the number of oligomers required is linear in the to large perturbations, and they are reached quickly even size of the network. Since then, molecular programming when starting from ambiguous configurations (Angluin has progressed significantly and two modern approaches et al. 2008). A third (undecided) state is critical for the will be discussed in detail in Sect. 3. functionality of the algorithm. Mapping this protocol to a biochemical reaction network produces a system described by 3 species (one per belief state) and 4 reactions (Fig. 2a). 2 Dynamical correspondence Initialised with n total molecules, this reaction network between biological and computing enjoys the same Oðlog nÞ convergence. While this basic networks network exhibits only the bistability aspect of a switch, external controls can be added to flip the system from one The primary mathematical feature of a switch is bistability, state to the other. which necessitates the existence of positive feedback loops. In the biological literature, the exact interaction pattern The simplest (bimolecular) chemical reaction network that of AM can be found in epigenetic switches, where DNA realizes a robust bistable switch is the Approximate histones can be in one of three states: (M)ethylated, Majority (AM) network, a system based on competing U(nmodified), or (A)cetylated (Dodd et al. 2007). A con- autocatalytic feedback loops (Fig. 2a). tiguous stretch of DNA consists of a population of histones The name Approximate Majority comes from its origin that should be uniformly methylated or acetylated. This is in distributed computing, where the algorithm is used by a achieved by the M and A states activating two proteins population of agents to reach consensus over one of two each that catalyse transitions between M–U–A states beliefs (states) that each agent can independently adopt through the whole population. The known properties of (Angluin et al. 2008). At steady state, the whole population AM imply robust uniform settling of the whole histone reaches the belief state that was initially in majority, but population into either M or A states, which is also the only approximately, since the algorithm is inherently interpretation suggested in Ref. Dodd et al. (2007). stochastic. Nevertheless, it has been shown that this algo- Many other biological switching systems employ sys- rithm asymptotically optimally convergences to one of two tems that can be related to the AM algorithm. Usually these stable steady states in Oðlog nÞ time with high probability appear in a less direct way, with multiple species involved (Angluin et al. 2008), where n is the population size in the feedback loops. Even though these more complicated A B Fig. 2 Structural morphism and emulation of AM by GW. a, b Wiring same dynamics and that the individual species in GW (X, R, Y, S) can diagrams of Approximate Majority (AM) network and a system be mapped to the different forms of AM. Active forms of X and R (x containing four species embedded in multiple feedback loops (GW). a and r ) and inactive forms of Y and S (y and s ) collapse into x from 0 2 2 0 The AM network shows the reactions involving the three forms of a AM. Inactive forms of X and R (x and r ) and active forms of Y and 2 2 single molecular species X (empty, ball ended arrows mean catalysis S(y and s ) collapse into x from AM. All intermediary forms ( ) 0 0 2 1 of a given reaction). b The GW network shows the interactions collapse with the intermediary form of AM. The similarity between between four species. Arrows indicate the interactions between them the networks of panel A and B represent a structural morphism and (filled, ball-end means activation and dash-end means inhibition). c, d the similarity of their dynamics mean network emulation exists Simulation traces of AM and GW show that they follow exactly the between these two systems 123 Computing with biological switches and clocks 767 systems may look quite different, it is possible to apply a the energy source decreases the system will switch to the model reduction technique that maps them down to the unmodified state OO. basic AM network (Cardelli 2014). Similar reductions can The TI system maintains its toggle-switch behaviour be shown for various models of the cell cycle switch even if some of the reaction paths are blocked (Hernansaiz- (Cardelli and Csikasz-Nagy 2012), and can be summarized Ballesteros et al. 2018). The switching behaviour is lost as follows. only when at least two reactions are removed, which then A trajectory is a time-course evolution of the concen- results in oscillatory behaviour. The Spontaneous Oscilla- tration of a single species. A complex network emulates a tor (SO) network (Fig. 3b) is the simplest oscillatory sys- simpler network if it can reproduce all the possible tra- tem that can be reached from TI by removal of reaction jectories of the simpler network, species by species, in the paths (Hernansaiz-Ballesteros et al. 2018). The oscillations following sense: for any initial conditions of the simple of SO autonomously follow the path OO ! OP ! PP ! network, there are initial conditions of the complex net- PO ! OO (Fig. 3b). Curiously, the SO network is work such that the set of trajectories of the complex net- remarkably similar to a well-known biological oscillator, work is (with replications) exactly the same as the set of the network driving the circadian clock of cyanobacteria trajectories of the simple network (Fig. 2c,d). In short, (Fig. 3c). Here, the autocatalytic molecule KaiC, with the emulation holds if the complex network can always mimic help of KaiA and KaiB, drives 24 h oscillations of phos- the simple network. Moreover, this emulation condition on phorylation cycles (Nakajima et al. 2005). It has been trajectories, which is predicated on all possible initial found that amongst the three components, KaiC is the most states, can be shown to hold just by examining the structure conserved, and sometimes appears in organisms without its of the networks (including rates and stoichiometry, but two partners (Loza-Correa et al. 2010). Thus it was pro- without considering initial conditions). In such a fashion it posed that KaiC-like molecules in primitive organisms can be shown that various idealized cell cycle switches could have adopted a topology similar to either the TI or emulate AM (Cardelli and Csikasz-Nagy 2012; Cardelli the SO systems, thus they could be working there either as 2014). For instance, the Greatwall network (GW) (Cardelli switches or oscillators respectively (Hernansaiz-Ballesteros and Csikasz-Nagy 2012) summarizes the interactions of the et al. 2018). cell cycle regulators Cdk, Wee1, Cdc25 and PP2a, corre- There is a critical interest in finding minimal networks sponding to species X, S, R and Y respectively (Fig. 2b). that can serve crucial biological functions. AM was already This network can emulate the behaviour of the AM net- shown to serve as a minimal switch (Cardelli and Csika ´sz- work (Fig. 2c,d). Nagy 2012), and we can now see that SO could serve as a minimal clock (Hernansaiz-Ballesteros et al. 2018). As the 2.1 From switch-like behaviours to oscillatory two can be converted to one another through reaction dynamics duplications and reaction removals, there is some sugges- tion of an evolutionary link between these architectures. Switch-like dynamics are widely exploited to control bio- This gives us a hope that these and other related systems logical systems requiring memory and decision making could be implemented in synthetic networks that can be (Tyson and Novak 2010). The AM system can efficiently used for complex biological or computing tasks. function as a bistable switch and its dynamics can be emu- lated by a large class of complex biological networks (Car- delli 2014). AM works with a single undecided state, but in a 3 Molecular programming real molecular system, the two modifications that lead to the two active forms of AM might not affect the same site. This Molecular Programming involves ‘‘the specification of led us to consider a Two Intermediates (TI) system with two structures, circuits, and behaviours both within living and intermediates (OP and PO) between the autocatalytic forms non-living systems–systems in which computing and deci- (OO and PP) (Fig. 3a). OO and PP can convert these species sion-making are carried out by chemical processes them- between the various forms producing a specific pattern of selves’’ (molecular-programming.org). Nucleic acids are modification: OO !OP !PP !PO !OO. From a currently the molecules of choice for molecular program- dynamical systems point of view, the TI system produces ming, due to their high degree of programmability via switch-like behaviour and emulates AM. In a biological Watson-Crick complementarity and their ability to directly context, this system has been proposed to function as a interface with biological components, with potential primitive sensor of the source of energy (Hernansaiz- applications in sensing, diagnosis and treatment of disease. Ballesteros et al. 2018). When energy level is above a critical A number of approaches have been proposed for imple- threshold TI will be in the fully modified state PP, while as menting computation in nucleic acids. Here we will sum- marise two of the main ones—DNA Strand Displacement 123 768 N. Dalchau et al. Fig. 3 A simple switch turned into an oscillator. a The Two cyanobacteria circadian clock (Loza-Correa et al. 2010), where KaiC Intermediates (TI) system, that is behaving like a switch and hexamers are helped to convert themselves between forms that are emulating the behaviour of AM. b The Spontaneous Oscillator (SO) phosphorylated an unphosphorylated at two critical sites (labelled T system is derived from TI and functions as robust oscillator. Solid and S). KaiA (blue triangle) facilitates the phosphorylation reactions, arrows represent catalytic transitions with ball end arrows showing while KaiB (yellow rod) helps the dephosphorylation reactions. the activator of transitions, grey empty arrows represent first order (Color figure online) conversions. c Representation of the KaiABC system of the and PEN DNA Toolbox—and describe how they have been DNA Strand Displacement scheme was proposed (Cardelli used to implement switches and clocks. 2013), which enabled gates to be manufactured using plasmid DNA grown in cell culture. Since the DNA 3.1 DNA strand displacement replication machinery of cells is substantially more accu- rate than existing DNA synthesis technology, particularly Pioneering theoretical work (Soloveichik et al. 2010) for long sequences, a large number of copies of the same showed how DNA could be used to implement a broad double-stranded DNA sequence can be clonally replicated range of computation, including any computation that can in cell culture. The culture is sequenced to check that no be expressed as a chemical reaction network. The mecha- errors have been introduced and, since the population is nism proposed was that of toehold-mediated DNA strand clonal, if the sample sequence is correct then all copies of displacement (Zhang and Seelig 2011), whose systematic the sequence are also highly likely to be correct. The use was pioneered by Yurke et al. (2000). During this 2-domain scheme was used to implement the computa- process, an invading single strand of DNA displaces an tional core of a switching network (Chen et al. 2013a) incumbent strand hybridized to a template (Fig. 4a). The (Fig. 6). Overall, one of the main advantages of using DNA process is mediated by a short exposed single-stranded region of DNA, referred to as a toehold. Various types of strand displacement for the design and implementation of computation have been implemented experimentally using molecular-scale computation is its high degree of pro- this approach, including elementary Boolean logic (Seelig grammability, since all interactions are precisely encoded et al. 2006), square root computation (Qian and Winfree by the choice of DNA sequence. Moreover, system 2011), neural network computation (Qian et al. 2011), dynamics can be accurately predicted from computational distributed consensus capable of switching (Chen et al. models of their components (Chen et al. 2013a; Srinivas 2013a), and oscillations (Srinivas et al. 2017). et al. 2017). Another important advantage is that the entire The general approach proposed by Soloveichik et al. computation can be implemented solely in terms of DNA, (2010) for implementing an arbitrary chemical reaction without requiring additional enzymes. This simplifies sys- network in DNA is based on a 4-domain scheme (Fig. 4). tem production, and also allows systems to be used in a This approach was subsequently used by Srinivas et al. broad range of biological contexts, with limited disruption. (2017) to implement an oscillator consisting solely of DNA One of the main challenges is the need to replenish DNA (Fig. 5). strands and complexes in cases where dynamic behaviour One of the potential drawbacks of the 4-domain needs to sustained for extended periods. To address this, scheme is that it requires synthetic DNA strands to be complexes and fuel strands could be replenished periodi- annealed. These synthetic strands can contain synthesis cally, or a system of buffered gates (Lakin et al. 2012) errors, which increase with strand length. A 2-domain could be used. Another challenge is that unintended 123 Computing with biological switches and clocks 769 12 23 (1) (2) (3) 1 23 12 3 1* 2* 3* 1* 2* 3* 23 12 single-reaction model 1* 2* 3* 1* 2* 3* species identifier q 27 3 14 0 11 ?1 2 3 * 2* 3* 2* 3* 1q q i i O G waste species species 6 9 identifier identifier 5 8 37 14 0 11 2 3 14 0 11 7 14 0 11 10 4 5 6 11 7 8 9 1* 0* 4 11*7* 3* 1* 0*4*1* 1 7 3* O X X 2 3 waste Fig. 4 A 4-domain scheme for implementing chemical reaction the formal unimolecular reaction X ! X þ X , with reaction index 1 2 3 networks in DNA, reproduced from Soloveichik et al. (2010). a An i. The species of this formal reaction are represented as DNA strands elementary DNA strand displacement interaction, modelled by the and highlighted by boxes, with X represented as \ ?1 23[, X as 1 2 chemical reaction X þ G ! Y þ H. Chemical species X denotes a \10 4 5 6[ and X as\11 7 8 9[. Black domains are assumed to be single DNA strand consisting of domains 1 and 2, where each domain unique to each reaction i, while green, red and blue domains are corresponds to a DNA sequence. The strand X is written \12[, associated to species X , X and X , respectively. The formal reaction 1 2 3 where the 3’ end of the strand is assumed to be on the right, X ! X þ X is implemented by two DNA complexes, which are 1 2 3 represented graphically by an arrowhead. The species G denotes a assumed to be present in excess and are consumed over time. The first complex consisting of strand\23[ hybridized to the strand\3* 2* complex G binds the species X and produces the intermediate O , 1 1 i 1*[, where the star (*) denotes Watson-Crick complementarity. The while the second complex T binds the intermediate O and produces i i reaction takes place in three steps: (1) The domain 1 binds to its the two species X and X . The additional intermediate step is needed 2 3 complement 1*. The reaction is reversible, since the domain 1 is to ensure that the reactant species X does not contain any assumed to be short enough to spontaneously unbind. These short overlapping domains with the product species X and X . Note that 2 3 domains are referred to as toeholds; (2) The domain 2 of strand\12[ the sequence of toehold domain 1 can also be adjusted to be only displaces the domain 2 of strand \23[ by a random walk process, partially complementary to domain 1, in order to tune the reaction rate referred to as branch migration; (3) The toehold domain 3 sponta- q . (Color figure online) neously unbinds from its complement 3*. b A 4-domain encoding of interactions between strands can lead to a decrease in feedback controller systems, and a comparison with alter- system performance, for instance due to blunt-end strand native nucleic acid implementation strategies. displacement interactions that occur in the absence of a toehold, also known as leaks. One strategy for mitigating 3.2 The polymerase-exonuclease-nickase these leaks involves the use of toehold clamps (Qian and dynamic network assembly (PEN-DNA) Winfree 2011), which can be used effectively in a sys- toolbox tematic way (Wang et al. 2017). Another approach for reducing unwanted interference between DNA molecules An alternative to DNA strand displacement for performing more generally is to localise the molecules to DNA origami molecular computation uses enzymes to manipulate DNA (Dalchau et al. 2015; Chatterjee et al. 2017), such that signals. The PEN-DNA (Polymerase—Exonuclease— strands which are meant to interact are placed close to each Nickase Dynamic Network Assembly) toolbox is a set of other. This increases the local concentration of interacting modules that can be composed to implement molecular strands, allowing fast computation, while reducing inter- programs (Fig. 7a) and, as we shall describe in this section, ference. See Yordanov et al. (2014) for a more in-depth has successfully been used to implement switches and discussion on the advantages and challenges of using DNA oscillators. strand displacement in the context of implementing 123 770 N. Dalchau et al. Fig. 5 Implementation of an oscillator using a 4-domain DNA strand similar to the one described in Fig. 4. Each molecular species is displacement scheme, reproduced from Srinivas et al. (2017). a The implemented as single DNA strand, and each reaction is implemented desired oscillatory dynamics are implemented by a molecular as a pair of DNA complexes together with an additional fuel strand. program, which is specified as a chemical reaction network. The For example, the reaction Aþ C ! 2A is implemented as a complex network consists of three species (A, B, C) and three autocatalytic that consumes the A and C strands to produce an intermediate strand, reactions, in which B converts A to itself, C converts B to itself, and and a complex that consumes the intermediate to produce two A A converts C to itself. This corresponds to the so-called rock-paper- strands, with the help of a fuel strand. The complexes and fuel strands scissors oscillator (Lachmann and Sella 1995). b The chemical are assumed to be present in excess and are consumed over time in a reaction network is then translated to a 4-domain DNA architecture, closed system, resulting in progressively slower oscillations Fig. 6 Implementation of a switch using a 2-domain DNA strand described in Fig. 5, the behaviour of the systems is specified as a displacement encoding, reproduced from Chen et al. (2013a). The chemical reaction network consisting of three reactions, in which X system takes as input two populations of signals, encoded as DNA and Y cancel each other out to produce two intermediates B, species strands, and uses a distributed consensus network to determine which X converts B to itself, and species Y converts B to itself. This is population is in the majority. The output of the system is a equivalent to the Approximate Majority network (Angluin et al. homogeneous population of strands, in which all of the minority 2008) described in Fig. 2 strands have been converted to the majority. As with the oscillator An activation module enables a short single-stranded b domain, producing a full duplex. The sequences of a and DNA (ssDNA) signal a to stimulate production of another b are chosen to enable a Nickase enzyme to bind and ssDNA signal b. This is achieved by a longer template convert the duplex into a nicked double-stranded molecule. strand a to b composed of two consecutive domains, one This separates the upper domains, such that their affinity complementary to a and the other complementary to b. for the template is reduced and they can more easily When a binds to the 3’ side of the atob template, Poly- unbind, leading to the release of the pre-existing a and de merase is recruited, and elongates the input strand over the novo synthesized b ssDNA signals. As such, a catalyses 123 Computing with biological switches and clocks 771 Fig. 7 The PEN-DNA toolbox. a Summary of the PEN-DNA toolbox state, red symbols represent the low a-high b state, and green/orange modules (reproduced from Meijer et al. 2017), with Polymerase (Pol), symbols are the external inputs. Measurements correspond to treating Exonuclease (Exo) and Nickase (Nick) enzymes. b The switchable with 2.5 nM or 5 nM of dtob, as indicated. All graphics are memory circuit from Padirac et al. (2012). In the network diagram, reproduced from Padirac et al. (2012). c The negative feedback loop blue symbols represent components associated with the high a-low b oscillator from Montagne et al. (2011). (Color figure online) the production of b, analogous to the reaction a ! aþ b. 3.2.1 Switches as memory devices A deactivation module implements the reaction a ! a , where a is notionally inactive. This is achieved by a A bistable switch was one of the first circuits constructed using the PEN-DNA toolbox (Padirac et al. 2012) pseudo-template pTa that extends a with a short oligonu- cleotide tail, preventing a from participating in activation (Fig. 7b). The circuit design combined self-activation with mutual inhibition, resembling the MI network described reactions. Finally, a 5’-3’ Exonuclease destroys all ssDNA signals, representing a non-specific degradation module. above. The inner mutual inhibition module was achieved using four template strands: two templates implemented self-activation for a (a to a) and b (b to b), while a further two templates implemented inhibition with the production 123 772 N. Dalchau et al. of inactive signals ia and ib, which block a and b templates Compared to oscillators constructed from purely DNA respectively. An additional two templates were then used to systems, the PEN-DNA systems exhibit temporal dynamics mediate inputs c and d that could switch the device that can be sustained for substantially longer time periods. between the a and b states. The authors demonstrated that a A feature of PEN-DNA that is likely to contribute to this is high concentration of external input could switch the the ability to synthesize new copies of the signal strands. device in approximately 200 minutes, but with lower This is not possible with a purely strand displacement concentrations leading only to a transient excursion and system, which produce new signal strands by releasing then return to the pre-existing stable state. While the them from previously constructed gate species, supplied as demonstration of the robustness of the switch is impressive, fuel. Accordingly, the gate species are consumed over time such a long switching time could prohibit its usage in some and oscillator amplitudes drop. The PEN-DNA systems applications/ Nevertheless, by this circuit being both also exhibit changes in dynamics over time as the supply of bistable and switchable, it can be used for long term nucleotides and other reagents is depleted, though this memory storage. A push-push memory device was also occurs on a longer time scale relative to the system constructed, which enabled switching back and forth in dynamics. response to the same input signal. Switches are fundamental building blocks for many computational devices, but their utilisation requires sensing 4 Future of biological computing of inputs and actuation. Recently, it was demonstrated how the PEN-DNA memory switch of Padirac et al. (2012) can 4.1 Molecular programming in cells be connected to downstream enzymatic actuators, enabling the connection of DNA-based memory devices to triggered Despite the limitations discussed above, there are consid- downstream signalling (Meijer et al. 2017). To achieve erable advantages to using DNA circuits to implement this, a translator module was developed that dynamically computation in cells. DNA offers a natural interface to the perceives the short single-stranded DNA molecules of the cellular machinery and is inherently biocompatible. After bistable switchable memory device described above, then several years of exploring the computational potential of produces longer DNA strands that can be used to control nucleic acid circuits in vitro, there are now efforts to the activation of two enzymes, NanoLuc and TEM1 b- deliver DNA circuits into live cells. In Groves et al. (2015), lactamase. Importantly, the translator was designed to a variety of methods were compared for delivering nucleic minimize retroactivity back to the memory switch, which acid circuits to mammalian (CHO and HeLa) cells, and it was demonstrated with a detailed experimental and theo- was shown that multi-input computation in live cells could retical characterization. Finally, the activation/inactivation be detected using flow cytometry. In the same study, of the enzymes relies on interactions with conjugated chemical modifications to DNA and RNA strands were oligonucleotides, which are modulated by the output of the shown to improve binding kinetics, most likely a result of translator module. This appears to be the first time memory reduced nuclease activity against the modified strands. This devices and actuators have been connected in a synthetic has stimulated more detailed characterization studies of molecular circuit, and is an important step towards realis- nuclease activity against nucleic acid circuits (Fern and ing more general molecular computers. Schulman 2017). Another fruitful strategy for delivering DNA circuits to live cells has been the use of DNA ori- 3.2.2 Limit cycle oscillators as clocks gami, which provides both a localizing and protective effect on circuit components, leading to faster circuit The first attempt to produce an oscillator using the PEN operation (Dalchau et al. 2015; Chatterjee et al. 2017), but toolbox approach was based on recapitulating a network also successful operation in a live animal (Amir et al. topology that is known to robustly produce oscillatory 2014). behaviours (Montagne et al. 2011). Subsequently, another Introducing molecular circuits based on the PEN-DNA network architecture based on a predator-prey interaction toolbox into cells is made challenging by the need to was developed (Fujii and Rondelez 2013). Using both express the PEN enzymes in the target cells. Enzymes strategies, the Rondelez group were able to sustain oscil- impose several design constraints on the selection of DNA lations for more than 10 cycles, with only a small ampli- sequences. Nicking enzymes have specific recognition tude loss. By taking advantage of molecular diffusion, and sites, which imposes a limit on the diversity of signal visualizing the solution between two glass slides, a follow- strands that can be used in a PEN-DNA circuit. In contrast, up work illustrated how these DNA-based oscillators can polymerase and exonuclease are non-specific, meaning that also produce travelling wave phenomena (Padirac et al. the activation and degradation reaction rates are difficult to 2013). control. While differential activation rates could be 123 Computing with biological switches and clocks 773 achieved by controlling activation template concentrations, Whitley and Sutton 2012; Yang 2014). Such advances will dynamic behaviours that require differential degradation continue, driven by the desire for scalability and robustness would be harder to engineer. as the complexity of solid state technology approaches that Nucleic acid circuits have the added benefit of requiring of biological systems. a reduced regulatory approval process compared with As precision in designing chemical systems increases, genetically modified organisms, for applications such as we look towards chemical computational units with which disease diagnosis and treatment. There have already been we may construct complex behaviours systematically. We several attempts to use nucleic acids circuits, combined have seen how computational DNA circuits and related with transcriptional machinery, for biosensing and diag- technologies can be used as flexible molecular mechanisms nosis (Pardee et al. 2016). Non-transcriptional nucleic acid to engineer switches, oscillators, and other computational circuits are in principle easier to program than transcrip- components in vitro, with efforts being made also in vivo. tional networks based on promoter regulation by proteins. Moreover, such computational units can be coupled with In part, this is due to transcriptional control requiring the molecular sensors, actuators, and scaffolding to provide pairing of a protein surface with a DNA binding motif, an complete nanoscale devices. Many such devices and interaction that is challenging to engineer synthetically. components can be individually designed and engineered However, new approaches based on CRISPR/dCas9 could using the DNA, RNA, and enzyme tricks of the biochem- lead to a more targeted way of engineering networks with ical trade. precise topologies. Finally, nucleic acid circuits are a convenient test framework for programmed genetic cir- 4.3 From single-cells to computational cuits. They force the engineer to consider energy/substrate communities economy and the physical limitations of molecular binding, which, for example, is analogous to ribosomal usage and Building on the fascinating advances in our ability to transcriptional and translational efficiency of synthetic program cell-autonomous behaviours, there are now sev- gene circuits. Much of what we have learned in the design, eral examples of establishing behaviours that rely on characterization and analysis of nucleic acid circuits can be multicellularity. Switches within individual cells can be applied to the engineering of computational circuits based linked via inter-cellular communication (see Hennig et al. on other biomolecular frameworks. 2015 for a thorough review), including natural quorum sensing molecules (Camilli and Bassler 2006) and artificial 4.2 From molecular networks to algorithms DNA messengers (Ortiz and Endy 2012; Gon ˜ i-Moreno et al. 2013). As such, it is possible to achieve behaviours of As we have seen above, algorithms that mimic the beha- distributed computing algorithms with cells. Based on viour of biological switches and clocks can be imple- temporal logic, it was shown how cell populations could be mented using DNA circuits, and the same dynamics can used for timing and recording chemical events (Hsiao et al. also be achieved using synthetic gene regulatory networks. 2016). It remains to be seen how more complex gene regulatory In additional to temporal control, intercellular commu- networks could implement more advanced algorithms, nication also enables spatial control, and therefore pro- enabled by advanced genome editing techniques (Cong grammed pattern formation. Already, this has enabled et al. 2013). More complex engineered networks of circuits that can detect spatial boundaries between an switches and clocks could also be combined with electronic environmental signal (light) (Tabor et al. 2009) and circuits (Cao et al. 2017) to serve as biosensors. These establish stripe patterns in expanding colonies (Liu et al. applications could have a major influence on disease 2011). More exploratory work with communicating bac- detection and treatment. However, to reach this stage terial populations has begun to shed light on how devel- requires a better understanding and control of elementary opmental patterns can be scale invariant (Cao et al. 2016), computing units. Thus, algorithmic thinking might be but also suggest a new platform for testing ecological leveraged to detect and ultimately treat complex disease theory, via synthetic ecosystems (Song et al. 2009). Fur- states, by combining switches and clocks with the existing thermore, techniques such as live cell lithography can logic circuit toolbox. create regular structures of communicating microbes at Historically, the analysis of biological mechanisms and resolutions of 5 lm (Mirsaidov et al. 2008). There is also collective behaviour from an algorithmic perspective led to work in controlling spatial distributions of DNA molecules simplified models, which aided understanding of informa- directly (Dalchau et al. 2014; calise and Schulman 2014), tion processing in natural systems. This laid the ground- which could be used to pre-pattern cellular systems. work for future breakthroughs across disciplines Put together, there is now real promise for designing cell (Marblestone et al. 2016; Navlakha and Bar-Joseph 2011; colonies that control their own temporal dynamics and 123 774 N. Dalchau et al. spatial positioning. This could be highly relevant to bio- understand the capability of synthetic multicellular logics production in bioreactors, where spatial hetero- platforms. geneity in resources and cell density could lead to inefficiencies. The advantages of automatic control can be 4.4 Learning from biological computing readily seen in more traditional control engineering appli- cations, and consequently, there is now rising interest of As we increasingly rely on computing to process large implementing control algorithms in biological circuits (Del datasets for everyday tasks at home and at work, power Vecchio et al. 2016). Earlier strategies were based on consumption will become a future limiting factor (Council transcriptional negative autoregulation (Becskei and Ser- 2011; Kamil et al. 2008). In fact the effects of thermody- rano 2000; Rosenfeld et al. 2002), but more recently, a namics—that is removing heat efficiently from semicon- more advanced integral control via negative feedback has ductor devices—has already driven the shift to multicore been demonstrated in metabolic circuits (Briat and chips and parallel computing, which can improve on the Khammash 2018), but also using optogenetics via in silico performance scaling of single processors, but will funda- controllers (Milias-Argeitis et al. 2016; Lugagne et al. mentally change how we develop programs (Council 2017). Automatic control will bring robust operation and 2011). Biological systems perform computations at much self-adaptation to biological circuits, which will help to lower levels of power consumption: estimates report 4 make biotechnology more efficient and ultimately more orders of magnitude for molecular machines (Nicolau et al. competitive in the marketplace (Del Vecchio et al. 2016). 2016) and up to 12 orders of magnitude for DNA com- Despite the promise of synthetic biology, significant puting (Adleman 1994). In addition, these computations challenges remain for regulating biological behaviours are carried out in a robust manner, embedded within fluc- with the insertion of designed networks of transcriptional tuating environments, and often utilising components that components. One challenge relates to timescale: tran- are unreliable and noisy (Sarpeshkar 2010). This incredible scriptional control is slow, though is the dominant mode of performance is achieved through multi-scale hybrid analog regulation in synthetic biology applications to date. Control and digital information processing. Biological computers algorithms are sometimes inefficient in the face of delays, have the additional advantage that they can interface and so their success might depend on establishing faster directly with living systems and therefore open up new modes of biological regulation. Here, molecular program- applications in biosensing with industrial and clinical rel- ming might provide a solution, as DNA-based circuits can evance. For example, signal processing in the ear has be localized, speeding up their operation (Chatterjee et al. already inspired electronics for low power cochlear 2017). Another challenge of using transcriptional regula- implants (Mandal et al. 2009) and pattern recognition by tion is that each additional component introduces a burden neurons led to a novel analog-to-digital converter (Yang on the host cell, which can lead to poor growth of the and Sarpeshkar 2006). These properties, combined with the colony, thus altering the performance of existing compo- high information storage density of DNA (Church et al. nents and/or reduce yields (Scott et al. 2010; Borkowski 2012; Goldman et al. 2013; Erlich and Zielinski 2017), et al. 2016; Wu et al. 2016). For example, inserting a provide exciting future directions for further research. component that leads to high levels of protein translation In this review we have highlighted how complex will impose a burden on the ribosome pool (Scott et al. biomolecular networks make use of switches and oscilla- 2010; Shachrai et al. 2010), high levels of transcription tors to perform computation. The continued understanding will impose a burden on RNA polymerase (Gyorgy et al. of how this information processing is achieved at such high 2015), and high levels of protein degradation will impose a levels of robustness and low power requirements will burden on proteases (Cookson et al. 2011). While some of require the concerted efforts of systems and synthetic these can be mitigated with quantification of the burden biology in addition to leveraging tools from engineering and careful design (Nielsen et al. 2016), establishing cel- and computer science. While it is unlikely that biological lular control with components that do not consume/occupy systems will ever replace silicon as our dominant com- shared cellular resources could be a major advantage. puting platform, learning how they compute could have a However, it remains unclear as to whether DNA circuits significant impact on future computing architectures. can operate reliably enough inside cells to rival existing Open Access This article is distributed under the terms of the Creative approaches to cellular control. Commons Attribution 4.0 International License (http://creative The extent to which spatiotemporal control can improve commons.org/licenses/by/4.0/), which permits unrestricted use, dis- biotechnology applications is relatively unexplored. tribution, and reproduction in any medium, provided you give Therefore, more theoretical work is needed to establish the appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were performance that can be achieved by algorithms based on made. chemistry and cellular communication, and therefore to 123 Computing with biological switches and clocks 775 Cardelli L (2014) Morphisms of reaction networks that couple References structure to function. BMC Syst Biol 8(1):84 Cardelli L, Csikasz-Nagy A (2012) The cell cycle switch computes Adleman LM (1994) Molecular computation of solutions to combi- approximate majority. Sci Rep 2(1):656 natorial problems. 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Published: Jun 1, 2018

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