Parallel Computations with DNA-Encoded Chemical Reaction Networks

Abstract

Molecular programs use chemical reactions as primitives to process information. An interesting property of many of these amorphous systems is their scale-invariant property: They can be split into sub-parts without affecting their function. In combination with emerging techniques to compartmentalize and manipulate extremely small volumes of liquid, this opens a route to parallel molecular computations involving possibly millions to billions of individual processors. In this short perspective, we use selected examples from the DNA-based molecular programming literature to discuss some of the technical aspects associated with distributing chemical computations in spatially defined microscopic sub-units. We also present some future directions to leverage the potential of parallel molecular networks in applications.

1 Harnessing Parallelization in Chemical Reaction Networks

1.1 D(R)NA-Based Deterministic Chemical Reaction Networks

D(R)NA-based artificial reaction networks are man-made, rationally designed biochemical systems targeting specific dynamical or computational behaviors. They use DNA or RNA as a substrate, as nucleic acids have proved incredibly versatile for storing information and executing chemical computations. Nucleic acids can be commercially synthetized with user-designed sequences, they can be tracked and characterized with great details (with fluorescence, sequencing, mass spectrometry, electrophoresis…) and can be conjugated to a large variety of other molecules.

These systems are based on modules (nodes or gates) that one can connect at will to create more-or-less arbitrary circuit architectures. This approach leverages the canonical programmability of DNA/DNA interactions—Watson–Crick rules—and the existence of generic reactions, which are agnostic to sequence. D(R)NA-based molecular programs take molecular signals as input, for example, the presence/absence of particular species or the concentration of these species, and process through a cascade of reactions—in many cases including feedbacks and multiple intermediates—down to the production of particular output species. The concentration of these output species, which can be monitored via physicochemical signals such as fluorescence, is then interpreted as the result of a computation. The computed function is encoded by the details of the reaction circuit, including its topology and the kinetic laws and parameters of the constituting reactions. A number of experimental toolboxes have been developed to experimentally assemble these architectures [1,2,3,4,5,6]. In principle, using these frameworks, one can basically set up a molecular system performing any computation of interest [7].

The fundamental building block of all reaction networking schemes is catalysis [8,9,10]. Catalysis allows one compound of the network to act on others, without being itself included in the transformation. For nucleic acid (NA)-based systems, catalysis is either related to mechanisms that can accelerate the slow reaction of strand exchange [4, 8, 9, 11] or to enzymatic manipulation of NA synthesis and degradation (e.g., polymerases, ligases and nucleases) [1, 2, 6].

In the case of enzymatic networking schemes, for example, genelets [1] use an RNA polymerase and one or two RNases, while the PEN toolbox [3, 6, 12] uses a DNA polymerase, a nickase and a DNA exonuclease. These enzymes can be seen as the hardware of a machine whose behavior is controlled by a DNA software consisting of synthetic templates. Although less explored than DNA-only systems, enzymatic approaches provide benefits in terms of compacity, ease of preparation, amplification folds and control of leaks. Importantly for the topic discussed here, some of them provide both a well-controlled kinetic bottleneck on the fuel consumption and an efficient chemical sink and are thus able to maintain an out-of-equilibrium state of long periods in a closed reactor. Demonstrated out-of-equilibrium DNA-encoded enzymatic networks include oscillators [3, 13, 14], inverters, memories and toggle switches [1, 12, 15]. Note that other NA-based molecular programming paradigms have been described and also experimentally validated [1, 2, 4, 7,8,9].

Chemical reaction networks (CRNs) share many formal similarities with other computational frameworks, such as electronic or mechanical circuits. They are modular, and computations are built by linking together simple computing modules (e.g., transistors in the case of electronic circuits and chemical reactions in the case of chemical reaction networks). However, contrary to these more classic approaches, CRNs run in a homogenous, liquid medium. In the general case, CRN-encoding compounds freely diffuse within this medium. Because of this, individual network connections within a CRN are not defined by spatial addresses, but rather by chemical recognition rules. A link between A and B in the network means a wire between the location of a single copy of A and a single copy of B for an electronic circuit, but, for a CRN, it means a specific (strong) chemical interaction between the molecules of type A and molecules of type B, both present in multiple, independent copies.

The standard DNA program runs in a test tube, that is, a typical volume of 10 s–100 s of microliters. One tube performs one—possibly complex—computation (a computation being defined here as a series of chemical reactions producing output species that depend on the input species). The computation is generally done only once, as in most cases resetting is not possible (i.e., regenerating the inputs if they have been consumed, erasing the outputs and restoring the intermediates species that drove the reaction). CRNs operate on molecular concentrations, in the sense that data flows are instantiated by changes in the concentration of some species over time, and the output is typically represented by the concentration of one or more specific species. The concentration of most compounds participating in a CRN needs to be in the nanomolar range or above to get appreciable kinetics, because most programmable reactions, including DNA hybridization [16], are limited by diffusion below this value. These typical volumes and concentrations imply that molecular counts are extremely high, typically 10⁹–10¹⁵ copies of each specific molecular type. The fact that computation by a bulk CRN involves the production of so many identical molecules naturally leads to consider the potential for parallel implementations.

1.2 CRNs Run on Inherently Parallel Processes

CRNs controlled by mass-action kinetics (see below for stochastic effects in very small volumes) are scale-free. Their behavior does not depend on the size of the system. This is because concentrations are intensive thermodynamic variables and leads to an intriguing property: the dynamical or information-processing functions of CRNs are independent of their size. For example, if the experimenter partitions a circuit from one large to two smaller containers, he will simply obtain two systems that are dynamically and computationally identical to the parent reaction. In other words, the function has not changed, but the number of threads has been doubled. Let us assume as an example that the CRN was running an addressable bistable system [12, 17], in order to maintain one bit of memory storage. The splitting in that case will simply lead to having two independent copies of the same memory element. Post splitting, one of them can in principle be reset to a different state. Altogether, one now disposes of two bits of memory. Given enough compartments, this operation can be repeated over and over.

Using microcompartmentalization techniques, where individual reactors’ volumes range from femtoliters to nanoliters, and using the above-mentioned test tube as starting material, it is possible to generate millions to billions of compartments. For example, the splitting of a bulk DNA-encoded enzymatic predator–prey oscillator into ~100 picoliter microdroplets, using a microfluidic approach, immediately generated many millions of independent networks, all displaying the same oscillatory behavior [18, 19].

This scale-freeness of CRNs is only true down to the stochastic limit, where volumes get so small that molecular counts are close to unity (Fig. 1). In this range, the continuous approximation breaks for concentrations and kinetics, which cannot be seen as deterministic anymore. Rather, they become discrete and stochastic: molecular counts are randomly updated by integer increments—which fundamentally alters the behaviors of CRN. For instance, in the deterministic regime and with conventional chemistry, it is not possible for a chemical species to reach its null-state in finite time (i.e., its concentration cannot get to 0). This implies that an autocatalytic system can always “regenerate” itself after dilution, because there are always some molecules around to seed the reaction. Yet in the stochastic regime, a species can permanently “crash” to zero with a non-null probability. Keeping the nanomolar concentration as a reference, the stochastic limit occurs around femtoliter volumes (the volume of a typical bacterium). Therefore, depending on compartment size, the splitting of molecular programs can either provide parallel circuits with classical behaviors or enable new, non-deterministic operations [20, 21].

Fig. 1

Splitting a sample containing a molecule at concentration C = 1 nM produces multiple compartments with the same average concentration and a coefficient of variation ${\text{CV}} = \frac{{\sqrt {\uplambda } }}{{\uplambda }}$, where ${\uplambda }$ is the average number of molecules per compartment. When the compartment volume reaches down to the femtoliter ${\uplambda }$~CV ~ 1, concentrations take discrete values and stochastic partitioning leads to strong inhomogeneity between compartments

To truly leverage the potential of CRNs for parallelism, one ideally wants to perform different sub-computations at each position of the distributed system. The way these sub-computations interact with each other through space (by free diffusion, through restricted diffusion, or not at all) will then define the various options for parallel molecular programming.

In this short and non-exhaustive contribution, we review experimental works that have explored the parallelization of DNA-encoded mass-action CRNs, focusing in particular on microcompartmentalization and high-throughput strategies. Based on these selected experimental approaches, we also suggest and discuss possible applications and future directions for parallelized molecular computing.

2 Creating Sub-Computations

A variety of approaches are suitable for the parallelization of molecular programs. Below, we group them into approaches that use impermeable physical boundaries (e.g., water-in-oil droplets), permeable boundaries or no boundaries at all (Fig. 2). Important characteristics associated with these technical choices are the size of the individual elements and the associated throughput (the number of compartments one can generate or manipulate in a standard experiment).

Fig. 2

Parallel molecular computations can be classified according to the diffusion rules between sub-units. a in the absence of boundaries, the behavior is governed by reaction–diffusion processes. Competition between reaction and diffusion determines the elementary length scale. b semi-permeable compartments, where the diffusion of molecular program components between partitions is permitted or not depending on the permeability rules (for example, size cutoff), can allow the emergence of new collective functions from simple sub-units. c impermeable compartments, where no diffusion is allowed between compartments, open the way to pure parallel processing

2.1 No-Diffusion (Leak–Tight) Compartments

A number of tight microcompartmentalization approaches have been explored. The absence of transport across the boundaries ensures that each microcompartment behaves as a fully independent computing element. On the other hand, it makes the delivery of specific inputs to each individual reactor more problematic. In the case of dynamical systems (out-of-equilibrium CRNs), it also mandates that the encapsulated chemistry be autonomous. For example, although many chemical (non-DNA) oscillators are known, most require continuous influx and outflux of reactants in open reactors, and only a handful are able to display (pseudo-) limit cycles in batch mode. Fortunately, several autonomous DNA circuits with non-trivial dynamics have been reported over the years and provide useful test cases for compartmentalization approaches (Fig. 3).

Fig. 3

Experimental approaches for independent compartments. a water-in-oil emulsions containing various DNA-encoded oscillatory networks, including genelets [22] and PEN-DNA circuits [18]. b microfabricated silicon chambers encapsulate IVTT-based functions, including oscillators [23]. c liposomes, used in this example as vehicles for IVTT-replication (IVTTR) gene amplification system [24]

2.1.1 Emulsions

Emulsions are made of a continuous and organic phase that contains many small water-in-oil droplets that can be considered as chemically independent (see [25, 26] for discussion of droplet-to-droplet exchange in some specific cases). Micro-partitioning a master mix using emulsions can be as simple as combining the aqueous reaction mix with oil and surfactant, using for example vortexing. Simmel, Winfree and colleagues used this approach to parallelize a genelet oscillator and reported the observation of microscopic droplets showing individual oscillatory behavior [22] (Fig. 3a). While many other emulsification techniques are possible, including the use of filters, mechanical mixers, bead shakers, sonication, etc., it is not yet clear how the harsh conditions they entail impact the macromolecules of the molecular programs. In addition, although they are very fast—with millions or billions of compartments created in seconds—these techniques do not provide precise control over the size distribution.

An alternative is droplet microfluidics [27]—in which reagents are controllably mixed and encapsulated at the microscale—which offers a better control on the size distribution and a gentler emulsification process. Although the compartments are produced in a sequential manner, generation rates reaching 10 s or 100 s of kHz can be achieved, and parallel designs [28] with tens of thousands of nozzles have been reported [29]. The use of microfluidic emulsions is well developed in the field of high-throughput directed evolution, combinatorial chemistry or droplet digital Polymerase Chain Reaction (ddPCR) [30]. In the latter case, a number of commercial solutions are available.

2.1.2 Liposomes

Liposomes more closely mimic the architecture of biological cells. While droplets are made of an aqueous compartment dispersed in oil, liposomes are aqueous compartments surrounded by a lipid membrane (a phospholipid bilayer) and dispersed in an aqueous phase. There are thus two aqueous phases: one inside each liposome and one outside the liposome. Since unmodified lipid bilayers are typically impermeant to DNA strands or large proteins, liposomes present in principle an attractive alternative to droplets for microcompartmentalization of molecular programs. Their generation is however more technical and delicate than droplets, especially when the size distribution of liposomes must be controlled [31]. This may explain why liposomes have been less explored for computational CRN [32], although there are some examples of liposome-compartmentalized complex biomolecular mixtures, generally designed as minimal artificial cells [33]. The group of Vincent Noireaux, among others, encapsulated In Vitro Transcription and Translation systems (IVTT) based on cell extract to recapitulate protein expression [34]. Danelon et al. went a step further by showing that genetic replication, supported by in situ expression of genetically encoded enzymatic activities, can be installed within IVTT-containing liposomes [24] (Fig. 3c). In principle, such minimal cells reproduce the basic functions necessary to enter a process of Darwinian evolution.

2.1.3 Microchambers

Microfabrication offers a top-down way to create microcompartments with precisely defined geometries, within which very small volumes of liquid can be enclosed [35]. This can be used for example to create partially confined reactors, able to support localized behaviors while still diffusively exchanging with a feeding tank. Bar-Ziv and colleagues leveraged this approach to carve microchambers and connecting channels inside a silicon wafer [23] (Fig. 3b). The chambers are patterned at their bottom with DNA brushes, which are dense monolayers of DNA strands’ coding for a gene expression CRN with positive or negative feedbacks. Each chamber is connected to a central feed channel that runs through the chip, acting as a chemical source and sink. The feed channel baths the chambers in a cell-free extract, which contains the molecular machinery to transcribe and translate the gene encoded by the DNA brush. This reaction is predominantly local, but species diffuse and escape over time to compartments nearby—creating a spatial network of connected compartments. The authors showed that the geometry of the channels and chamber controls the interplay between reaction and diffusion. For instance, a positive feedback loop network was unable to kick off when the channel connecting the chamber to the feed was too short. This was expected because the removal of signaling molecules dominated over their autocatalytic production. When the connecting channel was made longer, thereby decreasing the effective dilution rate, the positive feedback loop ignited and the chamber glowed green. The author extended this approach to create small spatial networks of microreactors, where each microreactor could contain a different set of encoding DNA modules (here, gene-encoding templates) [36]. In principle, this approach could allow the design of a variety of exotic dynamical behaviors, by controlling the relative position of each DNA node [37].

Note that some hybrid techniques, using both top-down micro-patterning and oil–water interfaces, can be used to create regular arrays containing millions of extremely small and monodisperse compartments (down to the femtoliter), compatible with biomolecular reactions [38].

2.2 Compartment-Free Approaches

Spatially resolved CRN behaviors can also be observed without any physical boundaries. This is well known in the community of nonlinear chemistry, which has studied a number of beautiful reaction–diffusion systems [39, 40]. In another field, chemical engineers are also interested by the emergence of localized behaviors, which in some cases may have deleterious consequences. In the absence of physical boundaries, whether or not local behaviors are possibly depends on the relative strength of chemical reactions and diffusion. This simple statement is captured by the so-called Damköhler number [41] which compares transport and reactive rates:

$$D_{a} = {\text{ reaction}}\,\,{\text{rate}}/{\text{transport}}\,\,{\text{rate}}.$$

Localized behaviors are possible when this dimensionless number is greater than 1, i.e., when reactions are faster than mixing. For diffusion-limited reactions involving short oligos, the hybridization rate (which is mostly independent of sequence, length and temperature) is in the order of 10⁶ M⁻¹ s⁻¹, whereas diffusion is around D∼10–100 μm² s⁻¹ (single- or double-stranded 10–100 mers) [42]. Knowing the concentrations of gate or node molecules, one can then assess the spatial scale of localized behaviors, in the absence of any mixing. For example, if the reaction rate is around 1 min⁻¹, this length scale is 10 µm; smaller reactors can be considered spontaneously well-mixed, whereas larger ones may generate reaction–diffusion systems (Fig. 4).

Fig. 4

Boundary-free spatial computations (reaction–diffusion systems). An initial state, taken as input, is transformed into dynamic or stationary patterns. a a spot of trigger molecules (orange spot) initiates the propagation of successive waves of species α (prey) and β (predator) in a predator–prey molecular system [44]. b a morphogen gradient (purple) is interpreted by a tristable system to create a three-stripe pattern, recapitulating the “French-Flag” embryogenesis [45]. c an incoherent feedforward loop coupled to differential diffusion coefficients allowed the transformation of an input pattern injected through UV-sensitive DNA modifications [46]

Similar to the case of well-mixed systems, the unfolding of a reaction–diffusion process can be interpreted as a computation, whose input will typically include geometrical clues. Biology provides a number of examples, such as the creation of concentration patterns during embryo morphogenesis via clock-and-wavefront, French-flag or Turing mechanisms, which will later on trigger cellular differentiation. At a simpler scale, the bacterial Min system performs an accurate determination of the geometric middle of a rod-shaped container using reaction–diffusion processes [43]. For molecular programming in reaction–diffusion settings (i.e., high Damköhler numbers), one needs to control, in addition to topology laws and rates, the diffusion characteristic of each species, as well as the boundary conditions.

For example, Padirac et al. spatialized a predator–prey oscillator by enclosing the corresponding DNA-encoded circuit in a flat chamber 200 µm thick and one centimeter wide, installed on a microscope stage. This chamber was locally seeded with prey, which created inhomogeneous initial conditions, and fluorescent reporters were used to observe the concentrations of both dynamic species. Incubation revealed traveling waves of prey, chased by waves of predators—reminiscent of their ecological counterparts (Fig. 4a). The waves traveled at a velocity of hundreds of micrometers per minute. These chemical waves result from the interplay between reaction and diffusion, and they transport information (e.g., the concentration of chemical species) over large distances (in the same way as light or electrical impulses could). Their velocity can be roughly predicted from simple scaling arguments $v = \sqrt {\left( {D/\tau } \right) = \sim 100}$ μm$\cdot$min⁻¹.

Similar PEN-toolbox traveling waves and fronts provide a useful primitive to build more complex spatial operations. Triggered at the entrance of a millimetric maze built of PDMS, a wavefront followed the walls of the channels, split into two at a junction and died when it reached a cul-de-sac [47]. The shape of the wavefront was sensitive to geometric clues such as the curvature of the channels. When the wavefront entered a turn with a short curvature radius, it showed a transient dispersion where the front on the outer end of the turn progressed faster than the front on the inner end. This dispersion was not observed in turns with larger radii.

Biological embryo development provides inspirational examples of how complex geometrical shapes can unfold from chemically encoded programs. The synthetic version, artificial morphogenesis thus represents an exciting frontier for molecular programming. The challenge is ambitious, because, in addition to topology, rates and laws, artificial morphogenesis requires the control of diffusion rates in a species-specific way. For example, Turing patterns generally require a marked difference between the diffusion rate of activating and inhibiting compounds; in the field of small-molecule CRN, a strategy to slow down the diffusion rate of inhibitory compounds has been instrumental to the engineering of the first synthetic Turing motifs [39]. For DNA-based approaches, the group of Estevez-Torres and Galas in Sorbonne Université/CNRS introduced some strategies for this purpose, based on immobilized binding (complementary) partners of the active DNA species [48]. They also studied the interaction between traveling fronts or confined them within guiding gels [49]. These efforts, reviewed in [50], culminated in an artificial reconstitution of the famous “French-Flag” embryo patterning algorithm, a system that takes a shallow 1D chemical gradient as input and outputs three sharply demarcated spatial regions (Fig. 4b) [45].

The diffusional coupling between reacting voxels (i.e., elementary reaction volumes) in reaction–diffusion systems can also be leveraged to compute fine spatial transformations (i.e., the transformation of a spatial pattern of concentrations into another pattern). Ellington and colleagues created a strand-displacement network that takes a 2D illumination pattern as input and outputs a species that delineates the edges of the pattern. This system is built around an incoherent feedforward loop (Fig. 4c) [46]; light both activates and inhibits the creation of a signal species. In area without illumination, nothing happens. The same is true for areas of homogenous illumination, where chemical activation and inhibition cancel each other. But, on the edges of an illuminated area, species that were activated by light diffuse to nearby dark area and escape photoinhibition, thus revealing edges. In principle, this approach could be generalized to more complex image processing and be connected to other chemical (like polymerization) or biological (like cell culture and differentiation) processes. This could enable wholly new ways to orchestrate complex chemistry or biology using spatially structured illumination to coordinate and manage complex processes.

2.3 Intermediate Cases: Some Species Diffuse, Some Do Not

In this section, we group approaches that are inbetween the two extreme cases presented above: completely tight compartments on the one hand and unrestricted diffusion on the other hand. Indeed, it is possible to imagine that the experimental design does not restrict diffusion of all species (Fig. 5). Although this situation may bring some issues (compartment content leaks out), it can also offer a number of advantages. As seen in the silicon microchambers example above, partial enclosing provides a strategy to deliver fuel molecules and implement a physical first-order decay process. This is very useful for systems that cannot sustain dynamical behavior on the long run in closed containers and is a strategy that has also been extensively used in the field of small-molecule nonlinear chemistry [39]. In addition, controlled leakage enables compartment-to-compartment communication and coupling, as well as the delivery of input signals.

Fig. 5

Strategies to create compartments with selective boundaries. a proteinosomes form compartments with size-selective boundaries. While streptavidin-tethered DNA species cannot cross the membrane, other DNA strands freely diffuse between compartments [51]. b a similar approach builds on microchambers with alginate walls, impermeable to polyacrylamide-grafted DNA strands [52]. c the attachment of DNA species directly to an immobile support (here, gel beads) prevents their diffusion, while input and output species can freely diffuse between the beads [41]. d lipid bilayers allow the passive diffusion of hydrophobic compounds while confining biomolecules [26]. e protein pores (e.g., α-hemolysin) can be inserted in the membrane allowing for the selective diffusion of molecules (e.g., arabinose) [26]

2.3.1 Proteinosomes

One approach uses semipermeable membranes that filter molecular species based on their sizes. Proteinosomes, for example, are artificial semipermeable microenclosure based on a layer of crosslinked proteins. They can be generated in a highly monodisperse way, and their membrane cutoff can be adjusted through the cross-link density. De Greef et al. created spatial arrays of proteinosomes containing non-enzymatic DNA networks (Fig. 5a) [51]. The compartmentalized circuit modules were trapped within the proteinosome, using affinity tagging to bulky partners, but small DNA signals could diffuse across the boundary, thus opening a communication channel.

2.3.2 Hydrogel Barriers

Hosoya et al. reported a different strategy to selectively permit signal transmission across different compartments, which uses the differential diffusion coefficients of DNA molecules across a gel matrix (Fig. 5b) [52]. Using an aluminum mold, they manufactured an array of millimetric-sized compartments separated by 500-µm thick alginate gel walls. While input/output single-stranded DNA can freely diffuse across the walls, DNA gates are grafted to polyacrylamide anchors that prevent their diffusion from compartment to compartment. By filling different compartments with different molecules (input, gates or catalyst), the authors created a primitive cellular automaton—termed gellular automaton—that forms specific patterns according to the position and type of the initialized cells. The work also showed that, in absence of an active signal amplification system (i.e., a positive feedback loop), diffusion is a poor mechanism to transmit information over large distances.

2.3.3 Liposomes and Lipid Bilayers

Although liposomes’ boundaries are impermeable to many hydrophilic or charged compounds, it is possible to engineer pores with soluble proteins that spontaneously insert in the bilayer—many of these proteins are toxins that bacteria use to vampirize target cells. Protein pores have an inner channel whose dimensions are well-defined and can be extremely selective in the size and type of molecules that they allow through the membrane. Some pores are controllable through external signals such as light [53]. Insertion of α-hemolysin pores in liposomes creates semi-opened liposomal compartments that exchange fuel and waste with the environment [54], extending the lifetime of the enclosed molecular network (Fig. 5e). In another study, the same pore was used to create a self-selection feedback for directed evolution [55]. However, α-hemolysin’s small size limits its use to transport DNA signals.

When brought in close contact, phospholipid-stabilized droplets form bilayers, known as Droplet Interface Bilayer (DIB), in which membrane pores can be inserted. Dupin et al. followed this approach to spatially array dozens of microdroplets connected again by α-hemolysin [26]. Since the inner channel of α-hemolysin is narrow, the study relied on small chemicals rather than DNA as signal molecules. The authors thus created interfacing modules to connect these signals to IVTT- or strand displacement-based circuits. In the case of IVTT, they showed that the protein pore itself can be one of the outputs of the circuit, allowing feedbacks that build on the reinforcement of the communication between two compartments. Pore insertion is a random phenomenon with a potential for strong signal amplification (given that an important chemical gradient exists across the membrane), and this led to the observation of the stochastic differentiation of initially identical microcompartments.

2.3.4 On-Support Immobilization of DNA Species

Since DNA-based networks always involve multicomponent reactions, an alternative to building (semi) permeable enclosures is to attach one (or more, but not all) of the reactive species to an immobile support [56]. This is an attractive option because many strategies and commercial modifications are available to graft DNA to various supports, and these chemical steps have been intensively studied for applications such as microarray and, more recently, Next-Generation Sequencing (NGS). In addition, a number of DNA amplification schemes or DNA reactions compatible with a solid support are available, including bridge PCR, primer walking reactions [56], primer grafted Recombinase Polymerase Amplification (RPA) or other enzymatic reactions [57].

This option was explored in [41], where porous microbeads carrying DNA instructions encoding autocatalytic CRNs were dispersed in a continuous layer of PEN-toolbox mixture (i.e., the dNTP and enzymes necessary to run the DNA instructions, Fig. 5c). In the simplest case, sharp and sustained gradients of concentrations were established around the active microbeads. In addition, various bead types, carrying different instruction sets, could be combined to create large scale collective behaviors. Precise mathematical formulas were derived to rationalize the observation of localized PEN out-of-equilibrium behaviors (depending on whether the geometry was 2D, 2.5D or 3D). A key insight from this study was that the kinetics of the reactions involved in the CRN impose a critical length scale for the emergence of localized behaviors in the absence of physical boundaries. In particular, DNA instructions-carrying beads have to be large enough to be able to maintain an individuality; if the bead is too small or if the chemistry is too slow compared to diffusion, then all beads perform identically, and the potential for parallelism is lost.

3 Discussion and Applications

Mass-action kinetic systems can be split without altering their dynamical properties, and this property extends to computational chemical networks. The insensitivity to scale is generally true down to microscopic length scales, offering the possibility for massive parallelism using the same amount of material as used for a single “classic” experiment (e.g., micro- to milliliters).

This property of CRNs is relatively unique in computational systems. It is alien to standard silicon-based hardware and in general from all computation devices based on physical processes (e.g., mechanical computers). However, being split-resilient is a property observed in many biological systems, not only unicellular, but also higher organisms including many plants, fungi and some animals: for these organisms, a splitting event creates two viable individuals from one, with properties identical to each other and to the parent. In many cases, the two parts will grow back to the size and shape (intensive variables) of their parent or at least have the potential to do so, if the conditions are favorable. In the animalia kingdom, the hydra is the classical example.

Beside the biological analogy, we believe this unique asset ought to be better explored and exploited in the future of artificial molecular computations. Depending on whether the sub-compartments are independent or not, we see three interesting directions to harness parallel CRNs (Fig. 6).

Fig. 6

Applications of parallelized molecular computations. a independent compartments containing an identical circuit but receiving different inputs. b independent compartments containing different circuits (e.g., from a parametric family) all working on the same inputs. c cross-talking compartments collaborating to compute a global response. d examples of input types

• i. Independent compartments containing an identical circuit but receiving different inputs

• ii. Independent compartments containing different circuits, all working on the same inputs

• iii. Cross-talking compartments collaborating to compute a global response.

3.1 Independent Compartments Containing an Identical Circuit but Receiving Different Inputs

In the simplest case, split resilience can be used to repeatedly perform the same operation on different inputs. Bacteria, for example, can be seen as vehicles of their genomes, each testing the reproductive success of a slightly different genome variant or testing the same variant under different external forcings.

The same idea can be used for microcompartmentalized artificial molecular programs. This is because microcompartmentalization itself is a way to diversify inputs. For a given reactor of volume V, as soon as input concentration gets close to the critical value C_c = (VN)⁻¹ (where N is Avogadro’s number), stochastic partitioning ensures that each compartment receives a different count of inputs. In the case where [inputs] << C_c, only two types of compartments are created, with or without one molecule of input. This latter case is of particular interest if input molecules come from a library: a collection of similar, yet distinct molecules—for example, a partially randomized DNA strand. Indeed, Poissonian partitioning ensures that all members of the library will be processed in an identical way and independently of all others.

Building on this idea, one of us reported a Positive Feedback Loop (PFL) network that tests the presence of a specific enzymatic activity and accordingly enables (or not) genetic amplification. Distributed in microdroplets together with a genetic library, this system implements an in vitro evolution algorithm, poised to select for a pre-defined catalytic activity. Over rounds of selection and diversification, this molecular algorithm will spontaneously ascend the local fitness landscape [58]. Although Directed Evolution experiments are not usually described in terms of an algorithmic search process, it is likely that the ability to perform precise computations on molecular signals, at a molecular level, and with a molecular outcome—i.e., molecular programming—can bring strong benefits to this field.

This molecular evolution approach could be extended to optimize DNA-based molecular programs themselves, since their behavior is also genetically encoded. An array of compartmentalized molecular programs could clone and differentiate, each new compartment computing a function in a slightly different manner. By applying a selection pressure, one could then optimize a given molecular program or discover new functional architectures. This idea has been applied in silico [59], but presents intimidating technical difficulties in vitro, since it requires one to engineer a feedback loop that affects the architecture of the molecular program itself.

In principle, different inputs can also be deterministically injected in the various sub-compartments. When working with very small volumes, it can be experimentally tricky to address each compartment individually, although various microfluidic or robotic platforms exist [60,61,62]. Approaches to create bead-displayed diversity, for example, using Split and Pool [63], could be explored in this respect. Given that the dominant application of molecular programming is to process input signals that are molecular—in an attempt to maintain the full sensing–processing–actuation chain at the molecular level—it becomes important to develop interfacing strategies for various types of molecules, including for example proteins [64, 65] and small molecules [66].

3.2 Independent Compartments Containing Different Circuits, All Working on the Same Inputs

The second option to harness the parallelism of molecular circuits is to create many compartmentalized reactors containing different circuits. This basically allows one to apply a family of functions to a common input condition—an approach that resembles the paradigm of Single Instruction Multiple Data in parallel computing.

Genot et al. demonstrated this idea by introducing a microfluidic droplet chip that scans up to three component concentrations simultaneously [21]. With this device, millions of droplets, each containing a different combination of the three compounds of interest, and collectively mapping any desired parameter subspace, were generated in less than one hour. Fluorescent inert dropcodes encoded the concentration of the parametric compounds and allowed one to recover the experimental condition for each droplet, even after they have been mixed and manipulated at will.

In the process of building a DNA-based reaction network, one must decide the concentration of each functional DNA strand, enzymes, additives, etc. Since all these parameters are described by continuous variables, this complexity leads to painstaking rounds of trial and error, before a functional region can be found in parameter space. The microfluidic platform was then used to map the experimental bifurcation diagram of a predator–prey oscillator, scanning simultaneously its principal control parameters: the prey reproduction rate, the global growth rate and the species lifetime (through the concentration of an exonuclease). The finesse of scanning exposed a tiny region of parameters with an exotic behavior: there, droplets would oscillate for some time, then stay completely flat for a number of periods, then resume strong regular oscillations. The observation of this mode, known as “hard excitable”, remains to date the only example in DNA-based circuits.

More generally, this droplet-scanning platform addresses a common issue of multicomponent systems which require the titration of many concentrations. In principle, parallelization using microcompartments could be used to expedite the optimization process, by testing different conditions in each microreactor. Note that this assumes that the compound of interest does not cross the compartment boundaries [25, 26].

3.3 Cross-Talking Compartments Collaborating to Compute a Global Response

Notwithstanding the examples presented above, it is still difficult to distribute a molecular program in many sub-compartments and simultaneously control the communication channels between these units. Pioneering works based on top-down microfluidics and microfabrication [23] involve a dozen of compartments at most, but it is likely that thousands—or even millions—of compartments would be needed for a powerful parallel computation to emerge.

On the bottom-up (self-assembly) side, the trafficking of molecules across vesicles or droplet interfaces is still challenging. Molecular pores, which spontaneously insert in lipid bilayers, provide an interesting option, but DNA strands are large macromolecules, and biological channel proteins do not naturally allow DNA traffic. For instance, the pores used in nanopore sequencing evolved to traffic small ions and organic molecules. It took a lot of protein engineering to thread DNA through them, and the process is not spontaneous: it requires a voltage difference as driving force and a polymerase for regulation [67]. The engineering of DNA-based membranes pores with larger apertures could provide some interesting options.

Here again, Nature could provide some inspiration, as cells do not use protein pores to traffic DNA, but instead the fusion and splitting of small vesicles—of which exosomes provide a prominent example. Exosomes are nanometer-sized (~40–200 nm) extracellular compartments that are secreted by some cells, enclosing biomolecules like RNA, DNA or proteins, and which are captured by other cells at remote locations. Although the exact mechanism regulating the production and absorption (endocytosis) is still being elucidated, exosomes seem to work as a “postal service” by which cells can send molecular messages to each other [68].

Finally, although we have focused here on the spatial parallelization of mass-action CRNs—that is, systems governed by concentrations and Ordinary Differential Equations (ODEs)—we stress that other approaches exploit the parallelism of computational chemical operations to manipulate complex libraries [69, 70]. One possibility is to perform the computation directly within a single (supra-) molecule in solution, such as a single DNA nanostructure [71,72,73]. Another approach would be to encode the computation in successive transformation of a single DNA sequence. For this purpose, the developing toolkit of solid-phase DNA manipulations [57] could enable sequential molecular transformations at tremendous throughputs.

What could be the future applications of parallel molecular computations? There are many tantalizing areas where it could solve open problems. In directed evolution, it could steer the evolution of DNA, RNA or proteins toward highly functional forms. Rather than screening for the absence or presence of a function in a molecule (single objective evolution), a molecular circuit could weigh multiple objectives (e.g., for an enzyme, it could assess both its thermodynamic constants, measured by its Michaelis–Menten constant Km, and its kinetic constant, measured by its turnover rate V) and assign an integrated fitness score to each compartment. After each round, a compartment would get a chance to be replicated according to its fitness, thus steering the population toward a region of desirable characteristics. Parallel molecular computations could also empower the nascent field of DNA data storage, for instance, to find the number of occurrences of a pattern in a database. A DNA database could be split and compartmentalized, and the same computation could be applied simultaneously to each compartment by a molecular program. For very large database (say in the Petabytes or Exabytes range or over), molecular computations may beat electronic computations in terms of energy-cost or speed, simply because their scaling is much better.