Spatial waves in synthetic biochemical networks

DNA-empowered synthetic cells as minimalistic life forms

Cells, the fundamental units of life, orchestrate intricate functions - motility, adaptation, replication, communication, and self-organization within tissues. Originating from spatiotemporally organized structures and machinery, coupled with information processing in signalling networks, cells embody the 'sensor-processor-actuator' paradigm. Can we glean insights from these processes to construct primitive artificial systems with life-like properties? Using de novo design approaches, what can we uncover about the evolutionary path of life? This Review discusses the strides made in crafting synthetic cells, utilizing the powerful toolbox of structural and dynamic DNA nanoscience. We describe how DNA can serve as a versatile tool for engineering entire synthetic cells or subcellular entities, and how DNA enables complex behaviour, including motility and information processing for adaptive and interactive processes. We chart future directions for DNA-empowered synthetic cells, envisioning interactive systems wherein synthetic cells communicate within communities and with living cells.

Artificial Homeostasis Systems Based on Feedback Reaction Networks: Design Principles and Future Promises

Feedback-controlled chemical reaction networks (FCRNs) are indispensable for various biological processes, such as cellular mechanisms, patterns, and signaling pathways. Through the intricate interplay of many feedback loops (FLs), FCRNs maintain a stable internal cellular environment. Currently, creating minimalistic synthetic cells is the long-term objective of systems chemistry, which is motivated by such natural integrity. The design, kinetic optimization, and analysis of FCRNs to exhibit functions akin to those of a cell still pose significant challenges. Indeed, reaching synthetic homeostasis is essential for engineering synthetic cell components. However, maintaining homeostasis in artificial systems against various agitations is a difficult task. Several biological events can provide us with guidelines for a conceptual understanding of homeostasis, which can be further applicable in designing artificial synthetic systems. In this regard, we organize our review with artificial homeostasis systems driven by FCRNs at different length scales, including homogeneous, compartmentalized, and soft material systems. First, we stretch a quick overview of FCRNs in different molecular and supramolecular systems, which are the essential toolbox for engineering different nonlinear functions and homeostatic systems. Moreover, the existing history of synthetic homeostasis in chemical and material systems and their advanced functions with self-correcting, and regulating properties are also emphasized.

Cell-Like Synthetic Supramolecular Soft Materials Realized in Multicomponent, Non-/Out-of-Equilibrium Dynamic Systems

Living cells are complex, nonequilibrium supramolecular systems capable of independently and/or cooperatively integrating multiple bio-supramolecules to execute intricate physiological functions that cannot be accomplished by individual biomolecules. These biological design strategies offer valuable insights for the development of synthetic supramolecular systems with spatially controlled hierarchical structures, which, importantly, exhibit cell-like responses and functions. The next grand challenge in supramolecular chemistry is to control the organization of multiple types of supramolecules in a single system, thus integrating the functions of these supramolecules in an orthogonal and/or cooperative manner. In this perspective, the recent progress in constructing multicomponent supramolecular soft materials through the hybridization of supramolecules, such as self-assembled nanofibers/gels and coacervates, with other functional molecules, including polymer gels and enzymes is highlighted. Moreover, results show that these materials exhibit bioinspired responses to stimuli, such as bidirectional rheological responses of supramolecular double-network hydrogels, temporal stimulus pattern-dependent responses of synthetic coacervates, and 3D hydrogel patterning in response to reaction-diffusion processes are presented. Autonomous active soft materials with cell-like responses and spatially controlled structures hold promise for diverse applications, including soft robotics with directional motion, point-of-care disease diagnosis, and tissue regeneration.

A DNA Nanodevice-Based Platform with Diverse Capabilities

Social biotic colonies often perform intricate tasks by interindividual communication and cooperation. Inspired by these biotic behaviors, a DNA nanodevice community is proposed as a universal and scalable platform. The modular nanodevice as the infrastructure of platform contains a DNA origami triangular prism framework and a hairpin-swing arm machinery core. By coding and decoding a signal domain on the shuttled output strand in different nanodevices, an orthogonal inter-nanodevice communication network is established to connect multi-nanodevices into a functional platform. The nanodevice platform enables implementation of diverse tasks, including signal cascading and feedback, molecular input recording, distributed logic computing, and modeling of simulation for virus transmission. The nanodevice platform with powerful compatibility and programmability presents an elegant example of the combination of the distributed operation of multiple devices and the complicated interdevice communication network, and may become a new generation of intelligent DNA nanosystems.

Multiscale Biofabrication: Integrating Additive Manufacturing with DNA-Programmable Self-Assembly

Structure and hierarchical organization are crucial elements of biological systems and are likely required when engineering synthetic biomaterials with life-like behavior. In this context, additive manufacturing techniques like bioprinting have become increasingly popular. However, 3D bioprinting, as well as other additive manufacturing techniques, show limited resolution, making it difficult to yield structures on the sub-cellular level. To be able to form macroscopic synthetic biological objects with structuring on this level, manufacturing techniques have to be used in conjunction with biomolecular nanotechnology. Here, a short overview of both topics and a survey of recent advances to combine additive manufacturing with microfabrication techniques and bottom-up self-assembly involving DNA, are given.

Nonlinear decision-making with enzymatic neural networks

Artificial neural networks have revolutionized electronic computing. Similarly, molecular networks with neuromorphic architectures may enable molecular decision-making on a level comparable to gene regulatory networks^1,2. Non-enzymatic networks could in principle support neuromorphic architectures, and seminal proofs-of-principle have been reported^3,4. However, leakages (that is, the unwanted release of species), as well as issues with sensitivity, speed, preparation and the lack of strong nonlinear responses, make the composition of layers delicate, and molecular classifications equivalent to a multilayer neural network remain elusive (for example, the partitioning of a concentration space into regions that cannot be linearly separated). Here we introduce DNA-encoded enzymatic neurons with tuneable weights and biases, and which are assembled in multilayer architectures to classify nonlinearly separable regions. We first leverage the sharp decision margin of a neuron to compute various majority functions on 10 bits. We then compose neurons into a two-layer network and synthetize a parametric family of rectangular functions on a microRNA input. Finally, we connect neural and logical computations into a hybrid circuit that recursively partitions a concentration plane according to a decision tree in cell-sized droplets. This computational power and extreme miniaturization open avenues to query and manage molecular systems with complex contents, such as liquid biopsies or DNA databases.

Programmable synthetic cell networks regulated by tuneable reaction rates

Coupled compartmentalised information processing and communication via molecular diffusion underpin network based population dynamics as observed in biological systems. Understanding how both compartmentalisation and communication can regulate information processes is key to rational design and control of compartmentalised reaction networks. Here, we integrate PEN DNA reactions into semi-permeable proteinosomes and characterise the effect of compartmentalisation on autocatalytic PEN DNA reactions. We observe unique behaviours in the compartmentalised systems which are not accessible under bulk conditions; for example, rates of reaction increase by an order of magnitude and reaction kinetics are more readily tuneable by enzyme concentrations in proteinosomes compared to buffer solution. We exploit these properties to regulate the reaction kinetics in two node compartmentalised reaction networks comprised of linear and autocatalytic reactions which we establish by bottom-up synthetic biology approaches.

Unraveling the physiochemical nature of colloidal motion waves among silver colloids

Traveling waves are common in biological and synthetic systems, including the recent discovery that silver (Ag) colloids form traveling motion waves in H₂O₂ and under light. Here, we show that this colloidal motion wave is a heterogeneous excitable system. The Ag colloids generate traveling chemical waves via reaction-diffusion, and either self-propel through self-diffusiophoresis ("ballistic waves") or are advected by diffusio-osmotic flows from gradients of neutral molecules ("swarming waves"). Key results include the experimental observation of traveling waves of OH^- with pH-sensitive fluorescent dyes and a Rogers-McCulloch model that qualitatively and quantitatively reproduces the key features of colloidal waves. These results are a step forward in elucidating the Ag-H₂O₂-light oscillatory system at individual and collective levels. In addition, they pave the way for using colloidal waves either as a platform for studying nonlinear phenomena, or as a tool for colloidal transport and for information transmission in microrobot ensembles.

Spatiotemporal Regulation of Hydrogel Actuators by Autocatalytic Reaction Networks

Regulating hydrogel actuators with chemical reaction networks is instrumental for constructing life-inspired smart materials. Herein, hydrogel actuators are engineered that are regulated by the autocatalytic front of thiols. The actuators consist of two layers. The first layer, which is regular polyacrylamide hydrogel, is in a strained conformation. The second layer, which is polyacrylamide hydrogel with disulfide crosslinks, maintains strain in the first layer. When thiols released by the autocatalytic front reduce disulfide crosslinks, the hydrogel actuates by releasing the mechanical strain in the first layer. The autocatalytic front is sustained by the reaction network, which uses thiouronium salts, disulfides of β-aminothiols, and maleimide as starting components. The gradual actuation by the autocatalytic front enables movements such as gradual unrolling, screwing, and sequential closing of "fingers." This actuation also allows the transmission of chemical signals in a relay fashion and the conversion of a chemical signal to an electrical signal. Locations and times of spontaneous initiation of autocatalytic fronts can be preprogrammed in the spatial distribution of the reactants in the hydrogel. To approach the functionality of living matter, the actuators triggered by an autocatalytic front can be integrated into smart materials regulated by chemical circuits.

Long-Lasting and Responsive DNA/Enzyme-Based Programs in Serum-Supplemented Extracellular Media

DNA molecular programs are emerging as promising pharmaceutical approaches due to their versatility for biomolecular sensing and actuation. However, the implementation of DNA programs has been mainly limited to serum-deprived in vitro assays due to the fast deterioration of the DNA reaction networks by the nucleases present in the serum. Here, we show that DNA/enzyme programs are functional in serum for 24 h but are later disrupted by nucleases that give rise to parasitic amplification. To overcome this, we implement three-letter code networks that suppress autocatalytic parasites while still conserving the functionality of DNA/enzyme programs for at least 3 days in the presence of 10% serum. In addition, we define a new buffer that further increases the biocompatibility and conserves responsiveness to changes in molecular composition across time. Finally, we demonstrate how serum-supplemented extracellular DNA molecular programs remain responsive to molecular inputs in the presence of living cells, having responses 6-fold faster than the cellular division rate, and are sustainable for at least three cellular divisions. This demonstrates the possibility of implementing in situ biomolecular characterization tools for serum-demanding in vitro models. We foresee that the coupling of chemical reactivity to our DNA programs by aptamers or oligonucleotide conjugations will allow the implementation of extracellular synthetic biology tools, which will offer new biomolecular pharmaceutical approaches and the emergence of complex and autonomous in vitro models.

Controlling The Synchronization of Molecular Oscillators Through Indirect Coupling

In this article, we study the coupling of a collection of molecular oscillators, called repressilators, interacting indirectly through enzymatic saturation. We extended a measure of autocorrelation to identify the period of the whole system and to detect coupling behaviors. We explored the parameter space of concentrations of molecular species in each oscillator versus enzymatic saturation, and observed regions of uncoupled, partially, or fully coupled systems. In particular, we found a region that provided a sharp transition between no coupling, two coupled oscillators, and full coupling. In practical applications, signals from the environment can directly affect parameters such as local enzymatic saturation, and thus switch the system from a coupled to an uncoupled regime and vice-versa. Our parameter exploration can be used to guide the design of complex molecular systems, such as active materials or molecular robot controllers.

Front speed and pattern selection of a propagating chemical front in an active fluid

Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly understood in general. In this analytical and numerical paper, we study an experimentally motivated minimal model of coupling between reaction-diffusion and active matter: a propagating front of an autocatalytic and stress-generating species. In the absence of activity, the front is described by the well-studied Kolmogorov, Petrovsky, and Piskunov equation. We find that front propagation is maintained even in active systems, with crucial differences: an extensile stress increases the front speed beyond a critical magnitude of the stress, while a contractile stress has no effect on the front speed but can generate a periodic instability in the high-concentration region behind the front. We expect our results to be useful in interpreting pattern formation in active systems with mechanochemical coupling in vivo and in vitro.

Programmed mechano-chemical coupling in reaction-diffusion active matter

Embryo morphogenesis involves a complex combination of self-organization mechanisms that generate a great diversity of patterns. However, classical in vitro patterning experiments explore only one self-organization mechanism at a time, thus missing coupling effects. Here, we conjugate two major out-of-equilibrium patterning mechanisms—reaction-diffusion and active matter—by integrating dissipative DNA/enzyme reaction networks within an active gel composed of cytoskeletal motors and filaments. We show that the strength of the flow generated by the active gel controls the mechano-chemical coupling between the two subsystems. This property was used to engineer a synthetic material where contractions trigger chemical reaction networks both in time and space, thus mimicking key aspects of the polarization mechanism observed in C. elegans oocytes. We anticipate that reaction-diffusion active matter will promote the investigation of mechano-chemical transduction and the design of new materials with life-like properties.

DNA-Controlled Spatiotemporal Patterning of a Cytoskeletal Active Gel

Living cells move and change their shape because signaling chemical reactions modify the state of their cytoskeleton, an active gel that converts chemical energy into mechanical forces. To create life-like materials, it is thus key to engineer chemical pathways that drive active gels. Here we describe the preparation of DNA-responsive surfaces that control the activity of a cytoskeletal active gel composed of microtubules: A DNA signal triggers the release of molecular motors from the surface into the gel bulk, generating forces that structure the gel. Depending on the DNA sequence and concentration, the gel forms a periodic band pattern or contracts globally. Finally, we show that the structuration of the active gel can be spatially controlled in the presence of a gradient of DNA concentration. We anticipate that such DNA-controlled active matter will contribute to the development of life-like materials with self-shaping properties.

Phototriggered Spatially Controlled Out-of-Equilibrium Patterns of Peptide Nanofibers in a Self-Sorting Double Network Hydrogel

Out-of-equilibrium patterns arising from diffusion processes are ubiquitous in nature, although they have not been fully exploited for the design of artificial materials. Here, we describe the formation of phototriggered out-of-equilibrium patterns using photoresponsive peptide-based nanofibers in a self-sorting double network hydrogel. Light irradiation using a photomask followed by thermal incubation induced the spatially controlled condensation of peptide nanofibers. According to confocal images and spectroscopic analyses, metastable nanofibers photodecomposed in the irradiated areas, where thermodynamically stable nanofibers reconstituted and condensed with a supply of monomers from the nonirradiated areas. These supramolecular events were regulated by light and diffusion to facilitate the creation of unique out-of-equilibrium patterns, including two lines from a one-line photomask and a line pattern of a protein immobilized in the hydrogel.

Reversible and spatiotemporal control of colloidal structure formation

Tuning colloidal structure formation is a powerful approach to building functional materials, as a wide range of optical and viscoelastic properties can be accessed by the choice of individual building blocks and their interactions. Precise control is achieved by DNA specificity, depletion forces, or geometric constraints and results in a variety of complex structures. Due to the lack of control and reversibility of the interactions, an autonomous oscillating system on a mesoscale without external driving was not feasible until now. Here, we show that tunable DNA reaction circuits controlling linker strand concentrations can drive the dynamic and fully reversible assembly of DNA-functionalized micron-sized particles. The versatility of this approach is demonstrated by programming colloidal interactions in sequential and spatial order to obtain an oscillatory structure formation process on a mesoscopic scale. The experimental results represent an approach for the development of active materials by using DNA reaction networks to scale up the dynamic control of colloidal self-organization.

Nucleic acid-based molecular computation heads towards cellular applications

Nucleic acids, with the advantages of programmability and biocompatibility, have been widely used to design different kinds of novel biocomputing devices. Recently, nucleic acid-based molecular computing has shown promise in making the leap from the test tube to the cell. Such molecular computing can perform logic analysis within the confines of the cellular milieu with programmable modulation of biological functions at the molecular level. In this review, we summarize the development of nucleic acid-based biocomputing devices that are rationally designed and chemically synthesized, highlighting the ability of nucleic acid-based molecular computing to achieve cellular applications in sensing, imaging, biomedicine, and bioengineering. Then we discuss the future challenges and opportunities for cellular and in vivo applications. We expect this review to inspire innovative work on constructing nucleic acid-based biocomputing to achieve the goal of precisely rewiring, even reconstructing cellular signal networks in a prescribed way.

Towards a synthetic cell cycle

Recent developments in synthetic biology may bring the bottom-up generation of a synthetic cell within reach. A key feature of a living synthetic cell is a functional cell cycle, in which DNA replication and segregation as well as cell growth and division are well integrated. Here, we describe different approaches to recreate these processes in a synthetic cell, based on natural systems and/or synthetic alternatives. Although some individual machineries have recently been established, their integration and control in a synthetic cell cycle remain to be addressed. In this Perspective, we discuss potential paths towards an integrated synthetic cell cycle.

Cascaded pattern formation in hydrogel medium using the polymerisation approach

Reaction-diffusion systems are one of the models of the formation process with various patterns found in nature. Inspired by natural pattern formation, several methods for designing artificial chemical reaction-diffusion systems have been proposed. DNA is a suitable building block to build such artificial systems owing to its programmability. Previously, we reported a line pattern formed due to the reaction and diffusion of synthetic DNA; however, the width of the line was too wide to be used for further applications such as parallel and multi-stage pattern formations. Here, we propose a novel method to programme a reaction-diffusion system in a hydrogel medium to realise a sharp line capable of forming superimposed and cascaded patterns. The mechanism of this system utilises a two-segment polymerisation of DNA caused by hybridisation. To superimpose the system, we designed orthogonal DNA sequences that formed two lines in different locations on the hydrogel. Additionally, we designed a reaction to release DNA and form a cascade pattern, in which the third line appears between the two lines. To explain the mechanism of our system, we modelled the system as partial differential equations, whose simulation results agreed well with the experimental data. Our method to fabricate cascaded patterns may inspire combinations of DNA-based technologies and expand the applications of artificial reaction-diffusion systems.

A theory of pattern formation for reaction–diffusion systems on temporal networks

Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over time. One area of active interest is pattern formation from reaction–diffusion systems, which themselves evolve over temporal networks. We derive analytical conditions for the onset of diffusive spatial and spatio-temporal pattern formation on undirected temporal networks through the Turing and Benjamin–Feir mechanisms, with the resulting pattern selection process depending strongly on the evolution of both global diffusion rates and the local structure of the underlying network. Both instability criteria are then extended to the case where the reaction–diffusion system is non-autonomous, which allows us to study pattern formation from time-varying base states. The theory we present is illustrated through a variety of numerical simulations which highlight the role of the time evolution of network topology, diffusion mechanisms and non-autonomous reaction kinetics on pattern formation or suppression. A fundamental finding is that Turing and Benjamin–Feir instabilities are generically transient rather than eternal, with dynamics on temporal networks able to transition between distinct patterns or spatio-temporal states. One may exploit this feature to generate new patterns, or even suppress undesirable patterns, over a given time interval.

Spatiotemporal Patterning of Living Cells with Extracellular DNA Programs

Reactive extracellular media focus on engineering reaction networks outside the cell to control intracellular chemical composition across time and space. However, current implementations lack the feedback loops and out-of-equilibrium molecular dynamics for encoding spatiotemporal control. Here, we demonstrate that enzyme-DNA molecular programs combining these qualities are functional in an extracellular medium where human cells can grow. With this approach, we construct an internalization program that delivers fluorescent DNA inside living cells and remains functional for at least 48 h. Its nonequilibrium dynamics allows us to control both the time and position of cell internalization. In particular, a spatially inhomogeneous version of this program generates a tunable reaction-diffusion two-band pattern of cell internalization. This demonstrates that a synthetic extracellular program can provide temporal and positional information to living cells, emulating archetypal mechanisms observed during embryo development. We foresee that nonequilibrium reactive extracellular media could be advantageously applied to in vitro biomolecular tracking, tissue engineering, or smart bandages.

Investigating the Evolution and Development of Biological Systems from the Perspective of Thermo-Kinetics and Systems Theory

Life itself is grander than the sum of its constituent molecules. Any living organism may be regarded as a part of a dissipative process that connects irreversible energy consumption with growth, reproduction, and evolution. Under energy-fuelled, far-from-equilibrium conditions, chemical systems capable of exponential growth can manifest a specific form of stability- dynamic kinetic stability (DKS) - indicating the persistence of self-reproducible entities. This kinetic behavior is associated with thermodynamic conditions far from equilibrium leading to an evolutionary view of the origin of life in which increasing entities have to be associated with the dissipation of free energy. This review aims to reformulate Darwinian theory in physicochemical terms so that it can handle both animate and inanimate systems, thus helping to overcome this theoretical divide. The expanded formulation is based on the principle of dynamic kinetic stability and evidence from the emerging field of systems chemistry. Although the classic Darwinian theory is useful for understanding the origins and evolution of species, it is not meant to primarily build an explicit framework for predicting potential evolution routes. Throughout the last century, the inherently systemic and dynamic nature of the biological systems has been brought to the attention of researchers. During the last decades, "systems" approaches to biology and genome evolution are gaining ever greater significance providing the possibility of a deeper interpretation of the basic concepts of life. Further progress of this approach depends on crossing disciplinary boundaries and complex simulations of biological systems. Evolutionary systems biology (ESB) through the integration of methods from evolutionary biology and systems biology aims to the understanding of the fundamental principles of life as well as the prediction of biological systems evolution.

Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

Programmable patterns in a DNA-based reaction-diffusion system

Biology offers compelling proof that macroscopic "living materials" can emerge from reactions between diffusing biomolecules. Here, we show that molecular self-organization could be a similarly powerful approach for engineering functional synthetic materials. We introduce a programmable DNA embedded hydrogel that produces tunable patterns at the centimeter length scale. We generate these patterns by implementing chemical reaction networks through synthetic DNA complexes, embedding the complexes in the hydrogel, and triggering with locally applied input DNA strands. We first demonstrate ring pattern formation around a circular input cavity and show that the ring width and intensity can be predictably tuned. Then, we create patterns of increasing complexity, including concentric rings and non-isotropic patterns. Finally, we show "destructive" and "constructive" interference patterns, by combining several ring-forming modules in the gel and triggering them from multiple sources. We further show that computer simulations based on the reaction-diffusion model can predict and inform the programming of target patterns.

Multimachine Communication Network That Mimics the Adaptive Immune Response

Biological organisms capable of controlling and performing a wide variety of functions have inspired attempts to mimic biological systems with designable intelligence. Here we develop a multimachine communication network (MMCN) to mimic the operation and function of adaptive immune response (AIR) via connecting three kinds of DNA machines built from module-functionalized gold nanoparticles. These machines simulate three critical immune cells, dendritic cells, T and B lymphocytes, and their differentiation and coordinated interaction upon exposure and response to an invading pathogen. MMCN is composed of standard modules with track, movement, and fuel components that allow for the (1) integration and adaptability of a single machine, (2) convenient spatiotemporal control of the sequential activation of a single machine, and (3) rapid reaction rate and high efficiency owing to an enhanced local concentration of interacting species. We show that the proposed network can sense and clear the corresponding pathogen via consecutive activation and connection of the machines, simultaneously forming a memory to respond more rapidly and effectively upon the second invasion of the pathogen. This system may be extended to construct powerful networks to execute more sophisticated tasks and accomplish diverse functions.

Dynamic Environments as a Tool to Preserve Desired Output in a Chemical Reaction Network

Current efforts to design functional molecular systems have overlooked the importance of coupling out-of-equilibrium behaviour with changes in the environment. Here, the authors use an oscillating reaction network and demonstrate that the application of environmental forcing, in the form of periodic changes in temperature and in the inflow of the concentration of one of the network components, removes the dependency of the periodicity of this network on temperature or flow rates and enforces a stable periodicity across a wide range of conditions. Coupling a system to a dynamic environment can thus be used as a simple tool to regulate the output of a network. In addition, the authors show that coupling can also induce an increase in behavioural complexity to include quasi-periodic oscillations.

Early warning signals in chemical reaction networks

Many natural and man-made complex systems display early warning signals when close to an abrupt shift in behaviour. Here we show that such early warning signals appear in a complex chemical reaction network.

DNA-based long-lived reaction-diffusion patterning in a host hydrogel

The development of living organisms is a source of inspiration for the creation of synthetic life-like materials. Embryo development is divided into three stages that are inextricably linked: patterning, differentiation and growth. During patterning, sustained out-of-equilibrium molecular programs interpret underlying molecular cues to create well-defined concentration profiles. Implementing this patterning stage in an autonomous synthetic material is a challenge that at least requires a programmable and long-lasting out-of-equilibrium chemistry compatible with a host material. Here, we show that DNA/enzyme reactions can create reaction-diffusion patterns that are extraordinarily long-lasting both in solution and inside an autonomous hydrogel. The life-time and stability of these patterns - here, traveling fronts and two-band patterns - are significantly increased by blocking parasitic side reactions and by dramatically reducing the diffusion coefficient of specific DNA strands. Immersed in oil, hydrogels pattern autonomously with limited evaporation, but can also exchange chemical information with other gels when brought into contact. Providing a certain degree of autonomy and being capable of interacting with each other, we believe these out-of-equilibrium hydrogels open the way for the rational design of primitive metabolic materials.

Modelling Bacteria-Inspired Dynamics with Networks of Interacting Chemicals

One approach to understanding how life-like properties emerge involves building synthetic cellular systems that mimic certain dynamical features of living cells such as bacteria. Here, we developed a model of a reaction network in a cellular system inspired by the ability of bacteria to form a biofilm in response to increasing cell density. Our aim was to determine the role of chemical feedback in the dynamics. The feedback was applied through the enzymatic rate dependence on pH, as pH is an important parameter that controls the rates of processes in cells. We found that a switch in pH can be used to drive base-catalyzed gelation or precipitation of a substance in the external solution. A critical density of cells was required for gelation that was essentially independent of the pH-driven feedback. However, the cell pH reached a higher maximum as a result of the appearance of pH oscillations with feedback. Thus, we conclude that while feedback may not play a vital role in some density-dependent behavior in cellular systems, it nevertheless can be exploited to activate internally regulated cell processes at low cell densities.

rEXPAR: An Isothermal Amplification Scheme That Is Robust to Autocatalytic Parasites

In the absence of DNA, a solution containing the four deoxynucleotidetriphosphates (dNTPs), a DNA polymerase, and a nicking enzyme generates a self-replicating mixture of DNA species called parasite. Parasites are problematic in template-based isothermal amplification schemes such as EXPAR as well as in related molecular programming approaches, such as the PEN DNA toolbox. Here we show that using a nicking enzyme with only three letters (C, G, T) in the top strand of its recognition site, such as Nb.BssSI, allows us to change the sequence design of EXPAR templates in a way that prevents the formation of parasites when dATP is removed from the solution. This method allows us to make the EXPAR reaction robust to parasite contamination, a common feature in the laboratory, while keeping it compatible with PEN programs, which we demonstrate by engineering a parasite-proof bistable reaction network.

Multivariate statistical analysis of chemical and electrochemical oscillators for an accurate frequency selection

The effect of experimental parameters on the frequency of chemical oscillators has been systematically studied since the first observations of clock reactions. The approach is mainly based on univariate changes in one specific parameter while others are kept constant. The frequency is then monitored and the effect of each parameter is discussed separately. This type of analysis, however, does not take into account the multiple interactions among the controllable parameters and the synergic responses on the oscillation frequency. We have carried out a multivariate statistical analysis of chemical (BZ-ferroin catalyzed reaction) and electrochemical (Cu/Cu₂O cathodic deposition) oscillators and identified the contributions of the experimental parameters on frequency variations. The BZ reaction presented a strong dependence on the initial concentration of sodium bromate and temperature, resulting in a frequency increase. The concentration of malonic acid, the organic substrate, affects the system but with lower intensity compared with the combination of sodium bromate and temperature. On the other hand, the Cu/Cu₂O electrochemical oscillator was shown to be less sensitive to changes in the temperature. The applied current density and pH were the two parameters which most perturbed the system. Interestingly, the frequency behaved nonmonotonically with a quadratic dependence. The multivariate analysis of both oscillators exhibited significant differences - while the homogenous oscillator displayed a linear dependence with the factors, the heterogeneous one revealed a more complex dependence with quadratic terms. Our results may contribute, for instance, in the synthesis of self-organized materials in which an accurate frequency selection is required and, depending on its value, different physicochemical properties are obtained.

Triggered reversible substitution of adaptive constitutional dynamic networks dictates programmed catalytic functions

The triggered substitution of networks and their resulting functions play an important mechanism in biological transformations, such as intracellular metabolic pathways and cell differentiation. We describe the triggered, cyclic, reversible intersubstitution of three nucleic acid-based constitutional dynamic networks (CDNs) and the programmed catalytic functions guided by the interconverting CDNs. The transitions between the CDNs are activated by nucleic acid strand displacement processes acting as triggers and counter triggers, leading to the adaptive substitution of the constituents and to emerging catalytic functions dictated by the compositions of the different networks. The quantitative evaluation of the compositions of the different CDNs is achieved by DNAzyme reporters and complementary electrophoresis experiments. By coupling a library of six hairpins to the interconverting CDNs, the CDN-guided, emerging, programmed activities of three different biocatalysts are demonstrated. The study has important future applications in the development of sensor systems, finite-state logic devices, and selective switchable catalytic assemblies.

Reverse and forward engineering of protein pattern formation

Living systems employ protein pattern formation to regulate important life processes in space and time. Although pattern-forming protein networks have been identified in various prokaryotes and eukaryotes, their systematic experimental characterization is challenging owing to the complex environment of living cells. In turn, cell-free systems are ideally suited for this goal, as they offer defined molecular environments that can be precisely controlled and manipulated. Towards revealing the molecular basis of protein pattern formation, we outline two complementary approaches: the biochemical reverse engineering of reconstituted networks and the de novo design, or forward engineering, of artificial self-organizing systems. We first illustrate the reverse engineering approach by the example of the Escherichia coli Min system, a model system for protein self-organization based on the reversible and energy-dependent interaction of the ATPase MinD and its activating protein MinE with a lipid membrane. By reconstituting MinE mutants impaired in ATPase stimulation, we demonstrate how large-scale Min protein patterns are modulated by MinE activity and concentration. We then provide a perspective on the de novo design of self-organizing protein networks. Tightly integrated reverse and forward engineering approaches will be key to understanding and engineering the intriguing phenomenon of protein pattern formation.This article is part of the theme issue 'Self-organization in cell biology'.

Two Synthetic Replicators Compete To Process a Dynamic Reagent Pool

Complementary building blocks, comprising a set of four aromatic aldehydes and a set of four nucleophiles-three anilines and one hydroxylamine-combine through condensation reactions to afford a dynamic covalent library (DCL) consisting of the eight starting materials and 16 condensation products. One of the aldehydes and, consequently, all of the DCL members derived from this compound bear an amidopyridine recognition site. Exposure of this DCL to two maleimides, M^p and M^m, each equipped with a carboxylic acid recognition site, results in the formation of a series of products through irreversible 1,3-dipolar cycloaddition reactions with the four nitrones present in the DCL. However, only the two cycloadducts in the product pool that incorporate both recognition sites, T^p and T^m, are self-replicators that can harness the DCL as feedstock for their own formation, facilitating their own synthesis via autocatalytic and cross-catalytic pathways. The ability of these replicators to direct their own formation from the components present in the dynamic reagent pool in response to the input of instructions in the form of preformed replicators is demonstrated through a series of quantitative ¹⁹F{¹H} NMR spectroscopy experiments. Simulations establish the critical relationships between the kinetic and thermodynamic parameters of the replicators, the initial reagent concentrations, and the presence or absence of the DCL and their influence on the competition between T^p and T^m. Thus, we establish the rules that govern the behavior of the competing replicators under conditions where their formation is coupled tightly to the processing of a DCL.

Accelerating DNA-Based Computing on a Supramolecular Polymer

Dynamic DNA-based circuits represent versatile systems to perform complex computing operations at the molecular level. However, the majority of DNA circuits relies on freely diffusing reactants, which slows down their rate of operation substantially. Here we introduce the use of DNA-functionalized benzene-1,3,5-tricarboxamide (BTA) supramolecular polymers as dynamic scaffolds to template DNA-based molecular computing. By selectively recruiting DNA circuit components to a supramolecular BTA polymer functionalized with 10-nucleotide handle strands, the kinetics of strand displacement and strand exchange reactions were accelerated 100-fold. In addition, strand exchange reactions were also favored thermodynamically by bivalent interactions between the reaction product and the supramolecular polymer. The noncovalent assembly of the supramolecular polymers enabled straightforward optimization of the polymer composition to best suit various applications. The ability of supramolecular BTA polymers to increase the efficiency of DNA-based computing was demonstrated for three well-known and practically important DNA-computing operations: multi-input AND gates, Catalytic Hairpin Assembly and Hybridization Chain Reactions. This work thus establishes supramolecular BTA polymers as an efficient platform for DNA-based molecular operations, paving the way for the construction of autonomous bionanomolecular systems that confine and combine molecular sensing, computation, and actuation.

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.

Diffusion modulation of DNA by toehold exchange

We propose a method to control the diffusion speed of DNA molecules with a target sequence in a polymer solution. The interaction between solute DNA and diffusion-suppressing DNA that has been anchored to a polymer matrix is modulated by the concentration of the third DNA molecule called the competitor by a mechanism called toehold exchange. Experimental results show that the sequence-specific modulation of the diffusion coefficient is successfully achieved. The diffusion coefficient can be modulated up to sixfold by changing the concentration of the competitor. The specificity of the modulation is also verified under the coexistence of a set of DNA with noninteracting base sequences. With this mechanism, we are able to control the diffusion coefficient of individual DNA species by the concentration of another DNA species. This methodology introduces a programmability to a DNA-based reaction-diffusion system.

Spatiotemporal control of DNA-based chemical reaction network via electrochemical activation in microfluidics

In recent years, DNA computing frameworks have been developed to create dynamical systems which can be used for information processing. These emerging synthetic biochemistry tools can be leveraged to gain a better understanding of fundamental biology but can also be implemented in biosensors and unconventional computing. Most of the efforts so far have focused on changing the topologies of DNA molecular networks or scaling them up. Several issues have thus received little attention and remain to be solved to turn them into real life technologies. In particular, the ability to easily interact in real-time with them is a key requirement. The previous attempts to achieve this aim have used microfluidic approaches, such as valves, which are cumbersome. We show that electrochemical triggering using DNA-grafted micro-fabricated gold electrodes can be used to give instructions to these molecular systems. We demonstrate how this approach can be used to release at specific times and locations DNA- based instructions. In particular, we trigger reaction-diffusion autocatalytic fronts in microfluidic channels. While limited by the stability of the Au-S bond, this easy to implement, versatile and scalable technique can be used in any biology laboratory to provide new ways to interact with any DNA-based computing framework.

First characterization of a biphasic, switch-like DNA amplification

We report the first DNA amplification chemistry with switch-like characteristics: the chemistry is biphasic, with an expected initial phase followed by an unprecedented high gain burst of product oligonucleotide in a second phase. The first and second phases are separated by a temporary plateau, with the second phase producing 10 to 100 times more product than the first. The reaction is initiated when an oligonucleotide binds and opens a palindromic looped DNA template with two binding domains. Upon loop opening, the oligonucleotide trigger is rapidly amplified through cyclic extension and nicking of the bound trigger. Loop opening and DNA association drive the amplification reaction, such that reaction acceleration in the second phase is correlated with DNA association thermodynamics. Without a palindromic sequence, the chemistry resembles the exponential amplification reaction (EXPAR). EXPAR terminates at the initial plateau, revealing a previously unknown phenomenon that causes early reaction cessation in this popular oligonucleotide amplification reaction. Here we present two distinct types of this biphasic reaction chemistry and propose dominant reaction pathways for each type based on thermodynamic arguments. These reactions create an endogenous switch-like output that reacts to approximately 1 pM oligonucleotide trigger. The chemistry is isothermal and can be adapted to respond to a broad range of input target molecules such as proteins, genomic bacterial DNA, viral DNA, and microRNA. This rapid DNA amplification reaction could potentially impact a variety of disciplines such as synthetic biology, biosensors, DNA computing, and clinical diagnostics.

Multiple scales in metapopulations of public goods producers

Multiple scales in metapopulations can give rise to paradoxical behavior: in a conceptual model for a public goods game, the species associated with a fitness cost due to the public good production can be stabilized in the well-mixed limit due to the mere existence of these scales. The scales in this model involve a length scale corresponding to separate patches, coupled by mobility, and separate time scales for reproduction and interaction with a local environment. Contrary to the well-mixed high mobility limit, we find that for low mobilities, the interaction rate progressively stabilizes this species due to stochastic effects, and that the formation of spatial patterns is not crucial for this stabilization.

Exploring the emergence of complexity using synthetic replicators

A significant number of synthetic systems capable of replicating themselves or entities that are complementary to themselves have appeared in the last 30 years. Building on an understanding of the operation of synthetic replicators in isolation, this field has progressed to examples where catalytic relationships between replicators within the same network and the extant reaction conditions play a role in driving phenomena at the level of the whole system. Systems chemistry has played a pivotal role in the attempts to understand the origin of biological complexity by exploiting the power of synthetic chemistry, in conjunction with the molecular recognition toolkit pioneered by the field of supramolecular chemistry, thereby permitting the bottom-up engineering of increasingly complex reaction networks from simple building blocks. This review describes the advances facilitated by the systems chemistry approach in relating the expression of complex and emergent behaviour in networks of replicators with the connectivity and catalytic relationships inherent within them. These systems, examined within well-stirred batch reactors, represent conceptual and practical frameworks that can then be translated to conditions that permit replicating systems to overcome the fundamental limits imposed on selection processes in networks operating under closed conditions. This shift away from traditional spatially homogeneous reactors towards dynamic and non-equilibrium conditions, such as those provided by reaction-diffusion reaction formats, constitutes a key change that mimics environments within cellular systems, which possess obvious compartmentalisation and inhomogeneity.

Programmable autonomous synthesis of single-stranded DNA

DNA performs diverse functional roles in biology, nanotechnology and biotechnology, but current methods for autonomously synthesizing arbitrary single-stranded DNA are limited. Here, we introduce the concept of primer exchange reaction (PER) cascades, which grow nascent single-stranded DNA with user-specified sequences following prescribed reaction pathways. PER synthesis happens in a programmable, autonomous, in situ and environmentally responsive fashion, providing a platform for engineering molecular circuits and devices with a wide range of sensing, monitoring, recording, signal-processing and actuation capabilities. We experimentally demonstrate a nanodevice that transduces the detection of a trigger RNA into the production of a DNAzyme that degrades an independent RNA substrate, a signal amplifier that conditionally synthesizes long fluorescent strands only in the presence of a particular RNA signal, molecular computing circuits that evaluate logic (AND, OR, NOT) combinations of RNA inputs, and a temporal molecular event recorder that records in the PER transcript the order in which distinct RNA inputs are sequentially detected.

Hierarchical control of enzymatic actuators using DNA-based switchable memories

Inspired by signaling networks in living cells, DNA-based programming aims for the engineering of biochemical networks capable of advanced regulatory and computational functions under controlled cell-free conditions. While regulatory circuits in cells control downstream processes through hierarchical layers of signal processing, coupling of enzymatically driven DNA-based networks to downstream processes has rarely been reported. Here, we expand the scope of molecular programming by engineering hierarchical control of enzymatic actuators using feedback-controlled DNA-circuits capable of advanced regulatory dynamics. We developed a translator module that converts signaling molecules from the upstream network to unique DNA strands driving downstream actuators with minimal retroactivity and support these findings with a detailed computational analysis. We show our modular approach by coupling of a previously engineered switchable memories circuit to downstream actuators based on β-lactamase and luciferase. To the best of our knowledge, our work demonstrates one of the most advanced DNA-based circuits regarding complexity and versatility.

Naturally evolved regulatory circuits have hierarchical layers of signal generation and processing. Here, the authors emulate these networks using feedback-controlled DNA circuits that convert upstream signaling to downstream enzyme activity in a switchable memories circuit.

Microscopic agents programmed by DNA circuits

Information stored in synthetic nucleic acids sequences can be used in vitro to create complex reaction networks with precisely programmed chemical dynamics. Here, we scale up this approach to program networks of microscopic particles (agents) dispersed in an enzymatic solution. Agents may possess multiple stable states, thus maintaining a memory and communicate by emitting various orthogonal chemical signals, while also sensing the behaviour of neighbouring agents. Using this approach, we can produce collective behaviours involving thousands of agents, for example retrieving information over long distances or creating spatial patterns. Our systems recapitulate some fundamental mechanisms of distributed decision making and morphogenesis among living organisms and could find applications in cases where many individual clues need to be combined to reach a decision, for example in molecular diagnostics.