Synthesis and materialization of a reaction-diffusion French flag pattern

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.

Delay-driven phase transitions in an epidemic model on time-varying networks

A complex networked system typically has a time-varying nature in interactions among its components, which is intrinsically complicated and therefore technically challenging for analysis and control. This paper investigates an epidemic process on a time-varying network with a time delay. First, an averaging theorem is established to approximate the delayed time-varying system using autonomous differential equations for the analysis of system evolution. On this basis, the critical time delay is determined, across which the endemic equilibrium becomes unstable and a phase transition to oscillation in time via Hopf bifurcation will appear. Then, numerical examples are examined, including a periodically time-varying network, a blinking network, and a quasi-periodically time-varying network, which are simulated to verify the theoretical results. Further, it is demonstrated that the existence of time delay can extend the network frequency range to generate Turing patterns, showing a facilitating effect on phase transitions.

DNA as a universal chemical substrate for computing and data storage

DNA computing and DNA data storage are emerging fields that are unlocking new possibilities in information technology and diagnostics. These approaches use DNA molecules as a computing substrate or a storage medium, offering nanoscale compactness and operation in unconventional media (including aqueous solutions, water-in-oil microemulsions and self-assembled membranized compartments) for applications beyond traditional silicon-based computing systems. To build a functional DNA computer that can process and store molecular information necessitates the continued development of strategies for computing and data storage, as well as bridging the gap between these fields. In this Review, we explore how DNA can be leveraged in the context of DNA computing with a focus on neural networks and compartmentalized DNA circuits. We also discuss emerging approaches to the storage of data in DNA and associated topics such as the writing, reading, retrieval and post-synthesis editing of DNA-encoded data. Finally, we provide insights into how DNA computing can be integrated with DNA data storage and explore the use of DNA for near-memory computing for future information technology and health analysis applications.

Orthogonal Light-Dependent Membrane Adhesion Induces Social Self-Sorting and Member-Specific DNA Communication in Synthetic Cell Communities

Developing orthogonal chemical communication pathways in diverse synthetic cell communities is a considerable challenge due to the increased crosstalk and interference associated with large numbers of different types of sender-receiver pairs. Herein, the authors control which sender-receiver pairs communicate in a three-membered community of synthetic cells through red and blue light illumination. Semipermeable protein-polymer-based synthetic cells (proteinosomes) with complementary membrane-attached protein adhesion communicate through single-stranded DNA oligomers and synergistically process biochemical information within a community consisting of one sender and two different receiver populations. Different pairs of red and blue light-responsive protein-protein interactions act as membrane adhesion mediators between the sender and receivers such that they self-assemble and socially self-sort into different multicellular structures under red and blue light. Consequently, distinct sender-receiver pairs come into the signaling range depending on the light illumination and are able to communicate specifically without activation of the other receiver population. Overall, this work shows how photoswitchable membrane adhesion gives rise to different self-sorting protocell patterns that mediate member-specific DNA-based communication in ternary populations of synthetic cells and provides a step towards the design of orthogonal chemical communication networks in diverse communities of synthetic cells.

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.

Communication and Cross-Regulation between Chemically Fueled Sender and Receiver Reaction Networks

Nature connects multiple fuel-driven chemical/enzymatic reaction networks (CRNs/ERNs) via cross-regulation to hierarchically control biofunctions for a tailored adaption in complex sensory landscapes. Herein, we introduce a facile example of communication and cross-regulation among two fuel-driven DNA-based ERNs regulated by a concatenated RNA transcription regulator. ERN1 ("sender") is designed for the fuel-driven promoter formation for T7 RNA polymerase, which activates RNA transcription. The produced RNA can deactivate or activate DNA in ERN2 ("receiver") by toehold-mediated strand displacement, leading to a communication between two ERNs. The RNA from ERN1 can repress or promote the fuel-driven state of ERN2; ERN2 in turn feedbacks to regulate the lifetime of ERN1. Furthermore, the incorporation of RNase H allows for RNA degradation and enables the autonomous recovery of ERN2. We believe that concatenation of multiple CRNs/ERNs provides a basis for the design of more elaborate autonomous regulatory mechanisms in systems chemistry and synthetic biology.

Steady-State Operation of a Cell-Free Genetic Band-Detection Circuit

Pattern formation processes play a decisive role during embryogenesis and involve the precise spatial and temporal orchestration of intricate gene regulatory processes. Synthetic gene circuits modeled after their biological counterparts can be used to investigate such processes under well-controlled conditions and may, in the future, be utilized for autonomous position determination in synthetic biological materials. Here, we investigated a three-node feed-forward gene regulatory circuit in vitro that generates three distinct fluorescent outputs in response to varying concentrations of a single externally supplied morphogen. The circuit acts as a band detector for the morphogen concentration and, in a spatial context, could serve as a stripe-forming gene circuit. We simulated the behavior of the genetic circuit in the presence of a morphogen gradient using a system of ordinary differential equations and determined optimal parameters for stripe-pattern formation using an evolutionary algorithm. To analyze the subcircuits of the system, we conducted cell-free characterization experiments and finally tested the whole genetic circuit in nanoliter-scale microfluidic flow reactors that provided a continuous supply of cell extract and metabolites and allowed removal of degradation products. To make use of the widely employed promoters P_LlacO-1 and P_LtetO-1 in our design, we removed LacI from our bacterial cell extract by genome engineering Escherichia coli using a pORTMAGE workflow. Our results show that the band-detector works as designed when operated out of equilibrium within the flow reactors. On the other hand, subcircuits of the system and the whole circuit fail to generate the desired gene expression response when operated in a closed reactor. Our work thus underlines the importance of out-of-equilibrium operation of complex gene circuits, which cannot settle to a steady-state expression pattern within the finite lifetime of a cell-free expression system.

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.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Reaction–Diffusion Patterning of DNA-Based Artificial Cells

Biological cells display complex internal architectures with distinct micro environments that establish the chemical heterogeneity needed to sustain cellular functions. The continued efforts to create advanced cell mimics, namely, artificial cells, demands strategies for constructing similarly heterogeneous structures with localized functionalities. Here, we introduce a platform for constructing membraneless artificial cells from the self-assembly of synthetic DNA nanostructures in which internal domains can be established thanks to prescribed reaction–diffusion waves. The method, rationalized through numerical modeling, enables the formation of up to five distinct concentric environments in which functional moieties can be localized. As a proof-of-concept, we apply this platform to build DNA-based artificial cells in which a prototypical nucleus synthesizes fluorescent RNA aptamers that then accumulate in a surrounding storage shell, thus demonstrating the spatial segregation of functionalities reminiscent of that observed in biological cells.

Standardized excitable elements for scalable engineering of far-from-equilibrium chemical networks

Engineered far-from-equilibrium synthetic chemical networks that pulse or switch states in response to environmental signals could precisely regulate the kinetics of chemical synthesis or self-assembly. Currently, such networks must be extensively tuned to compensate for the different activities of and unintended reactions between a network's various chemical components. Modular elements with standardized performance could be used to rapidly construct networks with designed functions. Here we develop standardized excitable chemical regulatory elements, termed genelets, and use them to construct complex in vitro transcriptional networks. We develop a protocol for identifying >15 interchangeable genelet elements with uniform performance and minimal crosstalk. These elements can be combined to engineer feedforward and feedback modules whose dynamics match those predicted by a simple kinetic model. Modules can then be rationally integrated and organized into networks that produce tunable temporal pulses and act as multistate switchable memories. Standardized genelet elements, and the workflow to identify more, should make engineering complex far-from-equilibrium chemical dynamics routine.

A model of spatio-temporal regulation within biomaterials using DNA reaction-diffusion waveguides

In multi-cellular organisms, cells and tissues coordinate biochemical signal propagation across length scales spanning micrometres to metres. Designing synthetic materials with similar capacities for coordinated signal propagation could allow these systems to adaptively regulate themselves across space and over time. Here, we combine ideas from cell signalling and electronic circuitry to propose a biochemical waveguide that transmits information in the form of a concentration of a DNA species on a directed path. The waveguide could be seamlessly integrated into a soft material because there is virtually no difference between the chemical or physical properties of the waveguide and the material it is embedded within. We propose the design of DNA strand displacement reactions to construct the system and, using reaction-diffusion models, identify kinetic and diffusive parameters that enable super-diffusive transport of DNA species via autocatalysis. Finally, to support experimental waveguide implementation, we propose a sink reaction and spatially inhomogeneous DNA concentrations that could mitigate the spurious amplification of an autocatalyst within the waveguide, allowing for controlled waveguide triggering. Chemical waveguides could facilitate the design of synthetic biomaterials with distributed sensing machinery integrated throughout their structure and enable coordinated self-regulating programmes triggered by changing environmental conditions.

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.

Catalytic DNA Polymerization Can Be Expedited by Active Product Release**

The sequence‐specific hybridization of DNA facilitates its use as a building block for designer nanoscale structures and reaction networks that perform computations. However, the strong binding energy of Watson–Crick base pairing that underlies this specificity also causes the DNA dehybridization rate to depend sensitively on sequence length and temperature. This strong dependency imposes stringent constraints on the design of multi‐step DNA reactions. Here we show how an ATP‐dependent helicase, Rep‐X, can drive specific dehybridization reactions at rates independent of sequence length, removing the constraints of equilibrium on DNA hybridization and dehybridization. To illustrate how this new capacity can speed up designed DNA reaction networks, we show that Rep‐X extends the range of conditions where the primer exchange reaction, which catalytically adds a domain provided by a hairpin template to a DNA substrate, proceeds rapidly.

Dissipative DNA nanotechnology

DNA nanotechnology has emerged as a powerful tool to precisely design and control molecular circuits, machines and nanostructures. A major goal in this field is to build devices with life-like properties, such as directional motion, transport, communication and adaptation. Here we provide an overview of the nascent field of dissipative DNA nanotechnology, which aims at developing life-like systems by combining programmable nucleic-acid reactions with energy-dissipating processes. We first delineate the notions, terminology and characteristic features of dissipative DNA-based systems and then we survey DNA-based circuits, devices and materials whose functions are controlled by chemical fuels. We emphasize how energy consumption enables these systems to perform work and cyclical tasks, in contrast with DNA devices that operate without dissipative processes. The ability to take advantage of chemical fuel molecules brings dissipative DNA systems closer to the active molecular devices that exist in nature.

Synthetic cell-based materials extract positional information from morphogen gradients

Biomaterials composed of synthetic cells have the potential to adapt and differentiate guided by physicochemical environmental cues. Inspired by biological systems in development, which extract positional information (PI) from morphogen gradients in the presence of uncertainties, we here investigate how well synthetic cells can determine their position within a multicellular structure. To calculate PI, we created and analyzed a large number of synthetic cellular assemblies composed of emulsion droplets connected via lipid bilayer membranes. These droplets contained cell-free feedback gene circuits that responded to gradients of a genetic inducer acting as a morphogen. PI is found to be limited by gene expression noise and affected by the temporal evolution of the morphogen gradient and the cell-free expression system itself. The generation of PI can be rationalized by computational modeling of the system. We scale our approach using three-dimensional printing and demonstrate morphogen-based differentiation in larger tissue-like assemblies.

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.

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.

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.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Feedback and Communication in Active Hydrogel Spheres with pH Fronts: Facile Approaches to Grow Soft Hydrogel Structures

Compartmentalized reaction networks regulating signal processing, communication and pattern formation are central to living systems. Towards achieving life-like materials, we compartmentalized urea-urease and more complex urea-urease/ester-esterase pH-feedback reaction networks into hydrogel spheres and investigate how fuel-driven pH fronts can be sent out from these spheres and regulated by internal reaction networks. Membrane characteristics are installed by covering urease spheres with responsive hydrogel shells. We then encapsulate the two networks (urea-urease and ester-esterase) separately into different hydrogel spheres to devise communication, pattern formation and attraction. Moreover, these pH fronts and patterns can be used for self-growing hydrogels, and for developing complex geometries from non-injectable hydrogels without 3D printing tools. This study opens possibilities for compartmentalized feedback reactions and their use in next generation materials fabrication.

DNAzyme- and light-induced dissipative and gated DNA networks

Nucleic acid-based dissipative, out-of-equilibrium systems are introduced as functional assemblies emulating transient dissipative biological transformations. One system involves a Pb²⁺-ion-dependent DNAzyme fuel strand-driven network leading to the transient cleavage of the fuel strand to “waste” products. Applying the Pb²⁺-ion-dependent DNAzyme to two competitive fuel strand-driven systems yields two parallel operating networks. Blocking the competitively operating networks with selective inhibitors leads, however, to gated transient operation of dictated networks, yielding gated catalytic operations. A second system introduces a “non-waste” generating out-of-equilibrium, dissipative network driven by light. The system consists of a trans-azobenzene-functionalized photoactive module that is reconfigured by light to an intermediary state consisting of cis-azobenzene units that are thermally recovered to the original trans-azobenzene-modified module. The cyclic transient photoinduced operation of the device is demonstrated. The kinetic simulation of the systems allows the prediction of the transient behavior of the networks under different auxiliary conditions.

Functional DNA modules are triggered in the presence of appropriate inhibitors to yield transient gated catalytic functions, and a photoresponsive DNA module leads to “waste-free” operation of transient, dissipative dynamic transitions.

A small-molecule chemical interface for molecular programs

In vitro molecular circuits, based on DNA-programmable chemistries, can perform an increasing range of high-level functions, such as molecular level computation, image or chemical pattern recognition and pattern generation. Most reported demonstrations, however, can only accept nucleic acids as input signals. Real-world applications of these programmable chemistries critically depend on strategies to interface them with a variety of non-DNA inputs, in particular small biologically relevant chemicals. We introduce here a general strategy to interface DNA-based circuits with non-DNA signals, based on input-translating modules. These translating modules contain a DNA response part and an allosteric protein sensing part, and use a simple design that renders them fully tunable and modular. They can be repurposed to either transmit or invert the response associated with the presence of a given input. By combining these translating-modules with robust and leak-free amplification motifs, we build sensing circuits that provide a fluorescent quantitative time-response to the concentration of their small-molecule input, with good specificity and sensitivity. The programmability of the DNA layer can be leveraged to perform DNA based signal processing operations, which we demonstrate here with logical inversion, signal modulation and a classification task on two inputs. The DNA circuits are also compatible with standard biochemical conditions, and we show the one-pot detection of an enzyme through its native metabolic activity. We anticipate that this sensitive small-molecule-to-DNA conversion strategy will play a critical role in the future applications of molecular-level circuitry.

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.

Information processing using an integrated DNA reaction network

Living organisms use interconnected chemical reaction networks (CRNs) to exchange information with the surrounding environment and respond to diverse external stimuli. Inspired by nature, numerous artificial CRNs with a complex information processing function have been recently introduced, with DNA as one of the most attractive engineering materials. Although much progress has been made in DNA-based CRNs in terms of controllable reaction dynamics and molecular computation, the effective integration of signal translation with information processing in a single CRN remains to be difficult. In this work, we introduced a stimuli-responsive DNA reaction network capable of integrated information translation and processing in a stepwise manner. This network is designed to integrate sensing, translation, and decision-making operations by independent modules, in which various logic units capable of performing different functions were realized, including information identification (YES and OR gates), integration (AND and AND-AND gates), integration-filtration (AND-AND-NOT gate), comparison (Comparator), and map-to-map analysis (Feynman gate). Benefitting from the modular and programmable design, continuous and parallel processing operations are also possible. With the innovative functions, we show that the DNA network is a highly useful addition to the current DNA-based CRNs by offering a bottom-up strategy to design devices capable of cascaded information processing with high efficiency.

Signaling in Systems Chemistry: Programing Gold Nanoparticles Formation and Assembly Using a Dynamic Bistable Network

Living cells exploit bistable and oscillatory behaviors as memory mechanisms, facilitating the integration of transient stimuli into sustained molecular responses that control downstream functions. Synthetic bistable networks have also been studied as memory entities, but have rarely been utilized to control orthogonal functions in coupled dynamic systems. We herein present a new cascade pathway, for which we have exploited a well-characterized switchable peptide-based replicating network, operating far from equilibrium, that yields two alternative steady-state outputs, which in turn serve as the input signals for consecutive processes that regulate various features of Au nanoparticle shape and assembly. This study further sheds light on how bridging together the fields of systems chemistry and nanotechnology may open up new opportunities for the dynamically controlled design of functional materials.

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.

Light-Activated Signaling in DNA-Encoded Sender-Receiver Architectures

Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver cells. A variety of nonliving artificial cell models have been developed in recent years that mimic various aspects of diffusion-based intercellular communication. However, localized secretion of diffusive signals from individual protocells, which is critical for mimicking biological sender-receiver systems, has remained challenging to control precisely. Here, we engineer light-responsive, DNA-encoded sender-receiver architectures, where protein-polymer microcapsules act as cell mimics and molecular communication occurs through diffusive DNA signals. We prepare spatial distributions of sender and receiver protocells using a microfluidic trapping array and set up a signaling gradient from a single sender cell using light, which activates surrounding receivers through DNA strand displacement. Our systematic analysis reveals how the effective signal range of a single sender is determined by various factors including the density and permeability of receivers, extracellular signal degradation, signal consumption, and catalytic regeneration. In addition, we construct a three-population configuration where two sender cells are embedded in a dense array of receivers that implement Boolean logic and investigate spatial integration of nonidentical input cues. The results offer a means for studying diffusion-based sender-receiver topologies and present a strategy to achieve the congruence of reaction-diffusion and positional information in chemical communication systems that have the potential to reconstitute collective cellular patterns.

A simple hydrogel device with flow-through channels to maintain dissipative non-equilibrium phenomena

The development of autonomous chemical systems that could imitate the properties of living matter, is a challenging problem at the meeting point of materials science and nonequilibrium chemistry. Here we design a multi-channel gel reactor in which out-of-equilibrium conditions are maintained by antagonistic chemical gradients. Our device is a rectangular hydrogel with two or more channels for the flows of separated reactants, which diffuse into the gel to react. The relative position of the channels acts as geometric control parameters, while the concentrations of the chemicals in the channels and the variable composition of the hydrogel, which affects the diffusivity of the chemicals, can be used as chemical control parameters. This flexibility allows finding easily the optimal conditions for the development of nonequilibrium phenomena. We demonstrate this straightforward operation by generating diverse spatiotemporal patterns in different chemical reactions. The use of additional channels can create interacting reaction zones.

Autonomous mesoscale positioning emerging from myelin filament self-organization and Marangoni flows

Out-of-equilibrium molecular systems hold great promise as dynamic, reconfigurable matter that executes complex tasks autonomously. However, translating molecular scale dynamics into spatiotemporally controlled phenomena emerging at mesoscopic scale remains a challenge-especially if one aims at a design where the system itself maintains gradients that are required to establish spatial differentiation. Here, we demonstrate how surface tension gradients, facilitated by a linear amphiphile molecule, generate Marangoni flows that coordinate the positioning of amphiphile source and drain droplets floating at air-water interfaces. Importantly, at the same time, this amphiphile leads, via buckling instabilities in lamellar systems of said amphiphile, to the assembly of millimeter long filaments that grow from the source droplets and get absorbed at the drain droplets. Thereby, the Marangoni flows and filament organization together sustain the autonomous positioning of interconnected droplet-filament networks at the mesoscale. Our concepts provide potential for the development of non-equilibrium matter with spatiotemporal programmability.

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.

ATP-powered molecular recognition to engineer transient multivalency and self-sorting 4D hierarchical systems

Biological systems organize multiple hierarchical structures in parallel, and create dynamic assemblies and functions by energy dissipation. In contrast, emerging artificial non-equilibrium self-assembling systems have remained relatively simplistic concerning hierarchical design, and non-equilibrium multi-component systems are uncharted territory. Here we report a modular DNA toolbox allowing to program transient non-equilibrium multicomponent systems across hierarchical length scales by introducing chemically fueled molecular recognition orchestrated by reaction networks of concurrent ATP-powered ligation and cleavage of freely programmable DNA building blocks. Going across hierarchical levels, we demonstrate transient side-chain functionalized nucleic acid polymers, and further introduce the concept of transient cooperative multivalency as a key to bridge length scales to pioneer fuel-driven encapsulation, self-assembly of colloids, and non-equilibrium transient narcissistic colloidal self-sorting on a systems level. The fully programmable and functionalizable DNA components pave the way to design chemically fueled 4D (3 space, 1 time) molecular multicomponent systems and autonomous materials.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Toward Engineering Biosystems With Emergent Collective Functions

Many complex behaviors in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans many length-scales. Here, we present a perspective on how some of these challenges could be overcome by using multi-agent modeling as a design framework within synthetic biology. Using case studies covering the construction of synthetic ecologies to biological computation and synthetic cellularity, we show how multi-agent modeling can capture the core features of complex multi-scale systems and provide novel insights into the underlying mechanisms which guide emergent functionalities across scales. The ability to unravel design rules underpinning these behaviors offers a means to take synthetic biology beyond single molecules or cells and toward the creation of systems with functions that can only emerge from collectives at multiple scales.

The New Age of Cell-Free Biology

The cell-free molecular synthesis of biochemical systems is a rapidly growing field of research. Advances in the Human Genome Project, DNA synthesis, and other technologies have allowed the in vitro construction of biochemical systems, termed cell-free biology, to emerge as an exciting domain of bioengineering. Cell-free biology ranges from the molecular to the cell-population scales, using an ever-expanding variety of experimental platforms and toolboxes. In this review, we discuss the ongoing efforts undertaken in the three major classes of cell-free biology methodologies, namely protein-based, nucleic acids–based, and cell-free transcription–translation systems, and provide our perspectives on the current challenges as well as the major goals in each of the subfields.

French flag gradients and Turing reaction-diffusion versus differentiation waves as models of morphogenesis

The Turing reaction-diffusion model and the French Flag Model are widely accepted in the field of development as the best models for explaining embryogenesis. Virtually all current attempts to understand cell differentiation in embryos begin and end with the assumption that some combination of these two models works. The result may become a bias in embryogenesis in assuming the problem has been solved by these two-chemical substance-based models. Neither model is applied consistently. We review the differences between the French Flag, Turing reaction-diffusion model, and a mechanochemical model called the differentiation wave/cell state splitter model. The cytoskeletal cell state splitter and the embryonic differentiation waves was first proposed in 1987 as a combined physics and chemistry model for cell differentiation in embryos, based on empirical observations on urodele amphibian embryos. We hope that the development of theory can be advanced and observations relevant to distinguishing the embryonic differentiation wave model from the French Flag model and reaction-diffusion equations will be taken up by experimentalists. Experimentalists rely on mathematical biologists for theory, and therefore depend on them for what parameters they choose to measure and ignore. Therefore, mathematical biologists need to fully understand the distinctions between these three models.

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.

Microfluidic platforms for the dynamic characterisation of synthetic circuitry

Generating novel functionality from well characterised synthetic parts and modules lies at the heart of synthetic biology. Ideally, circuitry is rationally designed in silico with quantitatively predictive models to predetermined design specifications. Synthetic circuits are intrinsically stochastic, often dynamically modulated and set in a dynamic fluctuating environment within a living cell. To build more complex circuits and to gain insight into context effects, intrinsic noise and transient performance, characterisation techniques that resolve both heterogeneity and dynamics are required. Here we review recent advances in both in vitro and in vivo microfluidic technologies that are suitable for the characterisation of synthetic circuitry, modules and parts.

Pattern localization to a domain edge

The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g., membrane-bound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud site in budding yeast and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can "sense" the edge of the template. A mechanism for how this edge sensing may work remains elusive. Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a two-component mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems and for the design of synthetic pattern forming systems.

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.

Tunable corrugated patterns in an active nematic sheet

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

Digital Maskless Photolithographic Patterning of DNA-Functionalized Poly(ethylene glycol) Diacrylate Hydrogels with Visible Light Enabling Photodirected Release of Oligonucleotides

Soft biomaterials possessing structural hierarchy have growing applications in lab-on-chip devices, artificial tissues, and micromechanical and chemomechanical systems. The ability to integrate sets of biomolecules, specifically DNA, within hydrogel substrates at precise locations could offer the potential to form and modulate complex biochemical processes with DNA-based molecular switches in such materials and provide a means of creating dynamic spatial patterns, thus enabling spatiotemporal control of a wide array of reaction-diffusion phenomena prevalent in biological systems. Here we develop a means of photopatterning two-dimensional DNA-functionalized poly(ethylene glycol) diacrylate (PEGDA) hydrogel architectures with an aim toward these applications. While PEGDA photopatterning methods are well-established for the fabrication of hydrogels, including those containing oligonucleotides, the photoinitiators typically used have significant crosstalk with many UV-photoswitchable chemistries including nitrobenzyl derivatives. We demonstrate the digital photopatterning of PEGDA-co-DNA hydrogels using a blue light-absorbing (470 nm peak) photoinitiator system and macromer comprised of camphorquinone, triethanolamine, and poly(ethylene glycol) diacrylate (M_n = 575) that minimizes absorption in the UV-A wavelength range commonly used to trigger photoswitchable chemistries. We demonstrate this method using digital maskless photolithography within microfluidic devices that allows for the reliable construction of multidomain structures. The method achieves feature resolutions as small as 25 μm, and the resulting materials allow for lateral isotropic bulk diffusion of short single-stranded (ss) DNA oligonucleotides. Finally, we show how the use of these photoinitiators allows for orthogonal control of photopolymerization and UV-photoscission of acrylate-modified DNA containing a 1-(2-nitrophenyl) ethyl spacer to selectively cleave DNA from regions of a PEGDA substrate.