Adaptive and Dissipative Hierarchical Population Crowding of Synthetic Protocells through Click-PISA under Gradient Energy Inputs.

The ability of living objects to respond rapidly en masse to various stimuli or stress is an important function in response to externally applied changes in the local environment. This occurs across many length scales, for instance, bacteria swarming in response to different stimuli or stress and macromolecular crowding within cells. Currently there are few mechanisms to induce similar autonomous behaviors within populations of synthetic protocells. Herein, we report a system in which populations of individual objects behave in a coordinated manner in response to changes in the energetic environment by the emergent self-organization of large object swarms. These swarms contain protocell populations of approximately 60 000 individuals. We demonstrate the dissipative nature of the hierarchical constructs, which persist under appropriate UV stimulation. Finally, we identify the ability of the object populations to change behaviors in an adaptive population-wide response to the local energetic environment.

Numerical and renormalization group analysis of the phase diagram of a stochastic cubic autocatalytic reaction-diffusion system.

The renormalization group is a set of tools that can be used to incorporate the effect of fluctuations in a dynamical system as a rescaling of the system's parameters. Here, we apply the renormalization group to a pattern-forming stochastic cubic autocatalytic reaction-diffusion model and compare its predictions with numerical simulations. Our results demonstrate a good agreement within the range of validity of the theory and show that external noise can be used as a control parameter in such systems.

Intermittent regimes as a synchronization phenomenon in two sets of nonlinear chemical oscillators.

Systems of nonlinear chemical oscillators can exhibit a large diversity of non-trivial states depending on the parameters that characterize them. Among these, a synchronization phenomenon is of special interest due to its direct link with chemical and biological processes in nature. We carry out numerical experiments for two different sets of chemical oscillators with different properties and immersed in a Belousov-Zhabotinsky solution. We document the emergence of different states of synchronization that depend on the parameters characterizing the solution. We also show that, in the interface regions, this system generates a stable dynamics of intermittency between the different synchronization states where interesting phenomena, such as the "devil's staircase," emerge. In general, the added complexity introduced with the additional set of oscillators results in more complex non-trivial synchronization states.

Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process.

A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.

Quantitative estimation of chemical microheterogeneity through the determination of fuzzy entropy.

Chemical micro-heterogeneity is an attribute of all living systems and most of the soft and crystalline materials. Its characterization requires a plethora of techniques. This work proposes a strategy for quantifying the degree of chemical micro-heterogeneity. First of all, our approach needs the collection of time-evolving signals that can be fitted through poly-exponential functions. The best fit is determined through the Maximum Entropy Method. The pre-exponential terms of the poly-exponential fitting function are used to estimate Fuzzy Entropy. Related to the possibility of implementing Fuzzy sets through the micro-heterogeneity of chemical systems. Fuzzy Entropy becomes a quantitative estimation of the Fuzzy Information that can be processed through micro-heterogeneous chemical systems. We conclude that our definition of Fuzzy Entropy can be extended to other kinds of data, such as morphological and structural distributions, spectroscopic bands and chromatographic peaks. The chemical implementation of Fuzzy sets and Fuzzy logic will promote the development of Chemical Artificial Intelligence.

Unified representation of Life's basic properties by a 3-species Stochastic Cubic Autocatalytic Reaction-Diffusion system of equations.

Today we can use physics to describe in great detail many of the phenomena intervening in the process of life. But no analogous unified description exists for the phenomenon of life itself. In spite of their complexity, all living creatures are out of equilibrium chemical systems sharing four fundamental properties: they (1) handle information, (2) metabolize, (3) self-reproduce and (4) evolve. This small number of features, which in terran life are implemented with biochemistry, point to an underlying simplicity that can be taken as a guide to motivate and implement a theoretical physics style unified description of life using tools from the non-equilibrium physical-chemistry of extended systems. Representing a system with general rules is a well stablished approach to model building and unification in physics, and we do this here to provide an abstract mathematical description of life. We start by reviewing the work of previous authors showing how the properties in the above list can be individually represented with stochastic reaction-diffusion kinetics using polynomial reaction terms. These include "switches" and computation, the kinetic representation of autocatalysis, Turing instability and adaptation in the presence of both deterministic and stochastic environments. Thinking of these properties as existing on a space-time lattice each of whose nodes are subject to a common mass-action kinetics compatible with the above, leads to a very rich dynamical system which, just as natural life, unifies the above properties and can therefore be interpreted as a high level or "outside-in" theoretical physics representation of life. Taking advantage of currently available advanced computational techniques and hardware, we compute the phase plane for this dynamical system both in the deterministic and stochastic cases. We do simulations and show numerically how the system works. We review how to extract useful information that can be mapped into emergent physical phenomena and attributes of importance in life such as the presence of a "membrane" or the time evolution of an individual system's negentropy or mass. Once these are available, we illustrate how to perform some basic phenomenology based on the model's numerical predictions. Applying the above to the idealization of the general Cell Division Cycle (CDC) given almost 25 years ago by Hunt and Murray, we show from the numerical simulations how this system executes a form of the idealized CDC. We also briefly discuss various simulations that show how other properties of living systems such as migration towards more favorable regions or the emergence of effective Lotka-Volterra populations are accounted for by this general and unified view from the "top" of the physics of life. The paper ends with some discussion, conclusions, and comments on some selected directions for future research. The mathematical techniques and powerful simulation tools we use are all well established and presented in a "didactical" style. We include a very rich but concise SI where the numerical details are thoroughly discussed in a way that anyone interested in studying or extending the results would be able to do so.

pH Oscillating System for Molecular Computation as a Chemical Turing Machine.

It has previously been demonstrated that native chemical Turing machines can be constructed by exploiting the nonlinear dynamics of the homogeneous oscillating Belousov-Zhabotinsky reaction. These Turing machines can perform word recognition of a Chomsky type 1 context sensitive language (CSL), demonstrating their high computing power. Here, we report on a chemical Turing machine that has been developed using the H2O2-H2SO4-SO3 2--CO3 2- pH oscillating system. pH oscillators are different to bromate oscillators in two key ways: the proton is the autocatalytic agent, and at least one of the reductants is always fully consumed in each turnover-meaning the system has to be operated as a flow reactor. Through careful design, we establish a system that can also perform Chomsky type 1 CSL word recognition and demonstrate its power through the testing of a series of in-language and out-of-language words.

Chemoadaptive Polymeric Assemblies by Integrated Chemical Feedback in Self-Assembled Synthetic Protocells.

The design and chemical synthesis of artificial material objects which can mimic the functions of living cells is an important ongoing scientific endeavor. A key challenge necessary for fulfilling the criteria for a system to be living currently regards evolution, which is derived from adaptivity. Integrated chemical loops capable of feedback control are required to achieve chemical systems which exhibit adaptivity. To explore this, we present an integrated, two-component orthogonal chemical process involving reversible addition-fragmentation chain transfer (RAFT) based polymerization-induced self-assembly (PISA) and a copper-catalyzed azide-alkyne click (CuAAC) coupling reaction. The chemical processes are linked through electron transfer from the activated chain-transfer agent (CTA) to the dormant Cu(II) precatalyst. We show that combining these complementary chemistries in a single reaction pot resulted in two primary outcomes: (i) simplification of the PISA process to synthesize the macro-CTA in situ from available nonamphiphilic components and (ii) routes to complexity and adaptation involving population dynamics, morphologies, and dissipative phenomena observed during in situ microscopy analysis.

Autonomous Low-Reynolds-Number Soft Robots with Structurally Encoded Motion and Their Thermodynamic Efficiency.

Soft low-Reynolds-number robotics hold the potential to significantly impact numerous fields including drug delivery, sensing, and diagnostics. Realizing this potential is predicated upon the ability to design soft robots tailored to their intended function. In this work, we identify the effect of different geometric and symmetry parameters on the motion of soft, autonomous robots that operate in the low-Reynolds-number regime and use organic fuel. The ability to power low-Reynolds-number soft robots using an organic fuel would provide a new avenue for their potential use in biomedical applications, as is the use of a polymeric biocompatible material as is done here. We introduce a simple and cost-effective 3D-printer-assisted method to fabricate robots of different shapes that is scalable and widely applicable for a variety of materials. The efficiency of chemical energy to mechanical energy conversion is measured in soft low-Reynolds-number robots for the first time, and their mechanism of motion is assessed. Motion is a result of a periodic and oscillatory change in the charge state of the gel. This work lays the groundwork for the structure-function design of soft, chemically operated, and autonomous low-Reynolds-number robots.

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review.

Computing with molecules is at the center of complex natural phenomena, where the information contained in ordered sequences of molecules is used to implement functionalities of synthesized materials or to interpret the environment, as in Biology. This uses large macromolecules and the hindsight of billions of years of natural evolution. But, can one implement computation with small molecules? If so, at what levels in the hierarchy of computing complexity? We review here recent work in this area establishing that all physically realizable computing automata, from Finite Automata (FA) (such as logic gates) to the Linearly Bound Automaton (LBA, a Turing Machine with a finite tape) can be represented/assembled/built in the laboratory using oscillatory chemical reactions. We examine and discuss in depth the fundamental issues involved in this form of computation exclusively done by molecules. We illustrate their implementation with the example of a programmable finite tape Turing machine which using the Belousov-Zhabotinsky oscillatory chemistry is capable of recognizing words in a Context Sensitive Language and rejecting words outside the language. We offer a new interpretation of the recognition of a sequence of chemicals representing words in the machine's language as an illustration of the "Maximum Entropy Production Principle" and concluding that word recognition by the Belousov-Zhabotinsky Turing machine is equivalent to extremal entropy production by the automaton. We end by offering some suggestions to apply the above to problems in computing, polymerization chemistry, and other fields of science.

Self-Organizing Microdroplet Protocells Displaying Light-Driven Oscillatory and Morphological Evolution.

The development of synthetic systems that enable the sustained active self-assembly of molecular blocks to mimic the complexity and dynamic behavior of living systems is of great interest in elucidating the origins of life, understanding the basic principles behind biological organization, and designing active materials. However, it remains a challenge to construct microsystems with dynamic behaviors and functions that are connected to molecular self-assembly processes driven by external energy. Here, an active self-assembly of microdroplet protocells with dynamic structure and high structural complexity through living radical polymerization under constant energy flux is reported. The active microdroplet protocells exhibit nonlinear behaviors including oscillatory growth and shrinkage. This relies on the transient stabilization of molecular assembly, which can channel the inflow of energy through noncovalent interactions of pure synthetic components. The intercommunication of microdroplet protocells through stochastic fusion leads to the formation of a variety of dynamic and higher-order biomimetic microstructures. This work constitutes an important step toward the realization of autonomous and dynamic microsystems and active materials with life-like properties.

Periodic Polymerization and the Generation of Polymer Giant Vesicles Autonomously Driven by pH Oscillatory Chemistry.

Using the radicals generated during pH oscillations, a semibatch pH oscillator is used as the chemical fuel and engine to drive polymerization induced self-assembly (PISA) for the one-pot autonomous synthesis of functional giant vesicles. Vesicles with diameters ranging from sub-micron to ∼5 µm are generated. Radical formation is found to be switched ON/OFF and be autonomously controlled by the pH oscillator itself, inducing a periodic polymerization process. The mechanism underlying these complex processes is studied and compared to conventional (non-oscillatory) initiation by the same redox pair. The pH oscillations along with the continuous increase in salt concentration in the semibatch reactor make the self-assembled objects undergo morphological evolution. This process provides a self-regulated means for the synthesis of soft giant polymersomes and opens the door for new applications of pH oscillators in a variety of contexts, from the exploration of new geochemical scenarios for the origin of life and the autonomous emergence of the necessary free-energy and proton gradients, to the creation of active functional microreactors and programmable release of cargo molecules for pH-responsive materials.

Exploring the symbol processing 'time interval' parametric constraint in a Belousov-Zhabotinsky operated chemical Turing machine.

Chemical reactions are powerful molecular recognition machines. This power has been recently harnessed to build actual instances of each class of experimentally realizable computing automata, using exclusively small-molecule chemistry (i.e. without requiring biomolecules). The most powerful of them, a programmable Turing machine, uses the Belousov-Zhabotinsky oscillatory chemistry, and accepts/rejects input sequences through a dual oscillatory and thermodynamic output signature. The time interval between the aliquots representing each letter of the input is the parameter that determines the time it takes to run the computation. Here, we investigate this critical performance parameter, and its effect not only on the computation speed, but also on the robustness of the accept/reject oscillatory and thermodynamic criteria. Our work demonstrates that the time interval is a non-trivial design parameter, whose choice should be made with great care. The guidelines we provide can be used in the optimization of the speed, robustness, and energy efficiency of chemical automata computations.

Photochemically induced cyclic morphological dynamics via degradation of autonomously produced, self-assembled polymer vesicles.

Autonomous and out-of-equilibrium vesicles synthesised from small molecules in a homogeneous aqueous medium are an emerging class of dynamically self-assembled systems with considerable potential for engineering natural life mimics. Here we report on the physico-chemical mechanism behind a dynamic morphological evolution process through which self-assembled polymeric structures autonomously booted from a homogeneous mixture, evolve from micelles to giant vesicles accompanied by periodic growth and implosion cycles when exposed to oxygen under light irradiation. The system however formed nano-objects or gelation under poor oxygen conditions or when heated. We determined the cause to be photoinduced chemical degradation within hydrated polymer cores inducing osmotic water influx and the subsequent morphological dynamics. The process also led to an increase in the population of polymeric objects through system self-replication. This study offers a new path toward the design of chemically self-assembled systems and their potential application in autonomous material artificial simulation of living systems.

In-vitro reconfigurability of native chemical automata, the inclusiveness of their hierarchy and their thermodynamics.

Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.

Renormalization of stochastic differential equations with multiplicative noise using effective potential methods.

We present a method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high-energy physics and has already been successfully applied to the renormalization of stochastic differential equations subjected to additive noise. We derive a general formula for the one-loop effective potential of a single ordinary stochastic differential equation (with arbitrary interaction terms) subjected to multiplicative Gaussian noise (provided the noise satisfies a certain normalization condition). To illustrate the usefulness (and limitations) of the method, we use the effective potential to renormalize a toy chemical model based on a simplified Gray-Scott reaction. In particular, we use it to compute the scale dependence of the toy model's parameters (in perturbation theory) when subjected to a Gaussian power-law noise with short time correlations.

Microcapsules with Distinct Dual-Layer Shells and Their Applications for the Encapsulation, Preservation, and Slow Release of Hydrophilic Small Molecules.

Microcapsules with two distinct layers of shells were fabricated using an approach combining microfluidics and photopolymerization. Unlike conventional microcapsules with a single shell, a fluorinated oil layer was introduced between the lumen and the outer polymer shell. The fluorinated oil layer significantly suppresses the leakage of the encapsulated ingredients in the lumen and consequently gives the microcapsules remarkable slow release capability for hydrophilic small molecule-based payloads, such as Rhodamine 6G. The release period of Rhodamine 6G can be up to 4 months when using a photocurable resin as the shell material, and the release of Rhodamine 6G can be regulated via the osmolality of the incubation solution for porous hydrogel microcapsules. Even under maximum hypotonic conditions, the release period of Rhodamine 6G in the hydrogel microcapsules is at least 10 days. The slow release capability can be significantly enhanced (6 weeks or longer) by increasing the thicknesses of the hydrogel shell and fluorinated oil layer.

From chemical soup to computing circuit: transforming a contiguous chemical medium into a logic gate network by modulating its external conditions.

It has been shown that it is possible to transform a well-stirred chemical medium into a logic gate simply by varying the chemistry's external conditions (feed rates, lighting conditions, etc.). We extend this work, showing that the same method can be generalized to spatially extended systems. We vary the external conditions of a well-known chemical medium (a cubic autocatalytic reaction-diffusion model), so that different regions of the simulated chemistry are operating under particular conditions at particular times. In so doing, we are able to transform the initially uniform chemistry, not just into a single logic gate, but into a functionally integrated network of diverse logic gates that operate as a basic computational circuit known as a full-adder.

Resonant Behavior in a Periodically Forced Nonisothermal Oregonator.

Nonisothermal chemical oscillators are poorly studied systems because chemical oscillations are conventionally studied under isothermal conditions. Coupling chemical reactions with heat generation and removal in a nonisothermal oscillatory system can lead to a highly nontrivial nonlinear dynamic behavior. For the current study, we considered the three-variable Oregonator model with the temperature incorporated as a variable (not a parameter), thus adding an energy balance to the set of equations. The effect of temperature on reaction rates is included through the temperature-dependent reaction rate coefficients (Arrhenius law). To model a continuous operation in a laboratory environment, the system was subjected to external forcing through the coolant temperature and infrared irradiation. By conducting numerical simulations and parametric studies, we found that the system is capable of a resonant behavior exhibiting induced oscillations. Our findings indicate that an external source of heat (e.g., via an infrared light emitting diode) can be used to induce a Hopf bifurcation under resonant conditions in an experimental Belousov-Zhabotinsky reactor.