Design and Implementation of a Highly Selective Minimal Self-Replicating System

Generalist versus Specialist Self-Replicators

Darwinian evolution, including the selection of the fittest species under given environmental conditions, is a major milestone in the development of synthetic living systems. In this regard, generalist or specialist behavior (the ability to replicate in a broader or narrower, more specific food environment) are of importance. Here we demonstrate generalist and specialist behavior in dynamic combinatorial libraries composed of a peptide-based and an oligo(ethylene glycol) based building block. Three different sets of macrocyclic replicators could be distinguished based on their supramolecular organization: two prepared from a single building block as well as one prepared from an equimolar mixture of them. Peptide-containing hexamer replicators were found to be generalists, i. e. they could replicate in a broad range of food niches, whereas the octamer peptide-based replicator and hexameric ethyleneoxide-based replicator were proven to be specialists, i. e. they only replicate in very specific food niches that correspond to their composition. However, sequence specificity cannot be demonstrated for either of the generalist replicators. The generalist versus specialist nature of these replicators was linked to their supramolecular organization. Assembly modes that accommodate structurally different building blocks lead to generalist replicators, while assembly modes that are more restrictive yield specialist replicators.

Out-of-Equilibrium Self-Replication Allows Selection for Dynamic Kinetic Stability in a System of Competing Replicators

Among the key characteristics of living systems are their ability to self‐replicate and the fact that they exist in an open system away from equilibrium. Herein, we show how the outcome of the competition between two self‐replicators, differing in size and building block composition, is different depending on whether the experiments are conducted in a closed vial or in an open and out‐of‐equilibrium replication–destruction regime. In the closed system, the slower replicator eventually prevails over the faster competitor. In a replication‐destruction regime, implemented through a flow system, the outcome of the competition is reversed and the faster replicator dominates. The interpretation of the experimental observations is supported by a mass‐action‐kinetics model. These results represent one of the few experimental manifestations of selection among competing self‐replicators based on dynamic kinetic stability and pave the way towards Darwinian evolution of abiotic systems.

Design of Subreplicating Systems from an Existing Self-Replicating Diels-Alder Reaction System by Isosteric Replacement

The key feature of non-enzymatic self-replicating systems is the formation of catalytically active ternary complexes in which product templates direct precursors into spatial proximity to allow the formation of new covalent bonds. It is possible to create new replicating species by simply evaluating the ternary active complex of an existing replicating system and applying proper isosteric replacements. In this study, we have evaluated the formerly reported self-replicating Diels-Alder reaction having 61 and 33% selectivity for two diastereomeric replicators. An isosteric replacement on the spacer part connecting recognition and reactive sites of the maleimide component was applied by considering the symmetry of catalytically active ternary complexes, and it was shown that self-replication was conserved. Analysis of the new system showed 77 and 21% diastereoselectivity for the two new replicating species. Seeding experiments indicated autocatalytic activity of both replicators. In other words, both replicators compete with each other by catalyzing their own formation from the same reagent source. Another modification was applied by aiming selective blocking of the autocatalytic cycle of the competing diastereomer. The new system showed a diastereoselectivity of about 94% for the favored replicator. The kinetic data of both systems were analyzed by modeling with SimFit simulations.

A Molecular Replication Process Drives Supramolecular Polymerization

Supramolecular polymers are materials in which the connections between monomers in the polymer main chain are non-covalent bonds. This area has seen rapid expansion in the last two decades and has been exploited in several applications. However, suitable contiguous hydrogen-bond arrays can be difficult to synthesize, placing some limitations on the deployment of supramolecular polymers. We have designed a hydrogen-bonded polymer assembled from a bifunctional monomer composed of two replicating templates separated by a rigid spacer. This design allows the autocatalytic formation of the polymer main chain through the self-templating properties of the replicators and drives the synthesis of the bifunctional monomer from its constituent components in solution. The template-directed 1,3-dipolar cycloaddition reaction between nitrone and maleimide proceeds with high diastereoselectivity, affording the bifunctional monomer. The high binding affinity between the self-complementary replicating templates that allows the bifunctional monomer to polymerize in solution is derived from the positive cooperativity associated with this binding process. The assembly of the polymer in solution has been investigated by diffusion-ordered NMR spectroscopy. Both microcrystalline and thin films of the polymeric material can be prepared readily and have been characterized by powder X-ray diffraction and scanning electron microscopy. These results demonstrate that the approach described here is a valid one for the construction of supramolecular polymers and can be extended to systems where the rigid spacer between the replicating templates is replaced by one carrying additional function.

Selection between Competing Self-Reproducing Lipids: Succession and Dynamic Activation

Models of chemical evolution are central to advancing origins of life research. To design more lifelike systems, we must expand our understanding of molecular selection mechanisms. Here, we show two selection modes that produce evolving populations of self-reproducing species, formed through thiol-disulfide exchange. Competition between thiol precursors can give clear succession patterns based on steric factors, an intrinsic property. A separate, emergent selection mechanism-dynamic activating metathesis-was found when exploring competing disulfide precursors. These experiments reveal that additional species generated in the mixture open up alternative reaction pathways to form self-reproducing products. Thus, increased compositional complexity provides certain species with a unique competitive advantage at the expense of others.

Re-Evaluation of a Fulvene-Based Self-Replicating Diels-Alder Reaction System

We re-evaluate our claim of a high diastereoselectivity in the self-relicating Diels-Alder reaction between maleimide 1 and fulvene 3. It was shown that the system has a diastereoselectivity of 1.8:1 for NN-4:NX-4, which is contrary to the 16:1 ratio claimed by Dieckmann et al. The analysis of ¹ H NMR monitoring of the reaction revealed that both replicators show sigmoidal growth which is typical for auto-catalytic systems.

Encoding Multiple Reactivity Modes within a Single Synthetic Replicator

Establishing programmable and self-sustaining replication networks in pools of chemical reagents is a key challenge in systems chemistry. Self-replicating templates are formed from two constituent components with complementary recognition and reactive sites via a slow bimolecular pathway and a fast template-directed pathway. Here, we re-engineer one of the components of a synthetic replicator to encode an additional recognition function, permitting the assembly of a binary complex between the components that mediates replicator formation through a template-independent pathway, which achieves maximum rate acceleration at early time points in the replication process. The complementarity between recognition sites creates a key conformational equilibrium between the catalytically inert product, formed via the template-independent pathway, and the catalytically active replicator that mediates the template-directed pathway. Consequently, the rapid formation of the catalytically inert isomer kick-starts replication through the template-directed pathway. Through kinetic analyses, we demonstrate that the presence of the two recognition-mediated reactivity modes results in enhanced template formation in comparison to that of systems capable of exploiting only a single recognition-mediated pathway. Finally, kinetic simulations reveal that the conformational equilibrium and both the relative and absolute efficiencies of the recognition-mediated pathways affect the extent to which self-replicating systems can benefit from this additional template-independent reactivity mode. These results allow us to formulate the rules that govern the coupling of replication processes to alternative recognition-mediated reactivity modes. The interplay between template-directed and template-independent pathways for replicator formation has significant relevance to ongoing efforts to design programmable and adaptable replicator networks.

Spontaneous formation of autocatalytic sets with self-replicating inorganic metal oxide clusters

Self-replication is an important property of life, yet no one knows how it arose, and the machinery found in modern cells is far too complex to have formed by chance. One suggestion is that simple networks may become able to cooperate and hence replicate together forming autocatalytic sets, but no simple systems have been found. Here we present an inorganic autocatalytic, based on molybdenum blue, that is formed spontaneously when a simple inorganic salt of sodium molybdate is reduced under acidic conditions. This study demonstrates how autocatalytic sets, based on simple inorganic salts, can lead to the spontaneous emergence of self-replicating systems and solves the mystery of how gigantic molecular nanostructures of molybdenum blue can form in the first place.

Here we show how a simple inorganic salt can spontaneously form autocatalytic sets of replicating inorganic molecules that work via molecular recognition based on the {PMo₁₂} ≡ [PMo₁₂O₄₀]^3– Keggin ion, and {Mo₃₆} ≡ [H₃Mo₅₇M₆(NO)₆O₁₈₃(H₂O)₁₈]^22– cluster. These small clusters are able to catalyze their own formation via an autocatalytic network, which subsequently template the assembly of gigantic molybdenum-blue wheel {Mo₁₅₄} ≡ [Mo₁₅₄O₄₆₂H₁₄(H₂O)₇₀]^14–, {Mo₁₃₂} ≡ [Mo^VI₇₂Mo^V₆₀O₃₇₂(CH₃COO)₃₀(H₂O)₇₂]^42– ball-shaped species containing 154 and 132 molybdenum atoms, and a {PMo₁₂}⊂{Mo₁₂₄Ce₄} ≡ [H₁₆Mo^VI₁₀₀Mo^V₂₄Ce₄O₃₇₆(H₂O)₅₆ (PMo^VI₁₀Mo^V₂O₄₀)(C₆H₁₂N₂O₄S₂)₄]^5– nanostructure. Kinetic investigations revealed key traits of autocatalytic systems including molecular recognition and kinetic saturation. A stochastic model confirms the presence of an autocatalytic network involving molecular recognition and assembly processes, where the larger clusters are the only products stabilized by the cycle, isolated due to a critical transition in the network.

Selection from a pool of self-assembling lipid replicators

Replication and compartmentalization are fundamental to living systems and may have played important roles in life’s origins. Selection in compartmentalized autocatalytic systems might provide a way for evolution to occur and for life to arise from non-living systems. Herein we report selection in a system of self-reproducing lipids where a predominant species can emerge from a pool of competitors. The lipid replicators are metastable and their out-of-equilibrium population can be sustained by feeding the system with starting materials. Phase separation is crucial for selective surfactant formation as well as autocatalytic kinetics; indeed, no selection is observed when all reacting species are dissolved in the same phase. Selectivity is attributed to a kinetically controlled process where the rate of monomer formation determines which replicator building blocks are the fittest. This work reveals how kinetics of a phase-separated autocatalytic reaction may be used to control the population of out-of-equilibrium replicators in time.

Selection in compartmentalized self-replicating systems might provide a way for life to arise from abiotic environments. Here, the authors explore selection in a system of transient autocatalytic lipids and find that autocatalytic kinetics and phase separation are the key selection factors.

Compositional Persistence in a Multicyclic Network of Synthetic Replicators

The emergence of collections of simple chemical entities that create self-sustaining reaction networks, embedding replication and catalysis, is cited as a potential mechanism for the appearance on the early Earth of systems that satisfy minimal definitions of life. In this work, a functional reaction network that creates and maintains a set of privileged replicator structures through auto- and cross-catalyzed reaction cycles is created from the pairwise combinations of four reagents. We show that the addition of individual preformed templates to this network, representing instructions to synthesize a specific replicator, induces changes in the output composition of the system that represent a network-level response. Further, we establish through sets of serial transfer experiments that the catalytic connections that exist between the four replicators in this network and the system-level behavior thereby encoded impose limits on the compositional variability that can be induced by repeated exposure to instructional inputs, in the form of preformed templates, to the system. The origin of this persistence is traced through kinetic simulations to the properties and inter-relationships between the critical ternary complexes formed by the auto- and crosscatalytic templates. These results demonstrate that in an environment where there is no continuous selection pressure the network connectivity, described by the catalytic relationships and system-level interactions between the replicators, is persistent, thereby limiting the ability of this network to adapt and evolve.

Open Prebiotic Environments Drive Emergent Phenomena and Complex Behavior

We have been studying simple prebiotic catalytic replicating networks as prototypes for modeling replication, complexification and Systems Chemistry. While living systems are always open and function far from equilibrium, these prebiotic networks may be open or closed, dynamic or static, divergent or convergent to a steady state. In this paper we review the properties of these simple replicating networks, and show, via four working models, how even though closed systems exhibit a wide range of emergent phenomena, many of the more interesting phenomena leading to complexification and emergence indeed require open systems.

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.

A transient self-assembling self-replicator

Developing physical models of complex dynamic systems showing emergent behaviour is key to informing on persistence and replication in biology, how living matter emerges from chemistry, and how to design systems with new properties. Herein we report a fully synthetic small molecule system in which a surfactant replicator is formed from two phase-separated reactants using an alkene metathesis catalyst. The replicator self-assembles into aggregates, which catalyse their own formation, and is thermodynamically unstable. Rather than replicating until the reactants are fully consumed, the metastable replicator is depleted in a second metathesis reaction, and closed system equilibrium is eventually reached. Mechanistic experiments suggest phase separation is responsible for both replicator formation and destruction.

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.

Chemical roots of biological evolution: the origins of life as a process of development of autonomous functional systems

In recent years, an extension of the Darwinian framework is being considered for the study of prebiotic chemical evolution, shifting the attention from homogeneous populations of naked molecular species to populations of heterogeneous, compartmentalized and functionally integrated assemblies of molecules. Several implications of this shift of perspective are analysed in this critical review, both in terms of the individual units, which require an adequate characterization as self-maintaining systems with an internal organization, and also in relation to their collective and long-term evolutionary dynamics, based on competition, collaboration and selection processes among those complex individuals. On these lines, a concrete proposal for the set of molecular control mechanisms that must be coupled to bring about autonomous functional systems, at the interface between chemistry and biology, is provided.

Generating System-Level Responses from a Network of Simple Synthetic Replicators

The creation of reaction networks capable of exhibiting responses that are properties of entire systems represents a significant challenge for the chemical sciences. The system-level behavior of a reaction network is linked intrinsically to its topology and the functional connections between its nodes. A simple network of chemical reactions constructed from four reagents, in which each reagent reacts with exactly two others, can exhibit up-regulation of two products even when only a single chemical reaction is addressed catalytically. We implement a system with this topology using two maleimides and two nitrones of different sizes-either short or long and each bearing complementary recognition sites-that react pairwise through 1,3-dipolar cycloaddition reactions to create a network of four length-segregated replicating templates. Comprehensive ¹H NMR spectroscopy experiments unravel the network topology, confirming that, in isolation, three out of four templates self-replicate, with the shortest template exhibiting the highest efficiency. The strongest template effects within the network are the mutually cross-catalytic relationships between the two templates of intermediate size. The network topology is such that the addition of different preformed templates as instructions to a mixture of all starting materials elicits system-level behavior. Instruction with a single template up-regulates the formation of two templates in a predictable manner. These results demonstrate that the rules governing system-level behavior can be unraveled through the application of wholly synthetic networks with well-defined chemistries and interactions.

pH controlled assembly of a self-complementary halogen-bonded dimer

Halogen bonding between an oxygen acceptor and an iodotriazole donor can be switched on an off by cycling the solution pH.

Phenols and their corresponding phenoxide anions can form halogen bonds with neutral iodotriazoles. The strength of these interactions depends critically on the protonation state of the oxygen atom – the interaction of the phenoxide anion is more than an order of magnitude stronger than the corresponding phenol. The assembly of a molecule bearing both an iodotriazole and a phenoxide anion into a self-complementary dimer, stabilised by two halogen bonds between the phenoxide anions and the neutral iodotriazoles has been demonstrated. The corresponding phenol shows no halogen bond mediated assembly either in the solid or in the solution state. This assembly process can be actuated simply by a change in protonation state – treatment of the phenol with one equivalent of base results in deprotonation and assembly of the dimer. The structure of the homodimer formed by the phenoxide-bearing iodotriazole has been determined in the solid state and ¹⁹F NMR spectroscopy demonstrates that the assembled dimer persists in solution and that it has significant stability. ¹⁹F NMR spectroscopy has also been used to demonstrate that the assembly process is completely reversible.

A Synthetic Replicator Drives a Propagating Reaction-Diffusion Front

A simple synthetic autocatalytic replicator is capable of establishing and driving the propagation of a reaction-diffusion front within a 50 μL syringe. This replicator templates its own synthesis through a 1,3-dipolar cycloaddition reaction between a nitrone component, equipped with a 9-ethynylanthracene optical tag, and a maleimide. Kinetic studies using NMR and UV-vis spectroscopies confirm that the replicator forms efficiently and with high diastereoselectivity, and this replication process brings about a dramatic change in optical properties of the sample-a change in the color of the fluorescence in the sample from yellow to blue. The addition of a small amount of the preformed replicator at a specific location within a microsyringe, filled with the reaction building blocks, results in the initiation and propagation of a reaction-diffusion front. The realization of a replicator capable of initiating a reaction-diffusion front provides a platform for the examination of interconnected replicating networks under out-of-equilibrium conditions involving diffusion processes.

Exploiting recognition-mediated assembly and reactivity in [2]rotaxane formation

A small molecular reaction network exploits recognition-mediated reactive processes in order to drive the assembly and formation of both a self-replicating linear template (thread) and a [2]rotaxane, in which the linear template is encircled by a diamide macrocycle. Complementary recognition sites, placed at strategic positions on the reactive building blocks, drive these assembly and replication processes. Template-instructed experiments show that the thread is capable of efficient self-replication and that no cross-catalytic relationships exist between the thread and the [2]rotaxane. The rate of [2]rotaxane formation is insensitive to the addition of a preformed template, however, [2]rotaxane formation does show enhanced diastereoselectivity, most likely originating from its recognition-mediated formation through a ternary reactive complex.

A recognition-mediated reaction drives amplification within a dynamic library

A single, appropriately designed, recognition event targets and transforms one of two reactive members of an exchanging pool of compounds through a recognition-mediated irreversible cycloaddition reaction, altering dramatically the final composition and kinetic behaviour of the dynamic library.

Template-Triggered Emergence of a Self-Replicator from a Dynamic Combinatorial Library

Self-assembly of a specific member of a dynamic combinatorial library (DCL) may lead to self-replication of this molecule. However, if the concentration of the potential replicator in the DCL fails to exceed its critical aggregation concentration (CAC), then self-replication will not occur. We now show how addition of a template can raise the concentration of a library member-template complex beyond its CAC, leading to the onset of self-replication. Once in existence, the replicator aggregates promote further replication also in the absence of the template that induced the initial emergence of the replicator.

Solvent composition dictates emergence in dynamic molecular networks containing competing replicators

In Darwinian evolution, species that are better adapted to their environment win the competition for common resources from less well-adapted competitors. Thus, in such scenarios the nature of the environment may dictate the outcome of the competition. We investigated to what degree these biological principles acting at the level of species extend to the molecular level into systems based on fully synthetic self-replicating molecules. We now report two systems in which two replicators compete for a common building block and where the environment dictates which of the two replicators wins. We observed that subtle changes in the environment can lead to dramatic differences in the outcome of the competition.

Improved Sommelet Reaction Catalysed by Lanthanum Triflate

An improved Sommelet reaction for the synthesis of araldehydes from benzyl halides and hexamethylenetetramine was achieved employing lanthanum triflate (3 mol%) as catalyst in water with sodium dodecyl sulfate (SDS, 2 wt%) as solubiliser. Good to excellent yields were obtained in most of the 18 examples.

Lipase-catalyzed asymmetric synthesis of oxathiazinanones through dynamic covalent kinetic resolution

A domino addition–lactonization pathway has been applied to a dynamic covalent resolution protocol, leading to efficient asymmetric synthesis of oxathiazinanones.

Supramolecular catalysis. Part 2: artificial enzyme mimics

The design of artificial catalysts able to compete with the catalytic proficiency of enzymes is an intense subject of research. Non-covalent interactions are thought to be involved in several properties of enzymatic catalysis, notably (i) the confinement of the substrates and the active site within a catalytic pocket, (ii) the creation of a hydrophobic pocket in water, (iii) self-replication properties and (iv) allosteric properties. The origins of the enhanced rates and high catalytic selectivities associated with these properties are still a matter of debate. Stabilisation of the transition state and favourable conformations of the active site and the product(s) are probably part of the answer. We present here artificial catalysts and biomacromolecule hybrid catalysts which constitute good models towards the development of truly competitive artificial enzymes.

Chelation-controlled additions to α-silyloxy aldehydes: an autocatalytic approach

The Felkin-Anh model has been widely accepted to describe stereochemical outcomes in nucleophilic additions to α-silyloxy carbonyl compounds. Herein, it is demonstrated that chelation-controlled additions can be performed using dialkylzinc reagents in the presence of chlorotrimethylsilane with good to excellent diastereoselectivities. Ethyl zinc chloride, the Lewis acid responsible for promoting chelation, is generated in situ in an autocatalytic fashion. This approach circumvents its use in stoichiometric amounts.

Uncovering the selection criteria for the emergence of multi-building-block replicators from dynamic combinatorial libraries

A family of self-replicating macrocycles was developed using dynamic combinatorial chemistry. Replication is driven by self-assembly of the replicators into fibrils and relies critically on mechanically induced fibril fragmentation. Analysis of separate dynamic combinatorial libraries made from one of six peptide-functionalized building blocks of different hydrophobicity revealed two selection criteria that govern the emergence of replicators from these systems. First, the replicators need to have a critical macrocycle size that endows them with sufficient multivalency to enable their self-assembly into fibrils. Second, efficient replication occurs only for library members that are of low abundance in the absence of a replication pathway. This work has led to spontaneous emergence of replicators with unrivalled structural complexity, being built from up to eight identical subunits and reaching a MW of up to 5.6 kDa. The insights obtained in this work provide valuable guidance that should facilitate future discovery of new complex self-replicating molecules. They may also assist in the development of new self-synthesizing materials, where self-assembly drives the synthesis of the very molecules that self-assemble. To illustrate the potential of this concept, the present system enables access to self-assembling materials made from self-synthesizing macrocycles with tunable ring size ranging from trimers to octamers.

Elucidating the origin of diastereoselectivity in a self-replicating system: selfishness versus altruism

We have investigated a diastereoselective self-replicating system based on a cycloaddition of a fulvene derivative and a maleimide using a two-pronged approach of combining NMR spectroscopy with computational modelling. Two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, one diastereomer takes over the resources as a "selfish" autocatalyst, while exploiting the competitor as a weak "altruist", resulting in a diastereoselectivity of 16:1. We applied 1D and 2D NMR spectroscopic techniques supported by ab initio chemical shifts as well as ab initio molecular dynamics simulations to study the structure and dynamics of the underlying network. This powerful combination allowed us to decipher the energetic and structural rationale behind the observed behaviour, while static computational methods currently used in the field did not.

A simple network of synthetic replicators can perform the logical OR operation

A small network of synthetic replicators is capable of responding to instructional inputs such that the output of the network is an excess of one of the replicators whenever the input contains either or both of the replicators, mirroring the OR boolean logic operation.