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 networks1,2. Non-enzymatic networks could in principle support neuromorphic architectures, and seminal proofs-of-principle have been reported3,4. 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.

Natural selection in compartmentalized environment with reshuffling.

The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic compartments-droplets of an emulsion. The selection of desirable variants is performed according to the phenotype of each compartment. The random partitioning leads to a fraction of compartments receiving more than one genotype making the whole process a lab implementation of the group selection. From a practical point of view (where efficient selection is typically sought), it is important to know the impact of the increase in the mean occupancy of compartments on the selection efficiency. We carried out a theoretical investigation of this problem in the context of selection dynamics for an infinite non-mutating subdivided population that randomly colonizes an infinite number of patches (compartments) at each reproduction cycle. We derive here an update equation for any distribution of phenotypes and any value of the mean occupancy. Using this result, we demonstrate that, for the linear additive fitness, the best genotype is still selected regardless of the mean occupancy. Furthermore, the selection process is remarkably resilient to the presence of multiple genotypes per compartments, and slows down approximately inversely proportional to the mean occupancy at high values. We extend out results to more general expressions that cover nonadditive and non-linear fitnesses, as well non-Poissonian distribution among compartments. Our conclusions may also apply to natural genetic compartmentalized replicators, such as viruses or early trans-acting RNA replicators.

Microscopic agents programmed by DNA circuits.

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

High-resolution mapping of bifurcations in nonlinear biochemical circuits.

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

Pursuit-and-Evasion Reaction-Diffusion Waves in Microreactors with Tailored Geometry.

Out-of-equilibrium chemical systems may self-organize into structures displaying spatiotemporal order, such as traveling waves and Turing patterns. Because of its predictable chemistry, DNA has recently appeared as an interesting candidate to engineer these spatiotemporal structures. However, in addition to the intrinsic chemical parameters, initial and boundary conditions have a major impact on the final structure. Here we take advantage of microfluidics to design controlled reactors and investigate pursuit-and-evasion chemical waves generated by a DNA-based reaction network with Predator-Prey dynamics. We first propose two complementary microfabrication strategies to either control the initial condition or the two-dimensional geometry of the reactor where the waves develop. We subsequently use them to investigate the effect of curvature in wave propagation. We finally show that DNA-based waves can compute the optimal path within a maze. We thus suggest that coupling configurable microfluidics to programmable DNA-based dissipative reaction networks is a powerful route to investigate spatiotemporal order formation in chemistry.

Biomimetic copper(I)--CO complexes: a structural and dynamic study of a cali.

Four novel calix[6]arene-based cuprous complexes are described. They present a biomimetic tris(imidazole) coordination core associated with a hydrophobic cavity that wraps the apical binding site. Each differs from the other by the methyl or ethyl substituents present on the phenoxyl groups (OR1) and on the imidazole arms (NR2) of the calix[6]arene structure. In solution, stable CO complexes were obtained. We have investigated their geometrical and dynamic properties with respect to the steric demand. IR and NMR studies revealed that, in solution, these complexes adopted two distinct conformations. The preferred conformation was dictated only by the size of the OR1 group. When R1 was an ethyl group, the complex preferentially adopted a flattened C3-symmetrical structure. The corresponding helical enantiomers were in conformational equilibrium, which, however, was slow on the 1H NMR time scale at -80 degrees C. When R1 was a methyl group, the low-temperature NMR spectra revealed the partial inclusion of one tBu group. The complex wobbled between three dissymmetric but equivalent conformations. Hence, small differences in the steric demand of the calixarene's skeleton changed the geometry and dynamics of the system. Indeed, this supramolecular control was promoted by the strong conformational coupling between the metal center and the host structure. Interestingly, this was not only the result of a covalent preorganization, but also stemmed from weak interactions within the hydrophobic pocket. The vibrational spectra of the bound CO were revealed to be a sensitive gauge of this supramolecular behavior, similar to copper proteins in which allosteric effects are common.