Nonlinear decision-making with enzymatic neural networks

Abstract

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][3][4] . Nonenzymatic networks could in principle support neuromorphic architectures, and seminal proof-of-principles have been reported 5,6 . However, leakages, as well as issues with sensitivity, speed, nonlinearities and preparation, make the composition of layers delicate, and molecular classifications equivalent to a multilayer neural network (e.g. nonlinear partitioning of a concentration space) remain elusive. Here we introduce DNA-encoded enzymatic neurons with tunable weights and biases, and which are assembled in multilayer architectures to classify nonlinearly separable regions. We first leverage the sharp decision margin of the neurons to compute various majority functions on 10 bits. We then compose neurons into a twolayer 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.Synthetic DNA has emerged as a versatile polymer to store and process information at the molecular scale. It has powered a rich library of computational molecular devices ranging from logic circuits 7-10 to self-assembling automata 11 . Departing from the biological model of computation, most DNA computing devices imitate the Boolean paradigm of electronics. However, their computing power has fallen short of the exponential growth of Moore's law: their size has been plateauing at ~5-10 logic gates for a decade 8 . In parallel, various groups have started looking at the brain, rather than the CPU, as an inspiration for computing with molecules 2,12,3-6 . This is because neuronal and chemical networks share striking similarities: massively parallel and recurrent architectures, analog and asynchronous operation, fault-tolerant and redundant computations (Figure S12)In 2018, Lopez et al. reported a DNA-based linear classifier 6 that performs all of its computations with a nonenzymatic mechanism: toehold-mediated strand displacement 13 . Using similar DNA-only mechanisms on many more inputs and taking inspiration from competitive neural networks 2,3 , Cherry and Qian reported in a tour de force a DNA classifier for the MNIST database 5 . Together, these molecular classifiers showcased the benefits of neuromorphic networks over Boolean circuits: massive parallelism, handling of analog inputs, and tolerance to corrupted patterns. However, these nonenzymatic classifiers had limited decision margins, i.e. they could not discriminate between two similar inputs belonging to different classes. They also suffered from leaks that made the compositio...

Toehold-Mediated Strand Displacement in Random Sequence Pools

“…This results in a complex of the invader and substrate and an unbound incumbent (Figure a). TMSD has been used in the implementation of a wide variety of in vitro molecular computing applications such as logic gates, − robotics, neural networks, − and other dynamic and complex functions. − The larger such systems grow, the higher the chance that different circuit components show undesired interactions with each other. In an in vitro context and in the absence of sequence constraints, such interactions can be explicitly designed against .…”

Molecular Computation for Molecular Classification

“…[ 46 ] E) Neural‐logic hybrid network capable of nonlinear space partitioning. [ 125 ] F) Riboregulator‐based perceptron for the classification of gene inputs. [ 20 ] G) Metabolic perceptron from enzymatic conversion and benzoate biosensor.…”

“…The PEN‐DNA toolbox also possesses the necessary building blocks to assemble a perceptron, namely input transduction, weighting, summation, and thresholded nonlinear activation function. [ 125 ] Weights are tuned by introducing decoy unproductive templates that compete for the inputs with cognate activator‐producing templates: As a result, the ratio of the two templates defines the weight of a given input. Negative weights can be implemented by using templates that produce anti‐activator strands, and thus does not require additional annihilation gates as used in enzyme‐free networks.…”

“…D) Neural sensor of lung cancer patient from 4 input circulating miRNAs [46]. E) Neural-logic hybrid network capable of nonlinear space partitioning [125]. F) Riboregulator-based perceptron for the classification of gene inputs [20].…”

Toehold-Mediated Strand Displacement in Random Sequence Pools

“…This results in a complex of the invader and substrate and an unbound incumbent (Figure 1a). This type of reaction, though simple in principle, has been used in the implementation of a wide variety of in vitro molecular computing applications such as logic gates [1][2][3] , robotics 4 , neural networks [5][6][7][8] and other dynamic and complex functions. [9][10][11][12] The larger such systems grow, the higher the chance that different circuit components show unwanted interactions with each other.…”