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Liu X, Parhi KK. DNA Memristors and Their Application to Reservoir Computing. ACS Synth Biol 2022; 11:2202-2213. [PMID: 35561249 DOI: 10.1021/acssynbio.2c00184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This paper introduces memristors realized by molecular and DNA reactions. Molecular memristors process one input molecule, generate two output molecules, and are realized using two molecular reactions with two different rate constants. The DNA memristors are realized using five DNA strand displacement (DSD) reactions with two effective rate constants. The hysteresis behavior is preserved in the proposed memristors, and this behavior can be altered by changing the ratios of the rate constants. The state of the memristor can be computed from the concentrations of the two output molecules using bipolar fractional coding. We describe how the proposed memristors can be used to learn the spatial and temporal properties of data via the reservoir computing (RC) model. An RC system can be divided into two parts: reservoir and readout layer. The first part transfers the information from the input space to a high-dimensional spatiotemporal feature space represented by the state of reservoirs. The connectivity structure of the reservoir will remain fixed through the dynamical evaluations. The readout layer effectively maps the projected features to the target output. A dynamical memristor array is used to implement an RC system that exploits the internal dynamical processes of the memristors. The readout layer implements a matrix-vector multiplication using molecular reactions, also based on bipolar fractional coding. All molecular reactions are mapped to DSD reactions. The RC system based on the DNA reservoir and the DNA readout layer is used to solve a handwritten digit recognition task and a second-order time series prediction task. The performance of the DNA RC system is comparable to that of an electronic memristor RC system for both tasks.
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Affiliation(s)
- Xingyi Liu
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota55455, United States
| | - Keshab K. Parhi
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota55455, United States
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van der Linden AJ, Pieters PA, Bartelds MW, Nathalia BL, Yin P, Huck WTS, Kim J, de Greef TFA. DNA Input Classification by a Riboregulator-Based Cell-Free Perceptron. ACS Synth Biol 2022; 11:1510-1520. [PMID: 35381174 PMCID: PMC9016768 DOI: 10.1021/acssynbio.1c00596] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The ability to recognize molecular patterns is essential for the continued survival of biological organisms, allowing them to sense and respond to their immediate environment. The design of synthetic gene-based classifiers has been explored previously; however, prior strategies have focused primarily on DNA strand-displacement reactions. Here, we present a synthetic in vitro transcription and translation (TXTL)-based perceptron consisting of a weighted sum operation (WSO) coupled to a downstream thresholding function. We demonstrate the application of toehold switch riboregulators to construct a TXTL-based WSO circuit that converts DNA inputs into a GFP output, the concentration of which correlates to the input pattern and the corresponding weights. We exploit the modular nature of the WSO circuit by changing the output protein to the Escherichia coli σ28-factor, facilitating the coupling of the WSO output to a downstream reporter network. The subsequent introduction of a σ28 inhibitor enabled thresholding of the WSO output such that the expression of the downstream reporter protein occurs only when the produced σ28 exceeds this threshold. In this manner, we demonstrate a genetically implemented perceptron capable of binary classification, i.e., the expression of a single output protein only when the desired minimum number of inputs is exceeded.
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Affiliation(s)
- Ardjan J. van der Linden
- Laboratory of Chemical Biology and Institute for Complex Molecular Systems, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Computational Biology Group, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Pascal A. Pieters
- Laboratory of Chemical Biology and Institute for Complex Molecular Systems, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Computational Biology Group, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Mart W. Bartelds
- Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands
| | - Bryan L. Nathalia
- Computational Biology Group, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Peng Yin
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts 02115, United States
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, United States
| | - Wilhelm T. S. Huck
- Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands
| | - Jongmin Kim
- Department of Life Sciences, Pohang University of Science and Technology, Pohang, Gyeongbuk 37673, Republic of Korea
| | - Tom F. A. de Greef
- Laboratory of Chemical Biology and Institute for Complex Molecular Systems, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Computational Biology Group, Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands
- Center for Living Technologies, Eindhoven-Wageningen-Utrecht Alliance, 3584 CB Utrecht, The Netherlands
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Abstract
This paper presents novel implementations for reservoir computing (RC) using DNA oscillators. An RC system consists of two parts: reservoir and readout layer. The reservoir projects input signals into a high-dimensional feature space which is formed by the state of the reservoir. The internal connectivity structure of the reservoir remains unchanged throughout computation. After training, the readout layer maps the projected features into the desired output. It has been shown in prior work that coupled deoxyribozyme oscillators can be used as the reservoir. In this paper, we utilize the n-phase molecular oscillator (n ≥ 3) presented in our prior work. The readout layer implements a matrix-vector multiplication using molecular reactions based on molecular analog multiplication. All molecular reactions are mapped to DNA strand displacement (DSD) reactions. We also introduce a novel encoding method that can significantly reduce the reaction time. The feasibility of the proposed RC systems based on the DNA oscillator is demonstrated for the handwritten digit recognition task and a second-order nonlinear prediction task.
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Affiliation(s)
- Xingyi Liu
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Keshab K. Parhi
- Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, United States
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Liu X, Parhi KK. Molecular and DNA Artificial Neural Networks via Fractional Coding. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 2020; 14:490-503. [PMID: 32149654 DOI: 10.1109/tbcas.2020.2979485] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article considers implementation of artificial neural networks (ANNs) using molecular computing and DNA based on fractional coding. Prior work had addressed molecular two-layer ANNs with binary inputs and arbitrary weights. In prior work using fractional coding, a simple molecular perceptron that computes sigmoid of scaled weighted sum of the inputs was presented where the inputs and the weights lie between [-1,1]. Even for computing the perceptron, the prior approach suffers from two major limitations. First, it cannot compute the sigmoid of the weighted sum, but only the sigmoid of the scaled weighted sum. Second, many machine learning applications require the coefficients to be arbitrarily positive and negative numbers that are not bounded between [-1,1]; such numbers cannot be handled by the prior perceptron using fractional coding. This paper makes four contributions. First molecular perceptrons that can handle arbitrary weights and can compute sigmoid of the weighted sums are presented. Thus, these molecular perceptrons are ideal for regression applications and multi-layer ANNs. A new molecular divider is introduced and is used to compute sigmoid(ax) where . Second, based on fractional coding, a molecular artificial neural network (ANN) with one hidden layer is presented. Third, a trained ANN classifier with one hidden layer from seizure prediction application from electroencephalogram is mapped to molecular reactions and DNA and their performances are presented. Fourth, molecular activation functions for rectified linear unit (ReLU) and softmax are also presented.
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Baek C, Lee SW, Lee BJ, Kwak DH, Zhang BT. Enzymatic Weight Update Algorithm for DNA-Based Molecular Learning. Molecules 2019; 24:molecules24071409. [PMID: 30974800 PMCID: PMC6479535 DOI: 10.3390/molecules24071409] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Revised: 04/03/2019] [Accepted: 04/04/2019] [Indexed: 01/16/2023] Open
Abstract
Recent research in DNA nanotechnology has demonstrated that biological substrates can be used for computing at a molecular level. However, in vitro demonstrations of DNA computations use preprogrammed, rule-based methods which lack the adaptability that may be essential in developing molecular systems that function in dynamic environments. Here, we introduce an in vitro molecular algorithm that ‘learns’ molecular models from training data, opening the possibility of ‘machine learning’ in wet molecular systems. Our algorithm enables enzymatic weight update by targeting internal loop structures in DNA and ensemble learning, based on the hypernetwork model. This novel approach allows massively parallel processing of DNA with enzymes for specific structural selection for learning in an iterative manner. We also introduce an intuitive method of DNA data construction to dramatically reduce the number of unique DNA sequences needed to cover the large search space of feature sets. By combining molecular computing and machine learning the proposed algorithm makes a step closer to developing molecular computing technologies for future access to more intelligent molecular systems.
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Affiliation(s)
- Christina Baek
- Interdisciplinary Program in Neuroscience, Seoul National University, Seoul 08826, Korea.
| | - Sang-Woo Lee
- School of Computer Science and Engineering, Seoul National University, Seoul 08826, Korea.
| | - Beom-Jin Lee
- School of Computer Science and Engineering, Seoul National University, Seoul 08826, Korea.
| | - Dong-Hyun Kwak
- Interdisciplinary Program in Neuroscience, Seoul National University, Seoul 08826, Korea.
| | - Byoung-Tak Zhang
- Interdisciplinary Program in Neuroscience, Seoul National University, Seoul 08826, Korea.
- School of Computer Science and Engineering, Seoul National University, Seoul 08826, Korea.
- Interdisciplinary Program in Cognitive Science, Seoul National University, Seoul 08826, Korea.
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Salehi SA, Liu X, Riedel MD, Parhi KK. Computing Mathematical Functions using DNA via Fractional Coding. Sci Rep 2018; 8:8312. [PMID: 29844537 PMCID: PMC5974329 DOI: 10.1038/s41598-018-26709-6] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Accepted: 05/18/2018] [Indexed: 12/22/2022] Open
Abstract
This paper discusses the implementation of mathematical functions such as exponentials, trigonometric functions, the sigmoid function and the perceptron function with molecular reactions in general, and DNA strand displacement reactions in particular. The molecular constructs for these functions are predicated on a novel representation for input and output values: a fractional encoding, in which values are represented by the relative concentrations of two molecular types, denoted as type-1 and type-0. This representation is inspired by a technique from digital electronic design, termed stochastic logic, in which values are represented by the probability of 1's in a stream of randomly generated 0's and 1's. Research in the electronic realm has shown that a variety of complex functions can be computed with remarkably simple circuitry with this stochastic approach. This paper demonstrates how stochastic electronic designs can be translated to molecular circuits. It presents molecular implementations of mathematical functions that are considerably more complex than any shown to date. All designs are validated using mass-action simulations of the chemical kinetics of DNA strand displacement reactions.
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Affiliation(s)
- Sayed Ahmad Salehi
- Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN, 55455, USA
| | - Xingyi Liu
- Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN, 55455, USA
| | - Marc D Riedel
- Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN, 55455, USA
| | - Keshab K Parhi
- Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN, 55455, USA.
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Lee JH, Lee SH, Baek C, Chun H, Ryu JH, Kim JW, Deaton R, Zhang BT. In vitro molecular machine learning algorithm via symmetric internal loops of DNA. Biosystems 2017; 158:1-9. [PMID: 28465242 DOI: 10.1016/j.biosystems.2017.04.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Revised: 04/12/2017] [Accepted: 04/24/2017] [Indexed: 01/11/2023]
Abstract
Programmable biomolecules, such as DNA strands, deoxyribozymes, and restriction enzymes, have been used to solve computational problems, construct large-scale logic circuits, and program simple molecular games. Although studies have shown the potential of molecular computing, the capability of computational learning with DNA molecules, i.e., molecular machine learning, has yet to be experimentally verified. Here, we present a novel molecular learning in vitro model in which symmetric internal loops of double-stranded DNA are exploited to measure the differences between training instances, thus enabling the molecules to learn from small errors. The model was evaluated on a data set of twenty dialogue sentences obtained from the television shows Friends and Prison Break. The wet DNA-computing experiments confirmed that the molecular learning machine was able to generalize the dialogue patterns of each show and successfully identify the show from which the sentences originated. The molecular machine learning model described here opens the way for solving machine learning problems in computer science and biology using in vitro molecular computing with the data encoded in DNA molecules.
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Affiliation(s)
- Ji-Hoon Lee
- Graduate Program in Bioinformatics, Seoul National University, Seoul, Republic of Korea
| | - Seung Hwan Lee
- School of Chemical and Biological Engineering, Seoul National University, Seoul, Republic of Korea
| | - Christina Baek
- Graduate Program in Brain Science, Seoul National University, Seoul, Republic of Korea
| | - Hyosun Chun
- School of Computer Science and Engineering, Seoul National University, Seoul, Republic of Korea
| | - Je-Hwan Ryu
- Graduate Program in Brain Science, Seoul National University, Seoul, Republic of Korea
| | - Jin-Woo Kim
- Biological and Agricultural Engineering, University of Arkansas, Fayetteville, AR, USA; Bio/Nano Technology Laboratory, Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, AR, USA
| | - Russell Deaton
- Electrical and Computer Engineering, University of Memphis, Memphis, TN,USA
| | - Byoung-Tak Zhang
- Graduate Program in Bioinformatics, Seoul National University, Seoul, Republic of Korea; Graduate Program in Brain Science, Seoul National University, Seoul, Republic of Korea; School of Computer Science and Engineering, Seoul National University, Seoul, Republic of Korea; Graduate Program in Cognitive Science, Seoul National University, Seoul, Republic of Korea.
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Noh YK, Lee DD, Yang KA, Kim C, Zhang BT. Molecular learning with DNA kernel machines. Biosystems 2015; 137:73-83. [PMID: 26163381 DOI: 10.1016/j.biosystems.2015.06.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2015] [Revised: 06/23/2015] [Accepted: 06/25/2015] [Indexed: 11/27/2022]
Abstract
We present a computational learning method for bio-molecular classification. This method shows how to design biochemical operations both for learning and pattern classification. As opposed to prior work, our molecular algorithm learns generic classes considering the realization in vitro via a sequence of molecular biological operations on sets of DNA examples. Specifically, hybridization between DNA molecules is interpreted as computing the inner product between embedded vectors in a corresponding vector space, and our algorithm performs learning of a binary classifier in this vector space. We analyze the thermodynamic behavior of these learning algorithms, and show simulations on artificial and real datasets as well as demonstrate preliminary wet experimental results using gel electrophoresis.
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Affiliation(s)
- Yung-Kyun Noh
- Department of Mechanical and Aerospace Engineering, Seoul National University, Republic of Korea
| | - Daniel D Lee
- Department of Electrical and Systems Engineering, University of Pennsylvania, USA
| | | | - Cheongtag Kim
- Department of Psychology, Seoul National University, Republic of Korea
| | - Byoung-Tak Zhang
- School of Computer Science and Engineering, Seoul National University, Republic of Korea.
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Non-linear molecular pattern classification using molecular beacons with multiple targets. Biosystems 2013; 114:206-13. [PMID: 23743339 DOI: 10.1016/j.biosystems.2013.05.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2012] [Revised: 01/15/2013] [Accepted: 05/21/2013] [Indexed: 11/24/2022]
Abstract
In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns.
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Genot AJ, Bath J, Turberfield AJ. Combinatorial Displacement of DNA Strands: Application to Matrix Multiplication and Weighted Sums. Angew Chem Int Ed Engl 2012. [DOI: 10.1002/ange.201206201] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Genot AJ, Bath J, Turberfield AJ. Combinatorial displacement of DNA strands: application to matrix multiplication and weighted sums. Angew Chem Int Ed Engl 2012. [PMID: 23208800 DOI: 10.1002/anie.201206201] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Anthony J Genot
- Oxford University, Department of Physics, Clarendon Laboratory, South Parks Road, Oxford OX1 3PU, UK
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Lim HW, Lee SH, Yang KA, Yoo SI, Park TH, Zhang BT. Biomolecular computation with molecular beacons for quantitative analysis of target nucleic acids. Biosystems 2012; 111:11-7. [PMID: 23123676 DOI: 10.1016/j.biosystems.2012.09.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2011] [Revised: 06/23/2012] [Accepted: 09/11/2012] [Indexed: 01/08/2023]
Abstract
Molecular beacons are efficient and useful tools for quantitative detection of specific target nucleic acids. Thanks to their simple protocol, molecular beacons have great potential as substrates for biomolecular computing. Here we present a molecular beacon-based biomolecular computing method for quantitative detection and analysis of target nucleic acids. Whereas the conventional quantitative assays using fluorescent dyes have been designed for single target detection or multiplexed detection, the proposed method enables us not only to detect multiple targets but also to compute their quantitative information by weighted-sum of the targets. The detection and computation are performed on a molecular level simultaneously, and the outputs are detected as fluorescence signals. Experimental results show the feasibility and effectiveness of our weighted detection and linear combination method using molecular beacons. Our method can serve as a primitive operation of molecular pattern analysis, and we demonstrate successful binary classifications of molecular patterns made of synthetic oligonucleotide DNA molecules.
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Affiliation(s)
- Hee-Woong Lim
- Center for Biointelligence Technology, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea.
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Neural network computation with DNA strand displacement cascades. Nature 2011; 475:368-72. [PMID: 21776082 DOI: 10.1038/nature10262] [Citation(s) in RCA: 593] [Impact Index Per Article: 45.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2010] [Accepted: 05/31/2011] [Indexed: 11/08/2022]
Abstract
The impressive capabilities of the mammalian brain--ranging from perception, pattern recognition and memory formation to decision making and motor activity control--have inspired their re-creation in a wide range of artificial intelligence systems for applications such as face recognition, anomaly detection, medical diagnosis and robotic vehicle control. Yet before neuron-based brains evolved, complex biomolecular circuits provided individual cells with the 'intelligent' behaviour required for survival. However, the study of how molecules can 'think' has not produced an equal variety of computational models and applications of artificial chemical systems. Although biomolecular systems have been hypothesized to carry out neural-network-like computations in vivo and the synthesis of artificial chemical analogues has been proposed theoretically, experimental work has so far fallen short of fully implementing even a single neuron. Here, building on the richness of DNA computing and strand displacement circuitry, we show how molecular systems can exhibit autonomous brain-like behaviours. Using a simple DNA gate architecture that allows experimental scale-up of multilayer digital circuits, we systematically transform arbitrary linear threshold circuits (an artificial neural network model) into DNA strand displacement cascades that function as small neural networks. Our approach even allows us to implement a Hopfield associative memory with four fully connected artificial neurons that, after training in silico, remembers four single-stranded DNA patterns and recalls the most similar one when presented with an incomplete pattern. Our results suggest that DNA strand displacement cascades could be used to endow autonomous chemical systems with the capability of recognizing patterns of molecular events, making decisions and responding to the environment.
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