Browsing by Subject "DNA computing"

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    Digital logic and signal processing computations with molecular reactions.
    (2012-05) Jiang, Hua
    Just as electronic systems implement computation in terms of voltage (energy per unit charge), molecular systems compute in terms of chemical concentrations (em molecules per unit volume). Broadly, the field strives for molecular implementations of computational processes -- that is to say processes that transform input concentrations of chemical types into output concentrations of chemical types. In this dissertation, we present methodologies to implement digital signal processing (DSP) operations, such as filtering and signal transformation, and digital logic operations, such as latching and flip-flopping, with molecular reactions. Molecular reactions that produce time-varying output quantities of molecules as a function of time-varying input quantities are designed according to a DSP or logic specification. Unlike all previous schemes for molecular computation, the methodology produces designs that are dependent only on coarse rate categories for the reactions ("fast" and "slow"). Given such categories, the computation is exact and independent of the specific reaction rates. We first present a methodology for implementing DSP through a globally synchronous, locally asynchornous scheme we call the RGB scheme. We then present a general methodology for implementing synchronous sequential computation. We generate a four-phase clock signal through robust, sustained chemical oscillations. We implement memory elements by transferring concentrations between molecular types in alternating phases of the clock. Thirdly, we propose a general methodology for implementing asynchronous sequential computation, including a method to schedule data flow for feed-forward systems and a method to implement systems with feedback loops. Finally, we present a methodology for systematic synthesis of various types of sequential digital logic. Given a system specification, a chemical reaction network is synthesized to perform the input/output logic functions. Synthesized systems are concise and robust in that computation accuracy does not depend on specific values of rate constants. All designs are mapped into DNA strand displacement reactions and validated through transient simulations of the chemical kinetics at the DNA reactions level.
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    A Framework for Computing Discrete-Time Systems and Functions using DNA
    (2017-07) Salehi, sayed ahmad
    Due to the recent advances in the field of synthetic biology, molecular computing has emerged as a non-conventional computing technology. A broad range of computational processes has been considered for molecular implementation. In this dissertation, we investigate the development of molecular systems for performing the following computations: signal processing, Markov chains, polynomials, and mathematical functions. First, we present a \textit{fully asynchronous} framework to design molecular signal processing algorithms. The framework maps each delay unit to two molecular types, i.e., first-type and second-type, and provides a 4-phase scheme to synchronize data flow for any multi-input/multi-output signal processing system. In the first phase, the input signal and values stored in all delay elements are consumed for computations. Results of computations are stored in the first-type molecules corresponding to the delay units and output variables. During the second phase, the values of the first-type molecules are transferred to the second-type molecules for the output variable. In the third phase, the concentrations of the first-type molecules are transferred to the second-type molecules associated with each delay element. Finally, in the fourth phase, the output molecules are collected. The method is illustrated by synthesizing a simple finite-impulse response (FIR) filter, an infinite-impulse response (IIR) filter, and an 8-point real-valued fast Fourier transform (FFT). The simulation results show that the proposed framework provides faster molecular signal processing systems compared to prior frameworks. We then present an overview of how continuous-time, discrete-time and digital signal processing systems can be implemented using molecular reactions. We also present molecular sensing systems where molecular reactions are used to implement analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). These converters can be used to design mixed-signal processing molecular systems. A complete example of the addition of two molecules using digital implementation is described where the concentrations of two molecules are converted to digital by two 3-bit ADCs, and the 4-bit output of the digital adder is converted to analog by a 4-bit DAC. Furthermore, we describe implementation of other forms of molecular computation. We propose an approach to implement any first-order Markov chain using molecular reactions in general and DNA in particular. The Markov chain consists of two parts: a set of states and state transition probabilities. Each state is modeled by a unique molecular type, referred to as a data molecule. Each state transition is modeled by a unique molecular type, referred to as a control molecule, and a unique molecular reaction. Each reaction consumes data molecules of one state and produces data molecules of another state. The concentrations of control molecules are initialized according to the probabilities of corresponding state transitions in the chain. The steady-state probability of the Markov chain is computed by the equilibrium concentration of data molecules. We demonstrate our method for the Gambler’s Ruin problem as an instance of the Markov chain process. We analyze the method according to both the stochastic chemical kinetics and the mass-action kinetics model. Additionally, we propose a novel {\em unipolar molecular encoding} approach to compute a certain class of polynomials. In this molecular encoding, each variable is represented using two molecular types: a \mbox{type-0} and a \mbox{type-1}. The value is the ratio of the concentration of type-1 molecules to the sum of the concentrations of \mbox{type-0} and \mbox{type-1} molecules. With the new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these polynomials can be expressed as linear combinations of Bernstein basis polynomials with positive coefficients less than or equal to 1. The proposed encoding naturally exploits the expansion of a power-form polynomial into a Bernstein polynomial. We present molecular encoders for converting any input in a standard representation to the fractional representation, as well as decoders for converting the computed output from the fractional to a standard representation. Lastly, we expand the unipolar molecular encoding for bipolar molecular encoding and propose simple molecular circuits that can compute multiplication and scaled addition. Using these circuits, we design molecular circuits to compute more complex mathematical functions such as $e^{-x}$, $\sin (x)$, and sigmoid$(x)$. According to this approach, we implement a molecular perceptron as a simple artificial neural network.
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    Machine Learning Systems Design using Molecular and DNA Reactions
    (2023-08) Liu, Xingyi
    There is a growing recognition that machine learning can play an important role in a wide range of critical applications, such as data mining, natural language processing, and biomedical applications. Design and synthesis of molecular machine learning systems are of interest as these have the potential to revolutionize applications such as in-situ protein monitoring, drug delivery, and molecular therapy. In modern practice, a disease is diagnosed by collecting data from a body sensor, analyzing the data in a computer or laboratory to diagnose a disease, and then delivering a therapy for either prevention or cure. In the proposed molecular biomedicine framework, the sensing, analytics, feature computation, and therapy would all be in the same place, i.e., in-vivo. In this dissertation, we synthesize different machine learning systems through molecular reactions, where inputs and outputs are chemical molecules, e.g., DNA strands. First, we propose a novel approach to synthesize molecular reactions to compute a radial basis function (RBF) support vector machine (SVM) kernel. The approach is based on fractional coding where a variable is represented by two molecules. The synergy between fractional coding in molecular computing and stochastic logic implementations in electronic computing is key to translating known stochastic logic circuits to molecular computing. We introduce a new explicit bipolar-to-unipolar molecular converter for intermediate format conversion. Two designs are presented; one is based on the explicit and the other is based on an implicit conversion from prior stochastic logic. When five support vectors are used, it is shown that the DNA RBF-SVM realized using the explicit format conversion has orders of magnitude less regression error than that based on implicit conversion. Second, we present an innovative method for synthesizing molecular reactions with the aim of training a perceptron, i.e., a single-layered neural network, with a sigmoidal activation function. The approach is also based on fractional coding. A new molecular scaler that performs multiplication by a factor greater than 1 is proposed based on fractional coding. The training of the perceptron proposed is based on a modified backpropagation equation as the exact equation cannot be easily mapped to molecular reactions using fractional coding. Third, we present the 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. We make 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 a > 1. 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. We then present 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. 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. We utilize the n-phase molecular oscillator (n >= 3). 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. Finally, we propose molecular and DNA memristors where the state is defined by a single output variable. Past molecular and DNA memristors defined the state of the memristor based on two output variables. The prior memristors cannot be cascaded because their input and output sizes are different. We introduce a different definition of state for the molecular and DNA memristors. This change allows cascading of memristors. The proposed memristors are used to build reservoir computing (RC) models. We also study the input-state characteristics of the cascaded memristors and show that the cascaded memristors retain the memristive behavior. The cascade connections in a reservoir can change dynamically; this allows the synthesis of a dynamic reservoir as opposed to a static one in the prior work. This reduces the number of memristors significantly compared to a static reservoir. The inputs to the readout layer correspond to one molecule per state instead of two; this significantly reduces the number of molecular and DNA reactions for the readout layer. A DNA RC system consisting of DNA memristors and a DNA readout layer can be used to solve the seizure detection task. We also demonstrate that a DNA RC system consisting of three cascaded DNA memristors and a DNA readout layer can be used to solve the time-series prediction task.