Synthetic Biology: A Unifying View and Review Using Analog Circuits

Synthetic biological neural networks: From current implementations to future perspectives

Artificial neural networks, inspired by the biological networks of the human brain, have become game-changing computing models in modern computer science. Inspired by their wide scope of applications, synthetic biology strives to create their biological counterparts, which we denote synthetic biological neural networks (SYNBIONNs). Their use in the fields of medicine, biosensors, biotechnology, and many more shows great potential and presents exciting possibilities. So far, many different synthetic biological networks have been successfully constructed, however, SYNBIONN implementations have been sparse. The latter are mostly based on neural networks pretrained in silico and being heavily dependent on extensive human input. In this paper, we review current implementations and models of SYNBIONNs. We briefly present the biological platforms that show potential for designing and constructing perceptrons and/or multilayer SYNBIONNs. We explore their future possibilities along with the challenges that must be overcome to successfully implement a scalable in vivo biological neural network capable of online learning.

Drug Cocktail Formulation via Circuit Design

Electronic circuits intuitively visualize and quantitatively simulate biological systems with nonlinear differential equations that exhibit complicated dynamics. Drug cocktail therapies are a powerful tool against diseases that exhibit such dynamics. We show that just six key states, which are represented in a feedback circuit, enable drug-cocktail formulation: 1) healthy cell number; 2) infected cell number; 3) extracellular pathogen number; 4) intracellular pathogenic molecule number; 5) innate immune system strength; and 6) adaptive immune system strength. To enable drug cocktail formulation, the model represents the effects of the drugs in the circuit. For example, a nonlinear feedback circuit model fits measured clinical data, represents cytokine storm and adaptive autoimmune behavior, and accounts for age, sex, and variant effects for SARS-CoV-2 with few free parameters. The latter circuit model provided three quantitative insights on the optimal timing and dosage of drug components in a cocktail: 1) antipathogenic drugs should be given early in the infection, but immunosuppressant timing involves a tradeoff between controlling pathogen load and mitigating inflammation; 2) both within and across-class combinations of drugs have synergistic effects; 3) if they are administered sufficiently early in the infection, anti-pathogenic drugs are more effective at mitigating autoimmune behavior than immunosuppressant drugs.

Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations

Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical equations describing the kinetics of biochemical reactions can be exactly mapped to the dynamics of voltages and currents in simple electronic circuits wherein voltages represent molecular concentrations and currents represent molecular fluxes. For example, we theoretically derive and experimentally verify accurate circuit models for Michaelis-Menten kinetics. Then, we show that such circuit models can be scaled via simple wiring among circuit motifs to represent more and arbitrarily complex reactions. Hence, we can directly map reaction networks to equivalent circuit schematics in a rapid, quantitatively accurate, and intuitive fashion without needing mathematical equations. We verify experimentally that these circuit models are quantitatively accurate. Examples include 1) different mechanisms of competitive, noncompetitive, uncompetitive, and mixed enzyme inhibition, important for understanding pharmacokinetics; 2) product-feedback inhibition, common in biochemistry; 3) reversible reactions; 4) multi-substrate enzymatic reactions, both important in many metabolic pathways; and 5) translation and transcription dynamics in a cell-free system, which brings insight into the functioning of all gene-protein networks. We envision that circuit modeling and simulation could become a powerful scientific communication language and tool for quantitative studies of kinetics in biology and related fields.

Catalyst-Based Biomolecular Logic Gates

Regulatory processes in biology can be re-conceptualized in terms of logic gates, analogous to those in computer science. Frequently, biological systems need to respond to multiple, sometimes conflicting, inputs to provide the correct output. The language of logic gates can then be used to model complex signal transduction and metabolic processes. Advances in synthetic biology in turn can be used to construct new logic gates, which find a variety of biotechnology applications including in the production of high value chemicals, biosensing, and drug delivery. In this review, we focus on advances in the construction of logic gates that take advantage of biological catalysts, including both protein-based and nucleic acid-based enzymes. These catalyst-based biomolecular logic gates can read a variety of molecular inputs and provide chemical, optical, and electrical outputs, allowing them to interface with other types of biomolecular logic gates or even extend to inorganic systems. Continued advances in molecular modeling and engineering will facilitate the construction of new logic gates, further expanding the utility of biomolecular computing.

Exponential Function Computation Based on DNA Strand Displacement Circuits

Due to its high programmability and storage, DNA circuits have been widely used in biological computing. In this paper, the addition, subtraction, multiplication, division, n-order and 1/n-order gates are built through DNA strand displacement reactions. The chemical reaction networks of the exponential function are established by using the six DNA analog computation gates. The integrated DNA strand displacement circuits are built through the chemical reaction networks. The exponential function polynomials can be computed through the integrated DNA strand displacement circuits. Finally, through visual DSD software verification, this design can realise the computation of exponential function polynomials, which provides a reference for solving exponential function equations and neural network computations in the future.

Accelerating Whole-Cell Simulations of mRNA Translation Using a Dedicated Hardware

In recent years, intracellular biophysical simulations have been used with increasing frequency not only for answering basic scientific questions but also in the field of synthetic biology. However, since these models include networks of interaction between millions of components, they are extremely time-consuming and cannot run easily on parallel computers. In this study, we demonstrate for the first time a novel approach addressing this challenge by using a dedicated hardware designed specifically to simulate such processes. As a proof of concept, we specifically focus on mRNA translation, which is the process consuming most of the energy in the cell. We design a hardware that simulates translation in Escherichia coli and Saccharomyces cerevisiae for thousands of mRNAs and ribosomes, which is in orders of magnitude faster than a similar software solution. With the sharp increase in the amount of genomic data available today and the complexity of the corresponding models inferred from them, we believe that the strategy suggested here will become common and can be used among others for simulating entire cells with all gene expression steps.

Measuring and modeling energy and power consumption in living microbial cells with a synthetic ATP reporter

Background

Adenosine triphosphate (ATP) is the main energy carrier in living organisms, critical for metabolism and essential physiological processes. In humans, abnormal regulation of energy levels (ATP concentration) and power consumption (ATP consumption flux) in cells is associated with numerous diseases from cancer, to viral infection and immune dysfunction, while in microbes it influences their responses to drugs and other stresses. The measurement and modeling of ATP dynamics in cells is therefore a critical component in understanding fundamental physiology and its role in pathology. Despite the importance of ATP, our current understanding of energy dynamics and homeostasis in living cells has been limited by the lack of easy-to-use ATP sensors and the lack of models that enable accurate estimates of energy and power consumption related to these ATP dynamics. Here we describe a dynamic model and an ATP reporter that tracks ATP in E. coli over different growth phases.

Results

The reporter is made by fusing an ATP-sensing rrnB P1 promoter with a fast-folding and fast-degrading GFP. Good correlations between reporter GFP and cellular ATP were obtained in E. coli growing in both minimal and rich media and in various strains. The ATP reporter can reliably monitor bacterial ATP dynamics in response to nutrient availability. Fitting the dynamics of experimental data corresponding to cell growth, glucose, acetate, dissolved oxygen, and ATP yielded a mathematical and circuit model. This model can accurately predict cellular energy and power consumption under various conditions. We found that cellular power consumption varies significantly from approximately 0.8 and 0.2 million ATP/s for a tested strain during lag and stationary phases to 6.4 million ATP/s during exponential phase, indicating ~ 8–30-fold changes of metabolic rates among different growth phases. Bacteria turn over their cellular ATP pool a few times per second during the exponential phase and slow this rate by ~ 2–5-fold in lag and stationary phases.

Conclusion

Our rrnB P1-GFP reporter and kinetic circuit model provide a fast and simple way to monitor and predict energy and power consumption dynamics in bacterial cells, which can impact fundamental scientific studies and applied medical treatments in the future.

Information processing based on DNA toehold-mediated strand displacement (TMSD) reaction

SemiSynBio is an emerging topic toward the construction of platforms for next-generation information processing. Recent research has indicated its promising prospect toward information processing including algorithm design and pattern manipulation with the DNA TMSD reaction, which is one of the cores of the SemiSynBio technology route. The DNA TMSD reaction is the process in which an invader strand displaces the incumbent strand from the gate strand through initiation at the exposed toehold domain. Also, the DNA TMSD reaction generally involves three processes: toehold association, branch migration and strand disassociation. Herein, we review the recent progress on information processing with the DNA TMSD reaction. We highlight the diverse developments on information processing with the logic circuit, analog circuit, combinational circuit and information relay with the DNA origami structure. Additionally, we explore the current challenges and various trends toward the design and application of the DNA TMSD reaction in future information processing.

Prediction of Cellular Burden with Host-Circuit Models

Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognized bottleneck in the design of robust circuits. In this tutorial we discuss the use of computational models that integrate gene circuits and the physiology of host cells. Through various use cases, we illustrate the power of host-circuit models to predict the impact of design parameters on both burden and circuit functionality. Our approach relies on a new generation of computational models for microbial growth that can flexibly accommodate resource bottlenecks encountered in gene circuit design. Adoption of this modeling paradigm can facilitate fast and robust design cycles in synthetic biology.

The Merging of Biological and Electronic Circuits

Biological circuits and systems within even a single cell need to be represented by large-scale feedback networks of nonlinear, stochastic, stiff, asynchronous, non-modular coupled differential equations governing complex molecular interactions. Thus, rational drug discovery and synthetic biological design is difficult. We suggest that a four-pronged interdisciplinary approach merging biology and electronics can help: (1) The mapping of biological circuits to electronic circuits via quantitatively exact schematics; (2) The use of existing electronic circuit software for hierarchical modeling, design, and analysis with such schematics; (3) The use of cytomorphic electronic hardware for rapid stochastic simulation of circuit schematics and associated parameter discovery to fit measured biological data; (4) The use of bio-electronic reporting circuits rather than bio-optical circuits for measurement. We suggest how these approaches can be combined to automate design, modeling, analysis, simulation, and quantitative fitting of measured data from a synthetic biological operational amplifier circuit in living microbial cells.

A compiler for biological networks on silicon chips

The explosive growth in semiconductor integrated circuits was made possible in large part by design automation software. The design and/or analysis of synthetic and natural circuits in living cells could be made more scalable using the same approach. We present a compiler which converts standard representations of chemical reaction networks and circuits into hardware configurations that can be used to simulate the network on specialized cytomorphic hardware. The compiler also creates circuit–level models of the target configuration, which enhances the versatility of the compiler and enables the validation of its functionality without physical experimentation with the hardware. We show that this compiler can translate networks comprised of mass–action kinetics, classic enzyme kinetics (Michaelis–Menten, Briggs–Haldane, and Botts–Morales formalisms), and genetic repressor kinetics, thereby allowing a large class of models to be transformed into a hardware representation. Rule–based models are particularly well–suited to this approach, as we demonstrate by compiling a MAP kinase model. Development of specialized hardware and software for simulating biological networks has the potential to enable the simulation of larger kinetic models than are currently feasible or allow the parallel simulation of many smaller networks with better performance than current simulation software.

We present a “silicon compiler” that is capable of translating biochemical models encoded in the SBML standard into specialized analog cytomorphic hardware and transfer function–level simulations of such hardware. We show how the compiler and hardware address challenges in analog computing: 1) We ensure that the integration of errors due to the mismatch between analog circuit parameters does not become infinite over time but always remains finite via the use of total variables (the solution of the “divergence problem”); 2) We describe the compilation process through a series of examples using building blocks of biological networks, and show the results of compiling two SBML models from the literature: the Elowitz repressilator model and a rule–based model of a MAP kinase cascade. Source code for the compiler is available at https://doi.org/10.5281/zenodo.3948393.

Circuits with broken fibration symmetries perform core logic computations in biological networks

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks in biological networks, and present a systematic route to design synthetic biological circuits.

We show that the core functional logic of genetic circuits arises from a fundamental symmetry breaking of the interactions of the biological network. The idea can be put into a hierarchy of symmetric genetic circuits that reveals their logical functions. We do so through a constructive procedure that naturally reveals a series of building blocks, widely present across species. This hierarchy maps to a progression of fundamental units of electronics, starting with the transistor, progressing to ring oscillators and current-mirror circuits and then to synchronized clocks, switches and finally to memory devices such as latches and flip-flops.

Molecular and DNA Artificial Neural Networks via Fractional Coding

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.

On signalling and estimation limits for molecular birth-processes

Understanding and uncovering the mechanisms or motifs that molecular networks employ to regulate noise is a key problem in cell biology. As it is often difficult to obtain direct and detailed insight into these mechanisms, many studies instead focus on assessing the best precision attainable on the signalling pathways that compose these networks. Molecules signal one another over such pathways to solve noise regulating estimation and control problems. Quantifying the maximum precision of these solutions delimits what is achievable and allows hypotheses about underlying motifs to be tested without requiring detailed biological knowledge. The pathway capacity, which defines the maximum rate of transmitting information along it, is a widely used proxy for precision. Here it is shown, for estimation problems involving elementary yet biologically relevant birth-process networks, that capacity can be surprisingly misleading. A time-optimal signalling motif, called birth-following, is derived and proven to better the precision expected from the capacity, provided the maximum signalling rate constraint is large and the mean one above a certain threshold. When the maximum constraint is relaxed, perfect estimation is predicted by the capacity. However, the true achievable precision is found highly variable and sensitive to the mean constraint. Since the same capacity can map to different combinations of rate constraints, it can only equivocally measure precision. Deciphering the rate constraints on a signalling pathway may therefore be more important than computing its capacity.

An Artificial Tissue Homeostasis Circuit Designed via Analog Circuit Techniques

Tissue homeostasis (feedback control) is an important mechanism that regulates the population of different cell types within a tissue. In type-1 diabetes, auto-immune attack and consequent death of pancreatic β cells result in the failure of homeostasis and loss of organ function. Synthetically engineered adult stem cells with homeostatic control based on digital logic have been proposed as a solution for regenerating β cells. Such previously proposed homeostatic control circuits have thus far been unable to reliably control both stem-cell proliferation and stem-cell differentiation. Using analog circuits and feedback systems analysis, we have designed an in silico circuit that performs homeostatic control by utilizing a novel scheme with both symmetric and asymmetric division of stem cells. The use of a variety of feedback systems analysis techniques, which is common in analog circuit design, including root-locus techniques, Bode plots of feedback-loop frequency response, compensation techniques for improving stability, and robustness analysis help us choose design parameters to meet desirable specifications. For example, we show that lead compensation in analog circuits instantiated as an incoherent feed-forward loop in the biological circuit improves stability, whereas simultaneously reducing steady-state tracking error. Our symmetric and asymmetric division scheme also improves phase margin in the feedback loop, and thus improves robustness. This paper could be useful in porting an analog-circuit design framework to synthetic biological applications of the future.

A Novel Bioelectronic Reporter System in Living Cells Tested with a Synthetic Biological Comparator

As the fields of biotechnology and synthetic biology expand, cheap and sensitive tools are needed to measure increasingly complicated genetic circuits. In order to bypass some drawbacks of optical fluorescent reporting systems, we have designed and created a co-culture microbial fuel cell (MFC) system for electronic reporting. This system leverages the syntrophic growth of Escheriachia. coli (E. coli) and an electrogenic bacterium Shewanella oneidensis MR-1 (S. oneidensis). The fermentative products of E. coli provide a carbon and electron source for S. oneidensis MR-1, which then reports on such activity electrically at the anode of the MFC. To further test the capability of electrical reporting of complicated synthetic circuits, a novel synthetic biological comparator was designed and tested with both fluorescent and electrical reporting systems. The results suggest that the electrical reporting system is a good alternative to commonly used optical fluorescent reporter systems since it is a non-toxic reporting system with a much wider dynamic range.

A Synthetic Close-Loop Controller Circuit for the Regulation of an Extracellular Molecule by Engineered Bacteria

Feedback control is ubiquitous in biological systems. It can also play a crucial role in the design of synthetic circuits implementing novel functions in living systems, to achieve self-regulation of gene expression, noise reduction, rise time decrease, or adaptive pathway control. Despite in vitro, in vivo, and ex vivo implementations have been successfully reported, the design of biological close-loop systems with quantitatively predictable behavior is still a major challenge. In this work, we tested a model-based bottom-up design of a synthetic close-loop controller in engineered Escherichia coli, aimed to automatically regulate the concentration of an extracellular molecule, N-(3-oxohexanoyl)-L-homoserine lactone (HSL), by rewiring the elements of heterologous quorum sensing/quenching networks. The synthetic controller was successfully constructed and experimentally validated. Relying on mathematical model and experimental characterization of individual regulatory parts and enzymes, we evaluated the predictability of the interconnected system behavior in vivo. The culture was able to reach an HSL steady-state level of 72 nM, accurately predicted by the model, and showed superior capabilities in terms of robustness against cell density variation and disturbance rejection, compared with a corresponding open-loop circuit. This engineering-inspired design approach may be adopted for the implementation of other close-loop circuits for different applications and contribute to decreasing trial-and-error steps.

A Synthetic Microbial Operational Amplifier

Synthetic biology has created oscillators, latches, logic gates, logarithmically linear circuits, and load drivers that have electronic analogs in living cells. The ubiquitous operational amplifier, which allows circuits to operate robustly and precisely has not been built with biomolecular parts. As in electronics, a biological operational-amplifier could greatly improve the predictability of circuits despite noise and variability, a problem that all cellular circuits face. Here, we show how to create a synthetic three-stage inducer-input operational amplifier with a fast CRISPR-based differential-input push-pull stage, a slow transcription-and-translation amplification stage, and a fast-enzymatic output stage. Our "Bio-OpAmp" uses only 5 proteins including dCas9. It expands the toolkit of fundamental analog circuits in synthetic biology and provides a simple circuit motif for robust and precise molecular homeostasis.

Designing miRNA-Based Synthetic Cell Classifier Circuits Using Answer Set Programming

Cell classifier circuits are synthetic biological circuits capable of distinguishing between different cell states depending on specific cellular markers and engendering a state-specific response. An example are classifiers for cancer cells that recognize whether a cell is healthy or diseased based on its miRNA fingerprint and trigger cell apoptosis in the latter case. Binarization of continuous miRNA expression levels allows to formalize a classifier as a Boolean function whose output codes for the cell condition. In this framework, the classifier design problem consists of finding a Boolean function capable of reproducing correct labelings of miRNA profiles. The specifications of such a function can then be used as a blueprint for constructing a corresponding circuit in the lab. To find an optimal classifier both in terms of performance and reliability, however, accuracy, design simplicity and constraints derived from availability of molcular building blocks for the classifiers all need to be taken into account. These complexities translate to computational difficulties, so currently available methods explore only part of the design space and consequently are only capable of calculating locally optimal designs. We present a computational approach for finding globally optimal classifier circuits based on binarized miRNA datasets using Answer Set Programming for efficient scanning of the entire search space. Additionally, the method is capable of computing all optimal solutions, allowing for comparison between optimal classifier designs and identification of key features. Several case studies illustrate the applicability of the approach and highlight the quality of results in comparison with a state of the art method. The method is fully implemented and a comprehensive performance analysis demonstrates its reliability and scalability.

A Digitally Programmable Cytomorphic Chip for Simulation of Arbitrary Biochemical Reaction Networks

Prior work has shown that compact analog circuits can faithfully represent and model fundamental biomolecular circuits via efficient log-domain cytomorphic transistor equivalents. Such circuits have emphasized basis functions that are dominant in genetic transcription and translation networks and deoxyribonucleic acid (DNA)-protein binding. Here, we report a system featuring digitally programmable 0.35 μm BiCMOS analog cytomorphic chips that enable arbitrary biochemical reaction networks to be exactly represented thus enabling compact and easy composition of protein networks as well. Since all biomolecular networks can be represented as chemical reaction networks, our protein networks also include the former genetic network circuits as a special case. The cytomorphic analog protein circuits use one fundamental association-dissociation-degradation building-block circuit that can be configured digitally to exactly represent any zeroth-, first-, and second-order reaction including loading, dynamics, nonlinearity, and interactions with other building-block circuits. To address a divergence issue caused by random variations in chip fabrication processes, we propose a unique way of performing computation based on total variables and conservation laws, which we instantiate at both the circuit and network levels. Thus, scalable systems that operate with finite error over infinite time can be built. We show how the building-block circuits can be composed to form various network topologies, such as cascade, fan-out, fan-in, loop, dimerization, or arbitrary networks using total variables. We demonstrate results from a system that combines interacting cytomorphic chips to simulate a cancer pathway and a glycolysis pathway. Both simulations are consistent with conventional software simulations. Our highly parallel digitally programmable analog cytomorphic systems can lead to a useful design, analysis, and simulation tool for studying arbitrary large-scale biological networks in systems and synthetic biology.

Cellular Biosensors with Engineered Genetic Circuits

An increasing interest in building novel biological devices with designed cellular functionalities has triggered the search of innovative tools for biocomputation. Utilizing the tools of synthetic biology, numerous genetic circuits have been implemented such as engineered logic operation in analog and digital circuits. Whole cell biosensors are widely used biological devices that employ several biocomputation tools to program cells for desired functions. Up to the present date, a wide range of whole-cell biosensors have been designed and implemented for disease theranostics, biomedical applications, and environmental monitoring. In this review, we investigated the recent developments in biocomputation tools such as analog, digital, and mix circuits, logic gates, switches, and state machines. Additionally, we stated the novel applications of biological devices with computing functionalities for diagnosis and therapy of various diseases such as infections, cancer, or metabolic diseases, as well as the detection of environmental pollutants such as heavy metals or organic toxic compounds. Current whole-cell biosensors are innovative alternatives to classical biosensors; however, there is still a need to advance decision making capabilities by developing novel biocomputing devices.

Bioelectronic measurement and feedback control of molecules in living cells

We describe an electrochemical measurement technique that enables bioelectronic measurements of reporter proteins in living cells as an alternative to traditional optical fluorescence. Using electronically programmable microfluidics, the measurement is in turn used to control the concentration of an inducer input that regulates production of the protein from a genetic promoter. The resulting bioelectronic and microfluidic negative-feedback loop then serves to regulate the concentration of the protein in the cell. We show measurements wherein a user-programmable set-point precisely alters the protein concentration in the cell with feedback-loop parameters affecting the dynamics of the closed-loop response in a predictable fashion. Our work does not require expensive optical fluorescence measurement techniques that are prone to toxicity in chronic settings, sophisticated time-lapse microscopy, or bulky/expensive chemo-stat instrumentation for dynamic measurement and control of biomolecules in cells. Therefore, it may be useful in creating a: cheap, portable, chronic, dynamic, and precise all-electronic alternative for measurement and control of molecules in living cells.

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Chemical reaction networks for computing logarithm

Living cells constantly process information from their living environment. It has recently been shown that a number of cell signaling mechanisms (e.g. G protein-coupled receptor and epidermal growth factor) can be interpreted as computing the logarithm of the ligand concentration. This suggests that logarithm is a fundamental computation primitive in cells. There is also an increasing interest in the synthetic biology community to implement analog computation and computing the logarithm is one such example. The aim of this article is to study how the computation of logarithm can be realized using chemical reaction networks (CRNs). CRNs cannot compute logarithm exactly. A standard method is to use power series or rational function approximation to compute logarithm approximately. Although CRNs can realize these polynomial or rational function computations in a straightforward manner, the issue is that in order to be able to compute logarithm accurately over a large input range, it is necessary to use high-order approximation that results in CRNs with a large number of reactions. This article proposes a novel method to compute logarithm accurately in CRNs while keeping the number of reactions in CRNs low. The proposed method can create CRNs that can compute logarithm to different levels of accuracy by adjusting two design parameters. In this article, we present the chemical reactions required to realize the CRNs for computing logarithm. The key contribution of this article is a novel method to create CRNs that can compute logarithm accurately over a wide input range using only a small number of chemical reactions.

Exploiting the dynamic properties of covalent modification cycle for the design of synthetic analog biomolecular circuitry

Background

Cycles of covalent modification are ubiquitous motifs in cellular signalling. Although such signalling cycles are implemented via a highly concise set of chemical reactions, they have been shown to be capable of producing multiple distinct input-output mapping behaviours – ultrasensitive, hyperbolic, signal-transducing and threshold-hyperbolic.

Results

In this paper, we show how the set of chemical reactions underlying covalent modification cycles can be exploited for the design of synthetic analog biomolecular circuitry. We show that biomolecular circuits based on the dynamics of covalent modification cycles allow (a) the computation of nonlinear operators using far fewer chemical reactions than purely abstract designs based on chemical reaction network theory, and (b) the design of nonlinear feedback controllers with strong performance and robustness properties.

Conclusions

Our designs provide a more efficient route for translation of complex circuits and systems from chemical reactions to DNA strand displacement-based chemistry, thus facilitating their experimental implementation in future Synthetic Biology applications.

Systematic Design of a Quorum Sensing-Based Biosensor for Enhanced Detection of Metal Ion in Escherichia Coli

With the recent industrial expansion, heavy metals and other pollutants have increasingly contaminated our living surroundings. The non-degradability of heavy metals may lead to accumulation in food chains and the resulting toxicity could cause damage in organisms. Hence, detection techniques have gradually received attention. In this study, a quorum sensing (QS)-based amplifier is introduced to improve the detection performance of metal ion biosensing. The design utilizes diffusible signal molecules, which freely pass through the cell membrane into the environment to communicate with others. Bacteria cooperate via the cell-cell communication process, thereby displaying synchronous behavior, even if only a minority of the cells detect the metal ion. In order to facilitate the design, the ability of the engineered biosensor to detect metal ion is described in a steady state model. The design can be constructed according to user-oriented specifications by selecting adequate components from corresponding libraries, with the help of a genetic algorithm (GA)-based design method. The experimental results validate enhanced efficiency and detection performance of the quorum sensing-based biosensor of metal ions.