Forward engineering of synthetic bio-logical AND gates

Modularized Design and Construction of Tunable Microbial Consortia with Flexible Topologies

Complex and fluid bacterial community compositions are critical to diversity, stability, and function. However, quantitative and mechanistic descriptions of the dynamics of such compositions are still lacking. Here, we develop a modularized design framework that allows for bottom-up construction and the study of synthetic bacterial consortia with different topologies. We showcase the microbial consortia design and building process by constructing amensalism and competition consortia using only genetic circuit modules to engineer different strains to form the community. Functions of modules and hosting strains are validated and quantified to calibrate dynamic parameters, which are then directly fed into a full mechanistic model to accurately predict consortia composition dynamics for both amensalism and competition without further fitting. More importantly, such quantitative understanding successfully identifies the experimental conditions to achieve coexistence composition dynamics. These results illustrate the process of both computationally and experimentally building up bacteria consortia complexity and hence achieve robust control of such fluid systems.

Reservoir Computing Using DNA Oscillators

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.

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.

Programming the Dynamic Control of Bacterial Gene Expression with a Chimeric Ligand- and Light-Based Promoter System

To program cells in a dynamic manner, synthetic biologists require precise control over the threshold levels and timing of gene expression. However, in practice, modulating gene expression is widely carried out using prototypical ligand-inducible promoters, which have limited tunability and spatiotemporal resolution. Here, we built two dual-input hybrid promoters, each retaining the function of the ligand-inducible promoter while being enhanced with a blue-light-switchable tuning knob. Using the new promoters, we show that both ligand and light inputs can be synchronously modulated to achieve desired amplitude or independently regulated to generate desired frequency at a specific amplitude. We exploit the versatile programmability and orthogonality of the two promoters to build the first reprogrammable logic gene circuit capable of reconfiguring into logic OR and N-IMPLY logic on the fly in both space and time without the need to modify the circuit. Overall, we demonstrate concentration- and time-based combinatorial regulation in live bacterial cells with potential applications in biotechnology and synthetic biology.

Computing Mathematical Functions using DNA via Fractional Coding

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.

Tuning the dynamic range of bacterial promoters regulated by ligand-inducible transcription factors

One challenge for synthetic biologists is the predictable tuning of genetic circuit regulatory components to elicit desired outputs. Gene expression driven by ligand-inducible transcription factor systems must exhibit the correct ON and OFF characteristics: appropriate activation and leakiness in the presence and absence of inducer, respectively. However, the dynamic range of a promoter (i.e., absolute difference between ON and OFF states) is difficult to control. We report a method that tunes the dynamic range of ligand-inducible promoters to achieve desired ON and OFF characteristics. We build combinatorial sets of AraC-and LasR-regulated promoters containing -10 and -35 sites from synthetic and Escherichia coli promoters. Four sequence combinations with diverse dynamic ranges were chosen to build multi-input transcriptional logic gates regulated by two and three ligand-inducible transcription factors (LacI, TetR, AraC, XylS, RhlR, LasR, and LuxR). This work enables predictable control over the dynamic range of regulatory components.

Multiplexing Engineered Receptors for Multiparametric Evaluation of Environmental Ligands

Engineered cell-based therapies comprise a promising, emerging biomedical technology. Broad utilization of this strategy will require new approaches for implementing sophisticated functional programs, such as sensing and responding to the environment in a defined fashion. Toward this goal, we investigated whether our self-contained receptor and signal transduction system (MESA) could be multiplexed to evaluate extracellular cues, with a focus on elucidating principles governing the integration of such engineered components. We first developed a set of hybrid promoters that exhibited AND gate activation by two transcription factors. We then evaluated these promoters when paired with two MESA receptors and various ligand combinations. Unexpectedly, although the multiplexed system exhibited distinct responses to ligands applied individually and in combination, the same synergy was not observed as when promoters were characterized with soluble transcription factors. Therefore, we developed a mechanistic computational model leveraging these observations, to both improve our understanding of how the receptors and promoters interface and to guide the design and implementation of future systems. Notably, the model explicitly accounts for the impact of intercellular variation on system characterization and performance. Model analysis identified key factors that affect the current receptors and promoters, and enabled an in silico exploration of potential modifications that inform the design of improved logic gates and their robustness to intercellular variation. Ultimately, this quantitative design-driven approach may guide the use and multiplexing of synthetic receptors for diverse custom biological functions beyond the case study considered here.

Novel Utilization of Terminators in the Design of Biologically Adjustable Synthetic Filters

Terminators, which signal the end of transcription processes, are typically placed behind the last coding sequence of an operon to prevent interference between transcript units in most biologically synthetic systems. Here, we seek to extend the usability of terminators in genetic system design by using terminators as regulatory genetic parts. Terminators with different impacts on their upstream and downstream genes are characterized in detail via dynamic modeling to predict the behavior of the overall genetic system. Some nonlinear effects of terminators observed in our terminator measurements potentially facilitate regulation of gene expression. Through dynamic modeling in silico, we find that such genetic systems may behave like genetic filters. In agreement with the simulations, we successfully implement genetic high-pass and bandpass filters in vivo, demonstrating the potential of using terminators as regulatory parts. The genetic bandpass filter in this work is implemented through the interdependence between genetic parts, in which the termination efficiency of a terminator varies with the strength of the upstream promoter. This design strategy for a bandpass filter requires fewer base pairs than the conventional strategy of concatenating high-pass and low-pass filters. Our results show that this novel utilization of terminators as regulatory parts may provide a new perspective for efficient design of genetic circuits. We believe that further exploration of the complicated dynamics of terminators is important in the development of synthetic biology.

Chemical master equation closure for computer-aided synthetic biology

With inexpensive DNA synthesis technologies, we can now construct biological systems by quickly piecing together DNA sequences. Synthetic biology is the promising discipline that focuses on the construction of these new biological systems. Synthetic biology is an engineering discipline, and as such, it can benefit from mathematical modeling. This chapter focuses on mathematical models of biological systems. These models take the form of chemical reaction networks. The importance of stochasticity is discussed and methods to simulate stochastic reaction networks are reviewed. A closure scheme solution is also presented for the master equation of chemical reaction networks. The master equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks for over 70 years. With the first complete solution of chemical master equations, a wide range of experimental observations of biomolecular interactions may be mathematically conceptualized. We anticipate that models based on the closure scheme described herein may assist in rationally designing synthetic biological systems.

Artificial cell-cell communication as an emerging tool in synthetic biology applications

Cell-cell communication is a widespread phenomenon in nature, ranging from bacterial quorum sensing and fungal pheromone communication to cellular crosstalk in multicellular eukaryotes. These communication modes offer the possibility to control the behavior of an entire community by modifying the performance of individual cells in specific ways. Synthetic biology, i.e., the implementation of artificial functions within biological systems, is a promising approach towards the engineering of sophisticated, autonomous devices based on specifically functionalized cells. With the growing complexity of the functions performed by such systems, both the risk of circuit crosstalk and the metabolic burden resulting from the expression of numerous foreign genes are increasing. Therefore, systems based on a single type of cells are no longer feasible. Synthetic biology approaches with multiple subpopulations of specifically functionalized cells, wired by artificial cell-cell communication systems, provide an attractive and powerful alternative. Here we review recent applications of synthetic cell-cell communication systems with a specific focus on recent advances with fungal hosts.

Investigation of Changes in Tetracycline Repressor Binding upon Mutations in the Tetracycline Operator

The tetracycline operon is an important gene network component, commonly used in synthetic biology applications because of its switch-like character. At the heart of this system is the highly specific interaction of the tet repressor protein (TetR) with its cognate DNA sequence (tetO). TetR binding on tetO practically stops expression of genes downstream of tetO by excluding RNA polymerase from binding the promoter and initiating transcription. Mutating the tetO sequence alters the strength of TetR-tetO binding and thus provides a tool to synthetic biologists to manipulate gene expression levels. We employ molecular dynamics (MD) simulations coupled with the free energy perturbation method to investigate the binding affinity of TetR to different tetO mutants. We also carry out in vivo tests in Escherichia coli for a series of promoters based on these mutants. We obtain reasonable agreement between experimental green fluorescent protein (GFP) repression levels and binding free energy differences computed from molecular simulations. In all cases, the wild-type tetO sequence yields the strongest TetR binding, which is observed both experimentally, in terms of GFP levels, and in simulation, in terms of free energy changes. Two of the four tetO mutants we tested yield relatively strong binding, whereas the other two mutants tend to be significantly weaker. The clustering and relative ranking of this subset of tetO mutants is generally consistent between our own experimental data, previous experiments with different systems and the free energy changes computed from our simulations. Overall, this work offers insights into an important synthetic biological system and demonstrates the potential, as well as limitations of molecular simulations to quantitatively explain biologically relevant behavior.

Modular, multi-input transcriptional logic gating with orthogonal LacI/GalR family chimeras

In prokaryotes, the construction of synthetic, multi-input promoters is constrained by the number of transcription factors that can simultaneously regulate a single promoter. This fundamental engineering constraint is an obstacle to synthetic biologists because it limits the computational capacity of engineered gene circuits. Here, we demonstrate that complex multi-input transcriptional logic gating can be achieved through the use of ligand-inducible chimeric transcription factors assembled from the LacI/GalR family. These modular chimeras each contain a ligand-binding domain and a DNA-binding domain, both of which are chosen from a library of possibilities. When two or more chimeras have the same DNA-binding domain, they independently and simultaneously regulate any promoter containing the appropriate operator site. In this manner, simple transcriptional AND gating is possible through the combination of two chimeras, and multiple-input AND gating is possible with the simultaneous use of three or even four chimeras. Furthermore, we demonstrate that orthogonal DNA-binding domains and their cognate operators allow the coexpression of multiple, orthogonal AND gates. Altogether, this work provides synthetic biologists with novel, ligand-inducible logic gates and greatly expands the possibilities for engineering complex synthetic gene circuits.

Optimal part and module selection for synthetic gene circuit design automation

An integral challenge in synthetic circuit design is the selection of optimal parts to populate a given circuit topology, so that the resulting circuit behavior best approximates the desired one. In some cases, it is also possible to reuse multipart constructs or modules that have been already built and experimentally characterized. Efficient part and module selection algorithms are essential to systematically search the solution space, and their significance will only increase in the following years due to the projected explosion in part libraries and circuit complexity. Here, we address this problem by introducing a structured abstraction methodology and a dynamic programming-based algorithm that guaranties optimal part selection. In addition, we provide three extensions that are based on symmetry check, information look-ahead and branch-and-bound techniques, to reduce the running time and space requirements. We have evaluated the proposed methodology with a benchmark of 11 circuits, a database of 73 parts and 304 experimentally constructed modules with encouraging results. This work represents a fundamental departure from traditional heuristic-based methods for part and module selection and is a step toward maximizing efficiency in synthetic circuit design and construction.

Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks

Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized.

Principles of genetic circuit design

Cells navigate environments, communicate and build complex patterns by initiating gene expression in response to specific signals. Engineers seek to harness this capability to program cells to perform tasks or create chemicals and materials that match the complexity seen in nature. This Review describes new tools that aid the construction of genetic circuits. Circuit dynamics can be influenced by the choice of regulators and changed with expression 'tuning knobs'. We collate the failure modes encountered when assembling circuits, quantify their impact on performance and review mitigation efforts. Finally, we discuss the constraints that arise from circuits having to operate within a living cell. Collectively, better tools, well-characterized parts and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the atomic manufacturing of functional materials.

Quorum sensing-modulated AND-gate promoters control gene expression in response to a combination of endogenous and exogenous signals

We have constructed and characterized two synthetic AND-gate promoters that require both a quorum-sensing (QS) signal and an exogenously added inducer to turn on gene expression. The engineered promoters, LEE and TTE, contain binding sites for the QS-dependent repressor, EsaR, and either LacI or TetR, and they are induced by an acyl-homoserine lactone (AHL) signal and IPTG or aTc. Although repression of both LEE and TTE by wild-type EsaR was observed, induction of gene expression at physiologically relevant concentrations of AHL required the use of an EsaR variant with higher signal sensitivity. Gene expression from both LEE and TTE was shown to require both signal molecules, and gene expression above background levels was not observed with either signal alone. We added endogenous production of AHL to evaluate the ability of the promoters to function in a QS-dependent manner and observed that gene expression increased as a function of cell density only in the presence of exogenously added IPTG or aTc. Cell-cell communication-dependent AND-gate behaviors were demonstrated using an agar plate assay, where cells containing the engineered promoters were shown to respond to AHL produced by a second E. coli strain only in the presence of exogenously added IPTG or aTc. The promoters described in this work demonstrate that EsaR and its target DNA sequence can be used to engineer new promoters to respond to cell density or cell-cell communication. Further, the AND-gate promoters described here may serve as a template for new regulatory systems that integrate QS and the presence of key metabolites or other environmental cues to enable dynamic changes in gene expression for metabolic engineering applications.

Discrete-time signal processing with DNA

We present a methodology for implementing discrete-time signal processing operations, such as filtering, with molecular reactions. The reactions produce time-varying output quantities of molecules as a function of time-varying input quantities according to a functional specification. This computation is robust and independent of the reaction rates, provided that the rate constants fall within coarse categories. We describe two approaches: one entails synchronization with a clock signal, implemented through sustained chemical oscillations; the other is "self-timed" or asynchronous. We illustrate the methodology by synthesizing a simple moving-average filter, a biquad filter, and a Fast Fourier Transform (FFT). Abstract molecular reactions for these filters and transforms are translated into DNA strand displacement reactions. The computation is validated through mass-action simulations of the DNA kinetics. Although a proof of concept for the time being, molecular filters and transforms have potential applications in fields such as biochemical sensing and drug delivery.

Directed evolution of the quorum-sensing regulator EsaR for increased signal sensitivity

The use of cell-cell communication or "quorum sensing (QS)" elements from Gram-negative Proteobacteria has enabled synthetic biologists to begin engineering systems composed of multiple interacting organisms. However, additional tools are necessary if we are to progress toward synthetic microbial consortia that exhibit more complex, dynamic behaviors. EsaR from Pantoea stewartii subsp. stewartii is a QS regulator that binds to DNA as an apoprotein and releases the DNA when it binds to its cognate signal molecule, 3-oxohexanoyl-homoserine lactone (3OC6HSL). In the absence of 3OC6HSL, EsaR binds to DNA and can act as either an activator or a repressor of transcription. Gene expression from P(esaR), which is repressed by wild-type EsaR, requires 100- to 1000-fold higher concentrations of signal than commonly used QS activators, such as LuxR and LasR. Here we have identified EsaR variants with increased sensitivity to 3OC6HSL using directed evolution and a dual ON/OFF screening strategy. Although we targeted EsaR-dependent derepression of P(esaR), our EsaR variants also showed increased 3OC6HSL sensitivity at a second promoter, P(esaS), which is activated by EsaR in the absence of 3OC6HSL. Here, the increase in AHL sensitivity led to gene expression being turned off at lower concentrations of 3OC6HSL. Overall, we have increased the signal sensitivity of EsaR more than 70-fold and generated a set of EsaR variants that recognize 3OC6HSL concentrations ranging over 4 orders of magnitude. QS-dependent transcriptional regulators that bind to DNA and are active in the absence of a QS signal represent a new set of tools for engineering cell-cell communication-dependent gene expression.

Stochastic model reduction using a modified Hill-type kinetic rate law

In the present work, we address a major challenge facing the modeling of biochemical reaction networks: when using stochastic simulations, the computational load and number of unknown parameters may dramatically increase with system size and complexity. A proposed solution to this challenge is the reduction of models by utilizing nonlinear reaction rate laws in place of a complex multi-reaction mechanism. This type of model reduction in stochastic systems often fails when applied outside of the context in which it was initially conceived. We hypothesize that the use of nonlinear rate laws fails because a single reaction is inherently Poisson distributed and cannot match higher order statistics. In this study we explore the use of Hill-type rate laws as an approximation for gene regulation, specifically transcription repression. We matched output data for several simple gene networks to determine Hill-type parameters. We show that the models exhibit inaccuracies when placed into a simple feedback repression model. By adding an additional abstract reaction to the models we account for second-order statistics. This split Hill rate law matches higher order statistics and demonstrates that the new model is able to more accurately describe the mean protein output. Finally, the modified Hill model is shown to be modular and models retain accuracy when placed into a larger multi-gene network. The work as presented may be used in gene regulatory or cell-signaling networks, where multiple binding events can be captured by Hill kinetics. The added benefit of the proposed split-Hill kinetics is the improved accuracy in modeling stochastic effects. We demonstrate these benefits with a few specific reaction network examples.

Modular control of multiple pathways using engineered orthogonal T7 polymerases

Synthetic genetic sensors and circuits enable programmable control over the timing and conditions of gene expression. They are being increasingly incorporated into the control of complex, multigene pathways and cellular functions. Here, we propose a design strategy to genetically separate the sensing/circuitry functions from the pathway to be controlled. This separation is achieved by having the output of the circuit drive the expression of a polymerase, which then activates the pathway from polymerase-specific promoters. The sensors, circuits and polymerase are encoded together on a 'controller' plasmid. Variants of T7 RNA polymerase that reduce toxicity were constructed and used as scaffolds for the construction of four orthogonal polymerases identified via part mining that bind to unique promoter sequences. This set is highly orthogonal and induces cognate promoters by 8- to 75-fold more than off-target promoters. These orthogonal polymerases enable four independent channels linking the outputs of circuits to the control of different cellular functions. As a demonstration, we constructed a controller plasmid that integrates two inducible systems, implements an AND logic operation and toggles between metabolic pathways that change Escherichia coli green (deoxychromoviridans) and red (lycopene). The advantages of this organization are that (i) the regulation of the pathway can be changed simply by introducing a different controller plasmid, (ii) transcription is orthogonal to host machinery and (iii) the pathway genes are not transcribed in the absence of a controller and are thus more easily carried without invoking evolutionary pressure.

Stochastic simulations of a synthetic bacteria-yeast ecosystem

BACKGROUND

The field of synthetic biology has greatly evolved and numerous functions can now be implemented by artificially engineered cells carrying the appropriate genetic information. However, in order for the cells to robustly perform complex or multiple tasks, co-operation between them may be necessary. Therefore, various synthetic biological systems whose functionality requires cell-cell communication are being designed. These systems, microbial consortia, are composed of engineered cells and exhibit a wide range of behaviors. These include yeast cells whose growth is dependent on one another, or bacteria that kill or rescue each other, synchronize, behave as predator-prey ecosystems or invade cancer cells.

RESULTS

In this paper, we study a synthetic ecosystem comprising of bacteria and yeast that communicate with and benefit from each other using small diffusible molecules. We explore the behavior of this heterogeneous microbial consortium, composed of Saccharomyces cerevisiae and Escherichia coli cells, using stochastic modeling. The stochastic model captures the relevant intra-cellular and inter-cellular interactions taking place in and between the eukaryotic and prokaryotic cells. Integration of well-characterized molecular regulatory elements into these two microbes allows for communication through quorum sensing. A gene controlling growth in yeast is induced by bacteria via chemical signals and vice versa. Interesting dynamics that are common in natural ecosystems, such as obligatory and facultative mutualism, extinction, commensalism and predator-prey like dynamics are observed. We investigate and report on the conditions under which the two species can successfully communicate and rescue each other.

CONCLUSIONS

This study explores the various behaviors exhibited by the cohabitation of engineered yeast and bacterial cells. The way that the model is built allows for studying the dynamics of any system consisting of two species communicating with one another via chemical signals. Therefore, key information acquired by our model may potentially drive the experimental design of various synthetic heterogeneous ecosystems.

proTeOn and proTeOff, new protein devices that inducibly activate bacterial gene expression

Using an original workflow, we have modeled, constructed, and characterized two new molecular devices that inducibly activate gene expression in Escherichia coli. The devices, prokaryotic-TetOn and prokaryotic-TetOff, were built by fusing an inducible DNA-binding protein domain to a transcription activation domain and constructing a complementary synthetic promoter sequence through which they could control downstream gene expression. In particular, the transactivators were built using variants of the tetracycline repressor, TetR, and the transactivating domain of the LuxR activator. The complementary promoter sequence included TetR's operator, tetO, and elements of the lux promoter. These specific protein domains and their operator sites were chosen as they have been thoroughly studied and well characterized. First, our methodology began with optimizing the geometry of the molecular components using molecular modeling. We did so to achieve an unprecedented combination of controllable and transactivating function in bacterial organisms. The devices were then built to activate the expression of green fluorescent protein. Their unique function was found to be robustly tight and activating many-fold increases of expressed gene levels, as measured by flow cytometry experiments. The devices were further characterized with stochastic kinetic models. The new devices presented herein may become useful additions to the molecular toolboxes used by biologists to control bacterial gene expression. The methodology used may also be a foundation for the design, development, and characterization of a library of such devices and more complex gene regulatory networks.

Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic biology

Modular and orthogonal genetic logic gates are essential for building robust biologically based digital devices to customize cell signalling in synthetic biology. Here we constructed an orthogonal AND gate in Escherichia coli using a novel hetero-regulation module from Pseudomonas syringae. The device comprises two co-activating genes hrpR and hrpS controlled by separate promoter inputs, and a σ⁵⁴-dependent hrpL promoter driving the output. The hrpL promoter is activated only when both genes are expressed, generating digital-like AND integration behaviour. The AND gate is demonstrated to be modular by applying new regulated promoters to the inputs, and connecting the output to a NOT gate module to produce a combinatorial NAND gate. The circuits were assembled using a parts-based engineering approach of quantitative characterization, modelling, followed by construction and testing. The results show that new genetic logic devices can be engineered predictably from novel native orthogonal biological control elements using quantitatively in-context characterized parts.

Biological digital sensors require the fabrication of modular genetic logic gates. Using the Pseudomonas syringae hrp system, Wang and colleagues generate AND, NOT and NAND gates, demonstrating the ability to engineer a modular system from biological elements.

SynBioSS-aided design of synthetic biological constructs

We present walkthrough examples of using SynBioSS to design, model, and simulate synthetic gene regulatory networks. SynBioSS stands for Synthetic Biology Software Suite, a platform that is publicly available with Open Licenses at www.synbioss.org. An important aim of computational synthetic biology is the development of a mathematical modeling formalism that is applicable to a wide variety of simple synthetic biological constructs. SynBioSS-based modeling of biomolecular ensembles that interact away from the thermodynamic limit and not necessarily at steady state affords for a theoretical framework that is generally applicable to known synthetic biological systems, such as bistable switches, AND gates, and oscillators. Here, we discuss how SynBioSS creates links between DNA sequences and targeted dynamic phenotypes of these simple systems.

Mechanism of transcriptional repression at a bacterial promoter by analysis of single molecules

The molecular basis for regulation of lactose metabolism in Escherichia coli is well studied. Nonetheless, the physical mechanism by which the Lac repressor protein prevents transcription of the lactose promoter remains unresolved. Using multi-wavelength single-molecule fluorescence microscopy, we visualized individual complexes of fluorescently tagged RNA polymerase holoenzyme bound to promoter DNA. Quantitative analysis of the single-molecule observations, including use of a novel statistical partitioning approach, reveals highly kinetically stable binding of polymerase to two different sites on the DNA, only one of which leads to transcription. Addition of Lac repressor directly demonstrates that bound repressor prevents the formation of transcriptionally productive open promoter complexes; discrepancies in earlier studies may be attributable to transcriptionally inactive polymerase binding. The single-molecule statistical partitioning approach is broadly applicable to elucidating mechanisms of regulatory systems including those that are kinetically rather than thermodynamically controlled.

Transient dynamics around unstable periodic orbits in the generalized repressilator model

We study the temporal dynamics of the generalized repressilator, a network of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a finite sequence of unstable periodic orbits that lead to reachable long-lived oscillating transients. Such transients dominate the finite time horizon dynamics that is relevant in confined, noisy environments such as bacterial cells (see our previous work [Strelkowa and Barahona, J. R. Soc. Interface 7, 1071 (2010)]), and are therefore of interest for bioengineering and synthetic biology. We show that the family of unstable orbits possesses spatial symmetries and can also be understood in terms of traveling wave solutions of kink-like topological defects. The long-lived oscillatory transients correspond to the propagation of quasistable two-kink configurations that unravel over a long time. We also assess the similarities between the generalized repressilator model and other unidirectionally coupled electronic systems, such as magnetic flux gates, which have been implemented experimentally.

Mathematical models in biology: from molecules to life

A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life's distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology.

Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics

The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.

Stochastic simulations of the tetracycline operon

Background

The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system.

Results

Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for Escherichia coli. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts.

Conclusions

Computer simulations of the tetracycline operon afford augmented insight into the interplay between its molecular components. They provide useful explanations of how the components and their interactions have evolved to best serve bacteria carrying this operon. Therefore, simulations may assist in designing novel gene network architectures consisting of tetracycline operon components.

Programming cells: towards an automated 'Genetic Compiler'

One of the visions of synthetic biology is to be able to program cells using a language that is similar to that used to program computers or robotics. For large genetic programs, keeping track of the DNA on the level of nucleotides becomes tedious and error prone, requiring a new generation of computer-aided design (CAD) software. To push the size of projects, it is important to abstract the designer from the process of part selection and optimization. The vision is to specify genetic programs in a higher-level language, which a genetic compiler could automatically convert into a DNA sequence. Steps towards this goal include: defining the semantics of the higher-level language, algorithms to select and assemble parts, and biophysical methods to link DNA sequence to function. These will be coupled to graphic design interfaces and simulation packages to aid in the prediction of program dynamics, optimize genes, and scan projects for errors.

Minimal genetic device with multiple tunable functions

The ability to design artificial genetic devices with predictable functions is critical to the development of synthetic biology. Given the highly variable requirements of biological designs, the ability to tune the behavior of a genetic device is also of key importance; such tuning will allow devices to be matched with other components into larger systems, and to be shifted into the correct parameter regimes to elicit desired behaviors. Here, we have developed a minimal synthetic genetic system that acts as a multifunction, tunable biodevice in the bacterium Escherichia coli. First, it acts as a biochemical AND gate, sensing the extracellular small molecules isopropyl β-D -1-thiogalactopyranoside and anhydrotetracycline as two input signals and expressing enhanced green fluorescent protein as an output signal. Next, the output signal of the AND gate can be amplified by the application of another extracellular chemical, arabinose. Further, the system can generate a wide range of chemically tunable single input-output response curves, without any genetic alteration of the circuit, by varying the concentrations of a set of extracellular small molecules. We have developed and parameterized a simple transfer function model for the system, and shown that the model successfully explains and predicts the quantitative relationships between input and output signals in the system.

SynBioSS designer: a web-based tool for the automated generation of kinetic models for synthetic biological constructs

Modeling tools can play an important role in synthetic biology the same way modeling helps in other engineering disciplines: simulations can quickly probe mechanisms and provide a clear picture of how different components influence the behavior of the whole. We present a brief review of available tools and present SynBioSS Designer. The Synthetic Biology Software Suite (SynBioSS) is used for the generation, storing, retrieval and quantitative simulation of synthetic biological networks. SynBioSS consists of three distinct components: the Desktop Simulator, the Wiki, and the Designer. SynBioSS Designer takes as input molecular parts involved in gene expression and regulation (e.g. promoters, transcription factors, ribosome binding sites, etc.), and automatically generates complete networks of reactions that represent transcription, translation, regulation, induction and degradation of those parts. Effectively, Designer uses DNA sequences as input and generates networks of biomolecular reactions as output. In this paper we describe how Designer uses universal principles of molecular biology to generate models of any arbitrary synthetic biological system. These models are useful as they explain biological phenotypic complexity in mechanistic terms. In turn, such mechanistic explanations can assist in designing synthetic biological systems. We also discuss, giving practical guidance to users, how Designer interfaces with the Registry of Standard Biological Parts, the de facto compendium of parts used in synthetic biology applications.

Computational methods in synthetic biology

We discuss how a theoretical synthetic biology research programme may liberate empiricism in biological sciences beyond the unaided human brain. Because synthetic biological systems are relatively small and largely independent of evolutionary contexts, they can be represented with mathematical models strongly founded on first principles of molecular biology and laws of statistical thermodynamics. A universal mathematical formalism for describing synthetic constructs may then be plausibly used to explain in unambiguous, quantitative terms how biological phenotypic complexity emerges as a result of well-defined biomolecular interactions. SynBioSS, a publicly available software package, is described that implements this mathematical formalism.