Deoxyribozyme-based three-input logic gates and construction of a molecular full adder

We have developed an array of seven deoxyribozyme-based molecular logic gates that behaves as a full adder in a single solution, with three oligonucleotides as inputs and two independent fluorogenic cleavage reactions as carry and sum outputs. The sum output consisted of four new deoxyribozyme-based logic gates: an ANDAND gate and three ANDNOTANDNOT gates. These gates required the design of a generic three-input deoxyribozyme-based logic gate that can use any three-way combination of activating or inactivating inputs. This generic gate design utilizes an additional inverting element that hybridizes to convert YES logic into NOT logic and vice versa. The system represents the first solution-phase, single test tube, enzymatic full adder and shows the complexity of control over molecular scale events that can be achieved with deoxyribozyme-based logic gates. Similar systems could be applied to control autonomous therapeutic and diagnostic devices.     

Modular approaches to expanding the functions of living matter

The synthesis of increasingly complex unnatural networks embedded in living matter is an emerging theme in synthetic biology. Synthetic networks have allowed the creation of organisms endowed with toggle switches, logic gates, pattern-forming systems, oscillators, cellular sensors, new modes of gene regulation and expanded genetic codes. A common challenge of this work is the addition of specific new functions to complex living organisms. This requires spatial and temporal control of molecular interactions and fluxes to achieve the desired outcomes. Here we review recent successes in this emerging field and discuss strategies for addressing the challenges of increasing network complexity.     

Development of genetic circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli

Analysis of the system design principles of signaling systems requires model systems where all components and regulatory interactions are known. Components of the Lac and Ntr systems were used to construct genetic circuits that display toggle switch or oscillatory behavior. Both devices contain an "activator module" consisting of a modified glnA promoter with lac operators, driving the expression of the activator, NRI. Since NRI activates the glnA promoter, this creates an autoactivated circuit repressible by LacI. The oscillator contains a "repressor module" consisting of the NRI-activated glnK promoter driving LacI expression. This circuitry produced synchronous damped oscillations in turbidostat cultures, with periods much longer than the cell cycle. For the toggle switch, LacI was provided constitutively; the level of active repressor was controlled by using a lacY mutant and varying the concentration of IPTG. This circuitry provided nearly discontinuous expression of activator.     

A computational method for the investigation of multistable systems and its application to genetic switches

Background

Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.

Results

Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.

Conclusions

Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.

     

Evolving digital circuits using hybrid particle swarm optimization and differential evolution

This paper presents the evolution of combinational logic circuits by a new hybrid algorithm known as the Differential Evolution Particle Swarm Optimization (DEPSO), formulated from the concepts of a modified particle swarm and differential evolution. The particle swarm in the hybrid algorithm is represented by a discrete 3-integer approach. A hybrid multi-objective fitness function is coined to achieve two goals for the evolution of circuits. The first goal is to evolve combinational logic circuits with 100% functionality, called the feasible circuits. The second goal is to minimize the number of logic gates needed to realize the feasible circuits. In addition, the paper presents modifications to enhance performance and robustness of particle swarm and evolutionary techniques for discrete optimization problems. Comparison of the performance of the hybrid algorithm to the conventional Karnaugh map and evolvable hardware techniques such as genetic algorithm, modified particle swarm, and differential evolution are presented on a number of case studies. Results show that feasible circuits are always achieved by the DEPSO algorithm unlike with other algorithms and the percentage of best solutions (minimal logic gates) is higher.     

A biomolecular implementation of logically reversible computation with minimal energy dissipation

Energy dissipation associated with logic operations imposes a fundamental physical limit on computation and is generated by the entropic cost of information erasure, which is a consequence of irreversible logic elements. We show how to encode information in DNA and use DNA amplification to implement a logically reversible gate that comprises a complete set of operators capable of universal computation. We also propose a method using this design to connect, or 'wire', these gates together in a biochemical fashion to create a logic network, allowing complex parallel computations to be executed. The architecture of the system permits highly parallel operations and has properties that resemble well known genetic regulatory systems.     

Synthetic genetic circuits for programmable biological functionalities

Living organisms evolve complex genetic networks to interact with the environment. Due to the rapid development of synthetic biology, various modularized genetic parts and units have been identified from these networks. They have been employed to construct synthetic genetic circuits, including toggle switches, oscillators, feedback loops and Boolean logic gates. Building on these circuits, complex genetic machines with capabilities in programmable decision-making could be created. Consequently, these accomplishments have led to novel applications, such as dynamic and autonomous modulation of metabolic networks, directed evolution of biological units, remote and targeted diagnostics and therapies, as well as biological containment methods to prevent release of engineered microorganisms and genetic materials. Herein, we outline the principles in genetic circuit design that have initiated a new chapter in transforming concepts to realistic applications. The features of modularized building blocks and circuit architecture that facilitate realization of circuits for a variety of novel applications are discussed. Furthermore, recent advances and challenges in employing genetic circuits to impart microorganisms with distinct and programmable functionalities are highlighted. We envision that this review gives new insights into the design of synthetic genetic circuits and offers a guideline for the implementation of different circuits in various aspects of biotechnology and bioengineering.     

Histone Variant HTZ1 Shows Extensive Epistasis with,but Does Not Increase Robustness to,New Mutations

Biological systems produce phenotypes that appear to be robust to perturbation by mutations and environmental variation. Prior studies identified genes that, when impaired, reveal previously cryptic genetic variation. This result is typically interpreted as evidence that the disrupted gene normally increases robustness to mutations, as such robustness would allow cryptic variants to accumulate. However, revelation of cryptic genetic variation is not necessarily evidence that a mutationally robust state has been made less robust. Demonstrating a difference in robustness requires comparing the ability of each state (with the gene perturbed or intact) to suppress the effects of new mutations. Previous studies used strains in which the existing genetic variation had been filtered by selection. Here, we use mutation accumulation (MA) lines that have experienced minimal selection, to test the ability of histone H2A.Z (HTZ1) to increase robustness to mutations in the yeast Saccharomyces cerevisiae. HTZ1, a regulator of chromatin structure and gene expression, represents a class of genes implicated in mutational robustness. It had previously been shown to increase robustness of yeast cell morphology to fluctuations in the external or internal microenvironment. We measured morphological variation within and among 79 MA lines with and without HTZ1. Analysis of within-line variation confirms that HTZ1 increases microenvironmental robustness. Analysis of between-line variation shows the morphological effects of eliminating HTZ1 to be highly dependent on the line, which implies that HTZ1 interacts with mutations that have accumulated in the lines. However, lines without HTZ1 are, as a group, not more phenotypically diverse than lines with HTZ1 present. The presence of HTZ1, therefore, does not confer greater robustness to mutations than its absence. Our results provide experimental evidence that revelation of cryptic genetic variation cannot be assumed to be caused by loss of robustness, and therefore force reevaluation of prior claims based on that assumption.     

Dynamics of a simple regulatory switch

We consider the dynamics of a model toggle switch abstracted from the genetic interactions operative in a fungal stress response circuit. The switch transduces an external signal and propagates it forward by mediating the transport between compartments of two interacting gene products. The transport between compartments is assumed to be related to the degree of association between the interacting proteins, a fact for which there exists a wealth of biological evidence. The ubiquity and modularity of this cellular control mechanism warrants a detailed study of the dynamics entailed by various modelling assumptions. Specifically, we consider a general gate model in which both of the associating proteins are freely transportable between compartments. A more restrictive, but biologically supported model, is considered in which only one of the two proteins undergoes transport. Under the strong assumption that the disassociation of the interacting proteins is unidirectional we show that the qualitative dynamics of the two models are similar; that is they both converge to unique periodic orbits. From a biophysical perspective the assumption of unidirectional dissociation is unrealistic. We show that the same result holds for the more restrictive model when one weakens the assumption of unidirectional binding or disassociation. We speculate that this is not true for the more general model. This difference in dynamics may have important biological implications and certainly points to promising avenues of research.     

An electrogenetic toggle switch model

Synthetic biology uses molecular biology to implement genetic circuits that perform computations. These circuits can process inputs and deliver outputs according to predefined rules that are encoded, often entirely, into genetic parts. However, the field has recently begun to focus on using mechanisms beyond the realm of genetic parts for engineering biological circuits. We analyse the use of electrogenic processes for circuit design and present a model for a merged genetic and electrogenetic toggle switch operating in a biofilm attached to an electrode. Computational simulations explore conditions under which bistability emerges in order to identify the circuit design principles for best switch performance. The results provide a basis for the rational design and implementation of hybrid devices that can be measured and controlled both genetically and electronically.     

The bacterial nanorecorder: engineering E. coli to function as a chemical recording device

Synthetic biology is an emerging branch of molecular biology that uses synthetic genetic constructs to create man-made cells or organisms that are capable of performing novel and/or useful applications. Using a synthetic chemically sensitive genetic toggle switch to activate appropriate fluorescent protein indicators (GFP, RFP) and a cell division inhibitor (minC), we have created a novel E. coli strain that can be used as a highly specific, yet simple and inexpensive chemical recording device. This biological "nanorecorder" can be used to determine both the type and the time at which a brief chemical exposure event has occurred. In particular, we show that the short-term exposure (15-30 min) of cells harboring this synthetic genetic circuit to small molecule signals (anhydrotetracycline or IPTG) triggered long-term and uniform cell elongation, with cell length being directly proportional to the time elapsed following a brief chemical exposure. This work demonstrates that facile modification of an existing genetic toggle switch can be exploited to generate a robust, biologically-based "nanorecorder" that could potentially be adapted to detect, respond and record a wide range of chemical stimuli that may vary over time and space.     

Implementation of a genetic logic circuit: bio-register

We introduce an idea of synthesizing a class of genetic registers based on the existing sequential biological circuits, which are composed of fundamental biological gates. In the renowned literature, biological gates and genetic oscillator have been unveiled and experimentally realized in recent years. These biological circuits have formed a basis for realizing a primitive biocomputer. In the traditional computer architecture, there is an intermediate load-store section, i.e. a register, which serves as a part of the digital processor. With which, the processor can load data from a larger memory into it and proceed to conduct necessary arithmetic or logic operations. Then, manipulated data are stored back to the memory by instruction via the register. We propose here a class of bio-registers for the biocomputer. Four types of register structures are presented. In silicon experiments illustrate results of the proposed design.     

An OR logic gate based on two molecular beacons

Design of elementary molecular logic gates is the key and the fundamental of performing complicated Boolean calculations. Herein, we report a strategy for constructing a DNA-based OR gate by using the mechanism of sequence recognition and the principle of fluorescence resonance energy transfer (FRET). In this system, the gate is entirely composed of a single strand of DNA (A, B and C) and the inputs are the molecular beacon probes (MB1 and MB2). Changes in fluorescence intensity confirm the realization of the OR logic operation and electrophoresis experiments verify these results. Our successful application of DNA to perform the binary operation represents that DNA can serve as an efficient biomaterial for designing molecular logic gates and devices.     

Implementing an OR-NOT (ORN) logic gate with components of the SOS regulatory network of Escherichia coli

Whether biological or electronic, man-engineered computation is based on logic circuits assembled with binary gates that are interconnected to perform Boolean operations. We report here the rewiring of the SOS system of Escherichia in a fashion that makes the output of both the recA and lexA promoters to faithfully follow the pattern of a binary composite OR-NOT gate (ORN) in which the inputs are DNA damage (e.g. nalidixic acid addition) and IPTG as an exogenous signal. Unlike other non-natural gates whose implementation requires changes in genes and promoters of the genome of the host cells, this ORN was brought about by the sole addition of wild-type bacteria with a plasmid encoding a module for LacI(q)-dependent expression of lexA. Specifically, we demonstrate that the interplay between native, chromosomally-encoded components of the SOS system and the extra parts engineered in such a plasmid made the desired performance to happen without any modification of the core DNA-damage response network. It is thus possible to artificially interface autonomous cell networks with a predetermined logic by means of Boolean gates built with regulatory elements already functioning in the recipient organism.     

Biological Signal Processing with a Genetic Toggle Switch

Complex gene regulation requires responses that depend not only on the current levels of input signals but also on signals received in the past. In digital electronics, logic circuits with this property are referred to as sequential logic, in contrast to the simpler combinatorial logic without such internal memory. In molecular biology, memory is implemented in various forms such as biochemical modification of proteins or multistable gene circuits, but the design of the regulatory interface, which processes the input signals and the memory content, is often not well understood. Here, we explore design constraints for such regulatory interfaces using coarse-grained nonlinear models and stochastic simulations of detailed biochemical reaction networks. We test different designs for biological analogs of the most versatile memory element in digital electronics, the JK-latch. Our analysis shows that simple protein-protein interactions and protein-DNA binding are sufficient, in principle, to implement genetic circuits with the capabilities of a JK-latch. However, it also exposes fundamental limitations to its reliability, due to the fact that biological signal processing is asynchronous, in contrast to most digital electronics systems that feature a central clock to orchestrate the timing of all operations. We describe a seemingly natural way to improve the reliability by invoking the master-slave concept from digital electronics design. This concept could be useful to interpret the design of natural regulatory circuits, and for the design of synthetic biological systems.     

A population‐based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events.     

Forward engineering of synthetic bio-logical AND gates

The field of synthetic biology has produced genetic circuits capable of emulating functional paradigms seen in digital electronic circuits. Examples are bistable switches, oscillators, and logic gates. The present work combines detailed mechanistic-kinetic models and stochastic simulation techniques as well as the techniques of in vivo molecular biology to study the potential of a synthetic, single promoter AND gate. This device is composed of elements of the tet, lac, and λ-phage promoters and is responsive to the commonly used inducers IPTG and aTc, producing GFP as an output signal. The quantitative behavior of the AND gate phenotype is studied both in numero and in vivo as a function of promoter topology. The model is constructed from kinetic data obtained from the literature and yields clearly defined ON/OFF logical behavior at realistic inducer concentrations. These behaviors are matched with observed in vivo data obtained through fluorescence-activated cell sorting. The effect of incomplete repression by weaker LacI repressor is also investigated and quantified. The simulation results, coupled with in vivo data, not only identify important design degrees of freedom, but also provide parameters that can be used to guide future synthetic designs using these common regulatory elements.     

Forward engineering of synthetic bio-logical AND gates

The field of synthetic biology has produced genetic circuits capable of emulating functional paradigms seen in digital electronic circuits. Examples are bistable switches, oscillators, and logic gates. The present work combines detailed mechanistic-kinetic models and stochastic simulation techniques as well as the techniques of in vivo molecular biology to study the potential of a synthetic, single promoter AND gate. This device is composed of elements of the tet, lac, and λ-phage promoters and is responsive to the commonly used inducers IPTG and aTc, producing GFP as an output signal. The quantitative behavior of the AND gate phenotype is studied both in numero and in vivo as a function of promoter topology. The model is constructed from kinetic data obtained from the literature and yields clearly defined ON/OFF logical behavior at realistic inducer concentrations. These behaviors are matched with observed in vivo data obtained through fluorescence-activated cell sorting. The effect of incomplete repression by weaker LacI repressor is also investigated and quantified. The simulation results, coupled with in vivo data, not only identify important design degrees of freedom, but also provide parameters that can be used to guide future synthetic designs using these common regulatory elements.