Toggle Switch Research Articles

Genetic Toggle Switch in the Absence of Cooperative Binding: Exact Results.

We present an analytical treatment of a genetic switch model consisting of two mutually inhibiting genes operating without cooperative binding of the corresponding transcription factors. Previous studies have numerically shown that these systems can exhibit bimodal dynamics without possessing two stable fixed points at the deterministic level. We analytically show that bimodality is induced by the noise and find the critical repression strength that controls a transition between the bimodal and nonbimodal regimes. We also identify characteristic polynomial scaling laws of the mean switching time between bimodal states. These results, independent of the model under study, reveal essential differences between these systems and systems with cooperative binding, where there is no critical threshold for bimodality and the mean switching time scales exponentially with the system size.

Spatiotemporal dynamics of distributed synthetic genetic circuits

We propose and study models of two distributed synthetic gene circuits, toggle-switch and oscillator, each split between two cell strains and coupled via quorum-sensing signals. The distributed toggle switch relies on mutual repression of the two strains, and oscillator is comprised of two strains, one of which acts as an activator for another that in turn acts as a repressor. Distributed toggle switch can exhibit mobile fronts, switching the system from the weaker to the stronger spatially homogeneous state. The circuit can also act as a biosensor, with the switching front dynamics determined by the properties of an external signal. Distributed oscillator system displays another biosensor functionality: oscillations emerge once a small amount of one cell strain appears amid the other, present in abundance. Distribution of synthetic gene circuits among multiple strains allows one to reduce crosstalk among different parts of the overall system and also decrease the energetic burden of the synthetic circuit per cell, which may allow for enhanced functionality and viability of engineered cells.

Limit load analysis of a spring-supported shallow arch of variable thickness given by a power-law, exponential, or logarithmic formula

Thin shallow arches may become unstable under transverse loading as the built-up internal compressive forces reach a limiting value beyond which the structure undergoes a sudden large displacement towards a new stable configuration. This phenomenon could be both desirable (in toggle switches) and disastrous (collapse of a dome or truss). Hence, it is important to carry out the so-called snap- or limit-load analysis to reveal the factors influence the phenomenon and to give guidelines in designing structures to behave favorably. Although energy methods are a common means of this analysis, the phenomenon could also be analyzed by considering the equations governing the displacement of the arch and by monitoring the load-displacement characteristic of the structure until it reaches the limit point. This is the procedure adopted here. Researches on the subject mostly consider constant thickness arches with common pin-ended or fixed supports. Here the thickness is varied along the arch in three forms: power-law, exponential, and logarithmic. The supports are considered to be nonrigid fixed; i.e., pinned ends are equipped with torsional springs with constant stiffness. By changing these stiffnesses, various combinations of pinned and/or fixed states, or an intermediate state at each end could be developed. By considering the analytical solution for the transverse displacement for the general power-law case, the limit-load is obtained by numerical solution of the limit-load condition, which is a highly complicated function of the derived displacement field. Several parameter studies, such as that of the effects of shallowness and slenderness of arch and spring stiffnesses on the critical load, are carried out. The results are verified by those of simpler cases available in the literature, as well as those from a finite-element approach.

Controlled switching of single-molecule junctions by mechanical motion of a phenyl ring.

Mechanical methods for single-molecule control have potential for wide application in nanodevices and machines. Here we demonstrate the operation of a single-molecule switch made functional by the motion of a phenyl ring, analogous to the lever in a conventional toggle switch. The switch can be actuated by dual triggers, either by a voltage pulse or by displacement of the electrode, and electronic manipulation of the ring by chemical substitution enables rational control of the on-state conductance. Owing to its simple mechanics, structural robustness, and chemical accessibility, we propose that phenyl rings are promising components in mechanical molecular devices.

Solution of the chemical master equation by radial basis functions approximation with interface tracking.

BackgroundThe chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level.ResultsWe introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space.DiscussionIn order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods.ConclusionsThe proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0210-y) contains supplementary material, which is available to authorized users.

Enhancement of 3-hydroxypropionic acid production from glycerol by using a metabolic toggle switch.

Background3-hydroxypropionic acid (3-HP) is an important platform for the production of C3 chemicals, including acrylic acid, methyl acrylate, and acrylamide. Microbial production of 3-HP is mainly due to glycerol metabolism. In this study, in order to improve microbial 3-HP production, we applied a metabolic toggle switch for controlling the glycerol metabolism to redirect the excess metabolic flux of central metabolic pathway toward an exogenous 3-HP producing pathway in Escherichia coli.ResultsThe metabolic toggle switch enables conditional repression of the expression of a target gene during the fermentation. We individually performed conditional repression of glpK, tpiA, and gapA, which are involved in glycerol metabolism. The conditional repression of glpK and tpiA was not effective for 3-HP production under our experimental conditions. However, gapA conditional repression contributed to improve 3-HP production (titer, 54.2 ± 1.5 mM; yield, 32.1 ± 1.3 %) compared with that for the wild type strain. Additional deletion of endogenous yqhD, which is responsible for the production of a major byproduct, 1,3-propandiol, further increased 3-HP production (titer, 67.3 ± 2.1 mM; yield, 51.5 ± 3.2 %). The titer and yield were 80 and 94 % higher than those of the wild type strain, respectively. The obtained 3-HP yield from glycerol is comparable with the highest yield ever reported for microbial 3-HP production using glycerol as a sole carbon source. The measurement of intracellular metabolites showed the metabolic toggle switch successfully controlled the metabolic flux.ConclusionThe conditional repression of gapA by using the metabolic toggle switch combined with deletion of endogeneous yqhD increased 3-HP production approximately twofold from glycerol. This result indicates the metabolic toggle switch can be applied in various bio-production using diverse substrates.

Yeast Replicator: A High-Throughput Multiplexed Microfluidics Platform for Automated Measurements of Single-Cell Aging.

The yeast Saccharomyces cerevisiae is a model organism for replicative aging studies; however, conventional lifespan measurement platforms have several limitations. Here, we present a microfluidics platform that facilitates simultaneous lifespan and gene expression measurements of aging yeast cells. Our multiplexed high-throughput platform offers the capability to perform independent lifespan experiments using different yeast strains or growth media. Using this platform in minimal media environments containing glucose, we measured the full lifespan of individual yeast cells in wild-type and canonical gene deletion backgrounds. Compared to glucose, in galactose we observed a 16.8% decrease in replicative lifespan accompanied by an ∼2-fold increase in single-cell oxidative stress levels reported by PSOD1-mCherry. Using PGAL1-YFP to measure the activity of the bistable galactose network, we saw that OFF and ON cells are similar in their lifespan. Our work shows that aging cells are committed to a single phenotypic state throughout their lifespan.

DNA-Binding Kinetics Determines the Mechanism of Noise-Induced Switching in Gene Networks

Gene regulatory networks are multistable dynamical systems in which attractor states represent cell phenotypes. Spontaneous, noise-induced transitions between these states are thought to underlie critical cellular processes, including cell developmental fate decisions, phenotypic plasticity in fluctuating environments, and carcinogenesis. As such, there is increasing interest in the development of theoretical and computational approaches that can shed light on the dynamics of these stochastic state transitions in multistable gene networks. We applied a numerical rare-event sampling algorithm to study transition paths of spontaneous noise-induced switching for a ubiquitous gene regulatory network motif, the bistable toggle switch, in which two mutually repressive genes compete for dominant expression. We find that the method can efficiently uncover detailed switching mechanisms that involve fluctuations both in occupancies of DNA regulatory sites and copy numbers of protein products. In addition, we show that the rate parameters governing binding and unbinding of regulatory proteins to DNA strongly influence the switching mechanism. In a regime of slow DNA-binding/unbinding kinetics, spontaneous switching occurs relatively frequently and is driven primarily by fluctuations in DNA-site occupancies. In contrast, in a regime of fast DNA-binding/unbinding kinetics, switching occurs rarely and is driven by fluctuations in levels of expressed protein. Our results demonstrate how spontaneous cell phenotype transitions involve collective behavior of both regulatory proteins and DNA. Computational approaches capable of simulating dynamics over many system variables are thus well suited to exploring dynamic mechanisms in gene networks.

Impact of the cell division cycle on gene circuits

In growing cells, protein synthesis and cell growth are typically not synchronous, and, thus, protein concentrations vary over the cell division cycle. We have developed a theoretical description of genetic regulatory systems in bacteria that explicitly considers the cell division cycle to investigate its impact on gene expression. We calculate the cell-to-cell variations arising from cells being at different stages in the division cycle for unregulated genes and for basic regulatory mechanisms. These variations contribute to the extrinsic noise observed in single-cell experiments, and are most significant for proteins with short lifetimes. Negative autoregulation buffers against variation of protein concentration over the division cycle, but the effect is found to be relatively weak. Stronger buffering is achieved by an increased protein lifetime. Positive autoregulation can strongly amplify such variation if the parameters are set to values that lead to resonance-like behaviour. For cooperative positive autoregulation, the concentration variation over the division cycle diminishes the parameter region of bistability and modulates the switching times between the two stable states. The same effects are seen for a two-gene mutual-repression toggle switch. By contrast, an oscillatory circuit, the repressilator, is only weakly affected by the division cycle.

A termination criterion for parameter estimation in stochastic models in systems biology

Parameter estimation procedures are a central aspect of modeling approaches in systems biology. They are often computationally expensive, especially when the models take stochasticity into account. Typically parameter estimation involves the iterative optimization of an objective function that describes how well the model fits some measured data with a certain set of parameter values. In order to limit the computational expenses it is therefore important to apply an adequate stopping criterion for the optimization process, so that the optimization continues at least until a reasonable fit is obtained, but not much longer. In the case of stochastic modeling, at least some parameter estimation schemes involve an objective function that is itself a random variable. This means that plain convergence tests are not a priori suitable as stopping criteria.This article suggests a termination criterion suited to optimization problems in parameter estimation arising from stochastic models in systems biology. The termination criterion is developed for optimization algorithms that involve populations of parameter sets, such as particle swarm or evolutionary algorithms. It is based on comparing the variance of the objective function over the whole population of parameter sets with the variance of repeated evaluations of the objective function at the best parameter set. The performance is demonstrated for several different algorithms. To test the termination criterion we choose polynomial test functions as well as systems biology models such as an Immigration-Death model and a bistable genetic toggle switch. The genetic toggle switch is an especially challenging test case as it shows a stochastic switching between two steady states which is qualitatively different from the model behavior in a deterministic model.

Synthesis of Genetic Clock with Combinational Biologic Circuits.

The potential of genetic clock lies in its role to triggering logic reaction for sequential biological circuits. In general, biochemical reaction of the biological system is extremely slow. However, a square wave generator used as a genetic clock the transient response should be fast enough to catch the reaction change between two logic levels. Therefore, the requirement for instantaneous changes in logic status is not likely to exist in biological systems. This paper presents a method of synthesizing a genetic clock generator based on the combination of a toggle switch with two biological logic gates. A dual repressor is used to connect the two fundamental biologic circuits. Analysis of the characteristic responses of this genetic clock with its relation to the key parameters is provided.

Numerical schemes for random ODEs with affine noise

Numerical schemes for random ordinary differential equations, abbreviated RODEs, with an affine structure can be derived in a similar way as for affine control systems using Taylor expansions that resemble stochastic Taylor expansions for Stratonovich stochastic differential equations. The driving noise processes can be quite general, such as Wiener processes or fractional Brownian motions with continuous sample paths or compound Poisson processes with piecewise constant sample paths, and even more general noises. Such affine-Taylor schemes of arbitrarily high order are constructed here. It is shown how their structure simplifies when the noise terms are additive or commutative. A derivative free counterpart is given and multi-step schemes are derived too. Numerical comparisons are provided for various explicit one-step and multi-step schemes in the context of a toggle switch model from systems biology.

Evolving modular genetic regulatory networks with a recursive, top-down approach.

Being able to design genetic regulatory networks (GRNs) to achieve a desired cellular function is one of the main goals of synthetic biology. However, determining minimal GRNs that produce desired time-series behaviors is non-trivial. In this paper, we propose a 'top-down' approach to evolving small GRNs and then use these to recursively boot-strap the identification of larger, more complex, modular GRNs. We start with relatively dense GRNs and then use differential evolution (DE) to evolve interaction coefficients. When the target dynamical behavior is found embedded in a dense GRN, we narrow the focus of the search and begin aggressively pruning out excess interactions at the end of each generation. We first show that the method can quickly rediscover known small GRNs for a toggle switch and an oscillatory circuit. Next we include these GRNs as non-evolvable subnetworks in the subsequent evolution of more complex, modular GRNs. Successful solutions found in canonical DE where we truncated small interactions to zero, with or without an interaction penalty term, invariably contained many excess interactions. In contrast, by incorporating aggressive pruning and the penalty term, the DE was able to find minimal or nearly minimal GRNs in all test problems.

Conserved molecular switch interactions in modeled cardioactive RF-NH2 peptide receptors: Ligand binding and activation

Peptides may act through G protein-coupled receptors to influence cardiovascular performance; thus, delineating mechanisms involved in signaling is a molecular-based strategy to influence health. Molecular switches, often represented by conserved motifs, maintain a receptor in an inactive state. However, once the switch is broken, the transmembrane regions move and activation occurs. The molecular switches of Drosophila melanogaster myosuppressin (MS) receptors were previously identified to include a unique ionic lock and novel 3-6 lock, as well as transmission and tyrosine toggle switches. In addition to MS, cardioactive ligands structurally related by a C-terminal RF-NH2 include sulfakinin, neuropeptide F (NPF), short NPF, and FMRF-NH2-containing peptide subfamilies. We hypothesized receptor molecular switch motifs were conserved within a RF-NH2 subfamily and across species. Thus, we investigated RF-NH2 receptor (RFa-R) molecular switches in D. melanogaster, Tribolium castaneum, Anopheles gambiae, Rhodnius prolixus, and Bombyx mori. Adipokinetic hormone (AKH), which does not contain a RF-NH2, was also examined. The tyrosine toggle switch and ionic lock showed a higher degree of conservation within a RF-NH2 subfamily than the transmission switch and 3-7 lock. AKH receptor motifs were not representative of a RF-NH2 subfamily. The motifs and interactions of switches in the RFa-Rs were consistent with receptor activation and ligand-specific binding.

Conserved Residues Control Activation of Mammalian G Protein-Coupled Odorant Receptors.

Odorant receptor (OR) genes and proteins represent more than 2% of our genome and 4% of our proteome and constitute the largest subgroup of G protein-coupled receptors (GPCRs). The mechanism underlying OR activation remains poorly understood, as they do not share some of the highly conserved motifs critical for activation of non-olfactory GPCRs. By combining site-directed mutagenesis, heterologous expression, and molecular dynamics simulations that capture the conformational change of constitutively active mutants, we tentatively identified crucial residues for the function of these receptors using the mouse MOR256-3 (Olfr124) as a model. The toggle switch for sensing agonists involves a highly conserved tyrosine residue in helix VI. The ionic lock is located between the "DRY" motif in helix III and a positively charged "R/K" residue in helix VI. This study provides an unprecedented model that captures the main mechanisms of odorant receptor activation.

Development of a stress-induced mutagenesis module for autonomous adaptive evolution of Escherichia coli to improve its stress tolerance.

BackgroundMicrobial tolerance to different environmental stresses is of importance for efficient production of biofuels and biochemical. Such traits are often improved by evolutionary engineering approaches including mutagen-induced mutagenesis and successive passage. In contrast to these approaches which generate mutations in rapidly growing cells, recent research showed that mutations could be generated in non-dividing cells under stressful but non-lethal conditions, leading to the birth of the theory of stress-induced mutagenesis (SIM). A molecular mechanism of SIM has been elucidated to be mutagenic repair of DNA breaks. This inspired us to develop a synthetic SIM module to simulate the mutagenic cellular response so as to accelerate microbial adaptive evolution for an improved stress tolerance.ResultsA controllable SIM evolution module was devised based on a genetic toggle switch in Escherichia coli. The synthetic module enables expression and repression of the genes related to up- and down-regulation responses during SIM in a bistable way. Upon addition of different inducers, the module can be turned on or off, triggering transition to a mutagenic or a high-fidelity state and thus allowing periodic adaptive evolution. Six genes (recA, dinB, umuD, ropS, ropE, and nusA) in the up-regulation responses were evaluated for their potentials to enhance the SIM rate. Expression of recA, dinB, or ropS alone increased the SIM rate by 4.5- to 13.7-fold, whereas their combined expression improved the rate by 31.9-fold. Besides, deletion of mutL increased the SIM rate by 82-fold. Assembly of these genes into the SIM module in the mutL-deletion E. coli strain elevated the SIM rate by nearly 3000-fold. Accelerated adaptive evolution of E. coli equipped with this synthetic SIM module was demonstrated under n-butanol stress, with the minimal inhibitory concentration of n-butanol increasing by 56 % within 2.5 months.ConclusionsA synthetic SIM module was constructed to simulate cellular mutagenic responses during SIM. Based on this, a novel evolutionary engineering approach—SIM-based adaptive evolution—was developed to improve the n-butanol tolerance of E. coli.Electronic supplementary materialThe online version of this article (doi:10.1186/s13068-015-0276-1) contains supplementary material, which is available to authorized users.

Using noise to control heterogeneity of isogenic populations in homogenous environments

We explore the extent to which the phenotypes of individual, genetically identical cells can be controlled independently from each other using only a single homogeneous environmental input. We show that such control is theoretically impossible if restricted to a deterministic setting, but it can be achieved readily if one exploits heterogeneities introduced at the single-cell level due to stochastic fluctuations in gene regulation. Using stochastic analyses of a bistable genetic toggle switch, we develop a control strategy that maximizes the chances that a chosen cell will express one phenotype, while the rest express another. The control mechanism uses UV radiation to enhance identically protein degradation in all cells. Control of individual cells is made possible only by monitoring stochastic protein fluctuations and applying UV control at favorable times and levels. For two identical cells, our stochastic control law can drive protein expression of a chosen cell above its neighbor with a better than 99% success rate. In a population of 30 identical cells, we can drive a given cell to remain consistently within the top 20%. Although cellular noise typically impairs predictability for biological responses, our results show that it can also simultaneously improve controllability for those same responses.

Synthesising gene clock with toggle switch and oscillator.

The usefulness of a genetic clock lies in its role to stimulate a sequence of logic reactions for sequential biological circuits. A clock signal is a periodic square wave, its amplitude alternates at a steady frequency between fixed minimal and maximal levels. Transition between the minimum and the maximum is instantaneous for an ideal square wave; however, the function is unrealisable in physical bio-systems. This research develops a new genetic clock generator based on a genetic oscillator, in which, a sine wave generator is adopted as a signal oscillator. It is shown that combination of a genetic oscillator with a toggle switch is able to generate clock signals forming an efficient way to generate a near square wave. In silico study confirms the proposed idea.

Colored Noise Induced Bistable Switch in the Genetic Toggle Switch Systems.

Noise can induce various dynamical behaviors in nonlinear systems. White noise perturbed systems have been extensively investigated during the last decades. In gene networks, experimentally observed extrinsic noise is colored. As an attempt, we investigate the genetic toggle switch systems perturbed by colored extrinsic noise and with kinetic parameters. Compared with white noise perturbed systems, we show there also exists optimal colored noise strength to induce the best stochastic switch behaviors in the single toggle switch, and the best synchronized switching in the networked systems, which demonstrate that noise-induced optimal switch behaviors are widely in existence. Moreover, under a wide range of system parameter regions, we find there exist wider ranges of white and colored noises strengths to induce good switch and synchronization behaviors, respectively; therefore, white noise is beneficial for switch and colored noise is beneficial for population synchronization. Our observations are very robust to extrinsic stimulus strength, cell density, and diffusion rate. Finally, based on the Waddington's epigenetic landscape and the Wiener-Khintchine theorem, physical mechanisms underlying the observations are interpreted. Our investigations can provide guidelines for experimental design, and have potential clinical implications in gene therapy and synthetic biology.

Cardiac contractility structure-activity relationship and ligand-receptor interactions; the discovery of unique and novel molecular switches in myosuppressin signaling.

Peptidergic signaling regulates cardiac contractility; thus, identifying molecular switches, ligand-receptor contacts, and antagonists aids in exploring the underlying mechanisms to influence health. Myosuppressin (MS), a decapeptide, diminishes cardiac contractility and gut motility. Myosuppressin binds to G protein-coupled receptor (GPCR) proteins. Two Drosophila melanogaster myosuppressin receptors (DrmMS-Rs) exist; however, no mechanism underlying MS-R activation is reported. We predicted DrmMS-Rs contained molecular switches that resembled those of Rhodopsin. Additionally, we believed DrmMS-DrmMS-R1 and DrmMS-DrmMS-R2 interactions would reflect our structure-activity relationship (SAR) data. We hypothesized agonist- and antagonist-receptor contacts would differ from one another depending on activity. Lastly, we expected our study to apply to other species; we tested this hypothesis in Rhodnius prolixus, the Chagas disease vector. Searching DrmMS-Rs for molecular switches led to the discovery of a unique ionic lock and a novel 3–6 lock, as well as transmission and tyrosine toggle switches. The DrmMS-DrmMS-R1 and DrmMS-DrmMS-R2 contacts suggested tissue-specific signaling existed, which was in line with our SAR data. We identified R. prolixus (Rhp)MS-R and discovered it, too, contained the unique myosuppressin ionic lock and novel 3–6 lock found in DrmMS-Rs as well as transmission and tyrosine toggle switches. Further, these motifs were present in red flour beetle, common water flea, honey bee, domestic silkworm, and termite MS-Rs. RhpMS and DrmMS decreased R. prolixus cardiac contractility dose dependently with EC50 values of 140 nM and 50 nM. Based on ligand-receptor contacts, we designed RhpMS analogs believed to be an active core and antagonist; testing on heart confirmed these predictions. The active core docking mimicked RhpMS, however, the antagonist did not. Together, these data were consistent with the unique ionic lock, novel 3–6 lock, transmission switch, and tyrosine toggle switch being involved in mechanisms underlying TM movement and MS-R activation, and the ability of MS agonists and antagonists to influence physiology.