Nonself RNA rewires IFN-ß signaling: A mathematical model of the innate immune response.

Type I interferons (IFNs) are key coordinators of the innate immune response to viral infection, which, through activation of the transcriptional regulators STAT1 and STAT2 (STAT1/2) in bystander cells, induce the expression of IFN-stimulated genes (ISGs). Here, we showed that in cells transfected with poly(I:C), an analog of viral RNA, the transcriptional activity of STAT1/2 was terminated because of depletion of the interferon-ß (IFN-ß) receptor, IFNAR. Activation of RNase L and PKR, products of two ISGs, not only hindered the replenishment of IFNAR but also suppressed negative regulators of IRF3 and NF-κB, consequently promoting IFNB transcription. We incorporated these findings into a mathematical model of innate immunity. By coupling signaling through the IRF3-NF-κB and STAT1/2 pathways with the activities of RNase L and PKR, the model explains how poly(I:C) switches the transcriptional program from being STAT1/2 induced to being IRF3 and NF-κB induced, which converts IFN-ß-responding cells to IFN-ß-secreting cells.

Single-Cell Measurements and Modeling and Computation of Decision-Making Errors in a Molecular Signaling System with Two Output Molecules.

A cell constantly receives signals and takes different fates accordingly. Given the uncertainty rendered by signal transduction noise, a cell may incorrectly perceive these signals. It may mistakenly behave as if there is a signal, although there is none, or may miss the presence of a signal that actually exists. In this paper, we consider a signaling system with two outputs, and introduce and develop methods to model and compute key cell decision-making parameters based on the two outputs and in response to the input signal. In the considered system, the tumor necrosis factor (TNF) regulates the two transcription factors, the nuclear factor κB (NFκB) and the activating transcription factor-2 (ATF-2). These two system outputs are involved in important physiological functions such as cell death and survival, viral replication, and pathological conditions, such as autoimmune diseases and different types of cancer. Using the introduced methods, we compute and show what the decision thresholds are, based on the single-cell measured concentration levels of NFκB and ATF-2. We also define and compute the decision error probabilities, i.e., false alarm and miss probabilities, based on the concentration levels of the two outputs. By considering the joint response of the two outputs of the signaling system, one can learn more about complex cellular decision-making processes, the corresponding decision error rates, and their possible involvement in the development of some pathological conditions.

Antagonism between viral infection and innate immunity at the single-cell level.

When infected with a virus, cells may secrete interferons (IFNs) that prompt nearby cells to prepare for upcoming infection. Reciprocally, viral proteins often interfere with IFN synthesis and IFN-induced signaling. We modeled the crosstalk between the propagating virus and the innate immune response using an agent-based stochastic approach. By analyzing immunofluorescence microscopy images we observed that the mutual antagonism between the respiratory syncytial virus (RSV) and infected A549 cells leads to dichotomous responses at the single-cell level and complex spatial patterns of cell signaling states. Our analysis indicates that RSV blocks innate responses at three levels: by inhibition of IRF3 activation, inhibition of IFN synthesis, and inhibition of STAT1/2 activation. In turn, proteins coded by IFN-stimulated (STAT1/2-activated) genes inhibit the synthesis of viral RNA and viral proteins. The striking consequence of these inhibitions is a lack of coincidence of viral proteins and IFN expression within single cells. The model enables investigation of the impact of immunostimulatory defective viral particles and signaling network perturbations that could potentially facilitate containment or clearance of the viral infection.

Predictive power of non-identifiable models.

Resolving practical non-identifiability of computational models typically requires either additional data or non-algorithmic model reduction, which frequently results in models containing parameters lacking direct interpretation. Here, instead of reducing models, we explore an alternative, Bayesian approach, and quantify the predictive power of non-identifiable models. We considered an example biochemical signalling cascade model as well as its mechanical analogue. For these models, we demonstrated that by measuring a single variable in response to a properly chosen stimulation protocol, the dimensionality of the parameter space is reduced, which allows for predicting the measured variable's trajectory in response to different stimulation protocols even if all model parameters remain unidentified. Moreover, one can predict how such a trajectory will transform in the case of a multiplicative change of an arbitrary model parameter. Successive measurements of remaining variables further reduce the dimensionality of the parameter space and enable new predictions. We analysed potential pitfalls of the proposed approach that can arise when the investigated model is oversimplified, incorrect, or when the training protocol is inadequate. The main advantage of the suggested iterative approach is that the predictive power of the model can be assessed and practically utilised at each step.

A plausible identifiable model of the canonical NF-κB signaling pathway.

An overwhelming majority of mathematical models of regulatory pathways, including the intensively studied NF-κB pathway, remains non-identifiable, meaning that their parameters may not be determined by existing data. The existing NF-κB models that are capable of reproducing experimental data contain non-identifiable parameters, whereas simplified models with a smaller number of parameters exhibit dynamics that differs from that observed in experiments. Here, we reduced an existing model of the canonical NF-κB pathway by decreasing the number of equations from 15 to 6. The reduced model retains two negative feedback loops mediated by IκBα and A20, and in response to both tonic and pulsatile TNF stimulation exhibits dynamics that closely follow that of the original model. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is both structurally and practically identifiable given measurements of 5 model variables from a simple TNF stimulation protocol. The reduced model is capable of reproducing different types of responses that are characteristic to regulatory motifs controlled by negative feedback loops: nearly-perfect adaptation as well as damped and sustained oscillations. It can serve as a building block of more comprehensive models of the immune response and cancer, where NF-κB plays a decisive role. Our approach, although may not be automatically generalized, suggests that models of other regulatory pathways can be transformed to identifiable, while retaining their dynamical features.

The MAPK/ERK channel capacity exceeds 6 bit/hour.

Living cells utilize signaling pathways to sense, transduce, and process information. As the extracellular stimulation often has rich temporal characteristics which may govern dynamic cellular responses, it is important to quantify the rate of information flow through the signaling pathways. In this study, we used an epithelial cell line expressing a light-activatable FGF receptor and an ERK activity reporter to assess the ability of the MAPK/ERK pathway to transduce signal encoded in a sequence of pulses. By stimulating the cells with random light pulse trains, we demonstrated that the MAPK/ERK channel capacity is at least 6 bits per hour. The input reconstruction algorithm detects the light pulses with 1-min accuracy 5 min after their occurrence. The high information transmission rate may enable the pathway to coordinate multiple processes including cell movement and respond to rapidly varying stimuli such as chemoattracting gradients created by other cells.

Respiratory Syncytial Virus Protects Bystander Cells against Influenza A Virus Infection by Triggering Secretion of Type I and Type III Interferons.

We observed the interference between two prevalent respiratory viruses, respiratory syncytial virus (RSV) and influenza A virus (IAV) (H1N1), and characterized its molecular underpinnings in alveolar epithelial cells (A549). We found that RSV induces higher levels of interferon beta (IFN-ß) production than IAV and that IFN-ß priming confers higher-level protection against infection with IAV than with RSV. Consequently, we focused on the sequential infection scheme of RSV and then IAV. Using A549 wild-type (WT), IFNAR1 knockout (KO), IFNLR1 KO, and IFNAR1-IFNLR1 double-KO cell lines, we found that both IFN-ß and IFN-λ are necessary for maximum protection against subsequent infection. Immunostaining revealed that preinfection with RSV partitions the cell population into a subpopulation susceptible to subsequent infection with IAV and an IAV-proof subpopulation. Strikingly, the susceptible cells turned out to be those already compromised and efficiently expressing RSV, whereas the bystander, interferon-primed cells are resistant to IAV infection. Thus, virus-virus exclusion at the cell population level is not realized through direct competition for a shared ecological niche (single cell) but rather is achieved with the involvement of specific cytokines induced by the host's innate immune response. IMPORTANCE Influenza A virus (IAV) and respiratory syncytial virus (RSV) are common recurrent respiratory infectants that show a relatively high coincidence. We demonstrated that preinfection with RSV partitions the cell population into a subpopulation susceptible to subsequent infection with IAV and an IAV-proof subpopulation. The susceptible cells are those already compromised and efficiently expressing RSV, whereas the bystander cells are resistant to IAV infection. The cross-protective effect critically depends on IFN-ß and IFN-λ signaling and thus ensues when the proportion of cells preinfected with RSV is relatively low yet sufficient to trigger a pervasive antiviral state in bystander cells. Our study suggests that mild, but not severe, respiratory infections may have a short-lasting protective role against more dangerous respiratory viruses, including severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).

The Spread of SARS-CoV-2 Variant Omicron with a Doubling Time of 2.0-3.3 Days Can Be Explained by Immune Evasion.

Omicron, the novel highly mutated SARS-CoV-2 Variant of Concern (VOC, Pango lineage B.1.1.529) was first collected in early November 2021 in South Africa. By the end of November 2021, it had spread and approached fixation in South Africa, and had been detected on all continents. We analyzed the exponential growth of Omicron over four-week periods in the two most populated of South Africa's provinces, Gauteng and KwaZulu-Natal, arriving at the doubling time estimates of, respectively, 3.3 days (95% CI: 3.2-3.4 days) and 2.7 days (95% CI: 2.3-3.3 days). Similar or even shorter doubling times were observed in other locations: Australia (3.0 days), New York State (2.5 days), UK (2.4 days), and Denmark (2.0 days). Log-linear regression suggests that the spread began in Gauteng around 11 October 2021; however, due to presumable stochasticity in the initial spread, this estimate can be inaccurate. Phylogenetics-based analysis indicates that the Omicron strain started to diverge between 6 October and 29 October 2021. We estimated that the weekly growth of the ratio of Omicron to Delta is in the range of 7.2-10.2, considerably higher than the growth of the ratio of Delta to Alpha (estimated to be in in the range of 2.5-4.2), and Alpha to pre-existing strains (estimated to be in the range of 1.8-2.7). High relative growth does not necessarily imply higher Omicron infectivity. A two-strain SEIR model suggests that the growth advantage of Omicron may stem from immune evasion, which permits this VOC to infect both recovered and fully vaccinated individuals. As we demonstrated within the model, immune evasion is more concerning than increased transmissibility, because it can facilitate larger epidemic outbreaks.

Slow nucleosome dynamics set the transcriptional speed limit and induce RNA polymerase II traffic jams and bursts.

Nucleosomes are recognized as key regulators of transcription. However, the relationship between slow nucleosome unwrapping dynamics and bulk transcriptional properties has not been thoroughly explored. Here, an agent-based model that we call the dynamic defect Totally Asymmetric Simple Exclusion Process (ddTASEP) was constructed to investigate the effects of nucleosome-induced pausing on transcriptional dynamics. Pausing due to slow nucleosome dynamics induced RNAPII convoy formation, which would cooperatively prevent nucleosome rebinding leading to bursts of transcription. The mean first passage time (MFPT) and the variance of first passage time (VFPT) were analytically expressed in terms of the nucleosome rate constants, allowing for the direct quantification of the effects of nucleosome-induced pausing on pioneering polymerase dynamics. The mean first passage elongation rate γ(hc, ho) is inversely proportional to the MFPT and can be considered to be a new axis of the ddTASEP phase diagram, orthogonal to the classical αß-plane (where α and ß are the initiation and termination rates). Subsequently, we showed that, for ß = 1, there is a novel jamming transition in the αγ-plane that separates the ddTASEP dynamics into initiation-limited and nucleosome pausing-limited regions. We propose analytical estimates for the RNAPII density ρ, average elongation rate v, and transcription flux J and verified them numerically. We demonstrate that the intra-burst RNAPII waiting times tin follow the time-headway distribution of a max flux TASEP and that the average inter-burst interval [Formula: see text] correlates with the index of dispersion De. In the limit γ→0, the average burst size reaches a maximum set by the closing rate hc. When α≪1, the burst sizes are geometrically distributed, allowing large bursts even while the average burst size [Formula: see text] is small. Last, preliminary results on the relative effects of static and dynamic defects are presented to show that dynamic defects can induce equal or greater pausing than static bottle necks.

SARS-CoV-2 Variant of Concern 202012/01 Has about Twofold Replicative Advantage and Acquires Concerning Mutations.

The novel SARS-CoV-2 Variant of Concern (VOC)-202012/01 (also known as B.1.1.7), first collected in United Kingdom on 20 September 2020, is a rapidly growing lineage that in January 2021 constituted 86% of all SARS-CoV-2 genomes sequenced in England. The VOC has been detected in 40 out of 46 countries that reported at least 50 genomes in January 2021. We have estimated that the replicative advantage of the VOC is in the range 1.83-2.18 [95% CI: 1.71-2.40] with respect to the 20A.EU1 variant that dominated in England in November 2020, and in range 1.65-1.72 [95% CI: 1.46-2.04] in Wales, Scotland, Denmark, and USA. As the VOC strain will likely spread globally towards fixation, it is important to monitor its molecular evolution. We have estimated growth rates of expanding mutations acquired by the VOC lineage to find that the L18F substitution in spike has initiated a fast growing VOC substrain. The L18F substitution is of significance because it has been found to compromise binding of neutralizing antibodies. Of concern are immune escape mutations acquired by the VOC: E484K, F490S, S494P (in the receptor binding motif of spike) and Q677H, Q675H (in the proximity of the polybasic cleavage site at the S1/S2 boundary). These mutants may hinder efficiency of existing vaccines and expand in response to the increasing after-infection or vaccine-induced seroprevalence.

Pareto-based evaluation of national responses to COVID-19 pandemic shows that saving lives and protecting economy are non-trade-off objectives.

Countries worldwide have adopted various strategies to minimize the socio-economic impact of the ongoing COVID-19 pandemic. Stringency of imposed measures universally reflects the standpoint from which protecting public health and avoiding damage to economy are seen as contradictory objectives. Based on epidemic trajectories of 25 highly developed countries and 10 US states in the (mobility reduction)-(reproduction number) plane we showed that delay in imposition of nation-wide quarantine elevates the number of infections and deaths, surge of which inevitably has to be suppressed by stringent and sustained lockdown. As a consequence, cumulative mobility reduction and population-normalized cumulative number of COVID-19-associated deaths are significantly correlated and this correlation increases with time. Overall, we demonstrated that, as long as epidemic suppression is the aim, the trade-off between the death toll and economic loss is illusory: high death toll correlates with deep and long-lasting lockdown causing a severe economic downturn.

Electrochemical Immunosensors Based on Screen-Printed Gold and Glassy Carbon Electrodes: Comparison of Performance for Respiratory Syncytial Virus Detection.

This paper presents the development and comparison of label-free electrochemical immunosensors based on screen-printed gold and glassy carbon (GC) disc electrodes for efficient and rapid detection of respiratory syncytial virus (RSV). Briefly, the antibody specific to the F protein of RSV was successfully immobilized on modified electrodes. Antibody coupling on the Au surface was conducted via 4-aminothiophenol (4-ATP) and glutaraldehyde (GA). The GC surface was modified with poly-L-lysine (PLL) for direct anti-RSV conjugation after EDC/NHS (1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide/N-Hydroxysuccinimide) activation. Electrochemical characterizations of the immunosensors were carried out by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). GC-based immunosensors show a dynamic range of antigen detection from 1.0 × 105 PFU/mL to 1.5×107 PFU/mL, more than 1.0 × 105 PFU/mL to 1.0 × 107 PFU/mL for the Au-based sensor. However, the GC platform is less sensitive and shows a higher detection limit (LOD) for RSV. The limit of detection of the Au immunosensor is 1.1 × 103 PFU/mL, three orders of magnitude lower than 2.85 × 106 PFU/mL for GC. Thus, the Au-based immunosensor has better analytical performance for virus detection than a carbon-based platform due to high sensitivity and very low RSV detection, obtained with good reproducibility.

Super-spreading events initiated the exponential growth phase of COVID-19 with ℛ0 higher than initially estimated.

The basic reproduction number R 0 of the coronavirus disease 2019 has been estimated to range between 2 and 4. Here, we used an SEIR model that properly accounts for the distribution of the latent period and, based on empirical estimates of the doubling time in the near-exponential phases of epidemic progression in China, Italy, Spain, France, UK, Germany, Switzerland and New York State, we estimated that R 0 lies in the range 4.7-11.4. We explained this discrepancy by performing stochastic simulations of model dynamics in a population with a small proportion of super-spreaders. The simulations revealed two-phase dynamics, in which an initial phase of relatively slow epidemic progression diverts to a faster phase upon appearance of infectious super-spreaders. Early estimates obtained for this initial phase may suggest lower R 0 .

Model-based optimization of combination protocols for irradiation-insensitive cancers.

Alternations in the p53 regulatory network may render cancer cells resistant to the radiation-induced apoptosis. In this theoretical study we search for the best protocols combining targeted therapy with radiation to treat cancers with wild-type p53, but having downregulated expression of PTEN or overexpression of Wip1 resulting in resistance to radiation monotherapy. Instead of using the maximum tolerated dose paradigm, we exploit stochastic computational model of the p53 regulatory network to calculate apoptotic fractions for both normal and cancer cells. We consider combination protocols, with irradiations repeated every 12, 18, 24, or 36 h to find that timing between Mdm2 inhibitor delivery and irradiation significantly influences the apoptotic cell fractions. We assume that uptake of the inhibitor is higher by cancer than by normal cells and that cancer cells receive higher irradiation doses from intersecting beams. These two assumptions were found necessary for the existence of protocols inducing massive apoptosis in cancer cells without killing large fraction of normal cells neighboring tumor. The best found protocols have irradiations repeated every 24 or 36 h with two inhibitor doses per irradiation cycle, and allow to induce apoptosis in more than 95% of cancer cells, killing less than 10% of normal cells.

Modeling and measurement of signaling outcomes affecting decision making in noisy intracellular networks using machine learning methods.

Characterization of decision-making in cells in response to received signals is of importance for understanding how cell fate is determined. The problem becomes multi-faceted and complex when we consider cellular heterogeneity and dynamics of biochemical processes. In this paper, we present a unified set of decision-theoretic, machine learning and statistical signal processing methods and metrics to model the precision of signaling decisions, in the presence of uncertainty, using single cell data. First, we introduce erroneous decisions that may result from signaling processes and identify false alarms and miss events associated with such decisions. Then, we present an optimal decision strategy which minimizes the total decision error probability. Additionally, we demonstrate how graphing receiver operating characteristic curves conveniently reveals the trade-off between false alarm and miss probabilities associated with different cell responses. Furthermore, we extend the introduced framework to incorporate the dynamics of biochemical processes and reactions in a cell, using multi-time point measurements and multi-dimensional outcome analysis and decision-making algorithms. The introduced multivariate signaling outcome modeling framework can be used to analyze several molecular species measured at the same or different time instants. We also show how the developed binary outcome analysis and decision-making approach can be extended to more than two possible outcomes. As an example and to show how the introduced methods can be used in practice, we apply them to single cell data of PTEN, an important intracellular regulatory molecule in a p53 system, in wild-type and abnormal cells. The unified signaling outcome modeling framework presented here can be applied to various organisms ranging from viruses, bacteria, yeast and lower metazoans to more complex organisms such as mammalian cells. Ultimately, this signaling outcome modeling approach can be utilized to better understand the transition from physiological to pathological conditions such as inflammation, various cancers and autoimmune diseases.

A shear stress micromodel of urinary tract infection by the Escherichia coli producing Dr adhesin.

In this study, we established a dynamic micromodel of urinary tract infection to analyze the impact of UT-segment-specific urinary outflow on the persistence of E. coli colonization. We found that the adherence of Dr+ E. coli to bladder T24 transitional cells and type IV collagen is maximal at lowest shear stress and is reduced by any increase in flow velocity. The analyzed adherence was effective in the whole spectrum of physiological shear stress and was almost irreversible over the entire range of generated shear force. Once Dr+ E. coli bound to host cells or collagen, they did not detach even in the presence of elevated shear stress or of chloramphenicol, a competitive inhibitor of binding. Investigating the role of epithelial surface architecture, we showed that the presence of budding cells-a model microarchitectural obstacle-promotes colonization of the urinary tract by E. coli. We report a previously undescribed phenomenon of epithelial cell "rolling-shedding" colonization, in which the detached epithelial cells reattach to the underlying cell line through a layer of adherent Dr+ E. coli. This rolling-shedding colonization progressed continuously due to "refilling" induced by the flow-perturbing obstacle. The shear stress of fluid containing free-floating bacteria fueled the rolling, while providing an uninterrupted supply of new bacteria to be trapped by the rolling cell. The progressive rolling allows for transfer of briefly attached bacteria onto the underlying monolayer in a repeating cascading event.

Limits to the rate of information transmission through the MAPK pathway.

Two important signalling pathways of NF-κB and ERK transmit merely 1 bit of information about the level of extracellular stimulation. It is thus unclear how such systems can coordinate complex cell responses to external cues. We analyse information transmission in the MAPK/ERK pathway that converts both constant and pulsatile EGF stimulation into pulses of ERK activity. Based on an experimentally verified computational model, we demonstrate that, when input consists of sequences of EGF pulses, transmitted information increases nearly linearly with time. Thus, pulse-interval transcoding allows more information to be relayed than the amplitude-amplitude transcoding considered previously for the ERK and NF-κB pathways. Moreover, the information channel capacity C, or simply bitrate, is not limited by the bandwidth B = 1/ τ, where τ ≈ 1 h is the relaxation time. Specifically, when the input is provided in the form of sequences of short binary EGF pulses separated by intervals that are multiples of τ/ n (but not shorter than τ), then for n = 2, C ≈ 1.39 bit h-1; and for n = 4, C ≈ 1.86 bit h-1. The capability to respond to random sequences of EGF pulses enables cells to propagate spontaneous ERK activity waves across tissue.

Sampling rare events in stochastic reaction-diffusion systems within trajectory looping.

In bistable reaction-diffusion systems, transitions between stable states typically occur on timescales orders of magnitude longer than the chemical equilibration time. Estimation of transition rates within explicit Brownian dynamics simulations is computationally prohibitively costly. We present a method that exploits a single trajectory, generated by a prior simulation of diffusive motions of molecules, to sample chemical kinetic processes on timescales several orders of magnitude longer than the duration of the diffusive trajectory. In this approach, we "loop" the diffusive trajectory by transferring chemical states of the molecules from the last to the first time step of the trajectory. Trajectory looping can be applied to enhance sampling of rare events in biochemical systems in which the number of reacting molecules is constant, as in cellular signal transduction pathways. As an example, we consider a bistable system of autophosphorylating kinases, for which we calculate state-to-state transition rates and traveling wave velocities. We provide an open-source implementation of the method.

Cell fate in antiviral response arises in the crosstalk of IRF, NF-κB and JAK/STAT pathways.

The innate immune system processes pathogen-induced signals into cell fate decisions. How information is turned to decision remains unknown. By combining stochastic mathematical modelling and experimentation, we demonstrate that feedback interactions between the IRF3, NF-κB and STAT pathways lead to switch-like responses to a viral analogue, poly(I:C), in contrast to pulse-like responses to bacterial LPS. Poly(I:C) activates both IRF3 and NF-κB, a requirement for induction of IFNß expression. Autocrine IFNß initiates a JAK/STAT-mediated positive-feedback stabilising nuclear IRF3 and NF-κB in first responder cells. Paracrine IFNß, in turn, sensitises second responder cells through a JAK/STAT-mediated positive feedforward pathway that upregulates the positive-feedback components: RIG-I, PKR and OAS1A. In these sensitised cells, the 'live-or-die' decision phase following poly(I:C) exposure is shorter-they rapidly produce antiviral responses and commit to apoptosis. The interlinked positive feedback and feedforward signalling is key for coordinating cell fate decisions in cellular populations restricting pathogen spread.

Genetic toggle switch controlled by bacterial growth rate.

BACKGROUND: In favorable conditions bacterial doubling time is less than 20 min, shorter than DNA replication time. In E. coli a single round of genome replication lasts about 40 min and it must be accomplished about 20 min before cell division. To achieve such fast growth rates bacteria perform multiple replication rounds simultaneously. As a result, when the division time is as short as 20 min E. coli has about 8 copies of origin of replication (ori) and the average copy number of the genes situated close to ori can be 4 times larger than those near the terminus of replication (ter). It implies that shortening of cell cycle may influence dynamics of regulatory pathways involving genes placed at distant loci. RESULTS: We analyze this effect in a model of a genetic toggle switch, i.e. a system of two mutually repressing genes, one localized in the vicinity of ori and the other localized in the vicinity of ter. Using a stochastic model that accounts for cell growth and divisions we demonstrate that shortening of the cell cycle can induce switching of the toggle to the state in which expression of the gene placed near ter is suppressed. The toggle bistability causes that the ratio of expression of the competing genes changes more than two orders of magnitude for a two-fold change of the doubling time. The increasing stability of the two toggle states enhances system sensitivity but also its reaction time. CONCLUSIONS: By fusing the competing genes with fluorescent tags this mechanism could be tested and employed to create an indicator of the doubling time. By manipulating copy numbers of the competing genes and locus of the gene situated near ter, one can obtain equal average expression of both genes for any doubling time T between 20 and 120 min. Such a toggle would accurately report departures of the doubling time from T.