Quantification of transcription noise's impact on cell fate commitment with digital resolutions.

MOTIVATION: Gene transcription is a random and noisy process. Tremendous efforts in single-cell studies have been mapping transcription noises to phenotypic variabilities between isogenic cells. However, the exact role of the noise in cell fate commitment remains largely descriptive or even controversial. RESULTS: For a specified cell fate, we define the jumping digit I of a critical gene as a statistical threshold that a single cell has approximately an equal chance to commit the fate as to have at least I transcripts of the gene. When the transcription is perturbed by a noise enhancer without changing the basal transcription level E0, we find a crossing digit k such that the noise catalyzes cell fate change when I > k while stabilizes the current state when I < k; k remains stable against enormous variations of kinetic rates. We further test the reactivation of latent HIV in 22 integration sites by noise enhancers paired with transcriptional activators. Strong synergistic actions are observed when the activators increase transcription burst frequency, whereas no synergism, but antagonism, is often observed if activators increase burst size. The synergistic efficiency can be predicted accurately by the ratio I/E0. When the noise enhancers double the noise, the activators double the burst frequency, and I/E0≥7, their combination is 10 times more effective than their additive effects across all 22 sites. AVAILABILITY AND IMPLEMENTATION: The jumping digit I may provide a novel probe to explore the phenotypic consequences of transcription noise in cell functions. Code is freely available at http://cam.gzhu.edu.cn/info/1014/1223.htm. The data underlying this article are available in the article and in its online supplementary material. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Incompatible and sterile insect techniques combined eliminate mosquitoes.

The radiation-based sterile insect technique (SIT) has successfully suppressed field populations of several insect pest species, but its effect on mosquito vector control has been limited. The related incompatible insect technique (IIT)-which uses sterilization caused by the maternally inherited endosymbiotic bacteria Wolbachia-is a promising alternative, but can be undermined by accidental release of females infected with the same Wolbachia strain as the released males. Here we show that combining incompatible and sterile insect techniques (IIT-SIT) enables near elimination of field populations of the world's most invasive mosquito species, Aedes albopictus. Millions of factory-reared adult males with an artificial triple-Wolbachia infection were released, with prior pupal irradiation of the released mosquitoes to prevent unintentionally released triply infected females from successfully reproducing in the field. This successful field trial demonstrates the feasibility of area-wide application of combined IIT-SIT for mosquito vector control.

The nonlinear dynamics and fluctuations of mRNA levels in cell cycle coupled transcription.

Gene transcription is a noisy process, and cell division cycle is an important source of gene transcription noise. In this work, we develop a mathematical approach by coupling transcription kinetics with cell division cycles to delineate how they are combined to regulate transcription output and noise. In view of gene dosage, a cell cycle is divided into an early stage [Formula: see text] and a late stage [Formula: see text]. The analytical forms for the mean and the noise of mRNA numbers are given in each stage. The analysis based on these formulas predicts precisely the fold change r* of mRNA numbers from [Formula: see text] to [Formula: see text] measured in a mouse embryonic stem cell line. When transcription follows similar kinetics in both stages, r* buffers against DNA dosage variation and r* ∈ (1, 2). Numerical simulations suggest that increasing cell cycle durations up-regulates transcription with less noise, whereas rapid stage transitions induce highly noisy transcription. A minimization of the transcription noise is observed when transcription homeostasis is attained by varying a single kinetic rate. When the transcription level scales with cellular volume, either by reducing the transcription burst frequency or by increasing the burst size in [Formula: see text], the noise shows only a minor variation over a wide range of cell cycle stage durations. The reduction level in the burst frequency is nearly a constant, whereas the increase in the burst size is conceivably sensitive, when responding to a large random variation of the cell cycle durations and the gene duplication time.

Use of age-stage structural models to seek optimal Wolbachia-infected male mosquito releases for mosquito-borne disease control.

Due to the lack of vaccines and effective clinical cures, current methods to control mosquito-borne viral diseases such as dengue and Zika are primarily targeting to eradicate the major mosquito vectors. However, traditional means, including larval source reduction and applications of insecticides etc, are not sufficient to keep vector population density below the epidemic risk threshold. An innovative and operational strategy is to release Wolbachia-infected male mosquitoes into wild areas to sterilize wild female mosquitoes by cytoplasmic incompatibility. To help design optimal release strategies before large scale and expensive operations, we started with an age-stage discrete model to track daily abundances of wild female mosquitoes, which fitted the field data collected by Guangzhou Center for Disease Control and Prevention from 2015 to 2017 with an average Pearson correlation coefficient 0.7283. Then, we modeled the Wolbachia interference by introducing the proportional releases of Wolbachia-infected males, and eight optimal release policies which guarantee more than 95% suppression efficiency were sought. Finally, we assessed the robustness of the optimality of the eight release policies by allowing the migration of females or the contamination of Wolbachia-infected females by two further extended mathematical models.

Linking dynamical complexities from activation signals to transcription responses.

The transcription of inducible genes involves signalling pathways that induce DNA binding of the downstream transcription factors to form functional promoter states. How the transcription dynamics is linked to the temporal variations of activation signals is far from being fully understood. In this work, we develop a mathematical model with multiple promoter states to address this question. Each promoter state has its own activation and inactivation rates and is selected randomly with a probability that may change in time. Under the activation of constant signals, our analysis shows that if only the activation rates differ among the promoter states, then the mean transcription level m(t) displays only a monotone or monophasic growth pattern. In a sharp contrast, if the inactivation rates change with the promoter states, then m(t) may display multiphasic growth patterns. Upon the activation of signals that oscillate periodically, m(t) also oscillates later, almost periodically at the same frequency, but the magnitude decreases with frequency and is almost completely attenuated at high frequencies. This gives a surprising indication that multiple promoter states could filter out the signal oscillation and the noise in the random promoter state selection, as observed in the transcription of a gene activated by p53 in breast carcinoma cells. Our approach may help develop a theoretical framework to integrate coherently the genetic circuit with the promoter states to elucidate the linkage from the activation signal to the temporal profile of transcription outputs.

Wolbachia spread dynamics in multi-regimes of environmental conditions.

Mosquito-borne diseases such as dengue fever and Zika kill more than 700,000 people each year in the world. A novel strategy to control these diseases employs the bacterium Wolbachia whose infection in mosquitoes blocks virus replication. The prerequisite for this measure is to release Wolbachia -infected mosquitoes to replace wild population. Due to the fluctuation of environmental conditions for mosquito growth, we develop and analyze a model of differential equations with parameters randomly changing over multiple environmental regimes. By comparing the dynamics between the stochastic system and constructed auxiliary systems, combined with other techniques, we provide sharp estimates on the threshold releasing level for Wolbachia fixation. We define the alarm period of disease transmission to measure the risk of mosquito-borne diseases. Our numerical simulations suggest that more frequent inter-regime transitions help reduce the alarm period, and the disease transmission is more sensitive to the average climatic conditions than the number of sub-regimes over a given time period. Further numerical examples also indicate that the reduction in the waiting time to suppress 95% of wild population is more evident when the releasing amount is increased up to a double of the wild population.

Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission.

Mosquitoes are primary vectors of life-threatening diseases such as dengue, malaria, and Zika. A new control method involves releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect wild mosquitoes and block disease transmission. In this work, we use differential equations to describe Wolbachia spreading dynamics, focusing on the poorly understood effect of imperfect maternal transmission. We establish two useful identities and employ them to prove that the system exhibits monomorphic, bistable, and polymorphic dynamics, and give sufficient and necessary conditions for each case. The results suggest that the largest maternal transmission leakage rate supporting Wolbachia spreading does not necessarily increase with the fitness of infected mosquitoes. The bistable dynamics is defined by the existence of two stable equilibria, whose basins of attraction are divided by the separatrix of a saddle point. By exploring the analytical property of the separatrix with some sharp estimates, we find that Wolbachia in a completely infected population could be wiped out ultimately if the initial population size is small. Surprisingly, when the infection shortens the lifespan of infected females that would impede Wolbachia spreading, such a reversion phenomenon does not occur.

Wolbachia spread dynamics in stochastic environments.

Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments.

Transcription dynamics of inducible genes modulated by negative regulations.

Gene transcription is a stochastic process in single cells, in which genes transit randomly between active and inactive states. Transcription of many inducible genes is also tightly regulated: It is often stimulated by extracellular signals, activated through signal transduction pathways and later repressed by negative regulations. In this work, we study the nonlinear dynamics of the mean transcription level of inducible genes modulated by the interplay of the intrinsic transcriptional randomness and the repression by negative regulations. In our model, we integrate negative regulations into gene activation process, and make the conventional assumption on the production and degradation of transcripts. We show that, whether or not the basal transcription is temporarily terminated when cells are stimulated, the mean transcription level grows in the typical up and down pattern commonly observed in immune response genes. With the help of numerical simulations, we clarify the delicate impact of the system parameters on the transcription dynamics, and demonstrate how our model generates the distinct temporal gene-induction patterns in mouse fibroblasts discerned in recent experiments.

The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway activated transcription.

Gene transcription is a stochastic process, and is often activated by multiple signal transduction pathways. In this work, we study gene transcription activated randomly by two cross-talking pathways, with the messenger RNA (mRNA) molecules being produced in a simple birth and death process. We derive the analytical formulas for the mean and the second moment of mRNA copy numbers and characterize the nature of transcription noise. We find that the stationary noise strength Φ is close to its baseline limit 1 when the mRNA level is high due to strong activation or stable transcription, or the mRNA level is low due to unstable transcription or ineffective mRNA production. If Φ stays well above 1, then the gene is infrequently active but mRNAs are accumulated rapidly once it is active. In this case, the system generates a transcriptional bursting, and the mean mRNA level peaks at a finite time. By examining the nonlinear dependance of Φ on transcriptional efficiency, we show that the maximum noise strength is attained only when the gene is silent in the majority of cells as observed in recent experiments. By comparing the current findings with our previous results in sequential pathway model, we come up with a profound conclusion that parallel, cross-talking pathways tend to increase transcription noise, whereas sequential pathways tend to reduce transcription noise. A further study on gene transcription activated by entangling pathways may help us reveal the subtle connection between the characteristics of transcription noise and the topology of genetic network.

The mean and noise of protein numbers in stochastic gene expression.

Gene expression is the central process in cells, and is stochastic in nature. In this work, we study the mean expression level of, and the expression noise in, a population of isogenic cells, assuming that transcription is activated by two sequential exponential processes of rates κ and λ. We find that the mean expression level often displays oscillatory dynamics, whereas most other models suggest that it always grows monotonically. We show that, given the same average gene off duration, the asymptotic expression noise increases with |κ - λ|, and is thus maximized when either κ → ∞ or λ → ∞, for which the two exponential processes approach to one process. It suggests that natural selection may favor two or more rate-limiting steps for gene transcription activation. Our analysis reveals that, at steady-state, the noise equals the inverse of the mean, plus the normalized covariance of the mRNA and protein copy numbers. This interesting identity partially explains a recent striking finding that the protein noises of many Escherichia coli genes were close to the inverse of the mean protein levels, and simultaneously, the protein and mRNA copy numbers within the individual cells were uncorrelated. We show further that the protein noise is close to the inverse of the mean if the gene is transcribed effectively and almost continuously, and the protein molecules are considerably more stable than the mRNAs. Such phenomenon has been observed repeatedly in the synthetic reporter genes controlled by strong promoters and tagged with fluorescent labels.

Modulation of gene transcription noise by competing transcription factors.

Sequence specific transcription factors (TFs) are critical to ensuring that genes are transcribed in the right cell at the right time. Often, the gene promoter is flanked by multiple binding sites, some of which can be bound by different types of TFs in the cell. To investigate how the transcription noise is modulated by the competition of these TFs at their shared binding sites, we model gene transcription as a renewal process where the time spent in each transcription cycle is assumed to be independently and identically distributed. With the help of the elementary renewal theorem and the central limit theorem, we prove that the stationary noise strength Φ of transcription frequency equals the noise η (2) of the time spent in a single transcription cycle. Subsequent analysis shows that competitive TF binding could produce an unbounded spectrum of Φ, in sharp contrast to the estimate 1/3 ≤ Φ < for single binding pattern activated transcription. We predict several mechanisms by which genes could stay away from abnormally noisy transcription while living with multiple binding patterns. The most efficient one is to maintain a relatively long engaged time by transcription pausing, interrupting, or other means. Alternatively, high noise strength is prevented if all binding patterns activate transcription strongly. When some binding patterns activate transcription weakly, low noise strength is ensured if the binding pattern with the weakest activation strength is utilized frequently.

Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways.

Gene transcription is a central cellular process and is stochastic in nature. The stochasticity has been studied in real cells and in theory, but often for the transcription activated by a single signaling pathway at steady-state. As transcription of many genes is involved with multiple pathways, we investigate how the transcription efficiency and noise is modulated by cross-talking pathways. We model gene transcription as a renewal process for which the gene can be turned on by different pathways. We determine the transcription efficiency by solving a system of differential equations, and obtain the mathematical formula of the noise strength by the Laplace transform and standard techniques in renewal theory. Our numerical examples demonstrate that cross-talking pathways are capable of inducing more cells to transcribe than the steady-state level after a short time period of signal transduction, and creating exceedingly high stationary transcription noise strength. In contrast, it is shown that one signaling pathway alone is unable to do so. Very strikingly, it is observed that the noise strength varies gradually over most values of the system parameters, but changes abruptly over a narrow range in the neighborhoods of some critical parameter values.

The mean frequency of transcriptional bursting and its variation in single cells.

The recent in vivo RNA detection technique has allowed real-time monitoring of gene transcription in individual living cells, revealing that genes can be transcribed randomly in a bursting fashion that short periods of rapid production of multiple transcripts are interspersed with relatively long periods of no production. In this work, we utilize the three state model to study how environmental signals and the intrinsic cellular contexts are combined to regulate stochastic gene transcription. We introduce a system of three master equations to model the stochastic occurrence of transcriptional bursting. As this system cannot be solved analytically, we introduce a linear operator, called the master operator. It is of significant mathematical interests of its own and transforms the mean frequency of transcriptional bursting mu(t) and the second moment mu2(t) into the unique solutions of the respective operator equations. Following this novel approach, we have found the exact forms of mu(t) and the variance sigma2(t). Our analysis shows that the three state transition process produces less noisy transcription than a single Poisson process does, and more transition steps average out rather than propagate fluctuations of transcripts among individual cells. The noise strength phi(t) = sigma2(t)/mu(t) displays highly non-trivial dynamics during the first two to three transcription cycles. It declines steeply from the beginning until reaching the absolute minimum value, and then bounces back suddenly to a flat level close to the steady-state. Our numerical simulations further demonstrate that the cellular signals that produce the least noisy population at steady-state may not generate the least noisy population in a finite time, and suggest that measurements at steady-state may not necessarily capture most essential features of transcription noise.

The mean and noise of stochastic gene transcription.

Gene transcription in single cells is inherently a probabilistic process. Even in a hypothetically homogeneous intracellular environment, the stochasticity of transcription would produce fluctuations in the number of transcripts, constituting the phenotypic heterogeneity in cell population. Noise, the variance normalized by the square of the mean, has typically been utilized to quantify the heterogeneity of transcript distribution. The noise has been thought to arise from random switching between gene on and gene off states, but what underlies the stochastic transition between the on state and the off state remains largely unknown. To examine how the environmental signals contribute to the gene transcription regulation, we employ a three states model to evaluate the dynamical and stationary mean transcript level, and the noise of transcript distribution. Our findings reinforce the assertion of Raser and O'Shea [2004. Control of stochasticity in eukaryotic gene expression. Science 304, 1811-1814] that two cells can produce the same mean mRNA population but display different noise characteristics. The theoretical analysis also brings new characteristics to the subtle correlations between the mean and the noise, which extends beyond the categorization of Raser and O'Shea.