Determining the Transcription Rates Yielding Steady-State Production of mRNA in the Lac Genetic Switch of Escherichia coli

To elucidate the regulatory dynamics of the gene expression activation and inactivation, an in silico biochemical model of the lac circuit in Escherichia coli was used to evaluate the transcription rates that yield the steady-state mRNA production in active and inactive states of the lac circuit. This result can be used in synthetic biology applications to understand the limits of the genetic synthesis. Since most genetic networks involve many interconnected components with positive and negative feedback control, intuitive understanding of their dynamics is often difficult to obtain. Although the kinetic model of the lac circuit considered involves only a single positive feedback, the developed computational framework can be used to evaluate supported ranges of other reaction rates in genetic circuits with more complex regulatory networks. More specifically, the inducible lac gene switch in E. coli is regulated by unbinding and binding of the inducer-repressor complexes to or from the DNA operator to switch the gene expression on and off. The dependency of mRNA production at steady state on different transcription rates and the repressor complexes has been studied by computer simulations in the Lattice Microbe software. Provided that the lac circuit is in active state, the transcription rate is independent of the inducer-repressor complexes present in the cell. In inactive state, the transcription rate is dependent on the specific inducer-repressor complex bound to the operator that inactivates the gene expression. We found that the repressor complex with the largest affinity to the operator yields the smallest range of the feasible transcription rates to yield the steady state while the lac circuit is in inactive state. In contrast, the steady state in active state can be obtained for any value of the transcription rate

Elucidating effects of reaction rates on dynamics of the lac circuit in Escherichia coli

Gene expression is regulated by a complex transcriptional network. It is of interest to quantify uncertainty of not knowing accurately reaction rates of underlying biochemical reactions, and to understand how they affect gene expression. Assuming a kinetic model of the lac circuit in Escherichia coli, regardless of how many reactions are involved in transcription regulation, transcription rate is shown to be the most important parameter affecting steady state production of mRNA and protein in the cell. In particular, doubling the transcription rate approximately doubles the number of mRNA synthesized at steady state for any rates of transcription inhibition and activation. On the other hand, increasing the rate of transcription inhibition by 10% reduces the average steady state count of mRNA by about 7%, whereas changes in the rate of transcription activation appear to have no such effect. Furthermore, for wide range of reaction rates in the kinetic model of the lac genetic switch considered, protein production was observed to always reach a maximum before the degradation reduces its count to zero, and this maximum was found to be always at least 27 protein molecules. Such value appears to be a fundamental structural property of genetic circuits making it very robust against changes in the internal and external conditions

Central Dogma at the Single-Molecule Level in Living Cells

Gene expression originates from individual DNA molecules within living cells. Like many single-molecule processes, gene expression and regulation are stochastic, that is, sporadic in time. This leads to heterogeneity in the messenger RNA and protein copy numbers in a population of cells with identical genomes. With advanced single-cell fluorescence microscopy, it is now possible to quantify transcriptomes and proteomes with single-molecule sensitivity. Dynamic processes such as transcription factor binding, transcription and translation can be monitored in real time, providing quantitative descriptions of gene expression and regulation, and the demonstration that a single-molecule event can determine the phenotype of a cell.Chemistry and Chemical Biolog

The Effect of Stochasticity on the Lac Operon: An Evolutionary Perspective

The role of stochasticity on gene expression is widely discussed. Both potential advantages and disadvantages have been revealed. In some systems, noise in gene expression has been quantified, in among others the lac operon of Escherichia coli. Whether stochastic gene expression in this system is detrimental or beneficial for the cells is, however, still unclear. We are interested in the effects of stochasticity from an evolutionary point of view. We study this question in the lac operon, taking a computational approach: using a detailed, quantitative, spatial model, we evolve through a mutation–selection process the shape of the promoter function and therewith the effective amount of stochasticity. We find that noise values for lactose, the natural inducer, are much lower than for artificial, nonmetabolizable inducers, because these artificial inducers experience a stronger positive feedback. In the evolved promoter functions, noise due to stochasticity in gene expression, when induced by lactose, only plays a very minor role in short-term physiological adaptation, because other sources of population heterogeneity dominate. Finally, promoter functions evolved in the stochastic model evolve to higher repressed transcription rates than those evolved in a deterministic version of the model. This causes these promoter functions to experience less stochasticity in gene expression. We show that a high repression rate and hence high stochasticity increases the delay in lactose uptake in a variable environment. We conclude that the lac operon evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers. In this particular system, we have shown that stochasticity is detrimental. Moreover, we demonstrate that in silico evolution in a quantitative model, by mutating the parameters of interest, is a promising way to unravel the functional properties of biological systems

Inferring distributions from observed mRNA and protein copy counts in genetic circuits

Defining distributions of molecule counts produced in the cell can elucidate stochastic dynamics of the underlying biological circuits. For genetic circuits, only a few distributions of messenger RNA and protein counts were reported in literature, so the task is to decide which of these candidate distributions best fit the observed data. In this paper, we present a statistical method to infer distributions of mRNA and protein counts from observed data. The main advantage of this method is that it does not require any prior assumptions or knowledge about underlying chemical reactions. In particular, a given distribution is fitted to the observed copy counts using a histogram with optimized bin sizes in order to reduce the fitting error. The goodness of fit is evaluated by Kolmogorov-Smirnov and chi-square statistical tests to accept or reject the hypothesis that observed molecule counts were generated from given distribution. The distribution fitting also yields the values of distribution parameters, or they can be estimated using the Bayes theorem. These parameters appear to be themselves random processes. The presented statistical framework for analyzing the observed mRNA and protein copy counts is illustrated for a simulated model of lac genetic circuit in Escherichia coli. For reaction rates assumed in the model, the results in literature predict that mRNA and protein counts at steady-state are gamma distributed. Our analysis shows that both mRNA and protein in the lac circuit model can be considered gamma distributed in at least 70% of times from the initial state until steady-state. The shape and scale parameters of observed gamma distributions are also gamma distributed, giving rise to double stochastic processes. More importantly, as shown previously, the distribution parameters are functions of transcription and translation rates, so presented statistical framework can be used to estimate or optimize reaction rates in biochemical systems

Operator Sequence Alters Gene Expression Independently of Transcription Factor Occupancy in Bacteria

A canonical quantitative view of transcriptional regulation holds that the only role of operator sequence is to set the probability of transcription factor binding, with operator occupancy determining the level of gene expression. In this work, we test this idea by characterizing repression in vivo and the binding of RNA polymerase in vitro in experiments where operators of various sequences were placed either upstream or downstream from the promoter in Escherichia coli. Surprisingly, we find that operators with a weaker binding affinity can yield higher repression levels than stronger operators. Repressor bound to upstream operators modulates promoter escape, and the magnitude of this modulation is not correlated with the repressor-operator binding affinity. This suggests that operator sequences may modulate transcription by altering the nature of the interaction of the bound transcription factor with the transcriptional machinery, implying a new layer of sequence dependence that must be confronted in the quantitative understanding of gene expression

Modelling and analysis of a genetic oscillator in E.coli

This thesis presents the modelling and analysis of an engineered genetic oscillator in E.coli. Genetic oscillators composed of transcriptional feedback loops are the central components of circadian clocks [16]. Thus understanding small genetic oscillators is key for understanding the complex regulatory networks of circadian clocks. In order to monitor clock function, a new colony based imaging assay was set up, based on luminescent transcriptional reporter constructs, that allows for automated data collection over long time spans and for the screening of clock mutants. Clock runs produced damped oscillatory behaviour after starting the clock by removal of the lac inducer IPTG or by giving a metabolic stimulus by transferring cells onto fresh agar plates. A detailed mathematical model of the clock was constructed, taking into account discrete and stochastic regulatory binding events at the promoter sites. From this model, using the theory of heterogeneous systems [69, 66], deterministic equations were derived and analysed to yield conditions for the occurrence of stable oscillations based on the system's nullclines. To facilitate the modelling, an algorithm was devised and implemented, that allows for automated construction of Markov chain models of gene activity states based on DNA binding events. In sum, the work constitutes the establishment and analysis of an integrated experimental and modelling system, which opens possibilities for further investigation in order to yield insight into the properties of genetic oscillators

Coupling Analysis, Simulation, and Experimentation in Natural and Engineered Biological Systems at the Molecular Scale

Cellular functions are controlled by genetic regulatory networks called gene circuits. Recently, there has been much interest in how gene circuits deal with or even exploit stochastic fluctuations in molecular species within the cellular environment. Through a coupling of analysis and simulation with experimentation, this dissertation work furthers the understanding of gene circuit noise behavior and makes significant contributions to the analytical and experimental tools that are currently available for the study and design of natural and synthetic gene circuits. In this study, models are developed for unregulated and autoregulated gene circuits. Results from the analysis are compared to computer simulations and experimental results. Exact stochastic simulations show that the derived analytical expressions are valid even for populations as low as 10 molecules, despite linear approximations made by the analysis. The experimental portion of this work presents a novel method for acquiring in vivo measurements of real-time gene expression. The techniques developed here are used to report the very first measurements of frequency content in gene circuit noise and verify theoretical predictions that negatively autoregulated gene circuits shift their noise spectra up to higher frequency. Through measured shifts in noise spectra, these frequency measurements can also reveal subtle and condition-dependent regulatory pathways. Measured noise spectra may also permit in vivo estimation of gene circuit kinetic rate parameters

Sequence-dependent noise filtering in small genetic motifs

The rates of intracellular processes are, in general, in constant change in response to environmental signals and other internal processes. To deal with noise in the input signals, filtering and decision-making circuits are needed. Motivated by recent evidences from in vivo measurements that the rate limiting steps in transcription initiation are critical in determine RNA and protein numbers, we study the effects of these steps on the behavior of three genetic circuits: a toggle switch, a genetic amplitude filter and a genetic frequency filter. We model these circuits, and from stochastic simulations, we study the performance of the filters and the stability of the switch. We find that these features degrade as the transcript levels are lowered. These effects can be alleviated by adding rate limiting steps to the transcription initiation process. In addition, we show that some features of the filters, such as cutoff levels, are affected by changes in mRNA production dynamics as well. In conclusion, our study shows that the kinetics of transcription initiation of the genes composing these circuits, which are largely determined by the promoter sequence, can be varied within realistic parameter ranges of values to alter considerably their behaviors