Noise in transcription negative feedback loops: simulation and experimental analysis

Negative feedback loops have been invoked as a way to control and decrease transcriptional noise. Here, we have built three circuits to test the effect of negative feedback loops on transcriptional noise of an autoregulated gene encoding a transcription factor (TF) and a downstream gene (DG), regulated by this TF. Experimental analysis shows that self-repression decreases noise compared to expression from a non-regulated promoter. Interestingly enough, we find that noise minimization by negative feedback loop is optimal within a range of repression strength. Repression values outside this range result in noise increase producing a U-shaped behaviour. This behaviour is the result of external noise probably arising from plasmid fluctuations as shown by simulation of the network. Regarding the target gene of a self-repressed TF (sTF), we find a strong decrease of noise when repression by the sTF is strong and a higher degree of noise anti-correlation between sTF and its target. Simulations of the circuits indicate that the main source of noise in these circuits could come from plasmid variation and therefore that negative feedback loops play an important role in suppressing both external and internal noise. An important observation is that DG expression without negative feedback exhibits bimodality at intermediate TF repression values. This bimodal behaviour seems to be the result of external noise as it can only be found in those simulations that include plasmid variation

A family tree of Markov models in systems biology

Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree'' for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.Comment: 18 pages, 2 figure

Strong negative self regulation of Prokaryotic transcription factors increases the intrinsic noise of protein expression

Background Many prokaryotic transcription factors repress their own transcription. It is often asserted that such regulation enables a cell to homeostatically maintain protein abundance. We explore the role of negative self regulation of transcription in regulating the variability of protein abundance using a variety of stochastic modeling techniques. Results We undertake a novel analysis of a classic model for negative self regulation. We demonstrate that, with standard approximations, protein variance relative to its mean should be independent of repressor strength in a physiological range. Consequently, in that range, the coefficient of variation would increase with repressor strength. However, stochastic computer simulations demonstrate that there is a greater increase in noise associated with strong repressors than predicted by theory. The discrepancies between the mathematical analysis and computer simulations arise because with strong repressors the approximation that leads to Michaelis-Menten-like hyperbolic repression terms ceases to be valid. Because we observe that strong negative feedback increases variability and so is unlikely to be a mechanism for noise control, we suggest instead that negative feedback is evolutionarily favoured because it allows the cell to minimize mRNA usage. To test this, we used in silico evolution to demonstrate that while negative feedback can achieve only a modest improvement in protein noise reduction compared with the unregulated system, it can achieve good improvement in protein response times and very substantial improvement in reducing mRNA levels. Conclusions Strong negative self regulation of transcription may not always be a mechanism for homeostatic control of protein abundance, but instead might be evolutionarily favoured as a mechanism to limit the use of mRNA. The use of hyperbolic terms derived from quasi-steady-state approximation should also be avoided in the analysis of stochastic models with strong repressors

Study of the interaction between a Zirconium thin film and an EN C100 steel substrate: temperature effect

Zirconium thin films were grown on high carbon steel substrates EN C100 (1 %wt. of carbon) by RF magnetron sputtering. In order to study the reactivity of the film/substrate system as a function of the temperature, one hour vacuum annealing was carried out for different temperatures between 600°C and 1100°C. The films were then analyzed by X-ray diffraction, scanning electron microscopy, glow discharge optical emission spectroscopy (GDOES) and nanoindentation. The obtained results showed a progressive transformation of zirconium film to zirconium carbide. Carbon atoms diffusion from substrate toward the film induced this transformation. The sample annealed at 900°C exhibited the best mechanicals properties (H =17 GPa and E = 220 GPa). Samples treated at higher temperature were affected by oxidation and high microporosity. Even if the conversion is uncomplete, annealing significantly promotes adhesion of the film on the substrate

Transcriptional Autoregulatory Loops Are Highly Conserved in Vertebrate Evolution

BACKGROUND: Feedback loops are the simplest building blocks of transcriptional regulatory networks and therefore their behavior in the course of evolution is of prime interest. METHODOLOGY: We address the question of enrichment of the number of autoregulatory feedback loops in higher organisms. First, based on predicted autoregulatory binding sites we count the number of autoregulatory loops. We compare it to estimates obtained either by assuming that each (conserved) gene has the same chance to be a target of a given factor or by assuming that each conserved sequence position has an equal chance to be a binding site of the factor. CONCLUSIONS: We demonstrate that the numbers of putative autoregulatory loops conserved between human and fugu, danio or chicken are significantly higher than expected. Moreover we show, that conserved autoregulatory binding sites cluster close to the factors' starts of transcription. We conclude, that transcriptional autoregulatory feedback loops constitute a core transcriptional network motif and their conservation has been maintained in higher vertebrate organism evolution

Frequency Domain Analysis Reveals External Periodic Fluctuations Can Generate Sustained p53 Oscillation

p53 is a well-known tumor suppressor protein that regulates many pathways, such as ones involved in cell cycle and apoptosis. The p53 levels are known to oscillate without damping after DNA damage, which has been a focus of many recent studies. A negative feedback loop involving p53 and MDM2 has been reported to be responsible for this oscillatory behavior, but questions remain as how the dynamics of this loop alter in order to initiate and maintain the sustained or undamped p53 oscillation. Our frequency domain analysis suggests that the sustained p53 oscillation is not completely dictated by the negative feedback loop; instead, it is likely to be also modulated by periodic DNA repair-related fluctuations that are triggered by DNA damage. According to our analysis, the p53-MDM2 feedback mechanism exhibits adaptability in different cellular contexts. It normally filters noise and fluctuations exerted on p53, but upon DNA damage, it stops performing the filtering function so that DNA repair-related oscillatory signals can modulate the p53 oscillation. Furthermore, it is shown that the p53-MDM2 feedback loop increases its damping ratio allowing p53 to oscillate at a frequency more synchronized with the other cellular efforts to repair the damaged DNA, while suppressing its inherent oscillation-generating capability. Our analysis suggests that the overexpression of MDM2, observed in many types of cancer, can disrupt the operation of this adaptive mechanism by making it less responsive to the modulating signals after DNA damage occurs

Induction level determines signature of gene expression noise in cellular systems

Noise in gene expression, either due to inherent stochasticity or to varying inter- and intracellular environment, can generate significant cell-to-cell variability of protein levels in clonal populations. We present a theoretical framework, based on stochastic processes, to quantify the different sources of gene expression noise taking cell division explicitly into account. Analytical, time-dependent solutions for the noise contributions arising from the major steps involved in protein synthesis are derived. The analysis shows that the induction level of the activator or transcription factor is crucial for the characteristic signature of the dominant source of gene expression noise and thus bridges the gap between seemingly contradictory experimental results. Furthermore, on the basis of experimentally measured cell distributions, our simulations suggest that transcription factor binding and promoter activation can be modelled independently of each other with sufficient accuracy

Phenotypic variability in synthetic biology applications:Dealing with noise in microbial gene expression

The stochasticity due to the infrequent collisions among low copy-number molecules within the crowded cellular compartment is a feature of living systems. Single cell variability in gene expression within an isogenic population (i.e. biological noise) is usually described as the sum of two independent components: intrinsic and extrinsic stochasticity. Intrinsic stochasticity arises from the random occurrence of events inherent to the gene expression process (e.g. the burst-like synthesis of mRNA and protein molecules). Extrinsic fluctuations reflect the state of the biological system and its interaction with the intra and extracellular environments (e.g. concentration of available polymerases, ribosomes, metabolites, and micro-environmental conditions). A better understanding of cellular noise would help synthetic biologists design gene circuits with well-defined functional properties. In silico modelling has already revealed several aspects of the network topology’s impact on noise properties; this information could drive the selection of biological parts and the design of reliably-engineered pathways. Importantly, while optimizing artificial gene circuitry for industrial applications, synthetic biology could also elucidate the natural mechanisms underlying natural phenotypic variability. In this review, we briefly summarize the functional roles of noise in unicellular organisms and address their relevance to synthetic network design. We will also consider how noise might influence the selection of network topologies supporting reliable functions, and how the variability of cellular events might be exploited when designing innovative biotechnology applications

Control of Hox transcription factor concentration and cell-to-cell variability by an auto-regulatory switch

The variability in transcription factor concentration among cells is an important developmental determinant, yet how variability is controlled remains poorly understood. Studies of variability have focused predominantly on monitoring mRNA production noise. Little information exists about transcription factor protein variability, as this requires the use of quantitative methods with single-molecule sensitivity. Using Fluorescence Correlation Spectroscopy (FCS), we have characterized the concentration and variability of 14 endogenously tagged TFs in live Drosophila imaginal discs. For the Hox TF Antennapedia, we investigated whether protein variability results from random stochastic events or is developmentally regulated. We found that Antennapedia transitioned from low concentration/high variability early, to high concentration/low variability later, in development. FCS and temporally resolved genetic studies uncovered that Antennapedia itself is necessary and sufficient to drive a developmental regulatory switch from auto-activation to auto-repression, thereby reducing variability. This switch is controlled by progressive changes in relative concentrations of preferentially activating and repressing Antennapedia isoforms, which bind chromatin with different affinities. Mathematical modeling demonstrated that the experimentally supported auto-regulatory circuit can explain the increase of Antennapedia concentration and suppression of variability over time