Recently, several studies have investigated the transcription process associated to specific genetic regulatory networks. In this work, we present a stochastic approach for analyzing the dynamics and effect of negative feedback loops (FBL) on the transcriptional noise. First, our analysis allows us to identify a bimodal activity depending of the strength of self-repression coupling D. In the strong coupling region D>>1, the variance of the transcriptional noise is found to be reduced a 28 % more than described earlier. Secondly, the contribution of the noise effect to the abundance of regulating protein becomes manifest when the coefficient of variation is computed. In the strong coupling region, this coefficient is found to be independent of all parameters and in fair agreement with the experimentally observed values. Finally, our analysis reveals that the regulating protein is significantly induced by the intrinsic and external noise in the strong coupling region. In short, it indicates that the existence of inherent noise in FBL makes it possible to produce a basal amount of proteins even though the repression level D is very strong.
Riboswitches, structured elements in the untranslated regions of messenger RNAs, regulate gene expression by binding specific metabolites. We introduce a kinetic network model that describes the functions of riboswitches at the systems level. Using experimental data for flavin mono nucleotide riboswitch as a guide we show that efficient function, implying a large dynamic range without compromising the requirement to suppress transcription, is determined by a balance between the transcription speed, the folding and unfolding rates of the aptamer, and the binding rates of the metabolite. We also…
Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually regulate each other's expression. We present a theoretical and numerical study of coherent mixed feedback loops of this type, in which both regulations are negative. Under suitable conditions, these feedback loops are expected to exhibit bistability, namely two stable states, one dominated by the transcriptional repressor and the other dominated by the sRNA. We…
We present a comparative analysis of large-scale topological and evolutionary properties of transcription networks in three species, the two distant bacteria E. coli and B. subtilis, and the yeast S. cerevisiae. The study focuses on the global aspects of feedback and hierarchy in transcriptional regulatory pathways. While confirming that gene duplication has a significant impact on the shaping of all the analyzed transcription networks, our results point to distinct trends between the bacteria, where time constraints in the transcription of downstream genes might be important in shaping the hi…
We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of oscillation. In one mode (mode 1) frequency remains constant over a wide range amplitude and in other mode (mode 2) the amplitude of oscillation remains constant over a wide range of frequency. Our study reproduces both features of oscillations in a single gene regulatory network and show that the negative plus positive feedback loops in gene regulatory network o…
Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and sufficiently strong nonlinearity in the transmission of the feedback signal in order to produce biochemical rhythms. A single gene with only positive transcriptional feedback does not produce oscillations. Here, we demonstrate that this single-gene network in conjunction with a simple negative interaction can also easily produce rhythms. We examine a model comprised of two well-differentiated parts. The first …
The E.coli transcription network has an essentially feedforward structure, with, however, abundant feedback at the level of self-regulations. Here, we investigate how these properties emerged during evolution. An assessment of the role of gene duplication based on protein domain architecture shows that (i) transcriptional autoregulators have mostly arisen through duplication, while (ii) the expected feedback loops stemming from their initial cross-regulation are strongly selected against. This requires a divergent coevolution of the transcription factor DNA-binding sites and their respective D…
We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show …
Gene expression via transcription-translation is the most fundamental reaction to sustain biological systems, and complex reactions such as this one occur in a small compartment of living cells. There is increasing evidence that t physical effects, such as molecular crowding or excluded volume effects of transcriptional-translational machinery, affect the yield of reaction products. On the other hand, transcriptional feedback that controls gene expression during mRNA synthesis is also a vital mechanism that regulates protein synthesis in cells. However, the excluded volume effect of spatial co…
Gene expression (GE) is an inherently random or stochastic or noisy process. The randomness in different steps of GE, e.g., transcription, translation, degradation, etc., leading to cell-to-cell variations in mRNA and protein levels. This variation appears in organisms ranging from microbes to metazoans. Stochastic gene expression has important consequences for cellular function. The random fluctuations in protein levels produce variability in cellular behavior. It is beneficial in some contexts and harmful to others. These situations include stress response, metabolism, development, cell cycl…
Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sit…
The molecular network in an organism consists of transcription/translation regulation, protein-protein interactions/modifications and a metabolic network, together forming a system that allows the cell to respond sensibly to the multiple signal molecules that exist in its environment. A key part of this overall system of molecular regulation is therefore the interface between the genetic and the metabolic network. A motif that occurs very often at this interface is a negative feedback loop used to regulate the level of the signal molecules. In this work we use mathematical models to investigat…
Recently, there has been a lot of effort in understanding sRNA mediated regulation of gene expression and how this mode of regulation differs from transcriptional regulation.In E.coli, in the presence of oxidative stress, the synthesis of sigma^s is regulated through an interesting mechanism involving both transcriptional and sRNA-mediated translational regulation. The key regulatory factors involved in transcriptional and translational regulation are ArcA and ArcB proteins and ArcZ sRNA, respectively. Phosphorylated ArcA, in a feedforward mechanism, represses the transcriptions sigma^s and Ar…
Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits have been increasingly used to test fundamental principles of genetic network dynamics. A recently developed fast, tunable genetic oscillator by Stricker et al.[23] has demonstrated robustness and tunability of oscillatory behavior by combining positive and negative feedback loops. This oscillator combining lacI (negative) and araC (positive) feedback loops, was however modeled …
We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-b…
Circadian (~24hr) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptional- translational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a…
A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression …
In the yeast Saccharomyces cerevisiae, the interplay between galactose, Gal3p, Gal80p and Gal4p determines the transcriptional status of the genes required for galactose utilization. After an increase in galactose concentration, galactose molecules bind onto Gal3p. This event leads via Gal80p to the activation of Gal4p, which then induces GAL3 and GAL80 gene transcription. Here we propose a qualitative dynamic model, whereby these molecular interaction events represent the first two stages of a functional feedback loop that closes with the capture of activated Gal4p by newly synthesized Gal3p …
Gene regulatory networks present a wide variety of dynamical responses to intrinsic and extrinsic perturbations. Arguably, one of the most important of such coordinated responses is the one of amplification cascades, in which activation of a few key-responsive transcription factors (termed master regulators, MRs) lead to a large series of transcriptional activation events. This is so since master regulators are transcription factors controlling the expression of other transcription factor molecules and so on. MRs hold a central position related to transcriptional dynamics and control of gene r…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily com…
We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point and a stable limit cycle coexist. At the bifurcation point the period of the oscillations diverges. Further, intrinsic noise can make the system switch between oscillatory state and the stationary state spontaneously. We find that this switching also occurs in previous models of circadian clocks that use this combination of positive and negative feedback. Ou…
According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit; the structure of a network predetermines the dynamic capacity of the network. We note that stochastic fluctuations can possibly confer a new dynamical capability to a network. Thus, it is of tremendous value to understand and be able to control the landscape of stochastic dynamical behaviors of a biochemical reaction network as a function of network architect…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein concentrations or gene expression levels are related to the presence of at least one negative feedback loop in the regulatory network. Here we study the dynamics of a very general class of negative feedback loops. Our main result is that in these systems the sequence of maxima and minima of the concentrations is uniquely determined by the topology of the loop …
Biochemical oscillation systems often consist of negative feedback loops with repressive transcription regulation. Such systems have distinctive characteristics in comparison with ordinary chemical systems: i) the numbers of molecules involved are small, ii) there are typically only a couple of genes in a cell with a finite regulation time scale. Due to the fluctuations caused by these features, the system behavior can be quite different from the one obtained by rate equations, because the rate equations ignore molecular fluctuations and thus are exact only in the infinite molecular number lim…
Noise in the expression of a gene produces fluctuations in the concentration of the gene product. These fluctuations can interfere with optimal function or can be exploited to generate beneficial diversity between cells; gene expression noise is therefore expected to be subject to evolutionary pressure. Shifts between modes of high and low rates of transcription initiation at a promoter appear to contribute to this noise both in eukaryotes and prokaryotes. However, models invoked for eukaryotic promoter noise such as stable activation scaffolds or persistent nucleosome alterations seem unlikel…
This paper compares the auto-repressed gene to a simple one (a gene without auto-regulation) in terms of response time and output noise under the assumption of fixed metabolic cost. The analysis shows that, in the case of non-vanishing leak expression rate, the negative feedback reduces both the switching on and switching off times of a gene. The noise of the auto-repressed gene will be lower than the one of the simple gene only for low leak expression rates. Summing up, for low, but non-vanishing leak expression rates, the auto-repressed gene is both faster and less noisier compared to the si…
A spontaneously patterning reaction diffusion network, containing an integrated activator inhibitor and substrate depletion mechanism, specifies trichoblast cell fate in Arabidopsis roots
Institute of Systems, Molecular and Integrative Biology. University of Liverpool（利物浦大学生物系统、分子与整合生物学研究所）；School of Biosciences. University of Nottingham（诺丁汉大学生物科学学院）
Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is exceedingly rare amongst the transcription factors of Saccharomyces cerevisiae.…
Understanding relationship between noisy dynamics and biological network architecture is a fundamentally important question, particularly in order to elucidate how cells encode and process information. We analytically and numerically investigate general network architectural conditions that are necessary to generate stochastic amplified and coherent oscillations. We enumerate all possible topologies of coupled negative feedbacks in the underlying biochemical networks with three components, negative feedback loops, and mass action kinetics. Using the linear noise approximation to analytically o…
By integrating heterogeneous functional genomic datasets, we have developed a new framework for detecting combinatorial control of gene expression, which includes estimating transcription factor activities using a singular value decomposition method and reducing high-dimensional input gene space by considering genomic properties of gene clusters. The prediction of cooperative gene regulation is accomplished by either Gaussian Graphical Models or Pairwise Mixed Graphical Models. The proposed framework was tested on yeast cell cycle datasets: (1) 54 known yeast cell cycle genes with 9 cell cycle…
The dynamic behaviors of microRNA and mRNA under external stress are studied with biological experiments and mathematics models. In this study, we developed a mathematic model to describe the biological phenomenon and for the first time reported that, as responses to external stress, the expression levels of microRNA and mRNA sustained oscillation. And the period of the oscillation is much shorter than several reported transcriptional regulation negative feedback loop.
A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the fact that detailed knowledge about intracellular networks is unavailable, integral-feedback controllers (IFCs) have been put forward for controlling molecular abundances. These controllers can maintain accuracy in spite of the uncertainties in the controlled networks. However, this desirable feature is achieved only if stability is also maintained. In this paper, we show that molecular IFCs can suffer from a hazard…
Feedback loops in a dynamic network play an important role in determining the dynamics of that network. Through a computational study, in this paper we show that networks with fewer independent negative feedback loops tend to exhibit more regular behavior than those with more negative loops. To be precise, we study the relationship between the number of independent feedback loops and the number and length of the limit cycles in the phase space of dynamic Boolean networks. We show that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to …
It is well-known that gene activation/deactivation dynamics may be a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we investigate the effect of realistic extrinsic noises acting on gene deactivation in a common network motif - the positive feedback of a transcription factor on its own synthesis - under a variety of settings, i.e., distinct cellular types, distribution of proteins and properties of the external perturbations. At variance with standard models where the perturbations are Gaussian unbounded, we …
The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed descript…
The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback. The latter is sufficient to originate a Hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback. We find a sharp bifurcation in parameter space, and define the threshold as the point in which the stationary distri…
Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in protein concentrations around optimal value. Due to the nonlinearities present in these feedbacks, moment dynamics are typically not closed, in the sense that the time derivative of the lower-order statistical moments of the protein copy number depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of …
Deterministic and stochastic Boolean network models are build for the dynamics of negative feedback loops of the p53 pathways. It is shown that the main function of the negative feedback in the p53 pathways is to keep p53 at a low steady state level, and each sequence of protein states in the negative feedback loops, is globally attracted to a closed cycle of the p53 dynamics after being perturbed by outside signal (e.g. DNA damage). Our theoretical and numerical studies show that both the biological stationary state and the biological oscillation after being perturbed are stable for a wide ra…
We present a minimal motif model for transmembrane cell signaling. The model assumes signaling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects can be modulated to provide a robust and high-fidelity response behavior without invoking sophisticated modeling of the signaling process as a sequence of cascade reactions and fine-tuned parameters. Our results show that the fact that the distributed signaling events take place in nanoclusters with a finite lifetime regulated by local production is sufficien…
Biological Regulatory Network Inference through Circular Causal Structure Learning
Data Science & Artificial Intelligence Research Institute, China Unicom（中国联通数据科学与人工智能研究院）；School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；International Center of Future Science, Jilin University（吉林大学未来科学国际中心）；Engineering Research Center of Knowledge-Driven Human-Machine Intelligence, MOE（教育部知识驱动人机智能工程研究中心）
Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback strengths is observed, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a re…
Genes and proteins regulate cellular functions through complex circuits of biochemical reactions. Fluctuations in the components of these regulatory networks result in noise that invariably corrupts the signal, possibly compromising function. Here, we create a practical formalism based on ideas introduced by Wiener and Kolmogorov (WK) for filtering noise in engineered communications systems to quantitatively assess the extent to which noise can be controlled in biological processes involving negative feedback. Application of the theory, which reproduces the previously proven scaling of the low…
