Feedback Regulation and its Efficiency in Biochemical Networks

Intracellular biochemical networks fluctuate dynamically due to various internal and external sources of fluctuation. Dissecting the fluctuation into biologically relevant components is important for understanding how a cell controls and harnesses noise and how information is transferred over apparently noisy intracellular networks. While substantial theoretical and experimental advancement on the decomposition of fluctuation was achieved for feedforward networks without any loop, we still lack a theoretical basis that can consistently extend such advancement to feedback networks. The main obstacle that hampers is the circulative propagation of fluctuation by feedback loops. In order to define the relevant quantity for the impact of feedback loops for fluctuation, disentanglement of the causally interlocked influence between the components is required. In addition, we also lack an approach that enables us to infer non-perturbatively the influence of the feedback to fluctuation as the dual reporter system does in the feedforward network. In this work, we resolve these problems by extending the work on the fluctuation decomposition and the dual reporter system. For a single-loop feedback network with two components, we define feedback loop gain as the feedback efficiency that is consistent with the fluctuation decomposition for feedforward networks. Then, we clarify the relation of the feedback efficiency with the fluctuation propagation in an open-looped FF network. Finally, by extending the dual reporter system, we propose a conjugate feedback and feedforward system for estimating the feedback efficiency only from the statistics of the system non-perturbatively

Optimal first-passage time in gene regulatory networks

The inherent probabilistic nature of the biochemical reactions, and low copy number of species can lead to stochasticity in gene expression across identical cells. As a result, after induction of gene expression, the time at which a specific protein count is reached is stochastic as well. Therefore events taking place at a critical protein level will see stochasticity in their timing. First-passage time (FPT), the time at which a stochastic process hits a critical threshold, provides a framework to model such events. Here, we investigate stochasticity in FPT. Particularly, we consider events for which controlling stochasticity is advantageous. As a possible regulatory mechanism, we also investigate effect of auto-regulation, where the transcription rate of gene depends on protein count, on stochasticity of FPT. Specifically, we investigate for an optimal auto-regulation which minimizes stochasticity in FPT, given fixed mean FPT and threshold. For this purpose, we model the gene expression at a single cell level. We find analytic formulas for statistical moments of the FPT in terms of model parameters. Moreover, we examine the gene expression model with auto-regulation. Interestingly, our results show that the stochasticity in FPT, for a fixed mean, is minimized when the transcription rate is independent of protein count. Further, we discuss the results in context of lysis time of an \textit{E. coli} cell infected by a $\lambda$ phage virus. An optimal lysis time provides evolutionary advantage to the $\lambda$ phage, suggesting a possible regulation to minimize its stochasticity. Our results indicate that there is no auto-regulation of the protein responsible for lysis. Moreover, congruent to experimental evidences, our analysis predicts that the expression of the lysis protein should have a small burst size.Comment: 8 pages, 3 figures, Submitted to Conference on Decision and Control 201

Noise control and utility: From regulatory network to spatial patterning

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network configurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent findings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning, and summarize key principles underlying noise control

Genetic noise control via protein oligomerization

Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions. Here we have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced). The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise

Gene autoregulation via intronic microRNAs and its functions

Background: MicroRNAs, post-transcriptional repressors of gene expression, play a pivotal role in gene regulatory networks. They are involved in core cellular processes and their dysregulation is associated to a broad range of human diseases. This paper focus on a minimal microRNA-mediated regulatory circuit, in which a protein-coding gene (host gene) is targeted by a microRNA located inside one of its introns. Results: Autoregulation via intronic microRNAs is widespread in the human regulatory network, as confirmed by our bioinformatic analysis, and can perform several regulatory tasks despite its simple topology. Our analysis, based on analytical calculations and simulations, indicates that this circuitry alters the dynamics of the host gene expression, can induce complex responses implementing adaptation and Weber's law, and efficiently filters fluctuations propagating from the upstream network to the host gene. A fine-tuning of the circuit parameters can optimize each of these functions. Interestingly, they are all related to gene expression homeostasis, in agreement with the increasing evidence suggesting a role of microRNA regulation in conferring robustness to biological processes. In addition to model analysis, we present a list of bioinformatically predicted candidate circuits in human for future experimental tests. Conclusions: The results presented here suggest a potentially relevant functional role for negative self-regulation via intronic microRNAs, in particular as a homeostatic control mechanism of gene expression. Moreover, the map of circuit functions in terms of experimentally measurable parameters, resulting from our analysis, can be a useful guideline for possible applications in synthetic biology.Comment: 29 pages and 7 figures in the main text, 18 pages of Supporting Informatio

Under-dominance constrains the evolution of negative autoregulation in diploids

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. This difference is all the more surprising because E. coli and S. cerevisiae otherwise have remarkably similar profiles of network motifs. In this study we first show that regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this fundamental difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution