Optimal Feedback Strength for Noise Suppression in Autoregulatory Gene Networks

Autoregulatory feedback loops, where the protein expressed from a gene inhibits or activates its own expression are common gene network motifs within cells. In these networks, stochastic fluctuations in protein levels are attributed to two factors: intrinsic noise (i.e., the randomness associated with mRNA/protein expression and degradation) and extrinsic noise (i.e., the noise caused by fluctuations in cellular components such as enzyme levels and gene-copy numbers). We present results that predict the level of both intrinsic and extrinsic noise in protein numbers as a function of quantities that can be experimentally determined and/or manipulated, such as the response time of the protein and the level of feedback strength. In particular, we show that for a fixed average number of protein molecules, decreasing response times leads to attenuation of both protein intrinsic and extrinsic noise, with the extrinsic noise being more sensitive to changes in the response time. We further show that for autoregulatory networks with negative feedback, the protein noise levels can be minimal at an optimal level of feedback strength. For such cases, we provide an analytical expression for the highest level of noise suppression and the amount of feedback that achieves this minimal noise. These theoretical results are shown to be consistent and explain recent experimental observations. Finally, we illustrate how measuring changes in the protein noise levels as the feedback strength is manipulated can be used to determine the level of extrinsic noise in these gene networks.     

Morphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation

Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multicellular organisms.     

Homeostatic Interplay between Bacterial Cell-Cell Signaling and Iron in Virulence

Pathogenic bacteria use interconnected multi-layered regulatory networks, such as quorum sensing (QS) networks to sense and respond to environmental cues and external and internal bacterial cell signals, and thereby adapt to and exploit target hosts. Despite the many advances that have been made in understanding QS regulation, little is known regarding how these inputs are integrated and processed in the context of multi-layered QS regulatory networks. Here we report the examination of the Pseudomonas aeruginosa QS 4-hydroxy-2-alkylquinolines (HAQs) MvfR regulatory network and determination of its interaction with the QS acyl-homoserine-lactone (AHL) RhlR network. The aim of this work was to elucidate paradigmatically the complex relationships between multi-layered regulatory QS circuitries, their signaling molecules, and the environmental cues to which they respond. Our findings revealed positive and negative homeostatic regulatory loops that fine-tune the MvfR regulon via a multi-layered dependent homeostatic regulation of the cell-cell signaling molecules PQS and HHQ, and interplay between these molecules and iron. We discovered that the MvfR regulon component PqsE is a key mediator in orchestrating this homeostatic regulation, and in establishing a connection to the QS rhlR system in cooperation with RhlR. Our results show that P. aeruginosa modulates the intensity of its virulence response, at least in part, through this multi-layered interplay. Our findings underscore the importance of the homeostatic interplay that balances competition within and between QS systems via cell-cell signaling molecules and environmental cues in the control of virulence gene expression. Elucidation of the fine-tuning of this complex relationship offers novel insights into the regulation of these systems and may inform strategies designed to limit infections caused by P. aeruginosa and related human pathogens.     

Modeling stochasticity and variability in gene regulatory networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.     

Quantification of mRNA and protein and integration with protein turnover in a bacterium

Biological function and cellular responses to environmental perturbations are regulated by a complex interplay of DNA, RNA, proteins and metabolites inside cells. To understand these central processes in living systems at the molecular level, we integrated experimentally determined abundance data for mRNA, proteins, as well as individual protein half‐lives from the genome‐reduced bacterium Mycoplasma pneumoniae. We provide a fine‐grained, quantitative analysis of basic intracellular processes under various external conditions. Proteome composition changes in response to cellular perturbations reveal specific stress response strategies. The regulation of gene expression is largely decoupled from protein dynamics and translation efficiency has a higher regulatory impact on protein abundance than protein turnover. Stochastic simulations using in vivo data show how low translation efficiency and long protein half‐lives effectively reduce biological noise in gene expression. Protein abundances are regulated in functional units, such as complexes or pathways, and reflect cellular lifestyles. Our study provides a detailed integrative analysis of average cellular protein abundances and the dynamic interplay of mRNA and proteins, the central biomolecules of a cell.     

Formulas for intrinsic noise evaluation in oscillatory genetic networks

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.     

Noise Management by Molecular Networks

Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise.