Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis

Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics – stationary pathway output, response amplitude, and relaxation time – in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role.     

Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.     

Predicting the magnitude of the reflex response to insertions in ubiquitin

The ability to predict the structural response of a protein to an insertion would be a significant advance for the fields of homology modeling and protein design. However, the effects of insertions on protein conformation are not well understood. Previous work has demonstrated that for two loops in ubiquitin, the primary determinant of the structural adaptation to insertions is the insertion site rather than the sequence of the insertion; this phenomenon was termed the reflex response of loops to insertions. We report herein the analysis of ubiquitin mutants with insertions in two other loops. This study demonstrates that the insertion site is the primary determinant of the response to insertions for these two new loops as well, which further supports the reflex response hypothesis. We also attempted to predict the relative magnitudes of the responses at each site but were unsuccessful. Using the additional data collected in this work, we have refined our predictive hypothesis.     

Nonadaptive Fluctuation in an Adaptive Sensory System: Bacterial Chemoreceptor

Background

Sensory systems often exhibit an adaptation or desensitization after a transient response, making the system ready to receive a new signal over a wide range of backgrounds. Because of the strong influence of thermal stochastic fluctuations on the biomolecules responsible for the adaptation, such as many membrane receptors and channels, their response is inherently noisy, and the adaptive property is achieved as a statistical average.

Methodology/Principal Findings

Here, we study a simple kinetic model characterizing the essential aspects of these adaptive molecular systems and show theoretically that, while such an adaptive sensory system exhibits a perfect adaptation property on average, its temporal stochastic fluctuations are able to be sensitive to the environmental conditions. Among the adaptive sensory systems, an extensively studied model system is the bacterial receptor responsible for chemotaxis. The model exhibits a nonadaptive fluctuation sensitive to the environmental ligand concentration, while perfect adaptation is achieved on average. Furthermore, we found that such nonadaptive fluctuation makes the bacterial behavior dependent on the environmental chemoattractant concentrations, which enhances the chemotactic performance.

Conclusions/Significance

This result indicates that adaptive sensory systems can make use of such stochastic fluctuation to carry environmental information, which is not possible by means of the average, while keeping responsive to the changing stimulus.     

Cooperative Adaptive Responses in Gene Regulatory Networks with Many Degrees of Freedom

Cells generally adapt to environmental changes by first exhibiting an immediate response and then gradually returning to their original state to achieve homeostasis. Although simple network motifs consisting of a few genes have been shown to exhibit such adaptive dynamics, they do not reflect the complexity of real cells, where the expression of a large number of genes activates or represses other genes, permitting adaptive behaviors. Here, we investigated the responses of gene regulatory networks containing many genes that have undergone numerical evolution to achieve high fitness due to the adaptive response of only a single target gene; this single target gene responds to changes in external inputs and later returns to basal levels. Despite setting a single target, most genes showed adaptive responses after evolution. Such adaptive dynamics were not due to common motifs within a few genes; even without such motifs, almost all genes showed adaptation, albeit sometimes partial adaptation, in the sense that expression levels did not always return to original levels. The genes split into two groups: genes in the first group exhibited an initial increase in expression and then returned to basal levels, while genes in the second group exhibited the opposite changes in expression. From this model, genes in the first group received positive input from other genes within the first group, but negative input from genes in the second group, and vice versa. Thus, the adaptation dynamics of genes from both groups were consolidated. This cooperative adaptive behavior was commonly observed if the number of genes involved was larger than the order of ten. These results have implications in the collective responses of gene expression networks in microarray measurements of yeast Saccharomyces cerevisiae and the significance to the biological homeostasis of systems with many components.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

Noise Propagation in Gene Regulation Networks Involving Interlinked Positive and Negative Feedback Loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.     

Trade-off between responsiveness and noise suppression in biomolecular system responses to environmental cues

When living systems detect changes in their external environment their response must be measured to balance the need to react appropriately with the need to remain stable, ignoring insignificant signals. Because this is a fundamental challenge of all biological systems that execute programs in response to stimuli, we developed a generalized time-frequency analysis (TFA) framework to systematically explore the dynamical properties of biomolecular networks. Using TFA, we focused on two well-characterized yeast gene regulatory networks responsive to carbon-source shifts and a mammalian innate immune regulatory network responsive to lipopolysaccharides (LPS). The networks are comprised of two different basic architectures. Dual positive and negative feedback loops make up the yeast galactose network; whereas overlapping positive and negative feed-forward loops are common to the yeast fatty-acid response network and the LPS-induced network of macrophages. TFA revealed remarkably distinct network behaviors in terms of trade-offs in responsiveness and noise suppression that are appropriately tuned to each biological response. The wild type galactose network was found to be highly responsive while the oleate network has greater noise suppression ability. The LPS network appeared more balanced, exhibiting less bias toward noise suppression or responsiveness. Exploration of the network parameter space exposed dramatic differences in system behaviors for each network. These studies highlight fundamental structural and dynamical principles that underlie each network, reveal constrained parameters of positive and negative feedback and feed-forward strengths that tune the networks appropriately for their respective biological roles, and demonstrate the general utility of the TFA approach for systems and synthetic biology.     

Stochastic resonance of localized activity driven by common noise

We study the influence of spatially correlated noise on the transient dynamics of a recurrent network with Mexican-Hat-type connectivity. We derive the closed form of the order parameter functional in the thermodynamical limit of neuron number N. Our analysis shows that network dynamics is qualitatively changed by the presence of common noise. Network dynamics driven by common noise obtains the global level of fluctuation, which is not observed in a network driven by independent noise only. We show that the optimal level of global fluctuation enhances the transition from non-localized firing states to spatially localized firing states, and also enhances the rotation speed of localized activity.     

The selective control of glycolysis,gluconeogenesis and glycogenesis by temporal insulin patterns

Insulin governs systemic glucose metabolism, including glycolysis, gluconeogenesis and glycogenesis, through temporal change and absolute concentration. However, how insulin‐signalling pathway selectively regulates glycolysis, gluconeogenesis and glycogenesis remains to be elucidated. To address this issue, we experimentally measured metabolites in glucose metabolism in response to insulin. Step stimulation of insulin induced transient response of glycolysis and glycogenesis, and sustained response of gluconeogenesis and extracellular glucose concentration (GLC _ex ). Based on the experimental results, we constructed a simple computational model that characterises response of insulin‐signalling‐dependent glucose metabolism. The model revealed that the network motifs of glycolysis and glycogenesis pathways constitute a feedforward (FF) with substrate depletion and incoherent feedforward loop (iFFL), respectively, enabling glycolysis and glycogenesis responsive to temporal changes of insulin rather than its absolute concentration. In contrast, the network motifs of gluconeogenesis pathway constituted a FF inhibition, enabling gluconeogenesis responsive to absolute concentration of insulin regardless of its temporal patterns. GLC _ex was regulated by gluconeogenesis and glycolysis. These results demonstrate the selective control mechanism of glucose metabolism by temporal patterns of insulin.     

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.     

Coupled feedback loops form dynamic motifs of cellular networks

Cellular networks are composed of complicated interconnections among components, and some subnetworks of particular functioning are often identified as network motifs. Among such network motifs, feedback loops are thought to play important dynamical roles. Intriguingly, such feedback loops are very often found as a coupled structure in cellular circuits. Therefore, we integrated all the scattered information regarding the coupled feedbacks in various cellular circuits and investigated the dynamical role of each coupled structure. Finally, we discovered that coupled positive feedbacks enhance signal amplification and bistable characteristics; coupled negative feedbacks realize enhanced homeostasis; coupled positive and negative feedbacks enable reliable decision-making by properly modulating signal responses and effectively dealing with noise.     

生物分子网络弹性研究进展

弹性是生物分子网络重要且基础的属性之一,一方面弹性赋予生物分子网络抵抗内部噪声与环境干扰并维持其自身基本功能的能力,另一方面,弹性为网络状态的恢复制造了阻力。生物分子网络弹性研究试图回答如下3个问题：a. 生物分子网络弹性的产生机理是什么？b. 弹性影响下生物分子网络的状态如何发生转移？c. 如何预测生物网络状态转换临界点,以防止系统向不理想的状态演化？因此,研究生物分子网络弹性有助于理解生物系统内部运作机理,同时对诸如疾病发生临界点预测、生物系统状态逆转等临床应用具有重要的指导意义。鉴于此,本文主要针对以上生物分子网络弹性领域的3个热点研究问题,在研究方法和生物学应用上进行了系统地综述,并对未来生物分子网络弹性的研究方向进行了展望。     

De Novo Evolution of Complex, Global and Hierarchical Gene Regulatory Mechanisms

Gene regulatory networks exhibit complex, hierarchical features such as global regulation and network motifs. There is much debate about whether the evolutionary origins of such features are the results of adaptation, or the by-products of non-adaptive processes of DNA replication. The lack of availability of gene regulatory networks of ancestor species on evolutionary timescales makes this a particularly difficult problem to resolve. Digital organisms, however, can be used to provide a complete evolutionary record of lineages. We use a biologically realistic evolutionary model that includes gene expression, regulation, metabolism and biosynthesis, to investigate the evolution of complex function in gene regulatory networks. We discover that: (i) network architecture and complexity evolve in response to environmental complexity, (ii) global gene regulation is selected for in complex environments, (iii) complex, inter-connected, hierarchical structures evolve in stages, with energy regulation preceding stress responses, and stress responses preceding growth rate adaptations and (iv) robustness of evolved models to mutations depends on hierarchical level: energy regulation and stress responses tend not to be robust to mutations, whereas growth rate adaptations are more robust and non-lethal when mutated. These results highlight the adaptive and incremental evolution of complex biological networks, and the value and potential of studying realistic in silico evolutionary systems as a way of understanding living systems.     

Memorizing environmental signals through feedback and feedforward loops

Cells in diverse organisms can store the information of previous environmental conditions for long periods of time. This form of cellular memory adjusts the cell's responses to future challenges, providing fitness advantages in fluctuating environments. Many biological functions, including cellular memory, are mediated by specific recurring patterns of interactions among proteins and genes, known as ‘network motifs.’ In this review, we focus on three well-characterized network motifs — negative feedback loops, positive feedback loops, and feedforward loops, which underlie different types of cellular memories. We describe the latest studies identifying these motifs in various molecular processes and discuss how the topologies and dynamics of these motifs can enable memory encoding and storage.     

GENETIC REGULATORY NETWORK MOTIFS CONSTRAIN ADAPTATION THROUGH CURVATURE IN THE LANDSCAPE OF MUTATIONAL (CO)VARIANCE

Systems biology is accumulating a wealth of understanding about the structure of genetic regulatory networks, leading to a more complete picture of the complex genotype–phenotype relationship. However, models of multivariate phenotypic evolution based on quantitative genetics have largely not incorporated a network‐based view of genetic variation. Here we model a set of two‐node, two‐phenotype genetic network motifs, covering a full range of regulatory interactions. We find that network interactions result in different patterns of mutational (co)variance at the phenotypic level (the M ‐matrix), not only across network motifs but also across phenotypic space within single motifs. This effect is due almost entirely to mutational input of additive genetic (co)variance. Variation in M has the effect of stretching and bending phenotypic space with respect to evolvability, analogous to the curvature of space–time under general relativity, and similar mathematical tools may apply in each case. We explored the consequences of curvature in mutational variation by simulating adaptation under divergent selection with gene flow. Both standing genetic variation (the G ‐matrix) and rate of adaptation are constrained by M , so that G and adaptive trajectories are curved across phenotypic space. Under weak selection the phenotypic mean at migration‐selection balance also depends on M .