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.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Stochastic Modeling of Autoregulatory Genetic Feedback Loops: A Review and Comparative Study

Autoregulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic parameters of the main biochemical steps. These models differ according to 1) which subcellular processes are explicitly modeled, 2) the modeling methodology employed (discrete, continuous, or hybrid), and 3) whether they can be analytically solved for the steady-state distribution of protein numbers. We discuss the assumptions and properties of the main models in the literature, summarize our current understanding of the relationship between them, and highlight some of the insights gained through modeling.     

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.     

When kinases meet mathematics: the systems biology of MAPK signalling

The mitogen activated protein kinase/extracellular signal regulated kinase pathway regulates fundamental cellular function such as cell proliferation, survival, differentiation and motility, raising the question how these diverse functions are specified and coordinated. They are encoded through the activation kinetics of the pathway, a multitude of feedback loops, scaffold proteins, subcellular compartmentalisation, and crosstalk with other pathways. These regulatory motifs alone or in combination can generate a multitude of complex behaviour. Systems biology tries to decode this complexity through mathematical modelling and prediction in order to gain a deeper insight into the inner works of signalling networks.     

On the dynamics of controlled metabolic network and cellular behavior

The existence of elaborate control mechanisms for the various biochemical processes inside and within living cells is responsible for the coherent behaviour observed in its spatio-temporal organisation. Stability and sensitivity are both necessary properties of living systems and these are achieved through negetive and positive feedback loops as in other control systems. We have studied a three-step reaction scheme involving a negative and a positive feedback loop in the form of end-product inhibition and allosteric activation. The variety of behaviour exhibited by this system, under different conditions, includes steady state, simple limit cycle oscillations, complex oscillations and period bifurcations leading to random oscillations or chaos. The system also shows the existence of two distinct chaotic regimes under the variation of a single parameter. These results, in comparison with single biochemical control loops, show that new behaviours can be exhibited in a more complex network which are not seen in the single control loops. The results are discussed in the light of a diverse variety of cellular functions in normal and altered cells indicating the role of controlled metabolic network as the underlying basis for cellular behaviour.     

microRNA调控网络与肿瘤

microRNA(miRNA)是一类长度约为22nt的小分子非编码RNA,对基因表达进行转录后调控。基因调控网络由各种回路,如前馈和反馈回路组成。它通过将外界刺激整合成合适的输出信号,控制细胞从增殖到死亡几乎所有的生命活动。已知基因调控网络的失调与肿瘤的发生发展密切相关。新近的实验证据表明,miRNA广泛参与基因调控网络中的反馈和前馈回路。该文主要介绍miRNA在基因表达调控网络中的作用及其与肿瘤发生发展的关系。     

Coherent coupling of feedback loops: a design principle of cell signaling networks

MOTIVATION: It is widely accepted that cell signaling networks have been evolved to be robust against perturbations. To investigate the topological characteristics resulting in such robustness, we have examined large-scale signaling networks and found that a number of feedback loops are present mostly in coupled structures. In particular, the coupling was made in a coherent way implying that same types of feedback loops are interlinked together. RESULTS: We have investigated the role of such coherently coupled feedback loops through extensive Boolean network simulations and found that a high proportion of coherent couplings can enhance the robustness of a network against its state perturbations. Moreover, we found that the robustness achieved by coherently coupled feedback loops can be kept evolutionarily stable. All these results imply that the coherent coupling of feedback loops might be a design principle of cell signaling networks devised to achieve the robustness.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

Signal transduction network motifs and biological memory

Memory is a ubiquitous phenomenon in biological systems, yet the mechanisms responsible for memory, and how to manipulate it at the subcellular level, remain poorly understood. Subjected to transient stimuli, biological systems can exhibit short early responses and/or prolonged (or permanent) late responses. Experimental evidence suggests that early responses (short-term memory) involve post-translational modification of existing proteins and/or their intracellular relocalization, whereas late responses (long-term memory) depend on new protein synthesis. Although this provides an intuitive explanation at the basic molecular level, it does little to clarify the important dynamics that actually maintain memory at the systems level. In this study, we use mathematical modeling to study dynamical mechanisms of biological memory. We first examined the response of four fundamental motifs (positive/negative feedforward and feedback) to external stimuli. Because motifs do not exist in isolation within the cell, we then combined these motifs to form signaling modules to understand how they confer biological memory. These motifs, and different combinations thereof, displayed distinct behavior in response to external stimuli. The principles described in this study have important implications for experimental approaches to identify the mechanisms for biological memory and for the development of therapeutic strategies to modulate signaling network responses in the setting of human disease.     

The regulatory circuits for hysteretic switching in cellular signal transduction pathways

Hysteresis can be found in many physical systems, and a hysteretic switch has been used for various mechanical and electrical systems. Such a hysteretic switch can be created by using a single positive feedback loop, as often used in engineering systems. It is, however, intriguing that various cellular signaling systems use coupled positive feedback loops to implement the hysteretic switch. A question then arises about the advantage of using coupled positive feedback loops instead of simple isolated positive feedback for an apparently equivalent hysteretic switch. Through mathematical simulations, we determined that cellular systems with coupled positive feedback loops show enhanced hysteretic switching, and can thereby make a more reliable decision under conditions of noisy signaling. As most intracellular processes are accompanied by intrinsic noise, important cellular decisions such as differentiation and apoptosis need to be highly robust to such noises. The coupled positive feedback loops might have been evolutionarily acquired to enable correct cell fate decisions to be made through enhanced hysteretic switching in noisy cellular environments.     

Emergence of robust regulatory motifs from in silico evolution of sustained oscillation

The relationship between robustness and evolvability (easiness to evolve), and the evolutionary emergence of robust genetic circuits in biology have attracted much attention in systems biology. This paper investigates in silico the influence of the cis-regulation logic and the coupling of feedback loops on the evolvability and robustness of gene regulatory motifs that can generate sustained oscillation. Our simulation results indicate that both evolvability and robustness of the considered regulatory motifs depend on the cis-regulation logic and the way in which positive and negative feedback loops are coupled. Most interestingly, our findings suggest that robust regulatory motifs can emerge from evolution without an explicit selection pressure on robustness and adding noise in the parameters during the evolution is likely to promote the evolution of sustained oscillation.     

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。