Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switch-like properties which are critical to their biological function. In this study, we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition, the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector.
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that propagate, amplify, and process signals work with noisy representations of that data. Biology must implement strategies that not only filter the noise, but also predict the current state of the environment based on information delayed due to the finite speed of chemical signaling. The idea of a biochemical noise filter is actually more than just a m…
In systems biology effective models are widely used due to the complexity of biological system. They result from a coarse-graining process which employs specific assumptions. Frequently one does not start with a model taking all details into account and then performs a coarse-graining process, but rather one starts right away with the effective equations and often the underlying assumptions remain hidden or unclear. We exemplify the analysis of an effective model by analyzing a time delay equation for the JAK/STAT5 signaling pathway and show how one can avoid wrong conclusions and obtain a dee…
Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical dynamics which dictate timing of cellular events. We propose that if a change of cell fate is triggered by the {\em time-integral} of the underlying stochastic biochemical signal, rather than the original signal, then a dramatic improvement in temporal specificity results. Exact analytical results for stochastic models of hourglass-timers and pendulum-clocks, two…
One of the ultimate goals in biology is to understand the design principles of biological systems. Such principles, if they exist, can help us better understand complex, natural biological systems and guide the engineering of de novo ones. Towards deciphering design principles, in silico evolution of biological systems with proper abstraction is a promising approach. Here, we demonstrate the application of in silico evolution combined with rule-based modelling for exploring design principles of cellular signaling networks. This application is based on a computational platform, called BioJazz, …
Signal transduction is an important and basic mechanism to cell life activities. The stochastic state transition of receptor induces the release of signaling molecular, which triggers the state transition of other receptors. It constructs a nonlinear sigaling network, and leads to robust switchlike properties which are critical to biological function. Network architectures and state transitions of receptor affect the performance of this biological network. In this work, we perform a study of nonlinear signaling on biological polymorphic network by analyzing network dynamics of the Ca$^{2+}$ in…
Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential advantages that signaling oscillations might have in cell function. The biological processes considered include tissue maintenance, embryonic development and wound healing. With the aid of mathematical modeling, we show that a common principle, namely delayed negative feedback, underpins this wide variety of phenomena.
We present DiSH-Sim, a simulator for large discrete models of biological signal transduction pathways, capable of simulating networks with multi-valued elements in both deterministic and stochastic manner. We focus on order of update and thus incorporate information about timing, taking into account that biological processes are not synchronized and certain biochemical changes occur slower than others. Another feature of our simulator is the use of grouped rules to model multi-valued elements and delays. The DiSH-Sim is publicly available and is being used to validate discrete cancer microenvi…
Biological signaling pathways based upon proteins binding to one another to relay a signal for genetic expression, such as the Bone Morphogenetic Protein (BMP) signaling pathway, can be modeled by mass action kinetics and conservation laws that result in non-closed form polynomial equations. Accurately determining parameters of biological pathways that represent physically relevant features, such as binding affinity of proteins and their associated uncertainty, presents a challenge for biological models lacking an explicit likelihood function. Additionally, parameterizing non-closed form biolo…
Dynamic models of signaling networks allow the formulation of hypotheses on the topology and kinetic rate laws characterizing a given molecular network, in-depth exploration and confrontation with kinetic biological data. Despite its standardization, dynamic modeling of signaling networks still requires successive technical steps that need to be carefully performed. Here, we detail these steps by going through the mathematical and statistical framework. We explain how it can be applied to the understanding of β-arrestin-dependent signaling networks. We illustrate our methodology through the mo…
With the tremendous increase in the amount of biological literature, developing automated methods for extracting big data from papers, building models and explaining big mechanisms becomes a necessity. We describe here our approach to translating machine reading outputs, obtained by reading bio- logical signaling literature, to discrete models of cellular networks. We use out- puts from three different reading engines, and describe our approach to translating their different features, using examples from reading cancer literature. We also outline several issues that still arise when assembling…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Morgridge Institute for Research（莫格里奇研究所）
Cells regulate themselves via dizzyingly complex biochemical processes called signaling pathways. These are usually depicted as a network, where nodes represent proteins and edges indicate their influence on each other. In order to understand diseases and therapies at the cellular level, it is crucial to have an accurate understanding of the signaling pathways at work. Since signaling pathways can be modified by disease, the ability to infer signaling pathways from condition- or patient-specific data is highly valuable. A variety of techniques exist for inferring signaling pathways. We build o…
Background: Networks in different domains are characterized by similar global characteristics while differing in local structures. To further extend this concept, we investigated network regularities on a fine scale in order to examine the functional impact of recurring motifs in signed oriented biological networks. In this work we generalize to signaling net works some considerations made on feedback and feed forward loops and extend them by adding a close scrutiny of Linear Triplets, which have not yet been investigate in detail. Results: We studied the role of triplets, either open or close…
Development of fast methods to conduct in silico experiments using computational models of cellular signaling is a promising approach toward advances in personalized medicine. However, software-based cellular network simulation has run-times plagued by wasted CPU cycles and unnecessary processes. Hardware-based simulation affords substantial speedup, but prior attempts at hardware-based biological simulation have been limited in scope and have suffered from inaccuracies due to poor random number generation. In this work, we propose several hardware-based simulation schemes utilizing novel rand…
This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of its constituent modules. The modular decomposition method developed here also has the property that any changes in the parameters of a chemical reaction only affect the dynamics of a single module. To illustrate our results, we define and analyze a few key biological modules that arise in gene regulation, enzymatic networks, and signaling pathways. We also pro…
Due to structural and functional abnormalities or genetic variations and mutations, there may be dysfunctional molecules within an intracellular signaling network that do not allow the network to correctly regulate its output molecules, such as transcription factors. This disruption in signaling interrupts normal cellular functions and may eventually develop some pathological conditions. In this paper, computation capacity of signaling networks is introduced as a fundamental limit on signaling capability and performance of such networks. The computation capacity measures the maximum number of …
Plants both lose water and take in carbon dioxide through microscopic stomatal pores, each of which is regulated by a surrounding pair of guard cells. During drought, the plant hormone abscisic acid (ABA) inhibits stomatal opening and promotes stomatal closure, thereby promoting water conservation. Here we synthesize experimental results into a consistent guard cell signal transduction network for ABA-induced stomatal closure, and develop a dynamic model of this process. Our model captures the regulation of more than forty identified network components, and accords well with previous experimen…
Setting Parameters for Biological Models With ANIMO
ANIMO（Analysis of Networks with Interactive Modeling）是一款用于建模生物网络的软件，例如信号，代谢或基因网络。ANIMO模型本质上是网络拓扑和许多交互参数的总和。拓扑结构以图形的形式描述生物实体之间的相互作用，而参数决定了这种相互作用发生的速度。当观察到ANIMO模型的行为与实验数据之间不匹配时，我们希望更新模型，以便它解释新数据。一般来说，模型的拓扑结构可以用新的（已知的或假设的）节点来扩展，并使其能够匹配实验数据。然而，无限制地向模型中添加新部分会导致两个问题：模型可能变得太复杂太快，以至于难以处理，并且太多标记为“假设”或“未知”的部分使模型变得不切实际。即使改变拓扑通常是更容易的任务，这些问题促使我们尝试更好的参数拟合作为第一步，并采取修改模型拓扑作为最后的资源。在本文中，我们展示了在ANIMO中添加的支持，以减轻扩展生物网络知识的任务，特别是集中在参数设置上。
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of individual nodes and network connectivity, possibly with additional information provided by statistical or descriptive metrics that characterize the network. But what can be inferred about network dynamics when there is no knowledge or information about the internal model or dynamics of participating nodes? Here, we explore how connected subsets of nodes co…
