Dynamic Behavior Of Network Research Articles

A Dynamic Analysis of IRS-PKR Signaling in Liver Cells: A Discrete Modeling Approach

A major challenge in systems biology is to develop a detailed dynamic understanding of the functions and behaviors in a particular cellular system, which depends on the elements and their inter-relationships in a specific network. Computational modeling plays an integral part in the study of network dynamics and uncovering the underlying mechanisms. Here we proposed a systematic approach that incorporates discrete dynamic modeling and experimental data to reconstruct a phenotype-specific network of cell signaling. A dynamic analysis of the insulin signaling system in liver cells provides a proof-of-concept application of the proposed methodology. Our group recently identified that double-stranded RNA-dependent protein kinase (PKR) plays an important role in the insulin signaling network. The dynamic behavior of the insulin signaling network is tuned by a variety of feedback pathways, many of which have the potential to cross talk with PKR. Given the complexity of insulin signaling, it is inefficient to experimentally test all possible interactions in the network to determine which pathways are functioning in our cell system. Our discrete dynamic model provides an in silico model framework that integrates potential interactions and assesses the contributions of the various interactions on the dynamic behavior of the signaling network. Simulations with the model generated testable hypothesis on the response of the network upon perturbation, which were experimentally evaluated to identify the pathways that function in our particular liver cell system. The modeling in combination with the experimental results enhanced our understanding of the insulin signaling dynamics and aided in generating a context-specific signaling network.

Vibration modes and natural frequencies of saddle form cable nets

The objective of this paper is to investigate the dynamic behaviour of cable networks, in terms of their natural frequencies and the corresponding vibration modes. A multi-degree-of-freedom cable net model is assumed, having circular plan view and the shape of a hyperbolic paraboloid surface. The cable supports are considered either rigid or flexible, thus accounting for the deformability of the edge ring. On the basis of numerical analyses, empirical formulae are proposed for the estimation of the linear natural frequencies, taking into account the mechanical and geometrical characteristics of the cable net and the ring, expressed in the form of appropriate non-dimensional parameters. The sequence of the symmetric and antisymmetric modes of the network and the occurrence of modal transition can be predicted in relation to one of these parameters, in analogy to single cables. The differences between a network with rigid cable supports and one with boundary ring, concerning the eigenmodes and the corresponding eigenfrequencies are identified.

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris–Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.

Dynamical Behavior of Phase Oscillator Networks on the Bethe Lattice

We study the dynamical nature of phase oscillator networks on a Bethe lattice. We derive self-consistent equations for the cavity fields (i.e. the oscillator probability distributions) by using the cavity method both in equilibrium and via an analytic approximation for non-equilibrium states. The order parameters and their evolution equations are obtained as functions of the cavity fields. The theoretical results and the accuracy of our approximations are confirmed by comparison with simulations involving direct integration of the Langevin equations describing the microscopic oscillator dynamics.

Performance evaluation of routing protocols for MANETs with known connectivity patterns using evolving graphs

The assessment of routing protocols for mobile wireless networks is a difficult task, because of the networks’ dynamic behavior and the absence of benchmarks. However, some of these networks, such as intermittent wireless sensors networks, periodic or cyclic networks, and some delay tolerant networks (DTNs), have more predictable dynamics, as the temporal variations in the network topology can be considered as deterministic, which may make them easier to study. Recently, a graph theoretic model—the evolving graphs—was proposed to help capture the dynamic behavior of such networks, in view of the construction of least cost routing and other algorithms. The algorithms and insights obtained through this model are theoretically very efficient and intriguing. However, there is no study about the use of such theoretical results into practical situations. Therefore, the objective of our work is to analyze the applicability of the evolving graph theory in the construction of efficient routing protocols in realistic scenarios. In this paper, we use the NS2 network simulator to first implement an evolving graph based routing protocol, and then to use it as a benchmark when comparing the four major ad hoc routing protocols (AODV, DSR, OLSR and DSDV). Interestingly, our experiments show that evolving graphs have the potential to be an effective and powerful tool in the development and analysis of algorithms for dynamic networks, with predictable dynamics at least. In order to make this model widely applicable, however, some practical issues still have to be addressed and incorporated into the model, like adaptive algorithms. We also discuss such issues in this paper, as a result of our experience.

On Stability Problems of Supply Networks Constrained With Transport Delay

Transportation is one of the most crucial components in supply networks. In transportation lines, there exists a finite time between products leaving a point and arriving to another point in the supply network. This period of time is the delay, which accompanies all transportation lines present in the entire network. Delay is a well-known limitation, which is inevitable and pervasive in the network causing synchronization problems, fluctuating or excessive inventories, and lack of robustness of inventories against cyclic perturbations. The end results of such undesirable effects directly reflect to costs. This paper is motivated to reveal the mechanisms leading to these problems by analytically characterizing qualitative behavior of supply network dynamics modeled by continuous-time differential equations. The presence of delay forms the main challenge in the analysis and this is tackled by developing/utilizing the tools emerging from delay systems and control theory. While the backbone of the paper addresses the qualitative behavior in presence of a single delay representing delays in all transportation paths, it also reveals how to choose production rates and transportation delay without inducing any undesirable effects mentioned. Thorough cases studies with single and multiple delays are presented to demonstrate the effectiveness of the approaches proposed.

Feedback Control Of Fluctuations In Gene Expression And Epigenetic Memory

Genes and proteins are organized into extensive networks that allow cells to respond and adapt to their environment. These networks are regulated through feedback loops. The dynamic behavior of a genetic network with a given architecture depends on stochastic fluctuations of the agents involved. However, it's still undetermined how the feedback strength and the noise levels couple to determine cellular behavior and its variability. In the present work, we analyze the stochastic dynamic behavior of the galactose uptake network of S. cerevisiae. We focus on how changing the strength of the positive and negative feedback loops influences circuit dynamics and adaptability, and how feedback controls the noise levels in the circuit. We show that when the strength of the negative feedback is increased, the capacity to display memory of the initial galactose consumption is lost compared to the wild type strain. On the other hand, by varying the strength of the positive feedback we observe the emergence of a region with stable memory. It has been shown that the capacity for cells to display memory depends on the stochastic fluctuations of the circuit, and hence we analyze the effect of feedback strength on transition rates between the alternative states ON/OFF. In this case we demonstrate that the switching rates between the two phenotypic states can be tuned by changing the strength of the feedbacks. These results reveal that the feedback strengths of the network regulate the dynamic behavior through modulation of the stochastic fluctuations of gene expression and the stability of different states of gene expression. This suggests that the strength of feedbacks may be tuned allowing a population to enhance its fitness under a certain frequency of environmental fluctuations, by changing the rate of stochastic transitions between different states.

Temperature Effect on the Dynamic Behavior of Tricarboxylic Acid Derivatives in Two-Dimensional Network Structures

The temperature effect on the adsorption behavior and the dynamic behavior of TCMB 2D network structure on the Au(111) substrate has been investigated. From the calculation of the adsorbed energy between the molecule and the Au(111) substrate, it can be found that there are significant changes in adsorbed energy as the temperature increase; moreover, different migration features are appeared at different specific temperature, owing to the deformation of the 2D network structure changed. The mean square displacement (MSD) and diffusion coefficient are calculated to study the migration property and dynamical behavior of 2D TCMB networks at specific temperatures.

Analytical estimates and proof of the scale-free character of efficiency and improvement in Barabási–Albert trees

Estimates for the efficiency of a tree are derived, leading to new analytical expressions for Barábasi–Albert trees efficiency. These expressions are used to investigate the dynamic behaviour of such networks. It is proved that the preferential attachment leads to an asymptotic conservation of efficiency as the Barábasi–Albert trees grow.

Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks

The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh-Hurwitz, Lyapunov criteria, Feinberg's Deficiency Zero theorem) would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.

Interplay between Topology and Dynamics in Excitation Patterns on Hierarchical Graphs.

In a recent publication (Müller-Linow et al., 2008) two types of correlations between network topology and dynamics have been observed: waves propagating from central nodes and module-based synchronization. Remarkably, the dynamic behavior of hierarchical modular networks can switch from one of these modes to the other as the level of spontaneous network activation changes. Here we attempt to capture the origin of this switching behavior in a mean-field model as well in a formalism, where excitation waves are regarded as avalanches on the graph.

Activating and inhibiting connections in biological network dynamics

BackgroundMany studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior – for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos.ResultsHere we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate.ConclusionThe activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks.ReviewersReviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon) Xia (nominated by Mark Gerstein). For the full reviews, please go to the Reviewers' comments section.

On Static and Dynamic Partitioning Behavior of Large-Scale P2P Networks

In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> (1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime.

Subnetwork analysis for multistationarity in mass action kinetics

Since quantitative knowledge of the complex (bio)chemical reaction networks is often very limited, formal methods that connect network structure and dynamic behavior are needed in mathematical modeling and analysis. Feinberg's Chemical Reaction Network Theory allows for the classification of the potential network behavior, for instance, with respect to the existence of multiple steady states, but is computationally limited to small systems. Here, we show that by analyzing subnetworks associated to stoichiometric generators, the applicability of the theory can be extended to more complex networks. Moreover, based on mild conditions regarding multiststionarity of such subnetworks, we present an algorithm which establishes multistationarity in the overall network.For example-networks inspired by cell cycle control in budding yeast, the approach allows for identification of key mechanisms for multistationarity, for model discrimination and for robustness analysis. The present paper continues and extends our work that has appeared in PNAS (cf. [6]).

Software for Automatic Coordination of Protection Devices in Distribution System

Among the several components of distribution systems, protection devices present a fundamental importance, since they aim at keeping the physical integrity not only of the system equipment, but also of the electricians team and the population in general. The existing tools today in the market that carry out the making of protection studies basically draw curves, and need direct user's interference for the protection devices adjustment and coordination analyses of selectivity, being susceptible to the user's mistakes and not always considering the best technical and economical application. In Brazil, the correct application of the protection devices demand a high amount of time, being extremely laborious due to the great number of devices (around 200 devices), besides the very dynamic behavior of distribution networks and the need for constant system expansion. This paper presents a computational tool developed with the objective of automatically determining the adjustments of all protection devices in the distribution networks to obtain the best technical application, optimizing its performance and making easier protection studies.

Inferring connectivity of interacting phase oscillators

The question as to how network topology properties influence network dynamical behavior has been extensively investigated. Here we treat the inverse problem, i.e., how to infer network connection topology from the dynamic evolution, and suggest a control based topology identification method. This method includes two steps: (i) driving the network to a steady state and (ii) inferring all elements of the connectivity matrix by exploiting information obtained from the observed steady state response of each node. We adopt different strategies for model-dependent (i.e., each local phase dynamics and coupling functions are known) and model-free (i.e., each local phase dynamics and coupling functions are unknown) cases and give detailed conditions for both cases under which network topology can be identified correctly. The influence of noise on topology identification is discussed as well. All proposed approaches are motivated and illustrated with networks of phase oscillators. We argue that these topology identification methods can be extended to general dynamical networks and are not restricted to only networks of phase oscillators.

Inference of an oscillating model for the yeast cell cycle

High-throughput techniques allow measurement of hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex regulatory processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods for estimating model parameters fail in this setting, since they overfit the data. This is even the case, if the focus is on modeling subnetworks of, at most, a few tens of components. In a Bayesian learning approach, this problem is avoided by a restriction of the search space with prior probability distributions over model parameters. This paper combines both differential equation models and a Bayesian approach. We model the periodic behavior of proteins involved in the cell cycle of the budding yeast Saccharomyces cerevisiae, with differential equations, which are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state, and lots of efforts have been made to explain the observed periodic behavior. We introduce an approach to infer an oscillating network from experimental data. First, an oscillating core network is learned. This is extended by further components by using a Bayesian approach in a second step. A specifically designed hierarchical prior distribution over interaction strengths prevents overfitting, and drives the solutions to sparse networks with only a few significant interactions. We apply our method to a simulated and a real world dataset and reveal main regulatory interactions. Moreover, we are able to reconstruct the dynamic behavior of the network.

Integrating metabolic, transcriptional regulatory and signal transduction models inEscherichia coli

The effort to build a whole-cell model requires the development of new modeling approaches, and in particular, the integration of models for different types of processes, each of which may be best described using different representation. Flux-balance analysis (FBA) has been useful for large-scale analysis of metabolic networks, and methods have been developed to incorporate transcriptional regulation (regulatory FBA, or rFBA). Of current interest is the integration of these approaches with detailed models based on ordinary differential equations (ODEs). We developed an approach to modeling the dynamic behavior of metabolic, regulatory and signaling networks by combining FBA with regulatory Boolean logic, and ordinary differential equations. We use this approach (called integrated FBA, or iFBA) to create an integrated model of Escherichia coli which combines a flux-balance-based, central carbon metabolic and transcriptional regulatory model with an ODE-based, detailed model of carbohydrate uptake control. We compare the predicted Escherichia coli wild-type and single gene perturbation phenotypes for diauxic growth on glucose/lactose and glucose/glucose-6-phosphate with that of the individual models. We find that iFBA encapsulates the dynamics of three internal metabolites and three transporters inadequately predicted by rFBA. Furthermore, we find that iFBA predicts different and more accurate phenotypes than the ODE model for 85 of 334 single gene perturbation simulations, as well for the wild-type simulations. We conclude that iFBA is a significant improvement over the individual rFBA and ODE modeling paradigms. All MATLAB files used in this study are available at http://www.simtk.org/home/ifba/. Supplementary data are available at Bioinformatics online.

Method for inferring and extracting reliable genetic interactions from time-series profile of gene expression

Recent advances in technologies such as DNA microarrays have provided an abundance of gene expression data on the genomic scale. One of the most important projects in the post-genome-era is the systemic identification of gene expression networks. However, inferring internal gene expression structure from experimentally observed time-series data are an inverse problem. We have therefore developed a system for inferring network candidates based on experimental observations. Moreover, we have proposed an analytical method for extracting common core binomial genetic interactions from various network candidates. Common core binomial genetic interactions are reliable interactions with a higher possibility of existence, and are important for understanding the dynamic behavior of gene expression networks. Here, we discuss an efficient method for inferring genetic interactions that combines a Step-by-step strategy (Y. Maki, Y. Takahashi, Y. Arikawa, S. Watanabe, K. Aoshima, Y. Eguchi, T. Ueda, S. Aburatani, S. Kuhara, M. Okamoto, An integrated comprehensive workbench for inferring genetic networks: Voyagene, Journal of Bioinformatics and Computational Biology 2(3) (2004) 533.) with an analysis method for extracting common core binomial genetic interactions.