Dynamics of Influenza Virus and Human Host Interactions During Infection and Replication Cycle

Madrahimov, Alex; Helikar, Tomáš; Kowal, Bryan; Lu, Guoqing; Rogers, Jim

doi:10.1007/s11538-012-9777-2

Cited by 28 publications

(18 citation statements)

References 80 publications

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“…For example, it would be interesting to compare the results of the fibroblast network to other networks such as the Boolean model of the influenza–host interactions during infection of an epithelial cell Madrahimov et al. (2013), to identify possible similarities and differences that may occur. At the same time, identifying possible classes of biological nodes/sub-networks obtained with the DP sub-network procedure in a variety of other networks could bring further clarifications on the advantages of the DP method.…”

Section: Final Commentsmentioning

confidence: 99%

Logical Reduction of Biological Networks to Their Most Determinative Components

Matache

2016

Bull Math Biol

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Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. The determinative power of a node is obtained by a summation of all mutual information quantities over all nodes having the chosen node as a common input, thus representing a measure of information gain obtained by the knowledge of the node under consideration. The determinative power of nodes has been considered in the literature under the assumption that the inputs are independent in which case one can use the Bahadur orthonormal basis. In this article, we relax that assumption and use a standard orthonormal basis instead. We use techniques of Hilbert space operators and harmonic analysis to generate formulas for the sensitivity to perturbations of nodes, quantified by the notions of influence, average sensitivity, and strength. Since we work on finite-dimensional spaces, our formulas and estimates can be and are formulated in plain matrix algebra terminology. We analyze the determinative power of nodes for a Boolean model of a signal transduction network of a generic fibroblast cell. We also show the similarities and differences induced by the alternative complete orthonormal basis used. Among the similarities, we mention the fact that the knowledge of the states of the most determinative nodes reduces the entropy or uncertainty of the overall network significantly. In a special case, we obtain a stronger result than in previous works, showing that a large information gain from a set of input nodes generates increased sensitivity to perturbations of those inputs.

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Section: Final Commentsmentioning

confidence: 99%

Logical Reduction of Biological Networks to Their Most Determinative Components

Matache

2016

Bull Math Biol

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“…On the theoretical side, it has been shown that the problem of finding, or even counting, steady states of Boolean networks is NP-hard [ 23 , 24 ], so that any algorithm for this problem will eventually encounter serious limitations. Since the size of published models has increased in recent years, including models with 100 or more nodes [ 15 , 17 , 21 , 22 ], it is important to develop more efficient methods that find all steady states of a Boolean model.…”

Section: Introductionmentioning

confidence: 99%

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

Veliz-Cuba

Aguilar

Hinkelmann³

et al. 2014

BMC Bioinformatics

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BackgroundA key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general.ResultsThis paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author.ConclusionsThe algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem.

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“…The model is available to the entire scientific community via the software for further expansion, refinements, as well as simulations and analyses. The user-friendly interface of the software allows users to make changes to the model without any need to enter complex mathematical equations or computer code, making it accessible to experimental scientists who have the most intimate knowledge of the local data to improve and grow this model (and others available in the software platform; e.g., [30], [43], [44]). …”

Section: Discussionmentioning

confidence: 99%

A Comprehensive, Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells

et al. 2013

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The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins and their post-translational modifications sites, and over 1,000 biochemical interactions. Using computer simulations of the model, we find it is able to reproduce a number of cellular phenomena. Furthermore, the model predicts that overexpression of Src results in increased endocytosis of EGFR in the absence/low amount of the epidermal growth factor (EGF). Our subsequent laboratory experiments also suggest increased internalization of EGFR upon Src overexpression under EGF-deprived conditions, further supporting this model-generated hypothesis.

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Dynamics of Influenza Virus and Human Host Interactions During Infection and Replication Cycle

Cited by 28 publications

References 80 publications

Logical Reduction of Biological Networks to Their Most Determinative Components

Logical Reduction of Biological Networks to Their Most Determinative Components

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

A Comprehensive, Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells

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