211 research outputs found
The effect of negative feedback loops on the dynamics of Boolean networks
Feedback loops in a dynamic network play an important role in determining the
dynamics of that network. Through a computational study, in this paper we show
that networks with fewer independent negative feedback loops tend to exhibit
more regular behavior than those with more negative loops. To be precise, we
study the relationship between the number of independent feedback loops and the
number and length of the limit cycles in the phase space of dynamic Boolean
networks. We show that, as the number of independent negative feedback loops
increases, the number (length) of limit cycles tends to decrease (increase).
These conclusions are consistent with the fact, for certain natural biological
networks, that they on the one hand exhibit generally regular behavior and on
the other hand show less negative feedback loops than randomized networks with
the same numbers of nodes and connectivity
Monotone and near-monotone biochemical networks
Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion
Structural and functional analysis of cellular networks with CellNetAnalyzer
BACKGROUND: Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking. RESULTS: Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks. CONCLUSION: CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use
Dynamics of Opinion Forming in Structurally Balanced Social Networks
A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends
Additive Edge Labelings
Let G=(V,E) be a graph and d a positive integer. We study the following
problem: for which labelings f_E: E \to Z_d is there a labeling f_V:V \to Z_d
such that f_E(i,j) = f_V(i) + f_V(j) (mod d), for every edge (i,j) in E? We
also explore the connections of the equivalent multiplicative version to toric
ideals. We derive a polynomial algorithm to answer these questions and to
obtain all possible solutions.Comment: 14 page
The structure of gene-gene networks beyond pairwise interactions
Despite its high and direct impact on nearly all biological processes, the
underlying structure of gene-gene interaction networks is investigated so far
according to pair connections. To address this, we explore the gene interaction
networks of the yeast Saccharomyces cerevisiae beyond pairwise interaction
using the structural balance theory (SBT). Specifically, we ask whether
essential and nonessential gene interaction networks are structurally balanced.
We study triadic interactions in the weighted signed undirected gene networks
and observe that balanced and unbalanced triads are over and underrepresented
in both networks, thus beautifully in line with the strong notion of balance.
Moreover, we note that the energy distribution of triads is significantly
different in both essential and nonessential networks compared with the
shuffled networks. Yet, this difference is greater in the essential network
regarding the frequency as well as the energy of triads. Additionally, results
demonstrate that triads in the essential gene network are more interconnected
through sharing common links, while in the nonessential network they tend to be
isolated. Last but not least, we investigate the contribution of all-length
signed walks and its impact on the degree of balance. Our findings reveal that
interestingly when considering longer cycles the nonessential gene network is
more balanced compared to the essential network.Comment: 16 pages, 5 figures, 4 table
Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks
<p>Abstract</p> <p>Background</p> <p>For large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.</p> <p>Results</p> <p>In this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.</p> <p>Conclusion</p> <p>In conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.</p
Methods of model reduction for large-scale biological systems: a survey of current methods and trends
Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed
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