66 research outputs found
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
Topology and dynamics of an artificial genetic regulatory network model
This thesis presents some of the methods of studying models of regulatory networks
using mathematical and computational formalisms. A basic review of the
biology behind gene regulation is introduced along with the formalisms used for modelling
networks of such regulatory interactions. Topological measures of large-scale
complex networks are discussed and then applied to a specific artificial regulatory network
model created through a duplication and divergence mechanism. Such networks
share topological features with natural transcriptional regulatory networks. Thus, it
may be the case that the topologies inherent in natural networks may be primarily
due to their method of creation rather than being exclusively shaped by subsequent
evolution under selection.
The evolvability of the dynamics of these networks are also examined by evolving
networks in simulation to obtain three simple types of output dynamics. The networks
obtained from this process show a wide variety of topologies and numbers of genes
indicating that it is relatively easy to evolve these classes of dynamics in this model
On the Origin of Biomolecular Networks
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pairwise interactions amongst biomolecules. Here, we explore the important and hitherto neglected role of information asymmetry in the genesis and evolution of such pairwise biomolecular interactions. Information asymmetry between sender and receiver genes is identified as a key feature distinguishing early biochemical reactions from abiotic chemistry, and a driver of network topology as biomolecular systems become more complex. In this context, we review how graph theoretical approaches can be applied not only for a better understanding of various proximate (mechanistic) relations, but also, ultimate (evolutionary) structures encoded in such networks from among all types of variations they induce. Among many possible variations, we emphasize particularly the essential role of gene duplication in terms of signaling game theory, whereby sender and receiver gene players accrue benefit from gene duplication, leading to a preferential attachment mode of network growth. The study of the resulting dynamics suggests many mathematical/computational problems, the majority of which are intractable yet yield to efficient approximation algorithms, when studied through an algebraic graph theoretic lens. We relegate for future work the role of other possible generalizations, additionally involving horizontal gene transfer, sexual recombination, endo-symbiosis, etc., which enrich the underlying graph theory even further
Functional Alignment of Regulatory Networks: A Study of Temperate Phages
The relationship between the design and functionality of molecular networks is now a key issue in biology. Comparison of regulatory networks performing similar tasks can provide insights into how network architecture is constrained by the functions it directs. Here, we discuss methods of network comparison based on network architecture and signaling logic. Introducing local and global signaling scores for the difference between two networks, we quantify similarities between evolutionarily closely and distantly related bacteriophages. Despite the large evolutionary separation between phage λ and 186, their networks are found to be similar when difference is measured in terms of global signaling. We finally discuss how network alignment can be used to pinpoint protein similarities viewed from the network perspective
Flow Motifs Reveal Limitations of the Static Framework to Represent Human interactions
Networks are commonly used to define underlying interaction structures where
infections, information, or other quantities may spread. Although the standard
approach has been to aggregate all links into a static structure, some studies
suggest that the time order in which the links are established may alter the
dynamics of spreading. In this paper, we study the impact of the time ordering
in the limits of flow on various empirical temporal networks. By using a random
walk dynamics, we estimate the flow on links and convert the original
undirected network (temporal and static) into a directed flow network. We then
introduce the concept of flow motifs and quantify the divergence in the
representativity of motifs when using the temporal and static frameworks. We
find that the regularity of contacts and persistence of vertices (common in
email communication and face-to-face interactions) result on little differences
in the limits of flow for both frameworks. On the other hand, in the case of
communication within a dating site (and of a sexual network), the flow between
vertices changes significantly in the temporal framework such that the static
approximation poorly represents the structure of contacts. We have also
observed that cliques with 3 and 4 vertices con- taining only low-flow links
are more represented than the same cliques with all high-flow links. The
representativity of these low-flow cliques is higher in the temporal framework.
Our results suggest that the flow between vertices connected in cliques depend
on the topological context in which they are placed and in the time sequence in
which the links are established. The structure of the clique alone does not
completely characterize the potential of flow between the vertices
Frequent Pattern Finding in Integrated Biological Networks
Biomedical research is undergoing a revolution with the advance of high-throughput technologies. A major challenge in the post-genomic era is to understand how genes, proteins and small molecules are organized into signaling pathways and regulatory networks. To simplify the analysis of large complex molecular networks, strategies are sought to break them down into small yet relatively independent network modules, e.g. pathways and protein complexes.
In fulfillment of the motivation to find evolutionary origins of network modules, a novel strategy has been developed to uncover duplicated pathways and protein complexes. This search was first formulated into a computational problem which finds frequent patterns in integrated graphs. The whole framework was then successfully implemented as the software package BLUNT, which includes a parallelized version.
To evaluate the biological significance of the work, several large datasets were chosen, with each dataset targeting a different biological question. An application of BLUNT was performed on the yeast protein-protein interaction network, which is described. A large number of frequent patterns were discovered and predicted to be duplicated pathways. To explore how these pathways may have diverged since duplication, the differential regulation of duplicated pathways was studied at the transcriptional level, both in terms of time and location.
As demonstrated, this algorithm can be used as new data mining tool for large scale biological data in general. It also provides a novel strategy to study the evolution of pathways and protein complexes in a systematic way. Understanding how pathways and protein complexes evolve will greatly benefit the fundamentals of biomedical research
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