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Making the right connections: biological networks in the light of evolution
 PROBLEMS AND PARADIGMS
"... Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein–protein interaction networks, we briefly survey the ways in which network ev ..."
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Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein–protein interaction networks, we briefly survey the ways in which network evolution is being addressed in the fields of systems biology, development and ecology. The approaches highlighted demonstrate a movement away from a focus on network topology towards a more integrated view, placing biological properties centrestage. We argue that there remains great potential in a closer synergy between evolutionary biology and biological network analysis, although that may require the development of novel approaches and even different analogies for biological networks themselves.
When is MenzerathAltmann law mathematically trivial? A new approach
 Statistical Applications in Genetics and Molecular Biology , 13
, 2014
"... Menzerath’s law, the tendency of Z, the mean size of the parts, to decrease as X, the number of parts, increases is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y/X, which would imply that ..."
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Menzerath’s law, the tendency of Z, the mean size of the parts, to decrease as X, the number of parts, increases is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y/X, which would imply that Z scales with X as Z ∼ 1/X. That scaling is a very particular case of MenzerathAltmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three nonparametric tests based upon different correlation metrics and one parametric test to evaluate if Z ∼ 1/X in genomes. The most powerful test is a new nonparametric based upon the correlation ratio, which is able to reject Z ∼ 1/X in nine out of eleven taxonomic groups and detect a borderline group. Rather than a fact, Z ∼ 1/X is a baseline that real genomes do not meet. The view of MenzerathAltmann law as inevitable is seriously flawed.
Convergence Properties of the Degree Distribution of Some Growing Network Models
, 2006
"... In this article we study a class of randomly grown graphs that includes some preferential attachment and uniform attachment models, as well as some evolving graph models that have been discussed previously in the literature. The degree distribution is assumed to form a Markov chain; this gives a pa ..."
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In this article we study a class of randomly grown graphs that includes some preferential attachment and uniform attachment models, as well as some evolving graph models that have been discussed previously in the literature. The degree distribution is assumed to form a Markov chain; this gives a particularly simple form for a stochastic recursion of the degree distribution. We show that for this class of models the empirical degree distribution tends almost surely and in norm to the expected degree distribution as the size of the graph grows to infinity and we provide a simple asymptotic expression for the expected degree distribution. Convergence of the empirical degree distribution has consequences for statistical analysis of network data in that it allows the full data to be summarized by the degree distribution of the nodes without losing the ability to obtain consistent estimates of parameters describing the network.
ANALYSIS OF BIOLOGICAL NETWORK DATA USING LIKELIHOODFREE INFERENCE TECHNIQUES
"... Biological Networks have received much attention in recent years, but statistical tools for network analysis are still in their infancy. In this paper we focus on Protein Interaction Networks (PINs) that typically comprise thousands of proteins and interactions. PINs are the result of long evolution ..."
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Biological Networks have received much attention in recent years, but statistical tools for network analysis are still in their infancy. In this paper we focus on Protein Interaction Networks (PINs) that typically comprise thousands of proteins and interactions. PINs are the result of long evolutionary histories. Here we adopt simple mathematical models that capture essentials of protein evolution and develop statistical methods to estimate evolutionary PIN parameters. Our initial approach is based on a recursion for the likelihood, but it becomes computationally intractable for reasonably sized networks. Our second approach is based on summary statistics and likelihoodfree inference. We discuss problems with selection of summaries, convergence, and credibility and apply the methods on Helicobacter pylori and Plasmodium falciparum data. 1.
Associate Editor: XXXXXXX
"... Motivation: Much of the largescale molecular data from living cells can be represented in terms of networks. Such networks occupy a central position in cellular systems biology. In the proteinprotein interaction (PPI) network, nodes represent proteins and edges represent connections between them, ..."
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Motivation: Much of the largescale molecular data from living cells can be represented in terms of networks. Such networks occupy a central position in cellular systems biology. In the proteinprotein interaction (PPI) network, nodes represent proteins and edges represent connections between them, based on experimental evidence. PPI networks are rich and complex, so that a mathematical model is sought to capture their properties and shed light on PPI evolution. The mathematical literature contains various generative models of random graphs. It is a major, still largely open question, which of these models (if any) can properly reproduce various biologicallyinteresting networks. Here we consider this problem where the graph at hand is the PPI network of Saccharomyces cerevisiae. We are trying to distinguishing between a model family which performs a process of copying neighbors, represented by the Duplication
Supplementary Material Variability in the degree distributions of subnets Sampling fraction 80% Sampling fraction 60%
"... Degree k Figure 1: Average degree distributions (black circles) and empirical 95 % confidence intervlas (dashed red lines) obtained from 1000 random subnets of the true S.cerevisiaeprotein interaction network. Also shown are the degree distributions of two random subnets. In figure 1 we show the ave ..."
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Degree k Figure 1: Average degree distributions (black circles) and empirical 95 % confidence intervlas (dashed red lines) obtained from 1000 random subnets of the true S.cerevisiaeprotein interaction network. Also shown are the degree distributions of two random subnets. In figure 1 we show the average degree distributions (black open circles), the 97.5 and 2.5 percentiles (red dashed lines) and the actual degree distributions of two random subnets. We find that the average (also shown in part A of figure 1) does describe the degree distributions well over a broad range of degrees, especially (and unsurprisingly) for larger.sampling fractions. The 95 % confidence interval always broadens at higher degrees, reflecting the broad tailed (though not scalefree [5]) nature of the degree distribution. In particular small values of the sampling fraction, the CIs indicate considerable variability in the tail of the degree distributions. 1 Predicting the clustering coefficient of the overall network
On the Use of ScaleFree Networks for Information Network Modelling
"... The notion of scalefree networks was created in the late 1990s when researchers at the University of Notre Dame investigated the distribution of the number of links connected to a node, i.e. the degree distribution of a network. For many realworld networks, they found a strong deviation from the ..."
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The notion of scalefree networks was created in the late 1990s when researchers at the University of Notre Dame investigated the distribution of the number of links connected to a node, i.e. the degree distribution of a network. For many realworld networks, they found a strong deviation from the random network model based on random graphs that had prevailed in network modelling until then. This finding led to the development of a novel approach which models the evolution of a network and is able to reproduce the observed degree distribution. In this paper, we briefly review the underlying principles of random graphs and scalefree networks. Furthermore, we give an overview of real world examples of scalefree networks from a biological and applicational perspective and present briefly an application of scalefree networks for the analysis of two types of information networks.
PREFACE The Workshop on Computational Systems Biology has been organized annually by the
"... Tampere University of Technology (TUT). The history of the workshop traces back to 2003, when it was organized for the first time as an internal meeting with some invited international collaborators. Since then the meeting has grown each year witnessing a rapid development in experimental bioscience ..."
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Tampere University of Technology (TUT). The history of the workshop traces back to 2003, when it was organized for the first time as an internal meeting with some invited international collaborators. Since then the meeting has grown each year witnessing a rapid development in experimental biosciences and growth in the research of computational methods in systems biology. This year the program committee set the target to making the event more international, as well as emphasizing the quality and significance of the research papers published in this proceedings book. Therefore in 2008 the workshop is organized in Leipzig, Institute for Medical Informatics, Statistics and Epidemiology (IMISE), Germany, together with collaborators from University of Leipzig and Dortmund University of Technology. The joint organization has proved to be smooth and successful we are having a record number of international participants. We have brought together the various communities involved in the different aspects of computational systems biology research, e.g. experimental biology, machine learning, signal processing, statistics and theoretical physics. The workshop program together with the range of published papers demonstrate
From evidence to inference: probing the . . .
, 2009
"... The evolutionary mechanisms by which protein interaction networks grow and change are beginning to be appreciated as a major factor shaping their presentday structures and properties. Starting with a consideration of the biases and errors inherent in our current views of these networks, we discuss ..."
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The evolutionary mechanisms by which protein interaction networks grow and change are beginning to be appreciated as a major factor shaping their presentday structures and properties. Starting with a consideration of the biases and errors inherent in our current views of these networks, we discuss the dangers of constructing evolutionary arguments from naïve analyses of network topology. We argue that progress in understanding the processes of network evolution is only possible when hypotheses are formulated as plausible evolutionary models and compared against the observed data within the framework of probabilistic modeling. The value of such models is expected to be greatly enhanced as they incorporate more of the details of the biophysical properties of interacting proteins, gene phylogeny, and measurement error and as more advanced methodologies emerge for model comparison and the inference of ancestral network states.