Disordered proteins and network disorder in network descriptions of protein structure, dynamics and function. Hypotheses and a comprehensive review

During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here we review the links between disordered proteins and the associated networks, and describe the consequences of local, mesoscopic and global network disorder on changes in protein structure and dynamics. We introduce a new classification of protein networks into ‘cumulus-type’, i.e., those similar to puffy (white) clouds, and ‘stratus-type’, i.e., those similar to flat, dense (dark) low-lying clouds, and relate these network types to protein disorder dynamics and to differences in energy transmission processes. In the first class, there is limited overlap between the modules, which implies higher rigidity of the individual units; there the conformational changes can be described by an ‘energy transfer’ mechanism. In the second class, the topology presents a compact structure with significant overlap between the modules; there the conformational changes can be described by ‘multi-trajectories’; that is, multiple highly populated pathways. We further propose that disordered protein regions evolved to help other protein segments reach ‘rarely visited’ but functionally-related states. We also show the role of disorder in ‘spatial games’ of amino acids; highlight the effects of intrinsically disordered proteins (IDPs) on cellular networks and list some possible studies linking protein disorder and protein structure networks

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Inferring complex networks from time series of dynamical systems: Pitfalls, misinterpretations, and possible solutions

Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated the development of sophisticated data analysis approaches adopting concepts from network theory: systems are considered to be composed of subsystems (nodes) which interact with each other (represented by edges). In many studies, such complex networks of interactions have been derived from empirical time series for various spatially extended systems and have been repeatedly reported to possess the same, possibly desirable, properties (e.g. small-world characteristics and assortativity). In this thesis we study whether and how interaction networks are influenced by the analysis methodology, i.e. by the way how empirical data is acquired (the spatial and temporal sampling of the dynamics) and how nodes and edges are derived from multivariate time series. Our modeling and numerical studies are complemented by field data analyses of brain activities that unfold on various spatial and temporal scales. We demonstrate that indications of small-world characteristics and assortativity can already be expected due solely to the analysis methodology, irrespective of the actual interaction structure of the system. We develop and discuss strategies to distinguish the properties of interaction networks related to the dynamics from those spuriously induced by the analysis methodology. We show how these strategies can help to avoid misinterpretations when investigating the dynamics of spatially extended systems.Comment: PhD thesis, University of Bonn (Germany), published in 2012, 141 page

Assortativity Effects on Diffusion-like Processes in Scale-free Networks

We study the variation in epidemic thresholds in complex networks with different assortativity properties. We determine the thresholds by applying spectral analysis to the matrices associated to the graphs. In order to produce graphs with a specific assortativity we introduce a procedure to sample the space of all the possible networks with a given degree sequence. Our analysis shows that while disassortative networks have an higher epidemiological threshold, assortative networks have a slower diffusion time for diseases. We also used these networks for evaluating the effects of assortativity in a specific dynamic model of sandpile. We show that immunization procedures give different results according to the assortativity of the network considered

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field

Information Theory for Complex Systems Scientists

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number of non-trivially interacting components whose collective behaviour can be difficult to predict. Information theory, a branch of mathematics historically associated with questions about encoding and decoding messages, has emerged as something of a lingua franca for those studying complex systems, far exceeding its original narrow domain of communication systems engineering. In the context of complexity science, information theory provides a set of tools which allow researchers to uncover the statistical and effective dependencies between interacting components; relationships between systems and their environment; mereological whole-part relationships; and is sensitive to non-linearities missed by commonly parametric statistical models. In this review, we aim to provide an accessible introduction to the core of modern information theory, aimed specifically at aspiring (and established) complex systems scientists. This includes standard measures, such as Shannon entropy, relative entropy, and mutual information, before building to more advanced topics, including: information dynamics, measures of statistical complexity, information decomposition, and effective network inference. In addition to detailing the formal definitions, in this review we make an effort to discuss how information theory can be interpreted and develop the intuition behind abstract concepts like "entropy," in the hope that this will enable interested readers to understand what information is, and how it is used, at a more fundamental level