Camellia Sarkar

Quantifying randomness in protein–protein interaction networks of different species: A random matrix approach

We analyze protein–protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics of random matrix theory. We demonstrate that spectral rigidity, which quantifies long range correlations in eigenvalues, for all protein–protein interaction networks follow random matrix prediction up to certain ranges indicating randomness in interactions. After this range, deviation from the universality evinces underlying structural features in network.

Uncovering randomness and success in society.

An understanding of how individuals shape and impact the evolution of society is vastly limited due to the unavailability of large-scale reliable datasets that can simultaneously capture information regarding individual movements and social interactions. We believe that the popular Indian film industry, “Bollywood”, can provide a social network apt for such a study. Bollywood provides massive amounts of real, unbiased data that spans more than 100 years, and hence this network has been used as a model for the present paper. The nodes which maintain a moderate degree or widely cooperate with the other nodes of the network tend to be more fit (measured as the success of the node in the industry) in comparison to the other nodes. The analysis carried forth in the current work, using a conjoined framework of complex network theory and random matrix theory, aims to quantify the elements that determine the fitness of an individual node and the factors that contribute to the robustness of a network. The authors of this paper believe that the method of study used in the current paper can be extended to study various other industries and organizations.

Unveiling the multi-fractal structure of complex networks

Abstract The fractal nature of graphs has traditionally been investigated by using the network’s nodes as the basic units. Here, instead, we propose to concentrate on the graph’s edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.

Multilayer network decoding versatility and trust

Despite large scale availability of social data, our understanding of the basic laws governing human behaviour remains limited, owing to the lack of a proper framework which can capture the interplay of various interdependent factors affecting social interactions. In the recent years, multilayer networks has increasingly been realized to provide an efficient framework for understanding the intricacies of complex real world systems. The present study encompasses the multilayer network analysis of Bollywood, the largest film industry of the world, comprising of a massive time-varying social data. Making around 1500 films annually, Bollywood has emerged as a globally recognized and appreciated platform for cultural exchange. This film industry acts as a mirror of the society and the rapidly changing nature of the society is reflected in the depictions of films. This renders this model system to provide a ripe platform to understand social behaviour by analyzing the patterns of evolution and the success of individuals in the society. Similarity in the degree distribution across the individual layers validates our basis of multilayering. While the degree-degree correlations of the whole networks reveal that in general nodes do not exhibit any particular preference for pairing up, multilayer framework indicates the gradual restoration of cooperation in the recent dataset. Working in more number of genres comes up as an intrinsic property of lead nodes. Further, versatility in pairs and triads has been shown to demonstrate its impact on the success of lead nodes. While repeated cooperation in pairs of dissimilar types of nodes has been shown to yield success to the lead nodes, triads of similar types of nodes turn out to be more successful. Weak ties analysis emphasize on the importance of every type of node in the society.In the recent years, the multilayer networks have increasingly been realized as a more realistic framework to understand emergent physical phenomena in complex real world systems. We analyze a massive time-varying social data drawn from the largest film industry of the world under multilayer network framework. The framework enables us to evaluate the versatility of actors, which turns out to be an intrinsic property of lead actors. Versatility in dimers suggests that working with different types of nodes are more beneficial than with similar ones. However, the triangles yield a different relation between type of co-actor and the success of lead nodes indicating the importance of higher order motifs in understanding the properties of the underlying system. Furthermore, despite the degree-degree correlations of entire networks being neutral, multilayering picks up different values of correlation indicating positive connotations like trust, in the recent years. Analysis of weak ties of the industry uncovers nodes from lower degree regime being important in linking Bollywood clusters. The framework and the tools used herein may be used for unraveling the complexity of other real world systems.

Social patterns revealed through random matrix theory

Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remain same throughout all datasets, random matrix theory provides insight into interaction pattern of individual of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remain same throughout all datasets, random matrix theory provides insight into interaction pattern of individual of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.

Optimization of synchronizability in multiplex networks

We investigate the optimization of synchronizability in multiplex networks and demonstrate that the interlayer coupling strength is the deciding factor for the efficiency of optimization. The optimized networks have homogeneity in the degree as well as in the betweenness centrality. Additionally, the interlayer coupling strength crucially affects various properties of individual layers in the optimized multiplex networks. We provide an understanding to how the emerged network properties are shaped or affected when the evolution renders them better synchronizable.

Randomness and Structure in Collaboration Networks: A Random Matrix Analysis

We investigate the Geom collaboration network under the random matrix theory framework. While the spectral density exhibiting triangular shape with high degeneracy at zero emphasizes on the complexity of interactions in underlying system, the spectral fluctuations provide a measure of the complexity. The short-range correlations follow the random matrix prediction, suggesting the existence of a minimal amount of randomness in the interactions between authors, whereas the long-range correlations deviating from the random matrix prediction implicate more directionality in collaboration behavior leading to less randomness. A higher degeneracy at -1 eigenvalue in the Geom collaboration network as compared with its configuration model indicates a large number of close to complete subgraphs in the network, suggesting collaboration groups among scientists. These structures can be considered to convey the same school of thoughts, whereas the randomness in spectra might be arising due to the intermingling of different collaboration modules. These results lead us to propagate that a blend of directional advancement and the mixing of schools of thoughts is essential for the steady development of a particular field of research.

Longitudinal network theory approaches identify crucial factors affecting sporulation efficiency in yeast

Integrating network theory approaches over longitudinal genome-wide gene expression data is a robust approach to understand the molecular underpinnings of a dynamic biological process. Here, we performed a network-based investigation of longitudinal gene expression changes during sporulation of a yeast strain, SK1. Using global network attributes, viz. clustering coefficient, degree distribution of a node, degree-degree mixing of the connected nodes and disassortativity, we observed dynamic changes in these parameters indicating a highly connected network with inter-module crosstalk. Analysis of local attributes, such as clustering coefficient, hierarchy, betweenness centrality and Granovetter9s weak ties showed that there was an inherent hierarchy under regulatory control that was determined by specific nodes. Biological annotation of these nodes indicated the role of specifically linked pairs of genes in meiosis. These genes act as crucial regulators of sporulation in the highly sporulating SK1 strain. An independent analysis of these network properties in a less efficient sporulating strain helped to understand the heterogeneity of network profiles. We show that comparison of network properties has the potential to identify candidate nodes contributing to the phenotypic diversity of developmental processes in natural populations. Therefore, studying these network parameters as described in this work for dynamic developmental processes, such as sporulation in yeast and eventually in disease progression in humans, can help in identifying candidate factors which are potential regulators of differences between normal and perturbed processes and can be causal targets for intervention.Using network theory on an integrated time-resolved genome-wide gene expression data, we investigated intricate dynamic regulatory relationships of transcription factors and target genes to unravel signatures that contribute to extreme phenotypic differences in yeast, Saccharomyces cerevisiae. We performed comparative analysis of gene expression profiles of two yeast strains SK1 and S288c, which lie at extreme ends of sporulation efficiency. The results based on various structural attributes of the networks, such as clustering coefficient, degree-degree correlations and betweenness centrality suggested that a delay in crosstalk between functional modules can be construed as one of the prime reasons behind low sporulation efficiency of S288c strain. A more hierarchical structure in late phase of sporulation in S288c seemed to be an outcome of a delayed response, resulting in initiation of modularity, which is a feature of early sporulation phase. Further, weak ties analysis revealed meiosis-associated genes for the high sporulating SK1 strain, while for the low sporulating S288c strain it revealed mitotic genes. This was a further indication of delay in regulatory activities essential to initiate sporulation in S288c strain. Our results demonstrate the potential of this framework in identifying candidate nodes contributing to phenotypic diversity in natural populations.

Codon based co-occurrence network motifs in human mitochondria

The nucleotide polymorphism in the human mitochondrial genome (mtDNA) tolled by codon position bias plays an indispensable role in human population dispersion and expansion. Herein, genome-wide nucleotide co-occurrence networks were constructed using data comprised of five different geographical regions and around 3000 samples for each region. We developed a powerful network model to describe complex mitochondrial evolutionary patterns among codon and non-codon positions. We found evidence that the evolution of human mitochondria DNA is dominated by adaptive forces, particularly mutation and selection, which was supported by many previous studies. The diversity observed in the mtDNA was compared with mutations, co-occurring mutations, network motifs considering codon positions as causing agent. This comparison showed that long-range nucleotide co-occurrences have a large effect on genomic diversity. Most notably, codon motifs apparently underpinned the preferences among codon positions for co-evolution which is probably highly biased during the origin of the genetic code. Our analysis also showed that variable nucleotide positions of different human sub-populations implemented the independent mtDNA evolution to its geographical dispensation. Ergo, this study has provided both a network framework and a codon glance to investigate co-occurring genomic variations that are critical in underlying complex mitochondrial evolution.