Modeling for evolving biological networks with scale-free connectivity, hierarchical modularity, and disassortativity

Mean field theory for biology inspired duplication-divergence network model

The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network-the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity-in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N∼10(4)), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks.

Preferential duplication of intermodular hub genes: an evolutionary signature in eukaryotes genome networks

Whole genome protein-protein association networks are not random and their topological properties stem from genome evolution mechanisms. In fact, more connected, but less clustered proteins are related to genes that, in general, present more paralogs as compared to other genes, indicating frequent previous gene duplication episodes. On the other hand, genes related to conserved biological functions present few or no paralogs and yield proteins that are highly connected and clustered. These general network characteristics must have an evolutionary explanation. Considering data from STRING database, we present here experimental evidence that, more than not being scale free, protein degree distributions of organisms present an increased probability for high degree nodes. Furthermore, based on this experimental evidence, we propose a simulation model for genome evolution, where genes in a network are either acquired de novo using a preferential attachment rule, or duplicated with a probability that linearly grows with gene degree and decreases with its clustering coefficient. For the first time a model yields results that simultaneously describe different topological distributions. Also, this model correctly predicts that, to produce protein-protein association networks with number of links and number of nodes in the observed range for Eukaryotes, it is necessary 90% of gene duplication and 10% of de novo gene acquisition. This scenario implies a universal mechanism for genome evolution.

Detecting breakdown points in metabolic networks

BACKGROUND

A complex network of biochemical reactions present in an organism generates various biological moieties necessary for its survival. It is seen that biological systems are robust to genetic and environmental changes at all levels of organization. Functions of various organisms are sustained against mutational changes by using alternative pathways. It is also seen that if any one of the paths for production of the same metabolite is hampered, an alternate path tries to overcome this defect and helps in combating the damage.

METHODOLOGY

Certain physical, chemical or genetic change in any of the precursor substrate of a biochemical reaction may damage the production of the ultimate product. We employ a quantitative approach for simulating this phenomena of causing a physical change in the biochemical reactions by performing external perturbations to 12 metabolic pathways under carbohydrate metabolism in Saccharomyces cerevisae as well as 14 metabolic pathways under carbohydrate metabolism in Homo sapiens. Here, we investigate the relationship between structure and degree of compatibility of metabolites against external perturbations, i.e., robustness. Robustness can also be further used to identify the extent to which a metabolic pathway can resist a mutation event. Biological networks with a certain connectivity distribution may be very resilient to a particular attack but not to another. The goal of this work is to determine the exact boundary of network breakdown due to both random and targeted attack, thereby analyzing its robustness. We also find that compared to various non-standard models, metabolic networks are exceptionally robust. Here, we report the use of a 'Resilience-based' score for enumerating the concept of 'network-breakdown'. We also use this approach for analyzing metabolite essentiality providing insight into cellular robustness that can be further used for future drug development.

RESULTS

We have investigated the behavior of metabolic pathways under carbohydrate metabolism in S. cerevisae and H. sapiens against random and targeted attack. Both random as well as targeted resilience were calculated by formulating a measure, that we termed as 'Resilience score'. Datasets of metabolites were collected for 12 metabolic pathways belonging to carbohydrate metabolism in S. cerevisae and 14 metabolic pathways belonging to carbohydrate metabolism in H. sapiens from Kyoto Encyclopedia for Genes and Genomes (KEGG).

Emergence of modularity and disassortativity in protein-protein interaction networks

In this paper, we present a simple evolution model of protein-protein interaction networks by introducing a rule of small-preference duplication of a node, meaning that the probability of a node chosen to duplicate is inversely proportional to its degree, and subsequent divergence plus nonuniform heterodimerization based on some plausible mechanisms in biology. We show that our model cannot only reproduce scale-free connectivity and small-world pattern, but also exhibit hierarchical modularity and disassortativity. After comparing the features of our model with those of real protein-protein interaction networks, we believe that our model can provide relevant insights into the mechanism underlying the evolution of protein-protein interaction networks.

Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture

Although several studies have provided important insights into the general principles of biological networks, the link between network organization and the genome-scale dynamics of the underlying entities (genes, mRNAs, and proteins) and its role in systems behavior remain unclear. Here we show that transcription factor (TF) dynamics and regulatory network organization are tightly linked. By classifying TFs in the yeast regulatory network into three hierarchical layers (top, core, and bottom) and integrating diverse genome-scale datasets, we find that the TFs have static and dynamic properties that are similar within a layer and different across layers. At the protein level, the top-layer TFs are relatively abundant, long-lived, and noisy compared with the core- and bottom-layer TFs. Although variability in expression of top-layer TFs might confer a selective advantage, as this permits at least some members in a clonal cell population to initiate a response to changing conditions, tight regulation of the core- and bottom-layer TFs may minimize noise propagation and ensure fidelity in regulation. We propose that the interplay between network organization and TF dynamics could permit differential utilization of the same underlying network by distinct members of a clonal cell population.

An evolving model of undirected networks based on microscopic biological interaction systems

With protein or gene interaction systems as the background, this paper proposes an evolving model of biological undirected networks, which are consistent with some plausible mechanisms in biology. Through introducing a rule of preferential duplication of a node inversely proportional to the degree of existing nodes and an attribute of the age of the node (the older, the more influence), by which the probability of a node receiving re-wiring links is chosen, the model networks generated in certain parameter conditions could reproduce series of statistic topological characteristics of real biological graphs, including the scale-free feature, small world effect, hierarchical modularity, limited structural robustness, and disassortativity of degree-degree correlation.

Regulation by transcription factors in bacteria: beyond description

Transcription is an essential step in gene expression and its understanding has been one of the major interests in molecular and cellular biology. By precisely tuning gene expression, transcriptional regulation determines the molecular machinery for developmental plasticity, homeostasis and adaptation. In this review, we transmit the main ideas or concepts behind regulation by transcription factors and give just enough examples to sustain these main ideas, thus avoiding a classical ennumeration of facts. We review recent concepts and developments: cis elements and trans regulatory factors, chromosome organization and structure, transcriptional regulatory networks (TRNs) and transcriptomics. We also summarize new important discoveries that will probably affect the direction of research in gene regulation: epigenetics and stochasticity in transcriptional regulation, synthetic circuits and plasticity and evolution of TRNs. Many of the new discoveries in gene regulation are not extensively tested with wetlab approaches. Consequently, we review this broad area in Inference of TRNs and Dynamical Models of TRNs. Finally, we have stepped backwards to trace the origins of these modern concepts, synthesizing their history in a timeline schema.