Complex networks and simple models in biology

Hypergraph animals

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighborhoods of nodes in hypergraphs. We establish their relationships to lattice animals and network motifs, and we develop their combinatorial properties for sparse and uncorrelated hypergraphs. We make use of the tight link of hypergraph animals to partition numbers, which opens up a vast mathematical framework for the analysis of hypergraph animals. We then study their abundances in random hypergraphs. Two transferable insights result from this analysis: (i) it establishes the importance of high-cardinality edges in ensembles of random hypergraphs that are inspired by the classical Erdös-Renyí random graphs; and (ii) there is a close connection between degree and hyperedge cardinality in random hypergraphs that shapes animal abundances and spectra profoundly. Both findings imply that hypergraph animals can have the potential to affect information flow and processing in complex systems. Our analysis also suggests that we need to spend more effort on investigating and developing suitable conditional ensembles of random hypergraphs that can capture real-world structures and their complex dependency structures.

Joint modeling of association networks and longitudinal biomarkers: An application to childhood obesity

The prevalence of chronic non-communicable diseases such as obesity has noticeably increased in the last decade. The study of these diseases in early life is of paramount importance in determining their course in adult life and in supporting clinical interventions. Recently, attention has been drawn to approaches that study the alteration of metabolic pathways in obese children. In this work, we propose a novel joint modeling approach for the analysis of growth biomarkers and metabolite associations, to unveil metabolic pathways related to childhood obesity. Within a Bayesian framework, we flexibly model the temporal evolution of growth trajectories and metabolic associations through the specification of a joint nonparametric random effect distribution, with the main goal of clustering subjects, thus identifying risk sub-groups. Growth profiles as well as patterns of metabolic associations determine the clustering structure. Inclusion of risk factors is straightforward through the specification of a regression term. We demonstrate the proposed approach on data from the Growing Up in Singapore Towards healthy Outcomes cohort study, based in Singapore. Posterior inference is obtained via a tailored MCMC algorithm, involving a nonparametric prior with mixed support. Our analysis has identified potential key pathways in obese children that allow for the exploration of possible molecular mechanisms associated with childhood obesity.

A Data-Driven Approach to Construct a Molecular Map of Trypanosoma cruzi to Identify Drugs and Vaccine Targets

Chagas disease (CD) is endemic in large parts of Central and South America, as well as in Texas and the southern regions of the United States. Successful parasites, such as the causative agent of CD, Trypanosoma cruzi have adapted to specific hosts during their phylogenesis. In this work, we have assembled an interactive network of the complex relations that occur between molecules within T. cruzi. An expert curation strategy was combined with a text-mining approach to screen 10,234 full-length research articles and over 200,000 abstracts relevant to T. cruzi. We obtained a scale-free network consisting of 1055 nodes and 874 edges, and composed of 838 proteins, 43 genes, 20 complexes, 9 RNAs, 36 simple molecules, 81 phenotypes, and 37 known pharmaceuticals. Further, we deployed an automated docking pipeline to conduct large-scale docking studies involving several thousand drugs and potential targets to identify network-based binding propensities. These experiments have revealed that the existing FDA-approved drugs benznidazole (Bz) and nifurtimox (Nf) show comparatively high binding energies to the T. cruzi network proteins (e.g., PIF1 helicase-like protein, trans-sialidase), when compared with control datasets consisting of proteins from other pathogens. We envisage this work to be of value to those interested in finding new vaccines for CD, as well as drugs against the T. cruzi parasite.

Study of interaction and complete merging of binary cyclones using complex networks

Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru-Kulap and Seroja-Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Entropic regression with neurologically motivated applications

The ultimate goal of cognitive neuroscience is to understand the mechanistic neural processes underlying the functional organization of the brain. The key to this study is understanding the structure of both the structural and functional connectivity between anatomical regions. In this paper, we use an information theoretic approach, which defines direct information flow in terms of causation entropy, to improve upon the accuracy of the recovery of the true network structure over popularly used methods for this task such as correlation and least absolute shrinkage and selection operator regression. The method outlined above is tested on synthetic data, which is produced by following previous work in which a simple dynamical model of the brain is used, simulated on top of a real network of anatomical brain regions reconstructed from diffusion tensor imaging. We demonstrate the effectiveness of the method of AlMomani et al. [Chaos 30, 013107 (2020)] when applied to data simulated on the realistic diffusion tensor imaging network, as well as on randomly generated small-world and Erdös-Rényi networks.

Analysis of Madrid Metro Network: From Structural to HJ-Biplot Perspective

With the growth of cities, urban traffic has increased and traffic congestion has become a serious problem. Due to their characteristics, metro systems are one of the most used public transportation networks in big cities. So, optimization and planning of metro networks are challenges which governments must focus on. The objective of this study was to analyze Madrid metro network using graph theory. Through complex network theory, the main structural and topological properties of the network as well as robustness characteristics were obtained. Furthermore, to inspect these results, multivariate analysis techniques were employed, specifically HJ-Biplot. This analysis tool allowed us to explore relationships between centrality measures and to classify stations according to their centrality. Therefore, it is a multidisciplinary study that includes network analysis and multivariate analysis. The study found that closeness and eccentricity were strongly negatively correlated. In addition, the most central stations were those located in the city center, that is, there is a relationship between centrality and geographic location. In terms of robustness, a highly agglomerated community structure was found.

NAIGO: An Improved Method to Align PPI Networks Based on Gene Ontology and Graphlets

With the development of high throughput technologies, there are more and more protein–protein interaction (PPI) networks available, which provide a need for efficient computational tools for network alignment. Network alignment is widely used to predict functions of certain proteins, identify conserved network modules, and study the evolutionary relationship across species or biological entities. However, network alignment is an NP-complete problem, and previous algorithms are usually slow or less accurate in aligning big networks like human vs. yeast. In this study, we proposed a fast yet accurate algorithm called Network Alignment by Integrating Biological Process (NAIGO). Specifically, we first divided the networks into subnets taking the advantage of known prior knowledge, such as gene ontology. For each subnet pair, we then developed a novel method to align them by considering both protein orthologous information and their local structural information. After that, we expanded the obtained local network alignments in a greedy manner. Taking the aligned pairs as seeds, we formulated the global network alignment problem as an assignment problem based on similarity matrix, which was solved by the Hungarian method. We applied NAIGO to align human and Saccharomyces cerevisiae S288c PPI network and compared the results with other popular methods like IsoRank, GRAAL, SANA, and NABEECO. As a result, our method outperformed the competitors by aligning more orthologous proteins or matched interactions. In addition, we found a few potential functional orthologous proteins such as RRM2B in human and DNA2 in S. cerevisiae S288c, which are related to DNA repair. We also identified a conserved subnet with six orthologous proteins EXO1, MSH3, MSH2, MLH1, MLH3, and MSH6, and six aligned interactions. All these proteins are associated with mismatch repair. Finally, we predicted a few proteins of S. cerevisiae S288c potentially involving in certain biological processes like autophagosome assembly.

Dynamics of the Global Stock Market Networks Generated by DCCA Methodology

A group of stock markets can be treated as a complex system. We tried to find the financial market crisis by constructing a global 24 stock market network while using detrended cross-correlation analysis. The community structures by the Girvan-Newman method are observed and other network properties, such as the average degree, clustering coefficient, efficiency, and modularity, are quantified. The criterion of correlation between any two markets on the detrended cross-correlation analysis was considered to be 0.7. We used the return (rt) and volatility (|rt|) time series for the periods of 1, 4, 10, and 20-year of composite stock price indices during 1997–2016. Europe (France, Germany, Netherland, UK), USA (USA1, USA2, USA3, USA4) and Oceania (Australia1, Australia2) have been confirmed to make a solid community. This approach also detected the signal of financial crisis, such as Asian liquidity crisis in 1997, world-wide dot-com bubble collapse in 2001, the global financial crisis triggered by the USA in 2008, European sovereign debt crisis in 2010, and the Chinese stock price plunge in 2015 by capturing the local maxima of average degree and efficiency.

Distribution of Node Characteristics in Evolving Tripartite Network

Many real-world networks have a natural tripartite structure. Investigating the structure and the behavior of actors in these networks is useful to gain a deeper understanding of their behavior and dynamics. In our paper, we describe an evolving tripartite network using a network model with preferential growth mechanisms and different rules for changing the strength of nodes and the weights of edges. We analyze the characteristics of the strength distribution and behavior of selected nodes and selected actors in this tripartite network. The distributions of these analyzed characteristics follow the power-law under different modeled conditions. Performed simulations have confirmed all these results. Despite its simplicity, the model expresses well the basic properties of the modeled network. It can provide further insights into the behavior of systems with more complex behaviors, such as the multi-actor e-commerce system that we have used as a real basis for the validation of our model.

Network Medicine in the Age of Biomedical Big Data

Network medicine is an emerging area of research dealing with molecular and genetic interactions, network biomarkers of disease, and therapeutic target discovery. Large-scale biomedical data generation offers a unique opportunity to assess the effect and impact of cellular heterogeneity and environmental perturbations on the observed phenotype. Marrying the two, network medicine with biomedical data provides a framework to build meaningful models and extract impactful results at a network level. In this review, we survey existing network types and biomedical data sources. More importantly, we delve into ways in which the network medicine approach, aided by phenotype-specific biomedical data, can be gainfully applied. We provide three paradigms, mainly dealing with three major biological network archetypes: protein-protein interaction, expression-based, and gene regulatory networks. For each of these paradigms, we discuss a broad overview of philosophies under which various network methods work. We also provide a few examples in each paradigm as a test case of its successful application. Finally, we delineate several opportunities and challenges in the field of network medicine. We hope this review provides a lexicon for researchers from biological sciences and network theory to come on the same page to work on research areas that require interdisciplinary expertise. Taken together, the understanding gained from combining biomedical data with networks can be useful for characterizing disease etiologies and identifying therapeutic targets, which, in turn, will lead to better preventive medicine with translational impact on personalized healthcare.

Using global modeling to unveil hidden couplings in small network motifs

One of the main tasks in network theory is to infer relations among interacting elements. We propose global modeling as a tool to detect links between nodes and their nature. Various situations using small network motifs are investigated under the assumption that the variable to be measured at each node provides full observability when isolated. Such a choice ensures no intrinsic difficulties for getting a global model in the coupled situation. As a first step toward unveiling the coupling function in larger network motifs, we consider three different scenarios involving Rössler systems diffusively coupled, in a couple or embedded in a network, or parametrically forced. We show that the global modeling is able to determine not only the existence of an interaction but also its functional form, to retrieve the dynamics of the whole system, and to extract the equations governing the single node dynamics as if it was isolated.

Gene regulatory and signaling networks exhibit distinct topological distributions of motifs

The biological processes of cellular decision making and differentiation involve a plethora of signaling pathways and gene regulatory circuits. These networks in turn exhibit a multitude of motifs playing crucial parts in regulating network activity. Here we compare the topological placement of motifs in gene regulatory and signaling networks and observe that it suggests different evolutionary strategies in motif distribution for distinct cellular subnetworks.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.

Comprehensive Map of Molecules Implicated in Obesity

Obesity is a global epidemic affecting over 1.5 billion people and is one of the risk factors for several diseases such as type 2 diabetes mellitus and hypertension. We have constructed a comprehensive map of the molecules reported to be implicated in obesity. A deep curation strategy was complemented by a novel semi-automated text mining system in order to screen 1,000 full-length research articles and over 90,000 abstracts that are relevant to obesity. We obtain a scale free network of 804 nodes and 971 edges, composed of 510 proteins, 115 genes, 62 complexes, 23 RNA molecules, 83 simple molecules, 3 phenotype and 3 drugs in "bow-tie" architecture. We classify this network into 5 modules and identify new links between the recently discovered fat mass and obesity associated FTO gene with well studied examples such as insulin and leptin. We further built an automated docking pipeline to dock orlistat as well as other drugs against the 24,000 proteins in the human structural proteome to explain the therapeutics and side effects at a network level. Based upon our experiments, we propose that therapeutic effect comes through the binding of one drug with several molecules in target network, and the binding propensity is both statistically significant and different in comparison with any other part of human structural proteome.

Genome scale modeling in systems biology: algorithms and resources

In recent years, in silico studies and trial simulations have complemented experimental procedures. A model is a description of a system, and a system is any collection of interrelated objects; an object, moreover, is some elemental unit upon which observations can be made but whose internal structure either does not exist or is ignored. Therefore, any network analysis approach is critical for successful quantitative modeling of biological systems. This review highlights some of most popular and important modeling algorithms, tools, and emerging standards for representing, simulating and analyzing cellular networks in five sections. Also, we try to show these concepts by means of simple example and proper images and graphs. Overall, systems biology aims for a holistic description and understanding of biological processes by an integration of analytical experimental approaches along with synthetic computational models. In fact, biological networks have been developed as a platform for integrating information from high to low-throughput experiments for the analysis of biological systems. We provide an overview of all processes used in modeling and simulating biological networks in such a way that they can become easily understandable for researchers with both biological and mathematical backgrounds. Consequently, given the complexity of generated experimental data and cellular networks, it is no surprise that researchers have turned to computer simulation and the development of more theory-based approaches to augment and assist in the development of a fully quantitative understanding of cellular dynamics.

Multi-tissue analysis of co-expression networks by higher-order generalized singular value decomposition identifies functionally coherent transcriptional modules

Recent high-throughput efforts such as ENCODE have generated a large body of genome-scale transcriptional data in multiple conditions (e.g., cell-types and disease states). Leveraging these data is especially important for network-based approaches to human disease, for instance to identify coherent transcriptional modules (subnetworks) that can inform functional disease mechanisms and pathological pathways. Yet, genome-scale network analysis across conditions is significantly hampered by the paucity of robust and computationally-efficient methods. Building on the Higher-Order Generalized Singular Value Decomposition, we introduce a new algorithmic approach for efficient, parameter-free and reproducible identification of network-modules simultaneously across multiple conditions. Our method can accommodate weighted (and unweighted) networks of any size and can similarly use co-expression or raw gene expression input data, without hinging upon the definition and stability of the correlation used to assess gene co-expression. In simulation studies, we demonstrated distinctive advantages of our method over existing methods, which was able to recover accurately both common and condition-specific network-modules without entailing ad-hoc input parameters as required by other approaches. We applied our method to genome-scale and multi-tissue transcriptomic datasets from rats (microarray-based) and humans (mRNA-sequencing-based) and identified several common and tissue-specific subnetworks with functional significance, which were not detected by other methods. In humans we recapitulated the crosstalk between cell-cycle progression and cell-extracellular matrix interactions processes in ventricular zones during neocortex expansion and further, we uncovered pathways related to development of later cognitive functions in the cortical plate of the developing brain which were previously unappreciated. Analyses of seven rat tissues identified a multi-tissue subnetwork of co-expressed heat shock protein (Hsp) and cardiomyopathy genes (Bag3, Cryab, Kras, Emd, Plec), which was significantly replicated using separate failing heart and liver gene expression datasets in humans, thus revealing a conserved functional role for Hsp genes in cardiovascular disease.

Molecular mechanisms of muscle plasticity with exercise

The skeletal muscle phenotype is subject to considerable malleability depending on use. Low-intensity endurance type exercise leads to qualitative changes of muscle tissue characterized mainly by an increase in structures supporting oxygen delivery and consumption. High-load strength-type exercise leads to growth of muscle fibers dominated by an increase in contractile proteins. In low-intensity exercise, stress-induced signaling leads to transcriptional upregulation of a multitude of genes with Ca(2+) signaling and the energy status of the muscle cells sensed through AMPK being major input determinants. Several parallel signaling pathways converge on the transcriptional co-activator PGC-1α, perceived as being the coordinator of much of the transcriptional and posttranscriptional processes. High-load training is dominated by a translational upregulation controlled by mTOR mainly influenced by an insulin/growth factor-dependent signaling cascade as well as mechanical and nutritional cues. Exercise-induced muscle growth is further supported by DNA recruitment through activation and incorporation of satellite cells. Crucial nodes of strength and endurance exercise signaling networks are shared making these training modes interdependent. Robustness of exercise-related signaling is the consequence of signaling being multiple parallel with feed-back and feed-forward control over single and multiple signaling levels. We currently have a good descriptive understanding of the molecular mechanisms controlling muscle phenotypic plasticity. We lack understanding of the precise interactions among partners of signaling networks and accordingly models to predict signaling outcome of entire networks. A major current challenge is to verify and apply available knowledge gained in model systems to predict human phenotypic plasticity.

Generative model selection using a scalable and size-independent complex network classifier

Real networks exhibit nontrivial topological features, such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are structurally similar to real networks. An important research problem is to identify the generative model that best fits to a target network. In this paper, we investigate this problem and our goal is to select the model that is able to generate graphs similar to a given network instance. By the means of generating synthetic networks with seven outstanding generative models, we have utilized machine learning methods to develop a decision tree for model selection. Our proposed method, which is named "Generative Model Selection for Complex Networks," outperforms existing methods with respect to accuracy, scalability, and size-independence.

Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks

We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species and reactions. If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values. On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. The technique is illustrated with a model of a bifunctional enzyme.

Approaches to modeling gene regulatory networks: a gentle introduction

This chapter is split into two main sections; first, I will present an introduction to gene networks. Second, I will discuss various approaches to gene network modeling which will include some examples for using different data sources. Computational modeling has been used for many different biological systems and many approaches have been developed addressing the different needs posed by the different application fields. The modeling approaches presented here are not limited to gene regulatory networks and occasionally I will present other examples. The material covered here is an update based on several previous publications by Thomas Schlitt and Alvis Brazma (FEBS Lett 579(8),1859-1866, 2005; Philos Trans R Soc Lond B Biol Sci 361(1467), 483-494, 2006; BMC Bioinformatics 8(suppl 6), S9, 2007) that formed the foundation for a lecture on gene regulatory networks at the In Silico Systems Biology workshop series at the European Bioinformatics Institute in Hinxton.

On the discovery of group-consistent graph substructure patterns from brain networks

Complex networks constitute a recurring issue in the analysis of neuroimaging data. Recently, network motifs have been identified as patterns of interconnections since they appear in a significantly higher number than in randomized networks, in a given ensemble of anatomical or functional connectivity graphs. The current approach for detecting and enumerating motifs in brain networks requires a predetermined motif repertoire and can operate only with motifs of small size (consisting of few nodes). There is a growing interest in methodologies for frequent graph-based pattern mining in large graph datasets that can facilitate adaptive design of motifs. The results presented in this paper are based on the graph-based Substructure pattern mining (gSpan) algorithm and introduce a manifold of ways to exploit it for data-driven motif extraction in connectomics research. Functional connectivity graphs from electroencephalographic (EEG) recordings during resting state and mental calculations are used to demonstrate our approach. Relying on either time-invariant or time-evolving graphs, characteristic motifs associated with various frequency bands were derived and compared. With a suitable manipulation, the gSpan discovers motifs which are specific to performing mental arithmetics. Finally, the subject-dependent temporal signatures of motifs' appearance revealed the transient nature of the evolving functional connectivity (math-related motifs "come and go").

Biological function through network topology: a survey of the human diseasome

Molecular network data are increasingly becoming available, necessitating the development of well performing computational tools for their analyses. Such tools enabled conceptually different approaches for exploring human diseases to be undertaken, in particular, those that study the relationship between a multitude of biomolecules within a cell. Hence, a new field of network biology has emerged as part of systems biology, aiming to untangle the complexity of cellular network organization. We survey current network analysis methods that aim to give insight into human disease.

The study of protein–protein interactions in bacteria

Many of the functions fulfilled by proteins in the cell require specific protein–protein interactions (PPI). During the last decade, the use of high-throughput experimental technologies, primarily based on the yeast 2-hybrid system, generated extensive data currently located in public databases. This information has been used to build interaction networks for different species. Unfortunately, due to the nature of the yeast 2-hybrid system, these databases contain many false positives and negatives, thus they require purging. A method for confirming these PPI is to test them using a technique that operates in vivo and detects binary PPI. This article comprises an overview of the study of PPI and describes the main techniques that have been used to identify bacterial PPI, prioritizing those that can be used for their verification, and it also mentions a number of PPI that have been identified or confirmed using these methods.

Randomly evolving idiotypic networks: modular mean field theory

We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular architectures, the building principles of which are known. The nodes of the network can be classified into groups of nodes, the modules, which share statistical properties. Each node experiences only the mean influence of the groups to which it is linked. Given the size of the groups and linking between them the statistical properties such as mean occupation, mean lifetime, and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations. For a pattern which consists of pairs of occupied nodes correlations are taken into account.

Randomly evolving idiotypic networks: structural properties and architecture

We consider a minimalistic dynamic model of the idiotypic network of B lymphocytes. A network node represents a population of B lymphocytes of the same specificity (idiotype), which is encoded by a bit string. The links of the network connect nodes with complementary and nearly complementary bit strings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists; otherwise it is empty. There is a continuous influx of new B lymphocytes of random idiotype from the bone marrow. B lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors; unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which make it possible to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.

Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks

Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of species where only one species moves is represented by a simple digraph and is modeled by a reaction-diffusion system with non-mass action kinetics. A graph-theoretic condition for potential Turing-Hopf instability that arises when a spatially homogeneous equilibrium loses its stability via a single pair of complex eigenvalues is obtained. This novel graph-theoretic condition is closely related to the negative cycle condition for oscillations in ordinary differential equation models and its generalizations, and requires the existence of a pair of subnetworks, each containing an even number of positive cycles. The technique is illustrated with a double-cycle Goodwin type model.

Evolutionary systems biology: historical and philosophical perspectives on an emerging synthesis

Systems biology (SB) is at least a decade old now and maturing rapidly. A more recent field, evolutionary systems biology (ESB), is in the process of further developing system-level approaches through the expansion of their explanatory and potentially predictive scope. This chapter will outline the varieties of ESB existing today by tracing the diverse roots and fusions that make up this integrative project. My approach is philosophical and historical. As well as examining the recent origins of ESB, I will reflect on its central features and the different clusters of research it comprises. In its broadest interpretation, ESB consists of five overlapping approaches: comparative and correlational ESB; network architecture ESB; network property ESB; population genetics ESB; and finally, standard evolutionary questions answered with SB methods. After outlining each approach with examples, I will examine some strong general claims about ESB, particularly that it can be viewed as the next step toward a fuller modern synthesis of evolutionary biology (EB), and that it is also the way forward for evolutionary and systems medicine. I will conclude with a discussion of whether the emerging field of ESB has the capacity to combine an even broader scope of research aims and efforts than it presently does.

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).

A differential network approach to exploring differences between biological states: an application to prediabetes

Background

Variations in the pattern of molecular associations are observed during disease development. The comprehensive analysis of molecular association patterns and their changes in relation to different physiological conditions can yield insight into the biological basis of disease-specific phenotype variation.

Methodology

Here, we introduce a formal statistical method for the differential analysis of molecular associations via network representation. We illustrate our approach with extensive data on lipoprotein subclasses measured by NMR spectroscopy in 4,406 individuals with normal fasting glucose, and 531 subjects with impaired fasting glucose (prediabetes). We estimate the pair-wise association between measures using shrinkage estimates of partial correlations and build the differential network based on this measure of association. We explore the topological properties of the inferred network to gain insight into important metabolic differences between individuals with normal fasting glucose and prediabetes.

Conclusions/Significance

Differential networks provide new insights characterizing differences in biological states. Based on conventional statistical methods, few differences in concentration levels of lipoprotein subclasses were found between individuals with normal fasting glucose and individuals with prediabetes. By performing the differential analysis of networks, several characteristic changes in lipoprotein metabolism known to be related to diabetic dyslipidemias were identified. The results demonstrate the applicability of the new approach to identify key molecular changes inaccessible to standard approaches.

Assessing coverage of protein interaction data using capture-recapture models

Protein interaction networks comprise thousands of individual binary links between distinct proteins. Whilst these data have attracted considerable attention and been the focus of many different studies, the networks, their structure, function, and how they change over time are still not fully known. More importantly, there is still considerable uncertainty regarding their size, and the quality of the available data continues to be questioned. Here, we employ statistical models of the experimental sampling process, in particular capture-recapture methods, in order to assess the false discovery rate and size of protein interaction networks. We uses these methods to gauge the ability of different experimental systems to find the true binary interactome. Our model allows us to obtain estimates for the size and false-discovery rate from simple considerations regarding the number of repeatedly interactions, and provides suggestions as to how we can exploit this information in order to reduce the effects of noise in such data. In particular our approach does not require a reference dataset. We estimate that approximately more than half of the true physical interactome has now been sampled in yeast.

Protein-protein interactions: making sense of networks via graph-theoretic modeling

The emerging area of network biology is seeking to provide insights into organizational principles of life. However, despite significant collaborative efforts, there is still typically a weak link between biological and computational scientists and a lack of understanding of the research issues across the disciplines. This results in the use of simple computational techniques of limited potential that are incapable of explaining these complex data. Hence, the danger is that the community might begin to view the topological properties of network data as mere statistics, rather than rich sources of biological information. A further danger is that such views might result in the imposition of scientific doctrines, such as scale-free-centric (on the modeling side) and genome-centric (on the biological side) opinions onto this area. Here, we take a graph-theoretic perspective on protein-protein interaction networks and present a high-level overview of the area, commenting on possible challenges ahead.

Detecting network communities: an application to phylogenetic analysis

This paper proposes a new method to identify communities in generally weighted complex networks and apply it to phylogenetic analysis. In this case, weights correspond to the similarity indexes among protein sequences, which can be used for network construction so that the network structure can be analyzed to recover phylogenetically useful information from its properties. The analyses discussed here are mainly based on the modular character of protein similarity networks, explored through the Newman-Girvan algorithm, with the help of the neighborhood matrix . The most relevant networks are found when the network topology changes abruptly revealing distinct modules related to the sets of organisms to which the proteins belong. Sound biological information can be retrieved by the computational routines used in the network approach, without using biological assumptions other than those incorporated by BLAST. Usually, all the main bacterial phyla and, in some cases, also some bacterial classes corresponded totally (100%) or to a great extent (>70%) to the modules. We checked for internal consistency in the obtained results, and we scored close to 84% of matches for community pertinence when comparisons between the results were performed. To illustrate how to use the network-based method, we employed data for enzymes involved in the chitin metabolic pathway that are present in more than 100 organisms from an original data set containing 1,695 organisms, downloaded from GenBank on May 19, 2007. A preliminary comparison between the outcomes of the network-based method and the results of methods based on Bayesian, distance, likelihood, and parsimony criteria suggests that the former is as reliable as these commonly used methods. We conclude that the network-based method can be used as a powerful tool for retrieving modularity information from weighted networks, which is useful for phylogenetic analysis.

Complex weighted networks have been applied to uncover organizing principles of complex biological, technological, and social systems. We propose herein a new method to identify communities in such structures and apply it to phylogenetic analysis. Recent studies using this theory in genomics and proteomics contributed to the understanding of the structure and dynamics of cellular complex interaction webs. Three main distinct molecular networks have been investigated based on transcriptional and metabolic activity, and on protein interaction. Here we consider the evolutionary relationship between proteins throughout phylogeny, employing the complex network approach to perform a comparative study of the enzymes related to the chitin metabolic pathway. We show how the similarity index of protein sequences can be used for network construction, and how the underlying structure is analyzed by the computational routines of our method to recover useful and sound information for phylogenetic studies. By focusing on the modular character of protein similarity networks, we were successful in matching the identified networks modules to main bacterial phyla, and even some bacterial classes. The network-based method reported here can be used as a new powerful tool for identifying communities in complex networks, retrieving useful information for phylogenetic studies.

Statistical inference of the time-varying structure of gene-regulation networks

Background

Biological networks are highly dynamic in response to environmental and physiological cues. This variability is in contrast to conventional analyses of biological networks, which have overwhelmingly employed static graph models which stay constant over time to describe biological systems and their underlying molecular interactions.

Methods

To overcome these limitations, we propose here a new statistical modelling framework, the ARTIVA formalism (Auto Regressive TIme VArying models), and an associated inferential procedure that allows us to learn temporally varying gene-regulation networks from biological time-course expression data. ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time. It allows us to recover the chronology of regulatory associations for individual genes involved in a specific biological process (development, stress response, etc.).

Results

We demonstrate that the ARTIVA approach generates detailed insights into the function and dynamics of complex biological systems and exploits efficiently time-course data in systems biology. In particular, two biological scenarios are analyzed: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning.

Conclusions

ARTIVA does recover essential temporal dependencies in biological systems from transcriptional data, and provide a natural starting point to learn and investigate their dynamics in greater detail.

Trees on networks: resolving statistical patterns of phylogenetic similarities among interacting proteins

Background

Phylogenies capture the evolutionary ancestry linking extant species. Correlations and similarities among a set of species are mediated by and need to be understood in terms of the phylogenic tree. In a similar way it has been argued that biological networks also induce correlations among sets of interacting genes or their protein products.

Results

We develop suitable statistical resampling schemes that can incorporate these two potential sources of correlation into a single inferential framework. To illustrate our approach we apply it to protein interaction data in yeast and investigate whether the phylogenetic trees of interacting proteins in a panel of yeast species are more similar than would be expected by chance.

Conclusions

While we find only negligible evidence for such increased levels of similarities, our statistical approach allows us to resolve the previously reported contradictory results on the levels of co-evolution induced by protein-protein interactions. We conclude with a discussion as to how we may employ the statistical framework developed here in further functional and evolutionary analyses of biological networks and systems.

Snazer: the simulations and networks analyzer

BACKGROUND

Networks are widely recognized as key determinants of structure and function in systems that span the biological, physical, and social sciences. They are static pictures of the interactions among the components of complex systems. Often, much effort is required to identify networks as part of particular patterns as well as to visualize and interpret them.From a pure dynamical perspective, simulation represents a relevant way-out. Many simulator tools capitalized on the "noisy" behavior of some systems and used formal models to represent cellular activities as temporal trajectories. Statistical methods have been applied to a fairly large number of replicated trajectories in order to infer knowledge.A tool which both graphically manipulates reactive models and deals with sets of simulation time-course data by aggregation, interpretation and statistical analysis is missing and could add value to simulators.

RESULTS

We designed and implemented Snazer, the simulations and networks analyzer. Its goal is to aid the processes of visualizing and manipulating reactive models, as well as to share and interpret time-course data produced by stochastic simulators or by any other means.

CONCLUSIONS

Snazer is a solid prototype that integrates biological network and simulation time-course data analysis techniques.

The challenges of informatics in synthetic biology: from biomolecular networks to artificial organisms

The field of synthetic biology holds an inspiring vision for the future; it integrates computational analysis, biological data and the systems engineering paradigm in the design of new biological machines and systems. These biological machines are built from basic biomolecular components analogous to electrical devices, and the information flow among these components requires the augmentation of biological insight with the power of a formal approach to information management. Here we review the informatics challenges in synthetic biology along three dimensions: in silico, in vitro and in vivo. First, we describe state of the art of the in silico support of synthetic biology, from the specific data exchange formats, to the most popular software platforms and algorithms. Next, we cast in vitro synthetic biology in terms of information flow, and discuss genetic fidelity in DNA manipulation, development strategies of biological parts and the regulation of biomolecular networks. Finally, we explore how the engineering chassis can manipulate biological circuitries in vivo to give rise to future artificial organisms.

The evolutionary dynamics of evolvability in a gene network model

Evolvability, the ability of populations to adapt, has recently emerged as a major unifying concept in biology. Although the study of evolvability offers new insights into many important biological questions, the conceptual bases of evolvability, and the mechanisms of its evolution, remain controversial. We used simulated evolution of a model of gene network dynamics to test the contentious hypothesis that natural selection can favour high evolvability, in particular in sexual populations. Our results conclusively demonstrate that fluctuating natural selection can increase the capacity of model gene networks to adapt to new environments. Detailed studies of the evolutionary dynamics of these networks establish a broad range of validity for this result and quantify the evolutionary forces responsible for changes in evolvability. Analysis of the genotype-phenotype map of these networks also reveals mechanisms connecting evolvability, genetic architecture and robustness. Our results suggest that the evolution of evolvability can have a pervasive influence on many aspects of organisms.

Protein-protein interactions: from global to local analyses

For the increasing number of species with complete genome sequences, the task of elucidating their complete proteomes and interactomes has attracted much recent interest. Although the proteome describes the complete repertoire of proteins expressed, the interactome comprises the pairwise protein-protein interactions that occur, or could occur, within an organism, and forms a large-scale sparse network. Here we discuss the challenges provided by present data, and outline a route from global analysis to more detailed and focused studies of protein-protein interactions. Carefully using protein-interaction data allows us to explore its potential fully alongside the evaluation of mechanistic hypotheses about biological systems.

Not all scale-free networks are born equal: the role of the seed graph in PPI network evolution

The (asymptotic) degree distributions of the best-known "scale-free" network models are all similar and are independent of the seed graph used; hence, it has been tempting to assume that networks generated by these models are generally similar. In this paper, we observe that several key topological features of such networks depend heavily on the specific model and the seed graph used. Furthermore, we show that starting with the "right" seed graph (typically a dense subgraph of the protein-protein interaction network analyzed), the duplication model captures many topological features of publicly available protein-protein interaction networks very well.

A general system for studying protein-protein interactions in Gram-negative bacteria

One of the most promising methods for large-scale studies of protein interactions is isolation of an affinity-tagged protein with its in vivo interaction partners, followed by mass spectrometric identification of the copurified proteins. Previous studies have generated affinity-tagged proteins using genetic tools or cloning systems that are specific to a particular organism. To enable protein-protein interaction studies across a wider range of Gram-negative bacteria, we have developed a methodology based on expression of affinity-tagged "bait" proteins from a medium copy-number plasmid. This construct is based on a broad-host-range vector backbone (pBBR1MCS5). The vector has been modified to incorporate the Gateway DEST vector recombination region, to facilitate cloning and expression of fusion proteins bearing a variety of affinity, fluorescent, or other tags. We demonstrate this methodology by characterizing interactions among subunits of the DNA-dependent RNA polymerase complex in two metabolically versatile Gram-negative microbial species of environmental interest, Rhodopseudomonas palustris CGA010 and Shewanella oneidensis MR-1. Results compared favorably with those for both plasmid and chromosomally encoded affinity-tagged fusion proteins expressed in a model organism, Escherichia coli.

Physiology of the prion protein

Prion diseases are transmissible spongiform encephalopathies (TSEs), attributed to conformational conversion of the cellular prion protein (PrP(C)) into an abnormal conformer that accumulates in the brain. Understanding the pathogenesis of TSEs requires the identification of functional properties of PrP(C). Here we examine the physiological functions of PrP(C) at the systemic, cellular, and molecular level. Current data show that both the expression and the engagement of PrP(C) with a variety of ligands modulate the following: 1) functions of the nervous and immune systems, including memory and inflammatory reactions; 2) cell proliferation, differentiation, and sensitivity to programmed cell death both in the nervous and immune systems, as well as in various cell lines; 3) the activity of numerous signal transduction pathways, including cAMP/protein kinase A, mitogen-activated protein kinase, phosphatidylinositol 3-kinase/Akt pathways, as well as soluble non-receptor tyrosine kinases; and 4) trafficking of PrP(C) both laterally among distinct plasma membrane domains, and along endocytic pathways, on top of continuous, rapid recycling. A unified view of these functional properties indicates that the prion protein is a dynamic cell surface platform for the assembly of signaling modules, based on which selective interactions with many ligands and transmembrane signaling pathways translate into wide-range consequences upon both physiology and behavior.

Estimating the size of the human interactome

After the completion of the human and other genome projects it emerged that the number of genes in organisms as diverse as fruit flies, nematodes, and humans does not reflect our perception of their relative complexity. Here, we provide reliable evidence that the size of protein interaction networks in different organisms appears to correlate much better with their apparent biological complexity. We develop a stable and powerful, yet simple, statistical procedure to estimate the size of the whole network from subnet data. This approach is then applied to a range of eukaryotic organisms for which extensive protein interaction data have been collected and we estimate the number of interactions in humans to be approximately 650,000. We find that the human interaction network is one order of magnitude bigger than the Drosophila melanogaster interactome and approximately 3 times bigger than in Caenorhabditis elegans.

Comparative analysis of the transcription-factor gene regulatory networks of E. coli and S. cerevisiae

Background

The regulatory interactions between transcription factors (TF) and regulated genes (RG) in a species genome can be lumped together in a single directed graph. The TF's and RG's conform the nodes of this graph, while links are drawn whenever a transcription factor regulates a gene's expression. Projections onto TF nodes can be constructed by linking every two nodes regulating a common gene. Similarly, projections onto RG nodes can be made by linking every two regulated genes sharing at least one common regulator. Recent studies of the connectivity pattern in the transcription-factor regulatory network of many organisms have revealed some interesting properties. However, the differences between TF and RG nodes have not been widely explored.

Results

After analysing the RG and TF projections of the transcription-factor gene regulatory networks of Escherichia coli and Saccharomyces cerevisiae, we found several common characteristic as well as some noticeable differences. To better understand these differences, we compared the properties of the E. coli and S. cerevisiae RG- and TF-projected networks with those of the corresponding projections built from randomized versions of the original bipartite networks. These last results indicate that the observed differences are mostly due to the very different ratios of TF to RG counts of the E. coli and S. cerevisiae bipartite networks, rather than to their having different connectivity patterns.

Conclusion

Since E. coli is a prokaryotic organism while S. cerevisiae is eukaryotic, there are important differences between them concerning processing of mRNA before translation, DNA packing, amount of junk DNA, and gene regulation. From the results in this paper we conclude that the most important effect such differences have had on the development of the corresponding transcription-factor gene regulatory networks is their very different ratios of TF to RG numbers. This ratio is more than three times larger in S. cerevisiae than in E. coli. Our calculations reveal that, both species' gene regulatory networks have very similar connectivity patterns, despite their very different TF to RG ratios. An this, to our consideration, indicates that the structure of both networks is optimal from an evolutionary viewpoint.

The evolution of genetic networks by non-adaptive processes

Although numerous investigators assume that the global features of genetic networks are moulded by natural selection, there has been no formal demonstration of the adaptive origin of any genetic network. This Analysis shows that many of the qualitative features of known transcriptional networks can arise readily through the non-adaptive processes of genetic drift, mutation and recombination, raising questions about whether natural selection is necessary or even sufficient for the origin of many aspects of gene-network topologies. The widespread reliance on computational procedures that are devoid of population-genetic details to generate hypotheses for the evolution of network configurations seems to be unjustified.