Lethality and centrality in protein networks

The structure of the protein universe and genome evolution

Despite the practically unlimited number of possible protein sequences, the number of basic shapes in which proteins fold seems not only to be finite, but also to be relatively small, with probably no more than 10,000 folds in existence. Moreover, the distribution of proteins among these folds is highly non-homogeneous -- some folds and superfamilies are extremely abundant, but most are rare. Protein folds and families encoded in diverse genomes show similar size distributions with notable mathematical properties, which also extend to the number of connections between domains in multidomain proteins. All these distributions follow asymptotic power laws, such as have been identified in a wide variety of biological and physical systems, and which are typically associated with scale-free networks. These findings suggest that genome evolution is driven by extremely general mechanisms based on the preferential attachment principle.

Computational systems biology

To understand complex biological systems requires the integration of experimental and computational research -- in other words a systems biology approach. Computational biology, through pragmatic modelling and theoretical exploration, provides a powerful foundation from which to address critical scientific questions head-on. The reviews in this Insight cover many different aspects of this energetic field, although all, in one way or another, illuminate the functioning of modular circuits, including their robustness, design and manipulation. Computational systems biology addresses questions fundamental to our understanding of life, yet progress here will lead to practical innovations in medicine, drug discovery and engineering.

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.

Infinite-order percolation and giant fluctuations in a protein interaction network

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.

Prediction, assessment and validation of protein interaction maps in bacteria

High-throughput proteomics technologies, especially the yeast two-hybrid system, produce large volumes of protein-protein interaction data organized in networks. The complete sequencing of many genomes raises questions about the extent to which such networks can be transferred between organisms. We attempted to answer this question using the experimentally derived Helicobacter pylori interaction map and the recently described interacting domain profile pair (IDPP) method to predict a virtual map for Escherichia coli. The extensive literature concerning E.coli was used to assess all predicted interactions and to validate the IDPP method, which clusters protein domains by sequence and connectivity similarities. The IDPP method has a much better heuristic value than methods solely based on protein homology. The IDPP method was further applied to Campylobacter jejuni to generate a virtual interaction map. An in-depth comparison of the chemotaxis pathways predicted in E.coli and C.jejuni led to the proposition of new functional assignments. Finally, the prediction of protein-protein interaction maps across organisms enabled us to validate some of the interactions on the original experimental map.

Expanding protein universe and its origin from the biological Big Bang

The bottom-up approach to understanding the evolution of organisms is by studying molecular evolution. With the large number of protein structures identified in the past decades, we have discovered peculiar patterns that nature imprints on protein structural space in the course of evolution. In particular, we have discovered that the universe of protein structures is organized hierarchically into a scale-free network. By understanding the cause of these patterns, we attempt to glance at the very origin of life.

Rational drug discovery: what can we learn from regulatory networks?

To enable the list of genes and proteins contained within genomic databases to be useful for drug discovery, we need to understand how the genome maps into the phenome. An essential, but not explicitly listed ingredient of the genome is the regulatory interactions between genes and proteins that form a genome-wide network. How can the concept of regulatory networks increase our understanding of living systems? Networks are more than just static "wiring diagrams". Gene interactions impose dynamic constraints, which, although obvious in emergent phenotypic properties, are not captured by traditional one gene-one trait approaches. Understanding the nature of these constraints in gene-activation state space will pave the way to a holistic yet formal and genomics-based approach to rational drug development.

Birth and death of protein domains: a simple model of evolution explains power law behavior

BACKGROUND

Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution.

RESULTS

A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered in details and the distributions of the equilibrium frequencies of domain families of different size are determined for each case. We apply the BDIM formalism to the analysis of the domain family size distributions in prokaryotic and eukaryotic proteomes and show an excellent fit between these empirical data and a particular form of the model, the second-order balanced linear BDIM. Calculation of the parameters of these models suggests surprisingly high innovation rates, comparable to the total domain birth (duplication) and elimination rates, particularly for prokaryotic genomes.

CONCLUSIONS

We show that a straightforward model of genome evolution, which does not explicitly include selection, is sufficient to explain the observed distributions of domain family sizes, in which power laws appear as asymptotic. However, for the model to be compatible with the data, there has to be a precise balance between domain birth, death and innovation rates, and this is likely to be maintained by selection. The developed approach is oriented at a mathematical description of evolution of domain composition of proteomes, but a simple reformulation could be applied to models of other evolving networks with preferential attachment.

Classification of scale-free networks

While the emergence of a power-law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the between ness centrality displays a power-law distribution with an exponent eta, which is robust, and use it to classify the scale-free networks. We have observed two universality classes with eta approximately equal 2.2(1) and 2.0, respectively. Real-world networks for the former are the protein-interaction networks, the metabolic networks for eukaryotes and bacteria, and the coauthorship network, and those for the latter one are the Internet, the World Wide Web, and the metabolic networks for Archaea. Distinct features of the mass-distance relation, generic topology of geodesics, and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes, while their degree exponents are tunable.

Food-web structure and network theory: The role of connectance and size

Networks from a wide range of physical, biological, and social systems have been recently described as "small-world" and "scale-free." However, studies disagree whether ecological networks called food webs possess the characteristic path lengths, clustering coefficients, and degree distributions required for membership in these classes of networks. Our analysis suggests that the disagreements are based on selective use of relatively few food webs, as well as analytical decisions that obscure important variability in the data. We analyze a broad range of 16 high-quality food webs, with 25-172 nodes, from a variety of aquatic and terrestrial ecosystems. Food webs generally have much higher complexity, measured as connectance (the fraction of all possible links that are realized in a network), and much smaller size than other networks studied, which have important implications for network topology. Our results resolve prior conflicts by demonstrating that although some food webs have small-world and scale-free structure, most do not if they exceed a relatively low level of connectance. Although food-web degree distributions do not display a universal functional form, observed distributions are systematically related to network connectance and size. Also, although food webs often lack small-world structure because of low clustering, we identify a continuum of real-world networks including food webs whose ratios of observed to random clustering coefficients increase as a power-law function of network size over 7 orders of magnitude. Although food webs are generally not small-world, scale-free networks, food-web topology is consistent with patterns found within those classes of networks.

Analyzing yeast protein-protein interaction data obtained from different sources

High-throughput methods for detecting protein interactions, such as mass spectrometry and yeast two-hybrid assays, continue to produce vast amounts of data that may be exploited to infer protein function and regulation. As this article went to press, the pool of all published interaction information on Saccharomyces cerevisiae was 15,143 interactions among 4,825 proteins, and power-law scaling supports an estimate of 20,000 specific protein interactions. To investigate the biases, overlaps, and complementarities among these data, we have carried out an analysis of two high-throughput mass spectrometry (HMS)-based protein interaction data sets from budding yeast, comparing them to each other and to other interaction data sets. Our analysis reveals 198 interactions among 222 proteins common to both data sets, many of which reflect large multiprotein complexes. It also indicates that a "spoke" model that directly pairs bait proteins with associated proteins is roughly threefold more accurate than a "matrix" model that connects all proteins. In addition, we identify a large, previously unsuspected nucleolar complex of 148 proteins, including 39 proteins of unknown function. Our results indicate that existing large-scale protein interaction data sets are nonsaturating and that integrating many different experimental data sets yields a clearer biological view than any single method alone.

Epidemic spreading in a variety of scale free networks

We have shown that the epidemic spreading in scale-free networks is very sensitive to the statistics of degree distribution characterized by the index gamma, the effective spreading rate lambda, the social strategy used by individuals to choose a partner, and the policy of administrating a cure to an infected node. Depending on the interplay of these four factors, the stationary fractions of infected population F(gamma) as well as the epidemic threshold properties can be essentially different. We have given an example of the evolutionary scale-free network which is disposed to the spreading and the persistence of infections at any spreading rate lambda>0 for any gamma. Probably, it is impossible to obtain a simple immunization program that can be simultaneously effective for all types of scale-free networks. We have also studied the dynamical solutions for the evolution equation governed by the epidemic spreading in scale-free networks and found that for the case of vanishingly small cure rate delta<<1 the initial configuration of infected nodes would feature the solution for very long times.

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabási and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. The load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, like the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than by preferential attachment (as defines the Barabási and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.

First- and second-order phase transitions in scale-free networks

We study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent gamma. Using the example of the q-state Potts model we derive a general self-consistency relation within the frame of the Weiss molecular-field approximation, which presumably leads to exact critical singularities. Depending on the value of gamma, we have found three different regimes of the phase diagram. As a general trend first-order transitions soften with decreasing gamma and the critical singularities at the second-order transitions are gamma dependent.

Evolving networks with disadvantaged long-range connections

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability of getting connected to a site at distance d is proportional to d(-alpha), where alpha is a tunable parameter of the model. We show that the properties of the networks grown with alpha<1 are close to those of the genuine scale-free construction, while for alpha>1 the structure of the network is quite different. Thus, in this regime, the node degree distribution is no longer a power law, and it is well represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of alpha.

Roles for the two-hybrid system in exploration of the yeast protein interactome

Comprehensive analysis of protein-protein interactions is a challenging endeavor of functional proteomics and has been best explored in the budding yeast. The yeast protein interactome analysis was achieved first by using the yeast two-hybrid system in a proteome-wide scale and next by large-scale mass spectrometric analysis of affinity-purified protein complexes. While these interaction data have led to a number of novel findings and the emergence of a single huge network containing thousands of proteins, they suffer many false signals and fall short of grasping the entire interactome. Thus, continuous efforts are necessary in both bioinformatics and experimentation to fully exploit these data and to proceed another step forward to the goal. Computational tools to integrate existing biological knowledge buried in literature and various functional genomic data with the interactome data are required for biological interpretation of the huge protein interaction network. Novel experimental methods have to be developed to detect weak, transient interactions involving low abundance proteins as well as to obtain clues to the biological role for each interaction. Since the yeast two-hybrid system can be used for the mapping of the interaction domains and the isolation of interaction-defective mutants, it would serve as a technical basis for the latter purpose, thereby playing another important role in the next phase of protein interactome research.

Spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

Cross signaling, cell specificity, and physiology

The literature on intracellular signal transduction presents a confusing picture: every regulatory factor appears to be regulated by all signal transduction cascades and to regulate all cell processes. This contrasts with the known exquisite specificity of action of extracellular signals in different cell types in vivo. The confusion of the in vitro literature is shown to arise from several causes: the inevitable artifacts inherent in reductionism, the arguments used to establish causal effect relationships, the use of less than adequate models (cell lines, transfections, acellular systems, etc.), and the implicit assumption that networks of regulations are universal whereas they are in fact cell and stage specific. Cell specificity results from the existence in any cell type of a unique set of proteins and their isoforms at each level of signal transduction cascades, from the space structure of their components, from their combinatorial logic at each level, from the presence of modulators of signal transduction proteins and of modulators of modulators, from the time structure of extracellular signals and of their transduction, and from quantitative differences of expression of similar sets of factors.

Network topology of a potential energy landscape: a static scale-free network

Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other scale-free networks, where the topology results from the dynamics of the network growth, the potential energy landscape is a static entity. Therefore, a fundamentally different organizing principle underlies this behavior: The potential energy landscape is highly heterogeneous with the low-energy minima having large basins of attraction and acting as the highly connected hubs in the network.

Scale-free network model of node and connection diversity

A network model with node and connection diversity is proposed in this paper. Distinctly from to other models whose nodes and connections are represented by identical simple points and lines, we investigate inhomogeneous networks with two kinds of sites and link by growth of preferential attachment. Scale-free networks with varied centralizations and exponents (ranging from 2.0 to theoretically infinity) are obtained, and the influences of the relative ratio of the two kinds of sites p, the number of links connected from each site m, and initial attractiveness delta are studied. A mean-field theory that agrees well with our numerical results was proposed and analyzed. The theory gives the analytical scaling exponent of the form gamma=2+p+delta/m-delta(1-p)/(mp+m+delta).

Vertex overload breakdown in evolving networks

We study evolving networks based on the Barabási-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case) is also studied. Implications on the growth of the Internet are discussed.

Computational methods for the prediction of protein interactions

Establishing protein interaction networks is crucial for understanding cellular operations. Detailed knowledge of the 'interactome', the full network of protein-protein interactions, in model cellular systems should provide new insights into the structure and properties of these systems. Parallel to the first massive application of experimental techniques to the determination of protein interaction networks and protein complexes, the first computational methods, based on sequence and genomic information, have emerged.

Specificity and stability in topology of protein networks

Molecular networks guide the biochemistry of a living cell on multiple levels: Its metabolic and signaling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network. To address topological properties of these two networks, we quantified correlations between connectivities of interacting nodes and compared them to a null model of a network, in which all links were randomly rewired. We found that for both interaction and regulatory networks, links between highly connected proteins are systematically suppressed, whereas those between a highly connected and low-connected pairs of proteins are favored. This effect decreases the likelihood of cross talk between different functional modules of the cell and increases the overall robustness of a network by localizing effects of deleterious perturbations.

Protein interactions: two methods for assessment of the reliability of high throughput observations

High throughput methods for detecting protein interactions require assessment of their accuracy. We present two forms of computational assessment. The first method is the expression profile reliability (EPR) index. The EPR index estimates the biologically relevant fraction of protein interactions detected in a high throughput screen. It does so by comparing the RNA expression profiles for the proteins whose interactions are found in the screen with expression profiles for known interacting and non-interacting pairs of proteins. The second form of assessment is the paralogous verification method (PVM). This method judges an interaction likely if the putatively interacting pair has paralogs that also interact. In contrast to the EPR index, which evaluates datasets of interactions, PVM scores individual interactions. On a test set, PVM identifies correctly 40% of true interactions with a false positive rate of approximately 1%. EPR and PVM were applied to the Database of Interacting Proteins (DIP), a large and diverse collection of protein-protein interactions that contains over 8000 Saccharomyces cerevisiae pairwise protein interactions. Using these two methods, we estimate that approximately 50% of them are reliable, and with the aid of PVM we identify confidently 3003 of them. Web servers for both the PVM and EPR methods are available on the DIP website (dip.doe-mbi.ucla.edu/Services.cgi).

Growing scale-free networks with small-world behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small-world effect. While the average shortest path length increases logarithmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive analytical expressions for the clustering coefficient in two limiting cases: random [C approximately (ln N)(2)/N] and highly clustered (C=5/6) scale-free networks.

Reverse engineering gene networks using singular value decomposition and robust regression

We propose a scheme to reverse-engineer gene networks on a genome-wide scale using a relatively small amount of gene expression data from microarray experiments. Our method is based on the empirical observation that such networks are typically large and sparse. It uses singular value decomposition to construct a family of candidate solutions and then uses robust regression to identify the solution with the smallest number of connections as the most likely solution. Our algorithm has O(log N) sampling complexity and O(N(4)) computational complexity. We test and validate our approach in a series of in numero experiments on model gene networks.

Evolutionary rate in the protein interaction network

High-throughput screens have begun to reveal the protein interaction network that underpins most cellular functions in the yeast Saccharomyces cerevisiae. How the organization of this network affects the evolution of the proteins that compose it is a fundamental question in molecular evolution. We show that the connectivity of well-conserved proteins in the network is negatively correlated with their rate of evolution. Proteins with more interactors evolve more slowly not because they are more important to the organism, but because a greater proportion of the protein is directly involved in its function. At sites important for interaction between proteins, evolutionary changes may occur largely by coevolution, in which substitutions in one protein result in selection pressure for reciprocal changes in interacting partners. We confirm one predicted outcome of this process-namely, that interacting proteins evolve at similar rates.

Wrestling with pleiotropy: genomic and topological analysis of the yeast gene expression network

The vast majority (>95%) of single-gene mutations in yeast affect not only the expression of the mutant gene, but also the expression of many other genes. These data suggest the presence of a previously uncharacterized "gene expression network"--a set of interactions between genes which dictate gene expression in the native cell environment. Here, we quantitatively analyze the gene expression network revealed by microarray expression data from 273 different yeast gene deletion mutants.(1) We find that gene expression interactions form a robust, error-tolerant "scale-free" network, similar to metabolic pathways(2) and artificial networks such as power grids and the internet.(3-5) Because the connectivity between genes in the gene expression network is unevenly distributed, a scale-free organization helps make organisms resistant to the deleterious effects of mutation, and is thus highly adaptive. The existence of a gene expression network poses practical considerations for the study of gene function, since most mutant phenotypes are the result of changes in the expression of many genes. Using principles of scale-free network topology, we propose that fragmenting the gene expression network via "genome-engineering" may be a viable and practical approach to isolating gene function.

Experimental genomic evolution: extensive compensation for loss of DNA ligase activity in a virus

Deletion of the viral ligase gene drastically reduced the fitness of bacteriophage T7 on a ligase-deficient host. Viral evolution recovered much of this fitness during long-term passage, but the final fitness remained below that of the intact virus. Compensatory changes occurred chiefly in genes involved in DNA metabolism: the viral endonuclease, helicase, and DNA polymerase. Two other compensatory changes of unknown function also occurred. Using a method to distinguish compensatory mutations from other beneficial mutations, five additional substitutions from the recovery were shown to enhance adaptation to culture conditions and were not compensatory for the deletion. In contrast to the few previous studies of viral recovery from deletions, the compensatory changes in T7 did not restore the deletion or duplicate major regions of the genome. The ability of this deleted genome to recover much of the lost fitness via mutations in its remaining genes reveals a considerable evolutionary potential to modify the interactions of its elements in maintaining an essential set of functions.

Scale-free networks in biology: new insights into the fundamentals of evolution?

Scale-free network models describe many natural and social phenomena. In particular, networks of interacting components of a living cell were shown to possess scale-free properties. A recent study((1)) compares the system-level properties of metabolic and information networks in 43 archaeal, bacterial and eukaryal species and claims that the scale-free organization of these networks is more conserved during evolution than their content.

Functional organization of the yeast proteome by systematic analysis of protein complexes

Most cellular processes are carried out by multiprotein complexes. The identification and analysis of their components provides insight into how the ensemble of expressed proteins (proteome) is organized into functional units. We used tandem-affinity purification (TAP) and mass spectrometry in a large-scale approach to characterize multiprotein complexes in Saccharomyces cerevisiae. We processed 1,739 genes, including 1,143 human orthologues of relevance to human biology, and purified 589 protein assemblies. Bioinformatic analysis of these assemblies defined 232 distinct multiprotein complexes and proposed new cellular roles for 344 proteins, including 231 proteins with no previous functional annotation. Comparison of yeast and human complexes showed that conservation across species extends from single proteins to their molecular environment. Our analysis provides an outline of the eukaryotic proteome as a network of protein complexes at a level of organization beyond binary interactions. This higher-order map contains fundamental biological information and offers the context for a more reasoned and informed approach to drug discovery.

Scale-free growing networks imply linear preferential attachment

It has been recognized for some time that a network grown by the addition of nodes with linear preferential attachment will possess a scale-free distribution of connectivities. Here we prove by some analytical arguments that the linearity is a necessary component to obtain this kind of distribution. However, the preferential linking rate does not necessarily apply to single nodes, but to groups of nodes of the same connectivity. We also point out that for a time-varying mean connectivity the linking rate will deviate from a linear expression by an extra asymptotically logarithmic term.

DIP, the Database of Interacting Proteins: a research tool for studying cellular networks of protein interactions

The Database of Interacting Proteins (DIP: http://dip.doe-mbi.ucla.edu) is a database that documents experimentally determined protein-protein interactions. It provides the scientific community with an integrated set of tools for browsing and extracting information about protein interaction networks. As of September 2001, the DIP catalogs approximately 11 000 unique interactions among 5900 proteins from >80 organisms; the vast majority from yeast, Helicobacter pylori and human. Tools have been developed that allow users to analyze, visualize and integrate their own experimental data with the information about protein-protein interactions available in the DIP database.

Mining DNA microarray data using a novel approach based on graph theory

The recent demonstration that biochemical pathways from diverse organisms are arranged in scale-free, rather than random, systems [Jeong et al., Nature 407 (2000) 651-654], emphasizes the importance of developing methods for the identification of biochemical nexuses--the nodes within biochemical pathways that serve as the major input/output hubs, and therefore represent potentially important targets for modulation. Here we describe a bioinformatics approach that identifies candidate nexuses for biochemical pathways without requiring functional gene annotation; we also provide proof-of-principle experiments to support this technique. This approach, called Nexxus, may lead to the identification of new signal transduction pathways and targets for drug design.

Synthetic cell biology

Synthesis of data into formal models of cellular function is rapidly becoming a necessary industry. The complexity of the interactions among cellular constituents and the quantity of data about these interactions hinders the ability to predict how cells will respond to perturbation and how they can be engineered for industrial or medical purposes. Models provide a systematic framework to describe and analyze these complex systems. In the past few years, models have begun to have an impact on mainstream biology by creating deeper insight into the design rules of cellular signal processing, providing a basis for rational engineering of cells, and for resolving debates about the root causes of certain cellular behaviors. This review covers some of the recent work and challenges in developing these "synthetic cell" models and their growing practical applications.

Probabilistic prediction of unknown metabolic and signal-transduction networks

Regulatory networks provide control over complex cell behavior in all kingdoms of life. Here we describe a statistical model, based on representing proteins as collections of domains or motifs, which predicts unknown molecular interactions within these biological networks. Using known protein-protein interactions of Saccharomyces cerevisiae as training data, we were able to predict the links within this network with only 7% false-negative and 10% false-positive error rates. We also use Markov chain Monte Carlo simulation for the prediction of networks with maximum probability under our model. This model can be applied across species, where interaction data from one (or several) species can be used to infer interactions in another. In addition, the model is extensible and can be analogously applied to other molecular data (e.g., DNA sequences).

Molecular biology of HMGA proteins: hubs of nuclear function

Members of the HMGA (a.k.a. HMGI/Y) family of 'high mobility group' (HMG) proteins participate in a wide variety of nuclear processes ranging from chromosome and chromatin mechanics to acting as architectural transcription factors that regulate the expression of numerous genes in vivo. As a consequence, they function in the cell as highly connected 'nodes' of protein-DNA and protein-protein interactions that influence a diverse array of normal biological processes including growth, proliferation, differentiation and death. The HMGA proteins, likewise, participate in pathological processes by, for example, acting as regulators of viral gene transcription and by serving as host-supplied proteins that facilitate retroviral integration. HMGA genes are bona fide proto-oncogenes that promote tumor progression and metastasis when overexpressed in cells. High constitutive HMGA protein levels are among the most consistent feature observed in all types of cancers with increasing concentrations being correlated with increasing malignancy. The intrinsic attributes that endow the HMGA proteins with these remarkable abilities are a combination of structural, biochemical and biological characteristics that are unique to these proteins. HMGA proteins have little, if any, secondary structure while free in solution but undergo disordered-to-ordered structural transitions when bound to substrates such as DNA or other proteins. Each protein contains three copies of a conserved DNA-binding peptide motif called the 'AT-hook' that preferentially binds to the minor groove of stretches of AT-rich sequence. In vivo HMGA proteins specifically interact with a large number of other proteins, most of which are transcription factors. They are also subject to many types of in vivo biochemical modifications that markedly influence their ability to interact with DNA substrates, other proteins and chromatin. And, most importantly, both the transcription of HMGA genes and the biochemical modifications of HMGA proteins are direct downstream targets of numerous signal transduction pathways making them exquisitely responsive to various environmental influences. This review covers recent advances that have contributed to our understanding of how this constellation of structural and biological features allows the HMGA proteins to serve as central 'hubs' of nuclear function.

Cancer proteomics: from signaling networks to tumor markers

Along with the great strides that have been made towards understanding cancer, has come a realization of the complexity of molecular events that lead to malignancy. Proteomics-based approaches, which enable the quantitative investigation of both cellular protein expression levels and protein-protein interactions involved in signaling networks, promise to define the molecules controlling the processes involved in cancer.

Insights into protein function through large-scale computational analysis of sequence and structure

Functional genomic and proteomic technologies are producing biological data relating to hundreds, or even thousands of proteins per experiment. Rapid and accurate computational analysis of the molecular function of these proteins is therefore crucial in order to interpret these data and prioritize further experiments.

Structural and functional linkages between subunit interfaces in mammalian pyruvate kinase

Mammalian pyruvate kinase (PK) is a four-domain enzyme that is active as a homo-tetramer. Tissue-specific isozymes of PK exhibit distinct levels of allosteric regulation. PK expressed in muscle tissue (M1-PK) shows hyperbolic steady-state kinetics, whereas PK expressed in kidney tissue (M2-PK) displays sigmoidal kinetics. Rabbit M1 and M2-PK are isozymes whose sequences differ in only 22 out of 530 residues per subunit, and these changes are localized in an inter-subunit interface. Previous studies have shown that a single amino acid mutation to M1-PK at either the Y (S402P) or Z (T340 M) subunit interface can confer a level of allosteric regulation that is intermediate to M1-PK and M2-PK. In an effort to elucidate the roles of the inter-subunit interaction in signal transmission and the functional/structural connectivity between these interfaces, the S402P mutant of M1-PK was crystallized and its structure resolved to 2.8 A. Although the overall S402P M1-PK structure is nearly identical with the wild-type structure within experimental error, significant differences in the conformation of the backbone are found at the site of mutation along the Y interface. In addition, there is a significant change along the Z interface, namely, a loss of an inter-subunit salt-bridge between Asp177 of domain B and Arg341 of domain A of the opposing subunit. Concurrent with the loss of the salt-bridge is an increase in the degree of rotational flexibility of domain B that constitutes the active site. Comparison of previous PK structures shows a correlation between an increase in this domain movement with the loss of the Asp177: Arg341 salt-bridge. These results identify the structural linkages between the Y and Z interfaces in regulating the interconversion of conformational states of rabbit M1-PK.

Pathway databases: a case study in computational symbolic theories

A pathway database (DB) is a DB that describes biochemical pathways, reactions, and enzymes. The EcoCyc pathway DB (see http://ecocyc.org) describes the metabolic, transport, and genetic-regulatory networks of Escherichia coli. EcoCyc is an example of a computational symbolic theory, which is a DB that structures a scientific theory within a formal ontology so that it is available for computational analysis. It is argued that by encoding scientific theories in symbolic form, we open new realms of analysis and understanding for theories that would otherwise be too large and complex for scientists to reason with effectively.

The art of the probable: system control in the adaptive immune system

The immune system provides very effective host defense against infectious agents. Although many details are known about the cells and molecules involved, a broader "systems engineering" view of this complex system is just beginning to emerge. Here the argument is put forward that stochastic events, potent amplification mechanisms, feedback controls, and heterogeneity arising from spatially dispersed cell interactions give rise to many of the gross properties of the immune system. A better appreciation of these underlying features will not only add to our basic understanding of how immunity develops or goes awry, but also illuminate new directions for manipulating the system in prophylactic and therapeutic settings.