Systems dynamics

System dynamics

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Biological systems are characterized by change over time. Such change may be a explicit to the system function, especially in growth and development, but also in signalling, or it may be an implicit consequence of homeostasis, where change is a response to perturbation. Thus the characterization of system dynamics is an essential component of understanding biological networks. This page also focusses on the question of party hubs and date hubs in network topology: whether the distinction is real and whether it is due to discretely different interaction types.

Introductory reading

Vinayagam et al. (2013) Protein complex-based analysis framework for high-throughput data sets. Sci Signal 6:rs5. (pmid: 23443684)

[ PubMed ] [ DOI ] Analysis of high-throughput data increasingly relies on pathway annotation and functional information derived from Gene Ontology. This approach has limitations, in particular for the analysis of network dynamics over time or under different experimental conditions, in which modules within a network rather than complete pathways might respond and change. We report an analysis framework based on protein complexes, which are at the core of network reorganization. We generated a protein complex resource for human, Drosophila, and yeast from the literature and databases of protein-protein interaction networks, with each species having thousands of complexes. We developed COMPLEAT (http://www.flyrnai.org/compleat), a tool for data mining and visualization for complex-based analysis of high-throughput data sets, as well as analysis and integration of heterogeneous proteomics and gene expression data sets. With COMPLEAT, we identified dynamically regulated protein complexes among genome-wide RNA interference data sets that used the abundance of phosphorylated extracellular signal-regulated kinase in cells stimulated with either insulin or epidermal growth factor as the output. The analysis predicted that the Brahma complex participated in the insulin response.

 

Contents

• Principles of dynamic regulation in networks
• To party or to date? An ongoing discussion how dynamic regulation influences network topology

   

Further reading and resources

Principles

Lipinski-Kruszka et al. (2015) Using dynamic noise propagation to infer causal regulatory relationships in biochemical networks. ACS Synth Biol 4:258-64. (pmid: 24967515)

[ PubMed ] [ DOI ] Cellular decision making is accomplished by complex networks, the structure of which has traditionally been inferred from mean gene expression data. In addition to mean data, quantitative measures of distributions across a population can be obtained using techniques such as flow cytometry that measure expression in single cells. The resulting distributions, which reflect a population's variability or noise, constitute a potentially rich source of information for network reconstruction. A significant portion of molecular noise in a biological process is propagated from the upstream regulators. This propagated component provides additional information about causal network connections. Here, we devise a procedure in which we exploit equations for dynamic noise propagation in a network under nonsteady state conditions to distinguish between alternate gene regulatory relationships. We test our approach in silico using data obtained from stochastic simulations as well as in vivo using experimental data collected from synthetic circuits constructed in yeast.

Gitter et al. (2010) Computational methods for analyzing dynamic regulatory networks. Methods Mol Biol 674:419-41. (pmid: 20827605)

[ PubMed ] [ DOI ] Regulatory and other networks in the cell change in a highly dynamic way over time and in response to internal and external stimuli. While several different types of high-throughput experimental procedures are available to study systems in the cell, most only measure static properties of such networks. Information derived from sequence data is inherently static, and most interaction data sets are measured in a static way as well. In this chapter we discuss one of the few abundant sources for temporal information, time series expression data. We provide an overview of the methods suggested for clustering this type of data to identify functionally related genes. We also discuss methods for inferring causality and interactions using lagged correlations and regression analysis. Finally, we present methods for combining time series expression data with static data to reconstruct dynamic regulatory networks. We point to software tools implementing the methods discussed in this chapter. As more temporal measurements become available, the importance of analyzing such data and of combining it with other types of data will greatly increase.

Przytycka et al. (2010) Toward the dynamic interactome: it's about time. Brief Bioinformatics 11:15-29. (pmid: 20061351)

[ PubMed ] [ DOI ] Dynamic molecular interactions play a central role in regulating the functioning of cells and organisms. The availability of experimentally determined large-scale cellular networks, along with other high-throughput experimental data sets that provide snapshots of biological systems at different times and conditions, is increasingly helpful in elucidating interaction dynamics. Here we review the beginnings of a new subfield within computational biology, one focused on the global inference and analysis of the dynamic interactome. This burgeoning research area, which entails a shift from static to dynamic network analysis, promises to be a major step forward in our ability to model and reason about cellular function and behavior.

Ideker et al. (2001) Integrated genomic and proteomic analyses of a systematically perturbed metabolic network. Science 292:929-34. (pmid: 11340206)

[ PubMed ] [ DOI ] We demonstrate an integrated approach to build, test, and refine a model of a cellular pathway, in which perturbations to critical pathway components are analyzed using DNA microarrays, quantitative proteomics, and databases of known physical interactions. Using this approach, we identify 997 messenger RNAs responding to 20 systematic perturbations of the yeast galactose-utilization pathway, provide evidence that approximately 15 of 289 detected proteins are regulated posttranscriptionally, and identify explicit physical interactions governing the cellular response to each perturbation. We refine the model through further iterations of perturbation and global measurements, suggesting hypotheses about the regulation of galactose utilization and physical interactions between this and a variety of other metabolic pathways.

Stability

Ma'ayan et al. (2008) Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks. Proc Natl Acad Sci U.S.A 105:19235-40. (pmid: 19033453)

[ PubMed ] [ DOI ] Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3-20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks.

Chen et al. (2009) Enhanced synchronizability in scale-free networks. Chaos 19:013105. (pmid: 19334969)

[ PubMed ] [ DOI ] We introduce a modified dynamical optimization coupling scheme to enhance the synchronizability in the scale-free networks as well as to keep uniform and converging intensities during the transition to synchronization. Further, the size of networks that can be synchronizable exceeds by several orders of magnitude the size of unweighted networks.

Oikonomou & Cross (2010) Frequency control of cell cycle oscillators. Curr Opin Genet Dev 20:605-12. (pmid: 20851595)

[ PubMed ] [ DOI ] The cell cycle oscillator, based on a core negative feedback loop and modified extensively by positive feedback, cycles with a frequency that is regulated by environmental and developmental programs to encompass a wide range of cell cycle times. We discuss how positive feedback allows frequency tuning, how size and morphogenetic checkpoints regulate oscillator frequency, and how extrinsic oscillators such as the circadian clock gate cell cycle frequency. The master cell cycle regulatory oscillator in turn controls the frequency of peripheral oscillators controlling essential events. A recently proposed phase-locking model accounts for this coupling.

Ratushny et al. (2011) Mathematical modeling of biomolecular network dynamics. Methods Mol Biol 781:415-33. (pmid: 21877294)

[ PubMed ] [ DOI ] Mathematical and computational models have become indispensable tools for integrating and interpreting heterogeneous biological data, understanding fundamental principles of biological system functions, genera-ting reliable testable hypotheses, and identifying potential diagnostic markers and therapeutic targets. Thus, such tools are now routinely used in the theoretical and experimental systematic investigation of biological system dynamics. Here, we discuss model building as an essential part of the theoretical and experimental analysis of biomolecular network dynamics. Specifically, we describe a procedure for defining kinetic equations and parameters of biomolecular processes, and we illustrate the use of fractional activity functions for modeling gene expression regulation by single and multiple regulators. We further discuss the evaluation of model complexity and the selection of an optimal model based on information criteria. Finally, we discuss the critical roles of sensitivity, robustness analysis, and optimal experiment design in the model building cycle.

The party/date controversy

Han et al. (2004) Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430:88-93. (pmid: 15190252)

[ PubMed ] [ DOI ] In apparently scale-free protein-protein interaction networks, or 'interactome' networks, most proteins interact with few partners, whereas a small but significant proportion of proteins, the 'hubs', interact with many partners. Both biological and non-biological scale-free networks are particularly resistant to random node removal but are extremely sensitive to the targeted removal of hubs. A link between the potential scale-free topology of interactome networks and genetic robustness seems to exist, because knockouts of yeast genes encoding hubs are approximately threefold more likely to confer lethality than those of non-hubs. Here we investigate how hubs might contribute to robustness and other cellular properties for protein-protein interactions dynamically regulated both in time and in space. We uncovered two types of hub: 'party' hubs, which interact with most of their partners simultaneously, and 'date' hubs, which bind their different partners at different times or locations. Both in silico studies of network connectivity and genetic interactions described in vivo support a model of organized modularity in which date hubs organize the proteome, connecting biological processes--or modules--to each other, whereas party hubs function inside modules.

Batada et al. (2006) Stratus not altocumulus: a new view of the yeast protein interaction network. PLoS Biol 4:e317. (pmid: 16984220)

[ PubMed ] [ DOI ] Systems biology approaches can reveal intermediary levels of organization between genotype and phenotype that often underlie biological phenomena such as polygenic effects and protein dispensability. An important conceptualization is the module, which is loosely defined as a cohort of proteins that perform a dedicated cellular task. Based on a computational analysis of limited interaction datasets in the budding yeast Saccharomyces cerevisiae, it has been suggested that the global protein interaction network is segregated such that highly connected proteins, called hubs, tend not to link to each other. Moreover, it has been suggested that hubs fall into two distinct classes: "party" hubs are co-expressed and co-localized with their partners, whereas "date" hubs interact with incoherently expressed and diversely localized partners, and thereby cohere disparate parts of the global network. This structure may be compared with altocumulus clouds, i.e., cotton ball-like structures sparsely connected by thin wisps. However, this organization might reflect a small and/or biased sample set of interactions. In a multi-validated high-confidence (HC) interaction network, assembled from all extant S. cerevisiae interaction data, including recently available proteome-wide interaction data and a large set of reliable literature-derived interactions, we find that hub-hub interactions are not suppressed. In fact, the number of interactions a hub has with other hubs is a good predictor of whether a hub protein is essential or not. We find that date hubs are neither required for network tolerance to node deletion, nor do date hubs have distinct biological attributes compared to other hubs. Date and party hubs do not, for example, evolve at different rates. Our analysis suggests that the organization of global protein interaction network is highly interconnected and hence interdependent, more like the continuous dense aggregations of stratus clouds than the segregated configuration of altocumulus clouds. If the network is configured in a stratus format, cross-talk between proteins is potentially a major source of noise. In turn, control of the activity of the most highly connected proteins may be vital. Indeed, we find that a fluctuation in steady-state levels of the most connected proteins is minimized.

Batada et al. (2007) Still stratus not altocumulus: further evidence against the date/party hub distinction. PLoS Biol 5:e154. (pmid: 17564494)

[ PubMed ] [ DOI ]

Jin et al. (2007) Hubs with network motifs organize modularity dynamically in the protein-protein interaction network of yeast. PLoS ONE 2:e1207. (pmid: 18030341)

[ PubMed ] [ DOI ] BACKGROUND: It has been recognized that modular organization pervades biological complexity. Based on network analysis, 'party hubs' and 'date hubs' were proposed to understand the basic principle of module organization of biomolecular networks. However, recent study on hubs has suggested that there is no clear evidence for coexistence of 'party hubs' and 'date hubs'. Thus, an open question has been raised as to whether or not 'party hubs' and 'date hubs' truly exist in yeast interactome. METHODOLOGY: In contrast to previous studies focusing on the partners of a hub or the individual proteins around the hub, our work aims to study the network motifs of a hub or interactions among individual proteins including the hub and its neighbors. Depending on the relationship between a hub's network motifs and protein complexes, we define two new types of hubs, 'motif party hubs' and 'motif date hubs', which have the same characteristics as the original 'party hubs' and 'date hubs' respectively. The network motifs of these two types of hubs display significantly different features in spatial distribution (or cellular localizations), co-expression in microarray data, controlling topological structure of network, and organizing modularity. CONCLUSION: By virtue of network motifs, we basically solved the open question about 'party hubs' and 'date hubs' which was raised by previous studies. Specifically, at the level of network motifs instead of individual proteins, we found two types of hubs, motif party hubs (mPHs) and motif date hubs (mDHs), whose network motifs display distinct characteristics on biological functions. In addition, in this paper we studied network motifs from a different viewpoint. That is, we show that a network motif should not be merely considered as an interaction pattern but be considered as an essential function unit in organizing modules of networks.

Applications

Taylor et al. (2009) Dynamic modularity in protein interaction networks predicts breast cancer outcome. Nat Biotechnol 27:199-204. (pmid: 19182785)

[ PubMed ] [ DOI ] Changes in the biochemical wiring of oncogenic cells drives phenotypic transformations that directly affect disease outcome. Here we examine the dynamic structure of the human protein interaction network (interactome) to determine whether changes in the organization of the interactome can be used to predict patient outcome. An analysis of hub proteins identified intermodular hub proteins that are co-expressed with their interacting partners in a tissue-restricted manner and intramodular hub proteins that are co-expressed with their interacting partners in all or most tissues. Substantial differences in biochemical structure were observed between the two types of hubs. Signaling domains were found more often in intermodular hub proteins, which were also more frequently associated with oncogenesis. Analysis of two breast cancer patient cohorts revealed that altered modularity of the human interactome may be useful as an indicator of breast cancer prognosis.

Buescher et al. (2012) Global network reorganization during dynamic adaptations of Bacillus subtilis metabolism. Science 335:1099-103. (pmid: 22383848)

[ PubMed ] [ DOI ] Adaptation of cells to environmental changes requires dynamic interactions between metabolic and regulatory networks, but studies typically address only one or a few layers of regulation. For nutritional shifts between two preferred carbon sources of Bacillus subtilis, we combined statistical and model-based data analyses of dynamic transcript, protein, and metabolite abundances and promoter activities. Adaptation to malate was rapid and primarily controlled posttranscriptionally compared with the slow, mainly transcriptionally controlled adaptation to glucose that entailed nearly half of the known transcription regulation network. Interactions across multiple levels of regulation were involved in adaptive changes that could also be achieved by controlling single genes. Our analysis suggests that global trade-offs and evolutionary constraints provide incentives to favor complex control programs.