Motifs, modules and games in bacteria

The evolution of modularity in bacterial metabolic networks

Deciphering the modular organization of metabolic networks and understanding how modularity evolves have attracted tremendous interest in recent years. Here, we present a comprehensive large scale characterization of modularity across the bacterial tree of life, systematically quantifying the modularity of the metabolic networks of >300 bacterial species. Three main determinants of metabolic network modularity are identified. First, network size is an important topological determinant of network modularity. Second, several environmental factors influence network modularity, with endosymbionts and mammal-specific pathogens having lower modularity scores than bacterial species that occupy a wider range of niches. Moreover, even among the pathogens, those that alternate between two distinct niches, such as insect and mammal, tend to have relatively high metabolic network modularity. Third, horizontal gene transfer is an important force that contributes significantly to metabolic modularity. We additionally reconstruct the metabolic network of ancestral bacterial species and examine the evolution of modularity across the tree of life. This reveals a trend of modularity decrease from ancestors to descendants that is likely the outcome of niche specialization and the incorporation of peripheral metabolic reactions.

Genetic-linkage mapping of complex hereditary disorders to a whole-genome molecular-interaction network

Common hereditary neurodevelopmental disorders such as autism, bipolar disorder, and schizophrenia are most likely both genetically multifactorial and heterogeneous. Because of these characteristics traditional methods for genetic analysis fail when applied to such diseases. To address the problem we propose a novel probabilistic framework that combines the standard genetic linkage formalism with whole-genome molecular-interaction data to predict pathways or networks of interacting genes that contribute to common heritable disorders. We apply the model to three large genotype-phenotype data sets, identify a small number of significant candidate genes for autism (24), bipolar disorder (21), and schizophrenia (25), and predict a number of gene targets likely to be shared among the disorders.

Spontaneous emergence of modularity in cellular networks

Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.

Sensing and integration of Erk and PI3K signals by Myc

The transcription factor Myc plays a central role in regulating cell-fate decisions, including proliferation, growth, and apoptosis. To maintain a normal cell physiology, it is critical that the control of Myc dynamics is precisely orchestrated. Recent studies suggest that such control of Myc can be achieved at the post-translational level via protein stability modulation. Myc is regulated by two Ras effector pathways: the extracellular signal-regulated kinase (Erk) and phosphatidylinositol 3-kinase (PI3K) pathways. To gain quantitative insight into Myc dynamics, we have developed a mathematical model to analyze post-translational regulation of Myc via sequential phosphorylation by Erk and PI3K. Our results suggest that Myc integrates Erk and PI3K signals to result in various cellular responses by differential stability control of Myc protein isoforms. Such signal integration confers a flexible dynamic range for the system output, governed by stability change. In addition, signal integration may require saturation of the input signals, leading to sensitive signal integration to the temporal features of the input signals, insensitive response to their amplitudes, and resistance to input fluctuations. We further propose that these characteristics of the protein stability control module in Myc may be commonly utilized in various cell types and classes of proteins.

Memory in microbes: quantifying history-dependent behavior in a bacterium

Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy.

Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis

Background

Few genome-scale models of organisms focus on the regulatory networks and none of them integrates all known levels of regulation. In particular, the regulations involving metabolite pools are often neglected. However, metabolite pools link the metabolic to the genetic network through genetic regulations, including those involving effectors of transcription factors or riboswitches. Consequently, they play pivotal roles in the global organization of the genetic and metabolic regulatory networks.

Results

We report the manually curated reconstruction of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis (transcriptional, translational and post-translational regulations and modulation of enzymatic activities). We provide a systematic graphic representation of regulations of each metabolic pathway based on the central role of metabolites in regulation. We show that the complex regulatory network of B. subtilis can be decomposed as sets of locally regulated modules, which are coordinated by global regulators.

Conclusion

This work reveals the strong involvement of metabolite pools in the general regulation of the metabolic network. Breaking the metabolic network down into modules based on the control of metabolite pools reveals the functional organization of the genetic and metabolic regulatory networks of B. subtilis.

Induction and relaxation dynamics of the regulatory network controlling the type III secretion system encoded within Salmonella pathogenicity island 1

Bacterial pathogenesis requires the precise spatial and temporal control of gene expression, the dynamics of which are controlled by regulatory networks. A network encoded within Salmonella Pathogenicity Island 1 controls the expression of a type III protein secretion system involved in the invasion of host cells. The dynamics of this network are measured in single cells using promoter-green fluorescent protein (gfp) reporters and flow cytometry. During induction, there is a temporal order of gene expression, with transcriptional inputs turning on first, followed by structural and effector genes. The promoters show varying stochastic properties, where graded inputs are converted into all-or-none and hybrid responses. The relaxation dynamics are measured by shifting cells from inducing to noninducing conditions and by measuring fluorescence decay. The gfp expressed from promoters controlling the transcriptional inputs (hilC and hilD) and structural genes (prgH) decay exponentially, with a characteristic time of 50-55 min. In contrast, the gfp expressed from a promoter controlling the expression of effectors (sicA) persists for 110+/-9 min. This promoter is controlled by a genetic circuit, formed by a transcription factor (InvF), a chaperone (SicA), and a secreted protein (SipC), that regulates effector expression in response to the secretion capacity of the cell. A mathematical model of this circuit demonstrates that the delay is due to a split positive feedback loop. This model is tested in a DeltasicA knockout strain, where sicA is complemented with and without the feedback loop. The delay is eliminated when the feedback loop is deleted. Furthermore, a robustness analysis of the model predicts that the delay time can be tuned by changing the affinity of SicA:InvF multimers for an operator in the sicA promoter. This prediction is used to construct a targeted library, which contains mutants with both longer and shorter delays. This combination of theory and experiments provides a platform for predicting how genetic perturbations lead to changes in the global dynamics of a regulatory network.

Biomedical implications of information processing in chemical systems: Non-classical approach to photochemistry of coordination compounds

Analogies between photoactive nitric oxide generators and various electronic devices: logic gates and operational amplifiers are presented. These analogies have important biological consequences: application of control parameters allows for better targeting and control of nitric oxide drugs. The same methodology may be applied in the future for other therapeutic strategies and at the same time helps to understand natural regulatory and signaling processes in biological systems.

Design and implementation of three incoherent feed-forward motif based biological concentration sensors

Synthetic biology is a useful tool to investigate the dynamics of small biological networks and to assess our capacity to predict their behavior from computational models. In this work we report the construction of three different synthetic networks in Escherichia coli based upon the incoherent feed-forward loop architecture. The steady state behavior of the networks was investigated experimentally and computationally under different mutational regimes in a population based assay. Our data shows that the three incoherent feed-forward networks, using three different macromolecular inhibitory elements, reproduce the behavior predicted from our computational model. We also demonstrate that specific biological motifs can be designed to generate similar behavior using different components. In addition we show how it is possible to tune the behavior of the networks in a predicable manner by applying suitable mutations to the inhibitory elements.

Coupled feedback loops form dynamic motifs of cellular networks

Cellular networks are composed of complicated interconnections among components, and some subnetworks of particular functioning are often identified as network motifs. Among such network motifs, feedback loops are thought to play important dynamical roles. Intriguingly, such feedback loops are very often found as a coupled structure in cellular circuits. Therefore, we integrated all the scattered information regarding the coupled feedbacks in various cellular circuits and investigated the dynamical role of each coupled structure. Finally, we discovered that coupled positive feedbacks enhance signal amplification and bistable characteristics; coupled negative feedbacks realize enhanced homeostasis; coupled positive and negative feedbacks enable reliable decision-making by properly modulating signal responses and effectively dealing with noise.

Coordination logic of the sensing machinery in the transcriptional regulatory network of Escherichia coli

The active and inactive state of transcription factors in growing cells is usually directed by allosteric physicochemical signals or metabolites, which are in turn either produced in the cell or obtained from the environment by the activity of the products of effector genes. To understand the regulatory dynamics and to improve our knowledge about how transcription factors (TFs) respond to endogenous and exogenous signals in the bacterial model, Escherichia coli, we previously proposed to classify TFs into external, internal and hybrid sensing classes depending on the source of their allosteric or equivalent metabolite. Here we analyze how a cell uses its topological structures in the context of sensing machinery and show that, while feed forward loops (FFLs) tightly integrate internal and external sensing TFs connecting TFs from different layers of the hierarchical transcriptional regulatory network (TRN), bifan motifs frequently connect TFs belonging to the same sensing class and could act as a bridge between TFs originating from the same level in the hierarchy. We observe that modules identified in the regulatory network of E. coli are heterogeneous in sensing context with a clear combination of internal and external sensing categories depending on the physiological role played by the module. We also note that propensity of two-component response regulators increases at promoters, as the number of TFs regulating a target operon increases. Finally we show that evolutionary families of TFs do not show a tendency to preserve their sensing abilities. Our results provide a detailed panorama of the topological structures of E. coli TRN and the way TFs they compose off, sense their surroundings by coordinating responses.

Current approaches to gene regulatory network modelling

Many different approaches have been developed to model and simulate gene regulatory networks. We proposed the following categories for gene regulatory network models: network parts lists, network topology models, network control logic models, and dynamic models. Here we will describe some examples for each of these categories. We will study the topology of gene regulatory networks in yeast in more detail, comparing a direct network derived from transcription factor binding data and an indirect network derived from genome-wide expression data in mutants. Regarding the network dynamics we briefly describe discrete and continuous approaches to network modelling, then describe a hybrid model called Finite State Linear Model and demonstrate that some simple network dynamics can be simulated in this model.

Environmental variability and modularity of bacterial metabolic networks

BACKGROUND

Biological systems are often modular: they can be decomposed into nearly-independent structural units that perform specific functions. The evolutionary origin of modularity is a subject of much current interest. Recent theory suggests that modularity can be enhanced when the environment changes over time. However, this theory has not yet been tested using biological data.

RESULTS

To address this, we studied the relation between environmental variability and modularity in a natural and well-studied system, the metabolic networks of bacteria. We classified 117 bacterial species according to the degree of variability in their natural habitat. We find that metabolic networks of organisms in variable environments are significantly more modular than networks of organisms that evolved under more constant conditions.

CONCLUSION

This study supports the view that variability in the natural habitat of an organism promotes modularity in its metabolic network and perhaps in other biological systems.

On the Long-Term Fitness of Cells in Periodically Switching Environments

Because all the cell populations are capable of making switches between different genetic expression states in response to the environmental change, Thattai and van Oudenaarden (Genetics 167, 523-530, 2004) have raised a very interesting question: In a constantly fluctuating environment, which type of cell population (heterogeneous or homogeneous) is fitter in the long term? This problem is very important to development and evolution biology. We thus take an extensive analysis about how the cell population evolves in a periodically switching environment either with symmetrical time-span or asymmetrical time-span. A complete picture of the phase diagrams for both cases is obtained. Furthermore, we find that the systems with time-dependent cellular transitions all collapse to the same set of dynamical equations with the modified parameters. Furthermore, we also explain in detail how the fitness problem bears much resemblance to the phenomenon, stochastic resonance, in physical sciences. Our results could be helpful for the biologists to design artificial evolution experiments and unveil the mystery of development and evolution.

A theoretical steady state analysis indicates that induction of Escherichia coli glnALG operon can display all-or-none behavior

The nitrogen starvation response in Escherichia coli is characterized by the enhanced expression of Ntr regulon, comprising hundreds of genes including the one coding for nitrogen-assimilating glutamine synthetase (GS) enzyme. The biosynthesis and activity of GS is regulated mainly by nitrogen and carbon levels in the cell and monitored by three functionally separable interconnected modules. Here, we present the steady-state modular analysis of this intricate network made up of a GS bicyclic closed-loop cascade, a NRII-NRI two-component system, and an autoregulated glnALG operon encoding genes for GS, NRII, and NRI. Our simulation results indicate that the transcriptional output of glnALG operon is discrete and switch-like, whereas the activation of transcription factor NRI is graded, and the inactivation of GS is moderately ultrasensitive to input stimulus glutamine. The autoregulation of the NRII-NRI two-component system was found to be essential for the all-or-none induction of the glnALG operon. Furthermore, we show that the autoregulated two-component system modulates the total active GS by delineating the GS activity from its biosynthetic regulation. Our analysis indicates that the exclusive relationship between GS activity and its synthesis is brought about by the autoregulated two-component system. The modularity of the network endows the system to respond differently to nitrogen depending on the carbon status of the cell. Through a system-level quantification, we conclude that the discrete switch-like transcriptional response of the E. coli glnALG operon to nutrient starvation prevents the premature initiation of transcription and may represent the desperate attempt by the cell to survive in limiting conditions.

Basal expression rate of comK sets a 'switching-window' into the K-state of Bacillus subtilis

Bacillus subtilis cell population divides into a competent fraction and a non-competent fraction in the stationary phase. The transition from the non-competent state (with basal ComK concentration) to the K-state (with high ComK concentration) behaves like a bistable switch. To better understand the mechanism that sets the fraction of cells that switch into the K-state (K-fraction), we characterized the basal comK expression in individual non-competent cells and found a large cell-to-cell variation. Basal expression rate increased exponentially, reached a maximum and decreased towards zero in the stationary phase. Concomitantly, the intrinsic switching rate increased and decreased with a time lag. When switching was induced prematurely by reduction of ComK proteolysis, the K-fraction increased strongly. Our data support a model in which the average basal level of ComK raises during late exponential phase and due to noise in basal comK expression only those cells that are on the high end of comK expression trigger the autocatalytic feedback for ComK transcription. We show that a subsequent shut-down of basal expression rate sets a 'time-window' for switching and is thus involved in determining the K-fraction in the bimodal population.

Network motifs: theory and experimental approaches

Transcription regulation networks control the expression of genes. The transcription networks of well-studied microorganisms appear to be made up of a small set of recurring regulation patterns, called network motifs. The same network motifs have recently been found in diverse organisms from bacteria to humans, suggesting that they serve as basic building blocks of transcription networks. Here I review network motifs and their functions, with an emphasis on experimental studies. Network motifs in other biological networks are also mentioned, including signalling and neuronal networks.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Random networks tossing biased coins

In statistical mechanical investigations of complex networks, it is useful to employ random graph ensembles as null models to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with asymptotically, scale-free out-degree and compact in-degree. Entries in each row of the adjacency matrix are set to 0 or 1 according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n approximately 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs. The technique is easily generalizable to different kinds of graphs.

Evolution of DNA double-strand break repair by gene conversion: coevolution between a phage and a restriction-modification system

The necessity to repair genome damage has been considered to be an immediate factor responsible for the origin of sex. Indeed, attack by a cellular restriction enzyme of invading DNA from several bacteriophages initiates recombinational repair by gene conversion if there is homologous DNA. In this work, we modeled the interaction between a bacteriophage and a bacterium carrying a restriction enzyme as antagonistic coevolution. We assume a locus on the bacteriophage genome has either a restriction-sensitive or a restriction-resistant allele, and another locus determines whether it is recombination/repair proficient or defective. A restriction break can be repaired by a co-infecting phage genome if one of them is recombination/repair proficient. We define the fitness of phage (resistant/sensitive and repair-positive/-negative) genotypes and bacterial (restriction-positive/-negative) genotypes by assuming random encounter of the genotypes, with given probabilities of single and double infections, and the costs of resistance, repair, and restriction. Our results show the evolution of the repair allele depends on b(1)/b(0), the ratio of the burst size b(1) under damage to host cell physiology induced by an unrepaired double-strand break to the default burst size b(0). It was not until this effect was taken into account that the evolutionary advantage of DNA repair became apparent.

A synthetic biology challenge: making cells compute

Advances in biology and engineering have enabled the reprogramming of cells with well-defined functions, leading to the emergence of synthetic biology. Early successes in this nascent field suggest its potential to impact diverse areas. Here, we examine the feasibility of engineering circuits for cell-based computation. We illustrate the basic concepts by describing the mapping of several computational problems to engineered gene circuits. Revolving around these examples and past studies, we discuss technologies and computational methods available to design, test, and optimize gene circuits. We conclude with discussion of challenges involved in a typical design cycle, as well as those specific to cellular computation.

Systems biology--an engineering perspective

The interdisciplinary field of systems biology has evolved rapidly over the last years. Different disciplines have aided the development of both its experimental and theoretical branches. One field, which has played a significant role is engineering science and, in particular chemical engineering. Here, we review and illustrate some of these contributions, ranging from modeling approaches to model analysis with a special focus on technique which have not yet been substantially exploited but can be potentially useful in the analysis of biochemical systems.

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called "inactive" components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation.

Fast, cheap and somewhat in control

Various practical challenges involved in controlling living organisms must be surmounted if synthetic biology is to be productive.

Efforts to manipulate living organisms have raised the question of whether engineering principles of hierarchy, abstraction and design can be applied to biological systems. Here, we consider the practical challenges to controlling living organisms that must be surmounted, or at least managed, if synthetic biology and cellular bioengineering are to be productive.

Evolutionary conservation and over-representation of functionally enriched network patterns in the yeast regulatory network

BACKGROUND

Localized network patterns are assumed to represent an optimal design principle in different biological networks. A widely used method for identifying functional components in biological networks is looking for network motifs - over-represented network patterns. A number of recent studies have undermined the claim that these over-represented patterns are indicative of optimal design principles and question whether localized network patterns are indeed of functional significance. This paper examines the functional significance of regulatory network patterns via their biological annotation and evolutionary conservation.

RESULTS

We enumerate all 3-node network patterns in the regulatory network of the yeast S. cerevisiae and examine the biological GO annotation and evolutionary conservation of their constituent genes. Specific 3-node patterns are found to be functionally enriched in different exogenous cellular conditions and thus may represent significant functional components. These functionally enriched patterns are composed mainly of recently evolved genes suggesting that there is no evolutionary pressure acting to preserve such functionally enriched patterns. No correlation is found between over-representation of network patterns and functional enrichment.

CONCLUSION

The findings of functional enrichment support the view that network patterns constitute an important design principle in regulatory networks. However, the wildly used method of over-representation for detecting motifs is not suitable for identifying functionally enriched patterns.

Deduction of intracellular sub-systems from a topological description of the network

Non-linear behaviour of biochemical networks, such as intracellular gene, protein or metabolic networks, is commonly represented using graphs of the underlying topology. Nodes represent abundance of molecules and edges interactions between pairs of molecules. These graphs are linear and thus based on an implicit linearization of the kinetic reactions in one or several dynamic modes of the total system. It is common to use data from different sources -- experiments conducted under different conditions or even on different species -- meaning that the graph will be a superposition of linearizations made in many different modes. The mixing of different modes makes it hard to identify functional modules, that is sub-systems that carry out a specific biological function, since the graph will contain many interactions that do not naturally occur at the same time. The ability to establish a boundary between the sub-system and its environment is critical in the definition of a module, contrary to a motif in which only internal interactions count. Identification of functional modules should therefore be done on graphs depicting the mode in which their function is carried out, i.e. graphs that only contain edges representing interactions active in the specific mode. In general, when an interaction between two molecules is established, one should always state the mode of the system in which it is active.

Modéliser les interactions moléculaires par la théorie des réseaux de jeux

We present a method to model biological systems, the theory of games networks. It extends game theory by multiplying the number of games, and by allowing agents to play several games simultaneously. Some important notions of biological systems, such as locality of interactions and modularity, can then be modelled.

Motif search in graphs: application to metabolic networks

The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks.

Transcriptional dynamics of the embryonic stem cell switch

Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4-SOX2-NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4-SOX2-NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG.

Dynamic changes in subgraph preference profiles of crucial transcription factors

Transcription factors with a large number of target genes—transcription hub(s), or THub(s)—are usually crucial components of the regulatory system of a cell, and the different patterns through which they transfer the transcriptional signal to downstream cascades are of great interest. By profiling normalized abundances (A_N) of basic regulatory patterns of individual THubs in the yeast Saccharomyces cerevisiae transcriptional regulation network under five different cellular states and environmental conditions, we have investigated their preferences for different basic regulatory patterns. Subgraph-normalized abundances downstream of individual THubs often differ significantly from that of the network as a whole, and conversely, certain over-represented subgraphs are not preferred by any THub. The THub preferences changed substantially when the cellular or environmental conditions changed. This switching of regulatory pattern preferences suggests that a change in conditions does not only elicit a change in response by the regulatory network, but also a change in the mechanisms by which the response is mediated. The THub subgraph preference profile thus provides a novel tool for description of the structure and organization between the large-scale exponents and local regulatory patterns.

Transcription factors are proteins that bind to short segments of DNA, thereby controlling transcription and expression of other genes. Transcription factors may control a number of other genes, and in turn be controlled by other transcription factors, thus forming an extensive transcriptional network of control and counter-control, which acts through space and time in the cell. In transcriptional networks, transcription factors and their target genes form various patterns (called subgraphs or motifs) that are suspected of being of importance to how transcription factors exert their control of cellular processes. Zhang and colleagues have studied how a subset of transcription factors (called transcription hubs) utilizes such subgraphs in networks generated from yeast cells under various cellular states and environmental conditions. Their analyses show that different transcription hubs in the same network prefer different types of subgraphs, and that these preferences are not governed by subgraph frequencies in the network. They further show that when cellular conditions change, the transcription hubs frequently change their subgraph preferences, indicating that different modes of control require different types of subgraph use. These findings could have implications for our understanding of the mechanisms that underlie the fine-tuned control systems that govern a cell or an organism.

Role of cascades in converting oscillatory signals into stationary step-like responses

In biological signal transduction pathways intermediates are often oscillatory and need to be converted into smooth output signals at the end. We show by mathematical modelling that protein kinase cascades enable converting oscillatory signals into sharp stationary step-like outputs. The importance of this result is demonstrated for the switch-like protein activation by calcium oscillations, which is of biological importance for regulating different cellular processes. In addition, we found that protein kinase cascades cause memory effects in the protein activation, which might be of a physiological advantage since a smaller amount of calcium transported in the cell is required for an effective activation of cellular processes.

Cell-signalling dynamics in time and space

The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signalling networks. Temporal dynamics are coupled to spatial gradients of signalling activities, which guide pivotal intracellular processes and tightly regulate signal propagation across a cell. Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.

Theodor Bücher Lecture. Metabolomics, modelling and machine learning in systems biology - towards an understanding of the languages of cells. Delivered on 3 July 2005 at the 30th FEBS Congress and the 9th IUBMB conference in Budapest

The newly emerging field of systems biology involves a judicious interplay between high-throughput 'wet' experimentation, computational modelling and technology development, coupled to the world of ideas and theory. This interplay involves iterative cycles, such that systems biology is not at all confined to hypothesis-dependent studies, with intelligent, principled, hypothesis-generating studies being of high importance and consequently very far from aimless fishing expeditions. I seek to illustrate each of these facets. Novel technology development in metabolomics can increase substantially the dynamic range and number of metabolites that one can detect, and these can be exploited as disease markers and in the consequent and principled generation of hypotheses that are consistent with the data and achieve this in a value-free manner. Much of classical biochemistry and signalling pathway analysis has concentrated on the analyses of changes in the concentrations of intermediates, with 'local' equations - such as that of Michaelis and Menten v=(Vmax x S)/(S+K m) - that describe individual steps being based solely on the instantaneous values of these concentrations. Recent work using single cells (that are not subject to the intellectually unsupportable averaging of the variable displayed by heterogeneous cells possessing nonlinear kinetics) has led to the recognition that some protein signalling pathways may encode their signals not (just) as concentrations (AM or amplitude-modulated in a radio analogy) but via changes in the dynamics of those concentrations (the signals are FM or frequency-modulated). This contributes in principle to a straightforward solution of the crosstalk problem, leads to a profound reassessment of how to understand the downstream effects of dynamic changes in the concentrations of elements in these pathways, and stresses the role of signal processing (and not merely the intermediates) in biological signalling. It is this signal processing that lies at the heart of understanding the languages of cells. The resolution of many of the modern and postgenomic problems of biochemistry requires the development of a myriad of new technologies (and maybe a new culture), and thus regular input from the physical sciences, engineering, mathematics and computer science. One solution, that we are adopting in the Manchester Interdisciplinary Biocentre (http://www.mib.ac.uk/) and the Manchester Centre for Integrative Systems Biology (http://www.mcisb.org/), is thus to colocate individuals with the necessary combinations of skills. Novel disciplines that require such an integrative approach continue to emerge. These include fields such as chemical genomics, synthetic biology, distributed computational environments for biological data and modelling, single cell diagnostics/bionanotechnology, and computational linguistics/text mining.

Effect of the MAPK cascade structure, nuclear translocation and regulation of transcription factors on gene expression

The mitogen activated protein kinase (MAP kinase) cascade system represents a highly conserved prototype of signal transduction by enzyme cascades. One of the best-studied properties of the MAPK system is its ability to convert graded input stimulus to switch-like all-or-none responses. Previous theoretical studies have centered on quantifying dual phosphorylated MAPK as a final output response and have not incorporated its influence on the regulation of gene expression. The main objective of the current work is to understand the regulatory effect of positive feedback loop embedded in the MAPK cascade, nuclear translocation of active MAPK, phosphorylation and activation of nuclear target proteins on the regulation of specific gene expression. To achieve this objective, we have simulated the MAPK cascade system, which resembles Hog1p activation pathway in yeast, at steady state. Thus, the input signal to the MAPK system is correlated with gene expression as a final system-level output response. The steady state simulation results suggest that other than regulating the signal propagation through cascades, the nuclear translocation of activated MAPK and subsequent regulation of gene expression represent one of the key modes to control the threshold level of response. This work proposes that, it is essential to consider the compartmental distributions of signaling species and the corresponding regulatory mechanisms of gene expression to study the system-level performance of signaling modules such as the MAPK cascade. Such an analysis will relate the extracellular cues to the final phenotypic response by capturing the mechanistic details of the signaling pathway.

Simulation of biochemical networks--cellular networks as dynamic control systems

It has been appreciated for at least a hundred years that biological organisms contain control systems that enable them to adapt to a changing environment and adjust their internal systems when they need to proliferate. Even so, we have little understanding of the role that many of the control systems play. It's only in recent years that mainstream science has begun to study biological systems qualitatively and to look specifically at dynamical responses. As a result it might be possible that future cancer therapies will operate by manipulating the control systems that have gone awry during uncontrolled proliferation. This is a long term goal because it would require a mind shift in the way some biologists approach such problems. In this short paper the author describes some of the main control elements found in biological systems and illustrate their use in biological networks. In addition the author discuss some of the strategies that one can use to build computational models.

Dynamic properties of network motifs contribute to biological network organization

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.

The authors model how network motifs respond to small-scale perturbations and find a strong correlation between motif stability and abundance in a network, suggesting that dynamic properties of network motifs may play a role in overall network structure.

Selective regulation of cellular processes via protein cascades acting as band-pass filters for time-limited oscillations

We show by mathematical modelling that a two-level protein cascade can act as a band-pass filter for time-limited oscillations. The band-pass filters are then combined into a network of three-level signalling cascades that by filtering the frequency of time-limited oscillations selectively switches cellular processes on and off. The physiological relevance for the selective regulation of cellular processes is demonstrated for the case of regulation by time-limited calcium oscillations.

Characterizing the Dynamics of the Quorum-Sensing System in Staphylococcus aureus

The virulence determinants of Staphylococcus aureus are expressed in a growth phase-dependent manner governed by the autoinducible quorum-sensing system agr. Activation of the agr system results in a rapid increase in the regulator RNAIII and occurs in response to accumulation of AIP. In order to activate the agr system, a basal transcription of agr components must be assumed. This basal transcription of agr components seems to be stimulated by sarA. To better understand how SarA would affect activation of the agr system by modulating the basal agr activity, a mathematical model for autoactivation of the agr system was set up. The model predicted that the agr system is hysteretic, meaning that the agr system is activated at a specific concentration of autoinducing peptide (AIP), whereas it is inactivated at a specific lower concentration of AIP. According to the model, changing the basal agr activity only had a marginal effect on steady-state levels of RNAIII but changed the sensitivity of the cells to AIP. This was supported by Northern blot analysis of RNAIII in S. aureus mutants with different levels of SarA expression. Since natural antagonistic AIPs have been demonstrated, the effect of adding inhibitors to the system was analyzed.

Toward predictive models of mammalian cells

Progress in experimental and theoretical biology is likely to provide us with the opportunity to assemble detailed predictive models of mammalian cells. Using a functional format to describe the organization of mammalian cells, we describe current approaches for developing qualitative and quantitative models using data from a variety of experimental sources. Recent developments and applications of graph theory to biological networks are reviewed. The use of these qualitative models to identify the topology of regulatory motifs and functional modules is discussed. Cellular homeostasis and plasticity are interpreted within the framework of balance between regulatory motifs and interactions between modules. From this analysis we identify the need for detailed quantitative models on the basis of the representation of the chemistry underlying the cellular process. The use of deterministic, stochastic, and hybrid models to represent cellular processes is reviewed, and an initial integrated approach for the development of large-scale predictive models of a mammalian cell is presented.

Phenotype analysis using network motifs derived from changes in regulatory network dynamics

The intrinsic dynamic response of a transcriptional regulatory network depends directly on molecular interactions in the cellular transcription, translation, and degradation machineries. These interactions can be incorporated into dynamic mathematical models of the biochemical system using the biophysical relationship with the model parameters. Modifications of such interactions bring changes to the biological behavior of the cells, and therefore, many normal and pathological cellular states depend on them. It is important for analysis, prediction, diagnosis, and treatment of cellular function to have an experimentally derived model with parameters that adequately represent the molecular interactions of interest. Finding the model and parameters of a transcriptional regulatory network is a difficult task that has been approached at different levels and with different techniques. We develop here a new analysis method (based on previous work on network inference, modeling, and parameter identification) that finds the most changed parameters from yeast oligonucleotide microarray expression patterns in cases where a phenotype difference exists between two samples. We then relate and examine the changed parameters with their associated genes, corresponding genetic functional categories, and particular subnetworks and connectivities. The biophysical bases for these changes are also identified by studying the relationship of the changed parameters with the transcription, translation, and degradation mechanisms. The method is improved to cases where there are two or more transcription factors influencing transcription, and a statistical analysis is performed to give a measurement of the uniqueness and robustness of the parameter fit.

Intracellular Signaling: Spatial and Temporal Control

Cells integrate many inputs through complex networks of interacting signaling pathways. Systems approaches as well as computer-aided reductionist approaches attempt to “untangle the wires” and gain an intimate understanding of cells. But “understanding” any system is just the way that the human mind gains the ability to predict behavior. Computer simulations are an alternative way to achieve this goal—quite possibly the only way for complex systems. We have new tools to probe large sets of unknown interactions, and we have amassed enough detailed information to quantitatively describe many functional modules. Cell physiology has passed the threshold: the time to begin modeling is now.

Metabolomics, machine learning and modelling: towards an understanding of the language of cells

In answering the question ‘Systems Biology – will it work?’ (which it self-evidently has already), it is appropriate to highlight advances in philosophy, in new technique development and in novel findings. In terms of philosophy, we see that systems biology involves an iterative interplay between linked activities – for instance, between theory and experiment, between induction and deduction and between measurements of parameters and variables – with more emphasis than has perhaps been common now being focused on the first in each of these pairs. In technique development, we highlight closed loop machine learning and its use in the optimization of scientific instrumentation, and the ability to effect high-quality and quasi-continuous optical images of cells. This leads to many important and novel findings. In the first case, these may involve new biomarkers for disease, whereas in the second case, we have determined that many biological signals may be frequency-rather than amplitude-encoded. This leads to a very different view of how signalling ‘works’ (equations such as that of Michaelis and Menten which use only amplitudes, i.e. concentrations, are inadequate descriptors), lays emphasis on the signal processing network elements that lie ‘downstream’ of what are traditionally considered the signals, and allows one simply to understand how cross-talk may be avoided between pathways which nevertheless use common signalling elements. The language of cells is much richer than we had supposed, and we are now well placed to decode it.

A hybrid systems framework for cellular processes

With the availability of technologies that allow us to obtain stimulus-response time series data for modeling and system identification, there is going to be an increasing need for conceptual frameworks in which to formulate and test hypotheses about intra- and inter-cellular dynamics, in general and not just dependent on a particular cell line, cell type, organism, or technology. While the semantics can be quite different, biologists and systems scientists use in many cases a similar language (notion of feedback, regulation, etc.). A more abstract system-theoretic framework for signals, systems, and control could provide the biologist with an interface between the domains. Apart from recent examples to identify functional elements and describing them in engineering terms, there have been various more abstract developments to describe dynamics at the cell level in the past. This includes Rosen's (M,R)-systems. This paper presents an abstract and general compact mathematical framework of intracellular dynamics, regulation and regime switching inspired by (M,R)-theory and based on hybrid automata.

Integration of the Gene Ontology into an object-oriented architecture

BACKGROUND

To standardize gene product descriptions, a formal vocabulary defined as the Gene Ontology (GO) has been developed. GO terms have been categorized into biological processes, molecular functions, and cellular components. However, there is no single representation that integrates all the terms into one cohesive model. Furthermore, GO definitions have little information explaining the underlying architecture that forms these terms, such as the dynamic and static events occurring in a process. In contrast, object-oriented models have been developed to show dynamic and static events. A portion of the TGF-beta signaling pathway, which is involved in numerous cellular events including cancer, differentiation and development, was used to demonstrate the feasibility of integrating the Gene Ontology into an object-oriented model.

RESULTS

Using object-oriented models we have captured the static and dynamic events that occur during a representative GO process, "transforming growth factor-beta (TGF-beta) receptor complex assembly" (GO:0007181).

CONCLUSION

We demonstrate that the utility of GO terms can be enhanced by object-oriented technology, and that the GO terms can be integrated into an object-oriented model by serving as a basis for the generation of object functions and attributes.