Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks

Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models. We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model     

Stochastic simulations of minimal self-reproducing cellular systems

This paper is a theoretical attempt to gain insight into the problem of how self-assembling vesicles (closed bilayer structures) could progressively turn into minimal self-producing and self-reproducing cells, i.e. into interesting candidates for (proto)biological systems. With this aim, we make use of a recently developed object-oriented platform to carry out stochastic simulations of chemical reaction networks that take place in dynamic cellular compartments. We apply this new tool to study the behaviour of different minimal cell models, making realistic assumptions about the physico-chemical processes and conditions involved (e.g. thermodynamic equilibrium/non-equilibrium, variable volume-to-surface relationship, osmotic pressure, solute diffusion across the membrane due to concentration gradients, buffering effect). The new programming platform has been designed to analyse not only how a single protometabolic cell could maintain itself, grow or divide, but also how a collection of these cells could 'evolve' as a result of their mutual interactions in a common environment.     

N.W. Thomas and colonial anthropology in British West Africa: reappraising a cautionary tale

As the first government anthropologist to be appointed by the British Colonial Office, Northcote Whitridge Thomas (1868‐1936) has earned a place in the footnotes of anthropological history. Historians of the discipline have discussed his career in West Africa in their wider explorations of the relationship between anthropology and colonial administration in the early twentieth century. Through this work, an orthodox account of Thomas has emerged as an eccentric dilettante who damaged the reputation of the discipline, setting back its adoption as a practical science of value to colonial governance by a generation or more. Adopting a micro‐historical approach, closer scrutiny of the archival evidence challenges this orthodoxy, and places Thomas more centrally within the professional networks and practices of British anthropology in the period 1900 to 1915. As well as correcting the record concerning Thomas's professional reputation, a more complex picture emerges regarding the colonial authorities’ attitudes towards anthropology and the reason why this early experiment in colonial anthropology failed.     

Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Efficient parametric analysis of the chemical master equation through model order reduction

ABSTRACT: BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. RESULTS: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.     

Ion mobility–mass spectrometry for structural proteomics

Ion mobility coupled to mass spectrometry has been an important tool in the fields of chemical physics and analytical chemistry for decades, but its potential for interrogating the structure of proteins and multiprotein complexes has only recently begun to be realized. Today, ion mobility–mass spectrometry is often applied to the structural elucidation of protein assemblies that have failed high-throughput crystallization or NMR spectroscopy screens. Here, we highlight the technology, approaches and data that have led to this dramatic shift in use, including emerging trends such as the integration of ion mobility–mass spectrometry data with more classical (e.g., ‘bottom-up’) proteomics approaches for the rapid structural characterization of protein networks.     

Does Habitat Variability Really Promote Metabolic Network Modularity?

The hypothesis that variability in natural habitats promotes modular organization is widely accepted for cellular networks. However, results of some data analyses and theoretical studies have begun to cast doubt on the impact of habitat variability on modularity in metabolic networks. Therefore, we re-evaluated this hypothesis using statistical data analysis and current metabolic information. We were unable to conclude that an increase in modularity was the result of habitat variability. Although horizontal gene transfer was also considered because it may contribute for survival in a variety of environments, closely related to habitat variability, and is known to be positively correlated with network modularity, such a positive correlation was not concluded in the latest version of metabolic networks. Furthermore, we demonstrated that the previously observed increase in network modularity due to habitat variability and horizontal gene transfer was probably due to a lack of available data on metabolic reactions. Instead, we determined that modularity in metabolic networks is dependent on species growth conditions. These results may not entirely discount the impact of habitat variability and horizontal gene transfer. Rather, they highlight the need for a more suitable definition of habitat variability and a more careful examination of relationships of the network modularity with horizontal gene transfer, habitats, and environments.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems

Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas’ conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.     

Hierarchical neuronal modeling of cognitive functions: from synaptic transmission to the Tower of London

Recent progress in the molecular biology of synaptic transmission, in particular of neurotransmitter receptors, offers novel information relevant to ‘realistic’ modeling of neural processes at the single cell and network level. Sophisticated computer analyses of 2D crystals by high resolution electron microscopy yield images of single neurotransmitter receptor molecules with tentative identifications of ligand binding sites and of conformational transitions. The dynamics of conformational changes can be accounted for by a ‘multistate allosteric network’ model. Allosteric receptors also possess the structural and functional properties required to serve as coincidence detectors between pre- and post-synaptic signals and, therefore, can be used as building blocks for a chemical Hebb synapse. These properties were introduced into networks of formal neurons capable of producing and detecting temporal sequences. In more elaborate models of pre-frontal cortex functions, allosteric receptors control the selection of transient ‘pre-representations’ and their stabilization by external or internal reward signals. We apply this scheme to Shallice's Tower of London test, and we show how a hierarchical neuronal architecture can implement executive or planning functions associated with frontal areas.     

Chemical Reaction Systems with Toric Steady States

Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.     

Adapting Agricultural Water Use to Climate Change in a Post-Soviet Context: Challenges and Opportunities in Southeast Kazakhstan

The convergence of climate change and post-Soviet socio-economic and institutional transformations has been underexplored so far, as have the consequences of such convergence on crop agriculture in Central Asia. This paper provides a place-based analysis of constraints and opportunities for adaptation to climate change, with a specific focus on water use, in two districts in southeast Kazakhstan. Data were collected by 2 multi-stakeholder participatory workshops, 21 semi-structured in-depth interviews, and secondary statistical data. The present-day agricultural system is characterised by enduring Soviet-era management structures, but without state inputs that previously sustained agricultural productivity. Low margins of profitability on many privatised farms mean that attempts to implement integrated water management have produced water users associations unable to maintain and upgrade a deteriorating irrigation infrastructure. Although actors engage in tactical adaptation measures, necessary structural adaptation of the irrigation system remains difficult without significant public or private investments. Market-based water management models have been translated ambiguously to this region, which fails to encourage efficient water use and hinders adaptation to water stress. In addition, a mutual interdependence of informal networks and formal institutions characterises both state governance and everyday life in Kazakhstan. Such interdependence simultaneously facilitates operational and tactical adaptation, but hinders structural adaptation, as informal networks exist as a parallel system that achieves substantive outcomes while perpetuating the inertia and incapacity of the state bureaucracy. This article has relevance for critical understanding of integrated water management in practice and adaptation to climate change in post-Soviet institutional settings more broadly.     

CheckShift improved: fast chemical shift reference correction with high accuracy

The construction of a consistent protein chemical shift database is an important step toward making more extensive use of this data in structural studies. Unfortunately, progress in this direction has been hampered by the quality of the available data, particularly with respect to chemical shift referencing, which is often either inaccurate or inconsistently annotated. Preprocessing of the data is therefore required to detect and correct referencing errors. In an earlier study we developed CheckShift, a program for performing this task automatically. Now we spent substantial effort in improving the running time of the CheckShift algorithm, which resulted in an running time decrease of 90%, thereby achieving equivalent quality to the former version of CheckShift. The reason for the running time decrease is twofold. Firstly we improved the search for the optimal re-referencing offset considerably. Secondly, as CheckShift is based on a secondary structure prediction from the amino acid sequence (formally PsiPred was used), we evaluated a wide range of available secondary structure prediction programs focusing on the special needs of the CheckShift algorithm. The results of this evaluation prove empirically that we can use faster secondary structure prediction programs than PsiPred without sacrificing CheckShift’s accuracy. Very recently Wang and Markley (2009) gave a small list of extreme outliers of the former version of the CheckShift web-server. Those were due to the empirical reduction of the search space implemented in the old version. The new version of CheckShift now gives very similar results to RefDB and LACS for all outliers mentioned in Table 1 of Wang and Markley (2009).     

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.     

Identification of functional differences in metabolic networks using comparative genomics and constraint-based models

Genome-scale network reconstructions are useful tools for understanding cellular metabolism, and comparisons of such reconstructions can provide insight into metabolic differences between organisms. Recent efforts toward comparing genome-scale models have focused primarily on aligning metabolic networks at the reaction level and then looking at differences and similarities in reaction and gene content. However, these reaction comparison approaches are time-consuming and do not identify the effect network differences have on the functional states of the network. We have developed a bilevel mixed-integer programming approach, CONGA, to identify functional differences between metabolic networks by comparing network reconstructions aligned at the gene level. We first identify orthologous genes across two reconstructions and then use CONGA to identify conditions under which differences in gene content give rise to differences in metabolic capabilities. By seeking genes whose deletion in one or both models disproportionately changes flux through a selected reaction (e.g., growth or by-product secretion) in one model over another, we are able to identify structural metabolic network differences enabling unique metabolic capabilities. Using CONGA, we explore functional differences between two metabolic reconstructions of Escherichia coli and identify a set of reactions responsible for chemical production differences between the two models. We also use this approach to aid in the development of a genome-scale model of Synechococcus sp. PCC 7002. Finally, we propose potential antimicrobial targets in Mycobacterium tuberculosis and Staphylococcus aureus based on differences in their metabolic capabilities. Through these examples, we demonstrate that a gene-centric approach to comparing metabolic networks allows for a rapid comparison of metabolic models at a functional level. Using CONGA, we can identify differences in reaction and gene content which give rise to different functional predictions. Because CONGA provides a general framework, it can be applied to find functional differences across models and biological systems beyond those presented here.