Maboss for HPC environments: implementations of the continuous time Boolean model simulator for large CPU clusters and GPU accelerators

BACKGROUND

Computational models in systems biology are becoming more important with the advancement of experimental techniques to query the mechanistic details responsible for leading to phenotypes of interest. In particular, Boolean models are well fit to describe the complexity of signaling networks while being simple enough to scale to a very large number of components. With the advance of Boolean model inference techniques, the field is transforming from an artisanal way of building models of moderate size to a more automatized one, leading to very large models. In this context, adapting the simulation software for such increases in complexity is crucial.

RESULTS

We present two new developments in the continuous time Boolean simulators: MaBoSS.MPI, a parallel implementation of MaBoSS which can exploit the computational power of very large CPU clusters, and MaBoSS.GPU, which can use GPU accelerators to perform these simulations.

CONCLUSION

These implementations enable simulation and exploration of the behavior of very large models, thus becoming a valuable analysis tool for the systems biology community.

Small-angle X-ray scattering intensity of multiscale models of spheroids

The microstructure of heterogeneous catalysts often consists of multiscale aggregates of nanoparticles, some of which are highly anisotropic. Therefore, small-angle X-ray scattering, in classical or anomalous mode, is a valuable tool to characterize this kind of material. Yet, the classical exploitation of the scattered intensities through form and structure factors or by means of Boolean models of spheres is questionable. Here, it is proposed to interpret the scattered intensities through the use of multiscale Boolean models of spheroids. The numerical procedure to compute scattered intensities of such models is given and then validated on asymptotic diluted Boolean models, and its applicability is demonstrated for the characterization of alumina catalyst supports.

Boolean modeling reveals that cyclic attractors in macrophage polarization serve as reservoirs of states to balance external perturbations from the tumor microenvironment

Cyclic attractors generated from Boolean models may explain the adaptability of a cell in response to a dynamical complex tumor microenvironment. In contrast to this idea, we postulate that cyclic attractors in certain cases could be a systemic mechanism to face the perturbations coming from the environment. To justify our conjecture, we present a dynamic analysis of a highly curated transcriptional regulatory network of macrophages constrained into a cancer microenvironment. We observed that when M1-associated transcription factors (STAT1 or NF-κB) are perturbed and the microenvironment balances to a hyper-inflammation condition, cycle attractors activate genes whose signals counteract this effect implicated in tissue damage. The same behavior happens when the M2-associated transcription factors are disturbed (STAT3 or STAT6); cycle attractors will prevent a hyper-regulation scenario implicated in providing a suitable environment for tumor growth. Therefore, here we propose that cyclic macrophage phenotypes can serve as a reservoir for balancing the phenotypes when a specific phenotype-based transcription factor is perturbed in the regulatory network of macrophages. We consider that cyclic attractors should not be simply ignored, but it is necessary to carefully evaluate their biological importance. In this work, we suggest one conjecture: the cyclic attractors can serve as a reservoir to balance the inflammatory/regulatory response of the network under external perturbations.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

Computational Verification of Large Logical Models-Application to the Prediction of T Cell Response to Checkpoint Inhibitors

At the crossroad between biology and mathematical modeling, computational systems biology can contribute to a mechanistic understanding of high-level biological phenomenon. But as knowledge accumulates, the size and complexity of mathematical models increase, calling for the development of efficient dynamical analysis methods. Here, we propose the use of two approaches for the development and analysis of complex cellular network models. A first approach, called "model verification" and inspired by unitary testing in software development, enables the formalization and automated verification of validation criteria for whole models or selected sub-parts. When combined with efficient analysis methods, this approach is suitable for continuous testing, thereby greatly facilitating model development. A second approach, called "value propagation," enables efficient analytical computation of the impact of specific environmental or genetic conditions on the dynamical behavior of some models. We apply these two approaches to the delineation and the analysis of a comprehensive model for T cell activation, taking into account CTLA4 and PD-1 checkpoint inhibitory pathways. While model verification greatly eases the delineation of logical rules complying with a set of dynamical specifications, propagation provides interesting insights into the different potential of CTLA4 and PD-1 immunotherapies. Both methods are implemented and made available in the all-inclusive CoLoMoTo Docker image, while the different steps of the model analysis are fully reported in two companion interactive jupyter notebooks, thereby ensuring the reproduction of our results.

Opportunities for multiscale computational modelling of serotonergic drug effects in Alzheimer's disease

Alzheimer's disease (AD) is an age-specific neurodegenerative disease that compromises cognitive functioning and impacts the quality of life of an individual. Pathologically, AD is characterised by abnormal accumulation of beta-amyloid (Aβ) and hyperphosphorylated tau protein. Despite research advances over the last few decades, there is currently still no cure for AD. Although, medications are available to control some behavioural symptoms and slow the disease's progression, most prescribed medications are based on cholinesterase inhibitors. Over the last decade, there has been increased attention towards novel drugs, targeting alternative neurotransmitter pathways, particularly those targeting serotonergic (5-HT) system. In this review, we focused on 5-HT receptor (5-HTR) mediated signalling and drugs that target these receptors. These pathways regulate key proteins and kinases such as GSK-3 that are associated with abnormal levels of Aβ and tau in AD. We then review computational studies related to 5-HT signalling pathways with the potential for providing deeper understanding of AD pathologies. In particular, we suggest that multiscale and multilevel modelling approaches could potentially provide new insights into AD mechanisms, and towards discovering novel 5-HTR based therapeutic targets.

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Alzheimer's disease (AD) drug treatment is limited, and alternatives are needed.

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Serotonin (5-HT) mediated signalling pathways may regulate Aβ and tau levels.

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5-HT based drugs have the potential to provide as novel therapeutics for AD.

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Complex 5-HT signalling mechanisms for AD and related drugs hinder understanding.

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Multiscale models may offer insights into mechanisms and therapeutic targets.

Multi-parameter exploration of dynamics of regulatory networks

Over the last twenty years advances in systems biology have changed our views on microbial communities and promise to revolutionize treatment of human diseases. In almost all scientific breakthroughs since time of Newton, mathematical modeling has played a prominent role. Regulatory networks emerged as preferred descriptors of how abundances of molecular species depend on each other. However, the central question on how cellular phenotypes emerge from dynamics of these network remains elusive. The principal reason is that differential equation models in the field of biology (while so successful in areas of physics and physical chemistry), do not arise from first principles, and these models suffer from lack of proper parameterization. In response to these challenges, discrete time models based on Boolean networks have been developed. In this review, we discuss an emerging modeling paradigm that combines ideas from differential equations and Boolean models, and has been developed independently within dynamical systems and computer science communities. The result is an approach that can associate a range of potential dynamical behaviors to a network, arrange the descriptors of the dynamics in a searchable database, and allows for multi-parameter exploration of the dynamics akin to bifurcation theory. Since this approach is computationally accessible for moderately sized networks, it allows, perhaps for the first time, to rationally compare different network topologies based on their dynamics.

Evolving Always-Critical Networks

Living beings share several common features at the molecular level, but there are very few large-scale “operating principles” which hold for all (or almost all) organisms. However, biology is subject to a deluge of data, and as such, general concepts such as this would be extremely valuable. One interesting candidate is the “criticality” principle, which claims that biological evolution favors those dynamical regimes that are intermediaries between ordered and disordered states (i.e., “at the edge of chaos”). The reasons why this should be the case and experimental evidence are briefly discussed, observing that gene regulatory networks are indeed often found on, or close to, the critical boundaries. Therefore, assuming that criticality provides an edge, it is important to ascertain whether systems that are critical can further evolve while remaining critical. In order to explore the possibility of achieving such “always-critical” evolution, we resort to simulated evolution, by suitably modifying a genetic algorithm in such a way that the newly-generated individuals are constrained to be critical. It is then shown that these modified genetic algorithms can actually develop critical gene regulatory networks with two interesting (and quite different) features of biological significance, involving, in one case, the average gene activation values and, in the other case, the response to perturbations. These two cases suggest that it is often possible to evolve networks with interesting properties without losing the advantages of criticality. The evolved networks also show some interesting features which are discussed.

Self-sustaining positive feedback loops in discrete and continuous systems

We consider a dynamic framework frequently used to model gene regulatory and signal transduction networks: monotonic ODEs that are composed of Hill functions. We derive conditions under which activity or inactivity in one system variable induces and sustains activity or inactivity in another. Cycles of such influences correspond to positive feedback loops that are self-sustaining and control-robust, in the sense that these feedback loops "trap" the system in a region of state space from which it cannot exit, even if the other system variables are externally controlled. To demonstrate the utility of this result, we consider prototypical examples of bistability and hysteresis in gene regulatory networks, and analyze a T-cell signal transduction ODE model from the literature.

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.

Gene regulatory network underlying the immortalization of epithelial cells

BACKGROUND

Tumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of spontaneous immortalization. This process is characterized by a series of cell-state transitions, in which normal epithelial cells acquire first a senescent state which is later surpassed to attain a mesenchymal stem-like phenotype with a potentially tumorigenic behavior. In this paper we aim to provide a system-level mechanistic explanation to the emergence of these cell types, and to the time-ordered transition patterns that are common to neoplasias of epithelial origin. To this end, we first integrate published functional and well-curated molecular data of the components and interactions that have been found to be involved in such cell states and transitions into a network of 41 molecular components. We then reduce this initial network by removing simple mediators (i.e., linear pathways), and formalize the resulting regulatory core into logical rules that govern the dynamics of each of the network components as a function of the states of its regulators.

RESULTS

Computational dynamic analysis shows that our proposed Gene Regulatory Network model recovers exactly three attractors, each of them defined by a specific gene expression profile that corresponds to the epithelial, senescent, and mesenchymal stem-like cellular phenotypes, respectively. We show that although a mesenchymal stem-like state can be attained even under unperturbed physiological conditions, the likelihood of converging to this state is increased when pro-inflammatory conditions are simulated, providing a systems-level mechanistic explanation for the carcinogenic role of chronic inflammatory conditions observed in the clinic. We also found that the regulatory core yields an epigenetic landscape that restricts temporal patterns of progression between the steady states, such that recovered patterns resemble the time-ordered transitions observed during the spontaneous immortalization of epithelial cells, both in vivo and in vitro.

CONCLUSION

Our study strongly suggests that the in vitro tumorigenic transformation of epithelial cells, which strongly correlates with the patterns observed during the pathological progression of epithelial carcinogenesis in vivo, emerges from underlying regulatory networks involved in epithelial trans-differentiation during development.

Stacking the odds for Golgi cisternal maturation

What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.

DOI:http://dx.doi.org/10.7554/eLife.16231.001

Wine glasses and hourglasses: Non-adaptive complexity of vesicle traffic in microbial eukaryotes

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We are motivated by the diversity of vesicle traffic systems in microbial parasites.

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We present a mathematical model of vesicle traffic in a manner accessible to a broad audience.

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We show that many complex features of vesicle traffic systems arise spontaneously due to molecular interactions.

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Traffic features such as compartmental maturation might arise non-adaptively and later be selected for function.

Microbial eukaryotes present a stunning diversity of endomembrane organization. From specialized secretory organelles such as the rhoptries and micronemes of apicomplexans, to peroxisome-derived metabolic compartments such as the glycosomes of kinetoplastids, different microbial taxa have explored different solutions to the compartmentalization and processing of cargo. The basic secretory and endocytic system, comprising the ER, Golgi, endosomes, and plasma membrane, as well as diverse taxon-specific specialized endomembrane organelles, are coupled by a complex network of cargo transport via vesicle traffic. It is tempting to connect form to function, ascribing biochemical roles to each compartment and vesicle of such a system. Here we argue that traffic systems of high complexity could arise through non-adaptive mechanisms via purely physical constraints, and subsequently be exapted for various taxon-specific functions. Our argument is based on a Boolean mathematical model of vesicle traffic: we specify rules of how compartments exchange vesicles; these rules then generate hypothetical cells with different types of endomembrane organization. Though one could imagine a large number of hypothetical vesicle traffic systems, very few of these are consistent with molecular interactions. Such molecular constraints are the bottleneck of a metaphorical hourglass, and the rules that make it through the bottleneck are expected to generate cells with many special properties. Sampling at random from among such rules represents an evolutionary null hypothesis: any properties of the resulting cells must be non-adaptive. We show by example that vesicle traffic systems generated in this random manner are reminiscent of the complex trafficking apparatus of real cells.

Morphological modelling of three-phase microstructures of anode layers using SEM images

A general method is proposed to model 3D microstructures representative of three-phases anode layers used in fuel cells. The models are based on SEM images of cells with varying morphologies. The materials are first characterized using three morphological measurements: (cross-)covariances, granulometry and linear erosion. They are measured on segmented SEM images, for each of the three phases. Second, a generic model for three-phases materials is proposed. The model is based on two independent underlying random sets which are otherwise arbitrary. The validity of this model is verified using the cross-covariance functions of the various phases. In a third step, several types of Boolean random sets and plurigaussian models are considered for the unknown underlying random sets. Overall, good agreement is found between the SEM images and three-phases models based on plurigaussian random sets, for all morphological measurements considered in the present work: covariances, granulometry and linear erosion. The spatial distribution and shapes of the phases produced by the plurigaussian model are visually very close to the real material. Furthermore, the proposed models require no numerical optimization and are straightforward to generate using the covariance functions measured on the SEM images.

Programmatic access to logical models in the Cell Collective modeling environment via a REST API

Cell Collective (www.cellcollective.org) is a web-based interactive environment for constructing, simulating and analyzing logical models of biological systems. Herein, we present a Web service to access models, annotations, and simulation data in the Cell Collective platform through the Representational State Transfer (REST) Application Programming Interface (API). The REST API provides a convenient method for obtaining Cell Collective data through almost any programming language. To ensure easy processing of the retrieved data, the request output from the API is available in a standard JSON format.

AVAILABILITY AND IMPLEMENTATION

The Cell Collective REST API is freely available at http://thecellcollective.org/tccapi. All public models in Cell Collective are available through the REST API. For users interested in creating and accessing their own models through the REST API first need to create an account in Cell Collective (http://thecellcollective.org).

CONTACT

thelikar2@unl.edu.

SUPPLEMENTARY INFORMATION

Technical user documentation: https://goo.gl/U52GWo.

Regulatory logic and pattern formation in the early sea urchin embryo

We model the endomesoderm tissue specification process in the vegetal half of the early sea urchin embryo using Boolean models with continuous-time updating to represent the regulatory network that controls gene expression. Our models assume that the network interaction rules remain constant over time and the dynamics plays out on a predetermined program of cell divisions. An exhaustive search of two-node models, in which each node may represent a module of several genes in the real regulatory network, yields a unique network architecture that can accomplish the pattern formation task at hand--the formation of three latitudinal tissue bands from an initial state with only two distinct cell types. Analysis of an eight-gene model constructed from available experimental data reveals that it has a modular structure equivalent to the successful two-node case. Our results support the hypothesis that the gene regulatory network provides sufficient instructions for producing the correct pattern of tissue specification at this stage of development (between the fourth and tenth cleavages in the urchin embryo).

Some perspectives on network modeling in therapeutic target prediction

Drug target identification is of significant commercial interest to pharmaceutical companies, and there is a vast amount of research done related to the topic of therapeutic target identification. Interdisciplinary research in this area involves both the biological network community and the graph algorithms community. Key steps of a typical therapeutic target identification problem include synthesizing or inferring the complex network of interactions relevant to the disease, connecting this network to the disease-specific behavior, and predicting which components are key mediators of the behavior. All of these steps involve graph theoretical or graph algorithmic aspects. In this perspective, we provide modelling and algorithmic perspectives for therapeutic target identification and highlight a number of algorithmic advances, which have gotten relatively little attention so far, with the hope of strengthening the ties between these two research communities.

A REDUCTION METHOD FOR BOOLEAN NETWORK MODELS PROVEN TO CONSERVE ATTRACTORS

Boolean models, wherein each component is characterized with a binary (ON or OFF) variable, have been widely employed for dynamic modeling of biological regulatory networks. However, the exponential dependencse of the size of the state space of these models on the number of nodes in the network can be a daunting prospect for attractor analysis of large-scale systems. We have previously proposed a network reduction technique for Boolean models and demonstrated its applicability on two biological systems, namely, the abscisic acid signal transduction network as well as the T-LGL leukemia survival signaling network. In this paper, we provide a rigorous mathematical proof that this method not only conserves the fixed points of a Boolean network, but also conserves the complex attractors of general asynchronous Boolean models wherein at each time step a randomly selected node is updated. This method thus allows one to infer the long-term dynamic properties of a large-scale system from those of the corresponding reduced model.

Boolean modeling of biological regulatory networks: a methodology tutorial

Given the complexity and interactive nature of biological systems, constructing informative and coherent network models of these systems and subsequently developing efficient approaches to analyze the assembled networks is of immense importance. The integration of network analysis and dynamic modeling enables one to investigate the behavior of the underlying system as a whole and to make experimentally testable predictions about less-understood aspects of the processes involved. In this paper, we present a tutorial on the fundamental steps of Boolean modeling of biological regulatory networks. We demonstrate how to infer a Boolean network model from the available experimental data, analyze the network using graph-theoretical measures, and convert it into a predictive dynamic model. For each step, the pitfalls one may encounter and possible ways to circumvent them are also discussed. We illustrate these steps on a toy network as well as in the context of the Drosophila melanogaster segment polarity gene network.