Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

Nets-within-nets for modeling emergent patterns in ontogenetic processes

Ontogenesis is the development of an organism from its earliest stage to maturity, including homeostasis maintenance throughout adulthood despite environmental perturbations. Almost all cells of a multicellular organism share the same genomic information. Nevertheless, phenotypic diversity and complex supra-cellular architectures emerge at every level, starting from tissues and organs. This is possible thanks to a robust and dynamic interplay of regulative mechanisms. To study ontogenesis, it is necessary to consider different levels of regulation, both genetic and epigenetic. Each cell undergoes a specific path across a landscape of possible regulative states affecting both its structure and its functions during development. This paper proposes using the Nets-Within-Nets formalism, which combines Petri Nets' simplicity with the capability to represent and simulate the interplay between different layers of regulation connected by non-trivial and context-dependent hierarchical relations. In particular, this work introduces a modeling strategy based on Nets-Within-Nets that can model several critical processes involved in ontogenesis. Moreover, it presents a case study focusing on the first phase of Vulval Precursor Cells specification in C.Elegans. The case study shows that the proposed model can simulate the emergent morphogenetic pattern corresponding to the observed developmental outcome of that phase, in both the physiological case and different mutations. The model presented in the results section is available online at https://github.com/sysbio-polito/NWN_CElegans_VPC_model/.

A framework for exhaustive modelling of genetic interaction patterns using Petri nets

MOTIVATION

Genetic interaction (GI) patterns are characterized by the phenotypes of interacting single and double mutated gene pairs. Uncovering the regulatory mechanisms of GIs would provide a better understanding of their role in biological processes, diseases and drug response. Computational analyses can provide insights into the underpinning mechanisms of GIs.

RESULTS

In this study, we present a framework for exhaustive modelling of GI patterns using Petri nets (PN). Four-node models were defined and generated on three levels with restrictions, to enable an exhaustive approach. Simulations suggest ∼5 million models of GIs. Generalizing these we propose putative mechanisms for the GI patterns, inversion and suppression. We demonstrate that exhaustive PN modelling enables reasoning about mechanisms of GIs when only the phenotypes of gene pairs are known. The framework can be applied to other GI or genetic regulatory datasets.

AVAILABILITY AND IMPLEMENTATION

The framework is available at http://www.ibi.vu.nl/programs/ExhMod.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Constructing and Analyzing Computational Models of Cell Signaling with BioModelAnalyzer

BioModelAnalyzer (BMA) is an open-source graphical tool for the development of executable models of protein and gene networks within cells. Based upon the Qualitative Networks formalism, the user can rapidly construct large networks, either manually or by connecting motifs selected from a built-in library. After the appropriate functions for each variable are defined, the user has access to three analysis engines to test the model. In addition to standard simulation tools, BMA includes an interface to the stability-testing algorithm and to a graphical Linear Temporal Logic (LTL) editor and analysis tool. Alongside this, we have developed a novel ChatBot to aid users constructing LTL queries and to explain the interface and run through tutorials. Here we present worked examples of model construction and testing via the interface. As an initial example, we discuss fate decisions in Dictyostelium discoidum and cAMP signaling. We go on to describe the workflow leading to the construction of a published model of the germline of C. elegans. Finally, we demonstrate how to construct simple models from the built-in network motif library. © 2020 by John Wiley & Sons, Inc. Basic Protocol 1: Modeling the signaling network of Dictyostelium discoidum Basic Protocol 2: Modeling the germline progression of Caenorhabditis elegans Basic Protocol 3: Constructing a model of the cell cycle using motifs.

Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.

The ability of transcription factors to differentially regulate gene expression is a crucial component of the mechanism underlying inversion, a frequently observed genetic interaction pattern

Genetic interactions, a phenomenon whereby combinations of mutations lead to unexpected effects, reflect how cellular processes are wired and play an important role in complex genetic diseases. Understanding the molecular basis of genetic interactions is crucial for deciphering pathway organization as well as understanding the relationship between genetic variation and disease. Several hypothetical molecular mechanisms have been linked to different genetic interaction types. However, differences in genetic interaction patterns and their underlying mechanisms have not yet been compared systematically between different functional gene classes. Here, differences in the occurrence and types of genetic interactions are compared for two classes, gene-specific transcription factors (GSTFs) and signaling genes (kinases and phosphatases). Genome-wide gene expression data for 63 single and double deletion mutants in baker's yeast reveals that the two most common genetic interaction patterns are buffering and inversion. Buffering is typically associated with redundancy and is well understood. In inversion, genes show opposite behavior in the double mutant compared to the corresponding single mutants. The underlying mechanism is poorly understood. Although both classes show buffering and inversion patterns, the prevalence of inversion is much stronger in GSTFs. To decipher potential mechanisms, a Petri Net modeling approach was employed, where genes are represented as nodes and relationships between genes as edges. This allowed over 9 million possible three and four node models to be exhaustively enumerated. The models show that a quantitative difference in interaction strength is a strict requirement for obtaining inversion. In addition, this difference is frequently accompanied with a second gene that shows buffering. Taken together, these results provide a mechanistic explanation for inversion. Furthermore, the ability of transcription factors to differentially regulate expression of their targets provides a likely explanation why inversion is more prevalent for GSTFs compared to kinases and phosphatases.

BioASF: a framework for automatically generating executable pathway models specified in BioPAX

Motivation: Biological pathways play a key role in most cellular functions. To better understand these functions, diverse computational and cell biology researchers use biological pathway data for various analysis and modeling purposes. For specifying these biological pathways, a community of researchers has defined BioPAX and provided various tools for creating, validating and visualizing BioPAX models. However, a generic software framework for simulating BioPAX models is missing. Here, we attempt to fill this gap by introducing a generic simulation framework for BioPAX. The framework explicitly separates the execution model from the model structure as provided by BioPAX, with the advantage that the modelling process becomes more reproducible and intrinsically more modular; this ensures natural biological constraints are satisfied upon execution. The framework is based on the principles of discrete event systems and multi-agent systems, and is capable of automatically generating a hierarchical multi-agent system for a given BioPAX model.

Results: To demonstrate the applicability of the framework, we simulated two types of biological network models: a gene regulatory network modeling the haematopoietic stem cell regulators and a signal transduction network modeling the Wnt/β-catenin signaling pathway. We observed that the results of the simulations performed using our framework were entirely consistent with the simulation results reported by the researchers who developed the original models in a proprietary language.

Availability and Implementation: The framework, implemented in Java, is open source and its source code, documentation and tutorial are available at http://www.ibi.vu.nl/programs/BioASF.

Contact:j.heringa@vu.nl

A computational model predicts genetic nodes that allow switching between species-specific responses in a conserved signaling network

Alterations to only specific parameters in a model including EGF, Wnt and Notch lead to cell behavior differences.

Construction and Experimental Validation of a Petri Net Model of Wnt/β-Catenin Signaling

The Wnt/β-catenin signaling pathway is important for multiple developmental processes and tissue maintenance in adults. Consequently, deregulated signaling is involved in a range of human diseases including cancer and developmental defects. A better understanding of the intricate regulatory mechanism and effect of physiological (active) and pathophysiological (hyperactive) WNT signaling is important for predicting treatment response and developing novel therapies. The constitutively expressed CTNNB1 (commonly and hereafter referred to as β-catenin) is degraded by a destruction complex, composed of amongst others AXIN1 and GSK3. The destruction complex is inhibited during active WNT signaling, leading to β-catenin stabilization and induction of β-catenin/TCF target genes. In this study we investigated the mechanism and effect of β-catenin stabilization during active and hyperactive WNT signaling in a combined in silico and in vitro approach. We constructed a Petri net model of Wnt/β-catenin signaling including main players from the plasma membrane (WNT ligands and receptors), cytoplasmic effectors and the downstream negative feedback target gene AXIN2. We validated that our model can be used to simulate both active (WNT stimulation) and hyperactive (GSK3 inhibition) signaling by comparing our simulation and experimental data. We used this experimentally validated model to get further insights into the effect of the negative feedback regulator AXIN2 upon WNT stimulation and observed an attenuated β-catenin stabilization. We furthermore simulated the effect of APC inactivating mutations, yielding a stabilization of β-catenin levels comparable to the Wnt-pathway activities observed in colorectal and breast cancer. Our model can be used for further investigation and viable predictions of the role of Wnt/β-catenin signaling in oncogenesis and development.

Logic programming to predict cell fate patterns and retrodict genotypes in organogenesis

Caenorhabditis elegans vulval development is a paradigm system for understanding cell differentiation in the process of organogenesis. Through temporal and spatial controls, the fate pattern of six cells is determined by the competition of the LET-23 and the Notch signalling pathways. Modelling cell fate determination in vulval development using state-based models, coupled with formal analysis techniques, has been established as a powerful approach in predicting the outcome of combinations of mutations. However, computing the outcomes of complex and highly concurrent models can become prohibitive. Here, we show how logic programs derived from state machines describing the differentiation of C. elegans vulval precursor cells can increase the speed of prediction by four orders of magnitude relative to previous approaches. Moreover, this increase in speed allows us to infer, or 'retrodict', compatible genomes from cell fate patterns. We exploit this technique to predict highly variable cell fate patterns resulting from dig-1 reduced-function mutations and let-23 mosaics. In addition to the new insights offered, we propose our technique as a platform for aiding the design and analysis of experimental data.

MODELING AND ANALYZING BIOLOGICAL SYSTEMS USING COLORED HIERARCHICAL PETRI NETS ILLUSTRATED BYC. ELEGANSVULVAL DEVELOPMENT

Colored Petri nets allow compact, parameterizable and scalable representations of large-scale biological models by encoding, e.g., species as colored tokens, and offer a variety of analysis techniques, e.g., structural analysis, simulation and model checking to analyze biological models. However, so far colored Petri nets have not been widely used and well explored in systems biology. In this paper, we aim to present a systematic approach to modeling and analyzing complex biological systems using colored Petri nets in order to help biologists to easily use them. We first describe a framework comprising a family of related colored Petri nets: colored qualitative Petri net (𝒬𝒫𝒩𝒞), colored stochastic Petri net (𝒮𝒫𝒩𝒞) and colored continuous Petri net (𝒞𝒫𝒩𝒞). They share structure, but are specialized by their kinetic information. Based on this framework, we present our colored Petri net approach to modeling and analyzing complex biological systems. First a biological system is modeled as a hierarchical 𝒬𝒫𝒩𝒞model, animated and analyzed by structural analysis; then it is converted into a 𝒮𝒫𝒩𝒞or 𝒞𝒫𝒩𝒞model, to be further analyzed using stochastic or continuous simulation, and simulative or numerical model checking. We demonstrate this approach using a nontrivial example, Caenorhabditis elegans vulval development.

Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model

Motivation: Combinatorial interactions of transcription factors with cis-regulatory elements control the dynamic progression through successive cellular states and thus underpin all metazoan development. The construction of network models of cis-regulatory elements, therefore, has the potential to generate fundamental insights into cellular fate and differentiation. Haematopoiesis has long served as a model system to study mammalian differentiation, yet modelling based on experimentally informed cis-regulatory interactions has so far been restricted to pairs of interacting factors. Here, we have generated a Boolean network model based on detailed cis-regulatory functional data connecting 11 haematopoietic stem/progenitor cell (HSPC) regulator genes.

Results: Despite its apparent simplicity, the model exhibits surprisingly complex behaviour that we charted using strongly connected components and shortest-path analysis in its Boolean state space. This analysis of our model predicts that HSPCs display heterogeneous expression patterns and possess many intermediate states that can act as ‘stepping stones’ for the HSPC to achieve a final differentiated state. Importantly, an external perturbation or ‘trigger’ is required to exit the stem cell state, with distinct triggers characterizing maturation into the various different lineages. By focusing on intermediate states occurring during erythrocyte differentiation, from our model we predicted a novel negative regulation of Fli1 by Gata1, which we confirmed experimentally thus validating our model. In conclusion, we demonstrate that an advanced mammalian regulatory network model based on experimentally validated cis-regulatory interactions has allowed us to make novel, experimentally testable hypotheses about transcriptional mechanisms that control differentiation of mammalian stem cells.

Contact:j.heringa@vu.nl or ioannis.xenarios@isb-sib.ch or bg200@cam.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Understanding cancer mechanisms through network dynamics

Cancer is a complex, multifaceted disease. Cellular systems are perturbed both during the onset and development of cancer, and the behavioural change of tumour cells usually involves a broad range of dynamic variations. To an extent, the difficulty of monitoring the systemic change has been alleviated by recent developments in the high-throughput technologies. At both the genomic as well as proteomic levels, the technological advances in microarray and mass spectrometry, in conjunction with computational simulations and the construction of human interactome maps have facilitated the progress of identifying disease-associated genes. On a systems level, computational approaches developed for network analysis are becoming especially useful for providing insights into the mechanism behind tumour development and metastasis. This review emphasizes network approaches that have been developed to study cancer and provides an overview of our current knowledge of protein-protein interaction networks, and how their systemic perturbation can be analysed by two popular network simulation methods: Boolean network and ordinary differential equations.

Modeling and analysis of biopathways dynamics

Cellular processes are governed and coordinated by a multitude of biopathways. A pathway can be viewed as a complex network of biochemical reactions. The dynamics of this network largely determines the functioning of the pathway. Hence the modeling and analysis of biochemical networks dynamics is an important problem and is an active area of research. Here we review quantitative models of biochemical networks based on ordinary differential equations (ODEs). We mainly focus on the parameter estimation and sensitivity analysis problems and survey the current methods for tackling them. In this context we also highlight a recently developed probabilistic approximation technique using which these two problems can be considerably simplified.

The role of proteosome-mediated proteolysis in modulating potentially harmful transcription factor activity in Saccharomyces cerevisiae

MOTIVATION

The appropriate modulation of the stress response to variable environmental conditions is necessary to maintain sustained viability in Saccharomyces cerevisiae. Particularly, controlling the abundance of proteins that may have detrimental effects on cell growth is crucial for rapid recovery from stress-induced quiescence.

RESULTS

Prompted by qualitative modeling of the nutrient starvation response in yeast, we investigated in vivo the effect of proteolysis after nutrient starvation showing that, for the Gis1 transcription factor at least, proteasome-mediated control is crucial for a rapid return to growth. Additional bioinformatics analyses show that potentially toxic transcriptional regulators have a significantly lower protein half-life, a higher fraction of unstructured regions and more potential PEST motifs than the non-detrimental ones. Furthermore, inhibiting proteasome activity tends to increase the expression of genes induced during the Environmental Stress Response more than those in the rest of the genome. Our combined results suggest that proteasome-mediated proteolysis of potentially toxic transcription factors tightly modulates the stress response in yeast.

CONTACT

jasmin.fisher@microsoft.com

Quantitative variation in autocrine signaling and pathway crosstalk in the Caenorhabditis vulval network

BACKGROUND

Biological networks experience quantitative change in response to environmental and evolutionary variation. Computational modeling allows exploration of network parameter space corresponding to such variations. The intercellular signaling network underlying Caenorhabditis vulval development specifies three fates in a row of six precursor cells, yielding a quasi-invariant 3°3°2°1°2°3° cell fate pattern. Two seemingly conflicting verbal models of vulval precursor cell fate specification have been proposed: sequential induction by the EGF-MAP kinase and Notch pathways, or morphogen-based induction by the former.

RESULTS

To study the mechanistic and evolutionary system properties of this network, we combine experimental studies with computational modeling, using a model that keeps the network architecture constant but varies parameters. We first show that the Delta autocrine loop can play an essential role in 2° fate specification. With this autocrine loop, the same network topology can be quantitatively tuned to use in the six-cell-row morphogen-based or sequential patterning mechanisms, which may act singly, cooperatively, or redundantly. Moreover, different quantitative tunings of this same network can explain vulval patterning observed experimentally in C. elegans, C. briggsae, C. remanei, and C. brenneri. We experimentally validate model predictions, such as interspecific differences in isolated vulval precursor cell behavior and in spatial regulation of Notch activity.

CONCLUSIONS

Our study illustrates how quantitative variation in the same network comprises developmental patterning modes that were previously considered qualitatively distinct and also accounts for evolution among closely related species.

Structural analysis to determine the core of hypoxia response network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network's dynamics. The question that begs for an answer is how to identify the core that is representative of a network's dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.