Rule-Based Modelling and Model Perturbation

Scalable reaction network modeling with automatic validation of consistency in Event-B

Constructing a large biological model is a difficult, error-prone process. Small errors in writing a part of the model cascade to the system level and their sources are difficult to trace back. In this paper we extend a recent approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to validate for model consistency step-by-step in an automated way. We demonstrate this approach on a model of the heat shock response in eukaryotes and its scalability on a model of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {ErbB}$$\end{document}ErbB signaling pathway. All consistency properties of the model were proved automatically with computer support.

Bio-Curation for Cellular Signalling: The KAMI Project

The general question of what constitutes bio-curation for rule-based modelling of cellular signalling is posed. A general approach to the problem is presented, based on rewriting in hierarchies of graphs, together with a specific instantiation of the methodology that addresses our particular bio-curation problem. The current state of the ongoing development of the KAMI bio-curation tool, based on this approach, is outlined along with our plans for future development.

Rule-based modelling provides an extendable framework for comparing candidate mechanisms underpinning clathrin polymerisation

Polymerisation of clathrin is a key process that underlies clathrin-mediated endocytosis. Clathrin-coated vesicles are responsible for cell internalization of external substances required for normal homeostasis and life –sustaining activity. There are several hypotheses describing formation of closed clathrin structures. According to one of the proposed mechanisms cage formation may start from a flat lattice buildup on the cellular membrane, which is later transformed into a curved structure. Creation of the curved surface requires rearrangement of the lattice, induced by additional molecular mechanisms. Different potential mechanisms require a modeling framework that can be easily modified to compare between them. We created an extendable rule-based model that describes polymerisation of clathrin molecules and various scenarios of cage formation. Using Global Sensitivity Analysis (GSA) we obtained parameter sets describing clathrin pentagon closure and the emergence/production and closure of large-size clathrin cages/vesicles. We were able to demonstrate that the model can reproduce budding of the clathrin cage from an initial flat array.

Generalizing Gillespie's Direct Method to Enable Network-Free Simulations

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

Dynamic Influence Networks for Rule-Based Models

We introduce the Dynamic Influence Network (DIN), a novel visual analytics technique for representing and analyzing rule-based models of protein-protein interaction networks. Rule-based modeling has proved instrumental in developing biological models that are concise, comprehensible, easily extensible, and that mitigate the combinatorial complexity of multi-state and multi-component biological molecules. Our technique visualizes the dynamics of these rules as they evolve over time. Using the data produced by KaSim, an open source stochastic simulator of rule-based models written in the Kappa language, DINs provide a node-link diagram that represents the influence that each rule has on the other rules. That is, rather than representing individual biological components or types, we instead represent the rules about them (as nodes) and the current influence of these rules (as links). Using our interactive DIN-Viz software tool, researchers are able to query this dynamic network to find meaningful patterns about biological processes, and to identify salient aspects of complex rule-based models. To evaluate the effectiveness of our approach, we investigate a simulation of a circadian clock model that illustrates the oscillatory behavior of the KaiC protein phosphorylation cycle.

From word models to executable models of signaling networks using automated assembly

Word models (natural language descriptions of molecular mechanisms) are a common currency in spoken and written communication in biomedicine but are of limited use in predicting the behavior of complex biological networks. We present an approach to building computational models directly from natural language using automated assembly. Molecular mechanisms described in simple English are read by natural language processing algorithms, converted into an intermediate representation, and assembled into executable or network models. We have implemented this approach in the Integrated Network and Dynamical Reasoning Assembler (INDRA), which draws on existing natural language processing systems as well as pathway information in Pathway Commons and other online resources. We demonstrate the use of INDRA and natural language to model three biological processes of increasing scope: (i) p53 dynamics in response to DNA damage, (ii) adaptive drug resistance in BRAF‐V600E‐mutant melanomas, and (iii) the RAS signaling pathway. The use of natural language makes the task of developing a model more efficient and it increases model transparency, thereby promoting collaboration with the broader biology community.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Kappa rule-based modeling in synthetic biology

Rule-based modeling, an alternative to traditional reaction-based modeling, allows us to intuitively specify biological interactions while abstracting from the underlying combinatorial complexity. One such rule-based modeling formalism is Kappa, which we introduce to readers in this chapter. We discuss the application of Kappa to three modeling scenarios in synthetic biology: a unidirectional switch based on nitrosylase induction in Saccharomyces cerevisiae, the repressilator in Escherichia coli formed from BioBrick parts, and a light-mediated extension to said repressilator developed by the University of Edinburgh team during iGEM 2010. The second and third scenarios in particular form a case-based introduction to the Kappa BioBrick Framework, allowing us to systematically address the modeling of devices and circuits based on BioBrick parts in Kappa. Through the use of these examples, we highlight the ease with which Kappa can model biological interactions both at the genetic and the protein-protein interaction level, resulting in detailed stochastic models accounting naturally for transcriptional and translational resource usage. We also hope to impart the intuitively modular nature of the modeling processes involved, supported by the introduction of visual representations of Kappa models. Concluding, we explore future endeavors aimed at making modeling of synthetic biology more user-friendly and accessible, taking advantage of the strengths of rule-based modeling in Kappa.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

Programming biological models in Python using PySB

PySB is a framework for creating biological models as Python programs using a high-level, action-oriented vocabulary that promotes transparency, extensibility and reusability. PySB interoperates with many existing modeling tools and supports distributed model development.

PySB models are programs and leverage existing programming tools for documentation, testing, and collaborative development.

Reusable functions can encode common low-level biochemical processes as well as high-level modules, making models transparent and concise.

Modeling workflow is accelerated through close integration with Python numerical tools and interoperability with existing modeling software.

We demonstrate the use of PySB to encode 15 alternative hypotheses for the mitochondrial regulation of apoptosis, including a new ‘Embedded Together' model based on recent biochemical findings.

Mathematical equations are fundamental to modeling biological networks, but as networks get large and revisions frequent, it becomes difficult to manage equations directly or to combine previously developed models. Multiple simultaneous efforts to create graphical standards, rule-based languages, and integrated software workbenches aim to simplify biological modeling but none fully meets the need for transparent, extensible, and reusable models. In this paper we describe PySB, an approach in which models are not only created using programs, they are programs. PySB draws on programmatic modeling concepts from little b and ProMot, the rule-based languages BioNetGen and Kappa and the growing library of Python numerical tools. Central to PySB is a library of macros encoding familiar biochemical actions such as binding, catalysis, and polymerization, making it possible to use a high-level, action-oriented vocabulary to construct detailed models. As Python programs, PySB models leverage tools and practices from the open-source software community, substantially advancing our ability to distribute and manage the work of testing biochemical hypotheses. We illustrate these ideas using new and previously published models of apoptosis.

Evolution of the cognitive proteome: from static to dynamic network models

Integrative analysis of the neuronal synapse proteome has uncovered an evolutionarily conserved signalling complex that underpins the cognitive capabilities of the brain. Highly dynamic, cell type specific and intricately regulated, the synaptic proteome presents many challenges to systems biology approaches, yet this is likely to be the best route to unlock a new generation of neuroscience research and CNS drug development that society so urgently demands. Most systems biology approaches today have focussed on exploiting protein-protein interaction data to their fullest extent within static interaction models. These have revealed structure-function relationships within the protein network, uncovered new candidate genes for genetic studies and drug research and development and finally provided a means to study the evolution of the system. The rapid maturation of medium and high-throughput biochemical technologies means that dissecting the synapse proteome's dynamic complexity is fast becoming a reality. Here we look at these new challenges and explore rule-based modelling as a basis for a new generation of synaptic models.

Towards a quantitative model of the post-synaptic proteome

The postsynaptic compartment of the excitatory glutamatergic synapse contains hundreds of distinct polypeptides with a wide range of functions (signalling, trafficking, cell-adhesion, etc.). Structural dynamics in the post-synaptic density (PSD) are believed to underpin cognitive processes. Although functionally and morphologically diverse, PSD proteins are generally enriched with specific domains, which precisely define the mode of clustering essential for signal processing. We applied a stochastic calculus of domain binding provided by a rule-based modelling approach to formalise the highly combinatorial signalling pathway in the PSD and perform the numerical analysis of the relative distribution of protein complexes and their sizes. We specified the combinatorics of protein interactions in the PSD by rules, taking into account protein domain structure, specific domain affinity and relative protein availability. With this model we interrogated the critical conditions for the protein aggregation into large complexes and distribution of both size and composition. The presented approach extends existing qualitative protein-protein interaction maps by considering the quantitative information for stoichiometry and binding properties for the elements of the network. This results in a more realistic view of the postsynaptic proteome at the molecular level.