An Introduction to Rule-based Modeling of Immune Receptor Signaling

Cells process external and internal signals through chemical interactions. Cells that constitute the immune system (e.g., antigen presenting cell, T-cell, B-cell, mast cell) can have different functions (e.g., adaptive memory, inflammatory response) depending on the type and number of receptor molecules on the cell surface and the specific intracellular signaling pathways activated by those receptors. Explicitly modeling and simulating kinetic interactions between molecules allows us to pose questions about the dynamics of a signaling network under various conditions. However, the application of chemical kinetics to biochemical signaling systems has been limited by the complexity of the systems under consideration. Rule-based modeling (BioNetGen, Kappa, Simmune, PySB) is an approach to address this complexity. In this chapter, by application to the Fc$\varepsilon$RI receptor system, we will explore the origins of complexity in macromolecular interactions, show how rule-based modeling can be used to address complexity, and demonstrate how to build a model in the BioNetGen framework. Open source BioNetGen software and documentation are available at http://bionetgen.org.Comment: 5 figure

Bayesian model comparison for compartmental models with applications in positron emission tomography

We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those that occur in the analysis of positron emission tomography (PET) data. Both modelling and computational issues are considered. Biophysically inspired informative priors are developed for the problem at hand, and by comparison with default vague priors it is shown that the proposed modelling is not overly sensitive to prior specification. It is also shown that an additive normal error structure does not describe measured PET data well, despite being very widely used, and that within a simple Bayesian framework simultaneous parameter estimation and model comparison can be performed with a more general noise model. The proposed approach is compared with standard techniques using both simulated and real data. In addition to good, robust estimation performance, the proposed technique provides, automatically, a characterisation of the uncertainty in the resulting estimates which can be considerable in applications such as PET

A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related (p)reprint

Advances in Rule-based Modeling: Compartments, Energy, and Hybrid Simulation, with Application to Sepsis and Cell Signaling

Biological systems are commonly modeled as reaction networks, which describe the system at the resolution of biochemical species. Cellular systems, however, are governed by events at a finer scale: local interactions among macromolecular domains. The multi-domain structure of macromolecules, combined with the local nature of interactions, can lead to a combinatorial explosion that pushes reaction network methods to their limits. As an alternative, rule-based models (RBMs) describe the domain-based structure and local interactions found in biological systems. Molecular complexes are represented by graphs: functional domains as vertices, macromolecules as groupings of vertices, and molecular bonding as edges. Reaction rules, which describe classes of reactions, govern local modifications to molecular graphs, such as binding, post-translational modification, and degradation. RBMs can be transformed to equivalent reaction networks and simulated by differential or stochastic methods, or simulated directly with a network-free approach that avoids the problem of combinatorial complexity. Although RBMs and network-free methods resolve many problems in systems modeling, challenges remain. I address three challenges here: (i) managing model complexity due to cooperative interactions, (ii) representing biochemical systems in the compartmental setting of cells and organisms, and (iii) reducing the memory burden of large-scale network-free simulations. First, I present a general theory of energy-based modeling within the BioNetGen framework. Free energy is computed under a pattern-based formalism, and contextual variations within reaction classes are enumerated automatically. Next, I extend the BioNetGen language to permit description of compartmentalized biochemical systems, with treatment of volumes, surfaces and transport. Finally, a hybrid particle/population method is developed to reduce memory requirements of network-free simulations. All methods are implemented and available as part of BioNetGen. The remainder of this work presents an application to sepsis and inflammation. A multi-organ model of peritoneal infection and systemic inflammation is constructed and calibrated to experiment. Extra-corporeal blood purification, a potential treatment for sepsis, is explored in silico. Model simulations demonstrate that removal of blood cytokines and chemokines is a sufficient mechanism for improved survival in sepsis. However, differences between model predictions and the latest experimental data suggest directions for further exploration

Simulating Apoptosis Using Discrete Methods: a Membrane System and a Stochastic Approach

Membrane Systems provide an intriguing method for modeling biological systems at a molecular level. The hierarchical structure of Membrane Systems lends itself readily to mimic the nature and behavior of cells.We have refined a technique for modeling the type I and type II FAS-induced apoptosis signalling cascade. Improve- ments over our previous modeling work on apoptosis include increased efficiency for storing and sorting waiting times of reactions, a nondeterministic approach for han- dling reactions competing over limited reactants and improvements, and refinements of the model reactions. The modular nature of our systems provides flexibility with respect to future discover- ies on the signal cascade. We provide a breakdown of our algorithms and explanations on improvements we have implemented. We also give an exhaustive comparison to an established ordinary differential equations technique. Based on the results of our sim- ulations, we conclude that Membrane Systems are a useful simulation tool in Systems Biology that could provide new insight into the subcellular processes, and provide also the argument that Membrane Systems may outperform ordinary differential equation simulations when simulating cascades of reactions (as they are observed in cells

Stochastic Approaches in P Systems for Simulating Biological Systems

Different stochastic strategies for modeling biological systems with P systems are reviewed in this paper, such as the multi-compartmental approach and dynamical probabilistic P systems. The respective results obtained from the simulations of a test case study (the quorum sensing phenomena in Vibrio Fischeri colonies) are shown, compared and discussed