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Mathematical Models for Immunology: Current State of the Art and Future Research Directions. Bull Math Biol 2016; 78:2091-2134. [PMID: 27714570 PMCID: PMC5069344 DOI: 10.1007/s11538-016-0214-9] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2016] [Accepted: 09/26/2016] [Indexed: 01/01/2023]
Abstract
The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.
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Chylek LA, Wilson BS, Hlavacek WS. Modeling biomolecular site dynamics in immunoreceptor signaling systems. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2015; 844:245-62. [PMID: 25480645 DOI: 10.1007/978-1-4939-2095-2_12] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.
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Affiliation(s)
- Lily A Chylek
- Department of Chemistry and Chemical Biology, Cornell University, 14853, Ithaca, NY, USA,
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Chylek LA, Holowka DA, Baird BA, Hlavacek WS. An Interaction Library for the FcεRI Signaling Network. Front Immunol 2014; 5:172. [PMID: 24782869 PMCID: PMC3995055 DOI: 10.3389/fimmu.2014.00172] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Accepted: 03/31/2014] [Indexed: 12/20/2022] Open
Abstract
Antigen receptors play a central role in adaptive immune responses. Although the molecular networks associated with these receptors have been extensively studied, we currently lack a systems-level understanding of how combinations of non-covalent interactions and post-translational modifications are regulated during signaling to impact cellular decision-making. To fill this knowledge gap, it will be necessary to formalize and piece together information about individual molecular mechanisms to form large-scale computational models of signaling networks. To this end, we have developed an interaction library for signaling by the high-affinity IgE receptor, FcεRI. The library consists of executable rules for protein–protein and protein–lipid interactions. This library extends earlier models for FcεRI signaling and introduces new interactions that have not previously been considered in a model. Thus, this interaction library is a toolkit with which existing models can be expanded and from which new models can be built. As an example, we present models of branching pathways from the adaptor protein Lat, which influence production of the phospholipid PIP3 at the plasma membrane and the soluble second messenger IP3. We find that inclusion of a positive feedback loop gives rise to a bistable switch, which may ensure robust responses to stimulation above a threshold level. In addition, the library is visualized to facilitate understanding of network circuitry and identification of network motifs.
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Affiliation(s)
- Lily A Chylek
- Department of Chemistry and Chemical Biology, Cornell University , Ithaca, NY , USA ; Los Alamos National Laboratory, Theoretical Division, Center for Non-linear Studies , Los Alamos, NM , USA
| | - David A Holowka
- Department of Chemistry and Chemical Biology, Cornell University , Ithaca, NY , USA
| | - Barbara A Baird
- Department of Chemistry and Chemical Biology, Cornell University , Ithaca, NY , USA
| | - William S Hlavacek
- Los Alamos National Laboratory, Theoretical Division, Center for Non-linear Studies , Los Alamos, NM , USA
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Chylek LA, Harris LA, Tung CS, Faeder JR, Lopez CF, Hlavacek WS. Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2014; 6:13-36. [PMID: 24123887 PMCID: PMC3947470 DOI: 10.1002/wsbm.1245] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2013] [Revised: 08/20/2013] [Accepted: 08/21/2013] [Indexed: 01/04/2023]
Abstract
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).
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Affiliation(s)
- Lily A. Chylek
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Leonard A. Harris
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania 15260, USA
| | - Chang-Shung Tung
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - James R. Faeder
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania 15260, USA
| | - Carlos F. Lopez
- Department of Cancer Biology and Center for Quantitative Sciences, Vanderbilt University School of Medicine, Nashville, Tennessee 37212, USA
| | - William S. Hlavacek
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Cheng X, Merchan L, Tchernookov M, Nemenman I. A large number of receptors may reduce cellular response time variation. Phys Biol 2013; 10:035008. [PMID: 23735700 DOI: 10.1088/1478-3975/10/3/035008] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Cells often have tens of thousands of receptors, even though only a few activated receptors can trigger full cellular responses. Reasons for the overabundance of receptors remain unclear. We suggest that, under certain conditions, the large number of receptors can result in a competition among receptors to be the first to activate the cell. The competition decreases the variability of the time to cellular activation, and hence results in a more synchronous activation of cells. We argue that, in simple models, this variability reduction does not necessarily interfere with the receptor specificity to ligands achieved by the kinetic proofreading mechanism. Thus cells can be activated accurately in time and specifically to certain signals. We predict the minimum number of receptors needed to reduce the coefficient of variation for the time to activation following binding of a specific ligand. Furthermore, we predict the maximum number of receptors so that the kinetic proofreading mechanism still can improve the specificity of the activation. These predictions fall in line with experimentally reported receptor numbers for multiple systems.
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Affiliation(s)
- Xiang Cheng
- Department of Physics, Emory University, Atlanta, GA 30322, USA.
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Blinov ML, Moraru II. Leveraging modeling approaches: reaction networks and rules. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2013; 736:517-30. [PMID: 22161349 DOI: 10.1007/978-1-4419-7210-1_30] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We have witnessed an explosive growth in research involving mathematical models and computer simulations of intracellular molecular interactions, ranging from metabolic pathways to signaling and gene regulatory networks. Many software tools have been developed to aid in the study of such biological systems, some of which have a wealth of features for model building and visualization, and powerful capabilities for simulation and data analysis. Novel high-resolution and/or high-throughput experimental techniques have led to an abundance of qualitative and quantitative data related to the spatiotemporal distribution of molecules and complexes, their interactions kinetics, and functional modifications. Based on this information, computational biology researchers are attempting to build larger and more detailed models. However, this has proved to be a major challenge. Traditionally, modeling tools require the explicit specification of all molecular species and interactions in a model, which can quickly become a major limitation in the case of complex networks - the number of ways biomolecules can combine to form multimolecular complexes can be combinatorially large. Recently, a new breed of software tools has been created to address the problems faced when building models marked by combinatorial complexity. These have a different approach for model specification, using reaction rules and species patterns. Here we compare the traditional modeling approach with the new rule-based methods. We make a case for combining the capabilities of conventional simulation software with the unique features and flexibility of a rule-based approach in a single software platform for building models of molecular interaction networks.
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Affiliation(s)
- Michael L Blinov
- Center for Cell Analysis and Modeling, University of Connecticut Health Center, Farmington, CT, USA.
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Kolczyk K, Samaga R, Conzelmann H, Mirschel S, Conradi C. The Process-Interaction-Model: a common representation of rule-based and logical models allows studying signal transduction on different levels of detail. BMC Bioinformatics 2012; 13:251. [PMID: 23020215 PMCID: PMC3598730 DOI: 10.1186/1471-2105-13-251] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2012] [Accepted: 09/21/2012] [Indexed: 02/07/2023] Open
Abstract
Background Signaling systems typically involve large, structured molecules each consisting of a large number of subunits called molecule domains. In modeling such systems these domains can be considered as the main players. In order to handle the resulting combinatorial complexity, rule-based modeling has been established as the tool of choice. In contrast to the detailed quantitative rule-based modeling, qualitative modeling approaches like logical modeling rely solely on the network structure and are particularly useful for analyzing structural and functional properties of signaling systems. Results We introduce the Process-Interaction-Model (PIM) concept. It defines a common representation (or basis) of rule-based models and site-specific logical models, and, furthermore, includes methods to derive models of both types from a given PIM. A PIM is based on directed graphs with nodes representing processes like post-translational modifications or binding processes and edges representing the interactions among processes. The applicability of the concept has been demonstrated by applying it to a model describing EGF insulin crosstalk. A prototypic implementation of the PIM concept has been integrated in the modeling software ProMoT. Conclusions The PIM concept provides a common basis for two modeling formalisms tailored to the study of signaling systems: a quantitative (rule-based) and a qualitative (logical) modeling formalism. Every PIM is a compact specification of a rule-based model and facilitates the systematic set-up of a rule-based model, while at the same time facilitating the automatic generation of a site-specific logical model. Consequently, modifications can be made on the underlying basis and then be propagated into the different model specifications – ensuring consistency of all models, regardless of the modeling formalism. This facilitates the analysis of a system on different levels of detail as it guarantees the application of established simulation and analysis methods to consistent descriptions (rule-based and logical) of a particular signaling system.
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Affiliation(s)
- Katrin Kolczyk
- Max Planck Institute Magdeburg, 39106 Magdeburg, Sandtorstr. 1, Germany.
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Barua D, Hlavacek WS, Lipniacki T. A computational model for early events in B cell antigen receptor signaling: analysis of the roles of Lyn and Fyn. THE JOURNAL OF IMMUNOLOGY 2012; 189:646-58. [PMID: 22711887 DOI: 10.4049/jimmunol.1102003] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
BCR signaling regulates the activities and fates of B cells. BCR signaling encompasses two feedback loops emanating from Lyn and Fyn, which are Src family protein tyrosine kinases (SFKs). Positive feedback arises from SFK-mediated trans phosphorylation of BCR and receptor-bound Lyn and Fyn, which increases the kinase activities of Lyn and Fyn. Negative feedback arises from SFK-mediated cis phosphorylation of the transmembrane adapter protein PAG1, which recruits the cytosolic protein tyrosine kinase Csk to the plasma membrane, where it acts to decrease the kinase activities of Lyn and Fyn. To study the effects of the positive and negative feedback loops on the dynamical stability of BCR signaling and the relative contributions of Lyn and Fyn to BCR signaling, we consider in this study a rule-based model for early events in BCR signaling that encompasses membrane-proximal interactions of six proteins, as follows: BCR, Lyn, Fyn, Csk, PAG1, and Syk, a cytosolic protein tyrosine kinase that is activated as a result of SFK-mediated phosphorylation of BCR. The model is consistent with known effects of Lyn and Fyn deletions. We find that BCR signaling can generate a single pulse or oscillations of Syk activation depending on the strength of Ag signal and the relative levels of Lyn and Fyn. We also show that bistability can arise in Lyn- or Csk-deficient cells.
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Affiliation(s)
- Dipak Barua
- Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Geier F, Fengos G, Iber D. A computational analysis of the dynamic roles of talin, Dok1, and PIPKI for integrin activation. PLoS One 2011; 6:e24808. [PMID: 22110576 PMCID: PMC3217926 DOI: 10.1371/journal.pone.0024808] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2011] [Accepted: 08/22/2011] [Indexed: 12/12/2022] Open
Abstract
Integrin signaling regulates cell migration and plays a pivotal role in developmental processes and cancer metastasis. Integrin signaling has been studied extensively and much data is available on pathway components and interactions. Yet the data is fragmented and an integrated model is missing. We use a rule-based modeling approach to integrate available data and test biological hypotheses regarding the role of talin, Dok1 and PIPKI in integrin activation. The detailed biochemical characterization of integrin signaling provides us with measured values for most of the kinetics parameters. However, measurements are not fully accurate and the cellular concentrations of signaling proteins are largely unknown and expected to vary substantially across different cellular conditions. By sampling model behaviors over the physiologically realistic parameter range we find that the model exhibits only two different qualitative behaviors and these depend mainly on the relative protein concentrations, which offers a powerful point of control to the cell. Our study highlights the necessity to characterize model behavior not for a single parameter optimum, but to identify parameter sets that characterize different signaling modes.
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Affiliation(s)
- Florian Geier
- Department of Biosystems Science and Engineering (D-BSSE), ETH Zürich, Basel, Switzerland
| | - Georgios Fengos
- Department of Biosystems Science and Engineering (D-BSSE), ETH Zürich, Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering (D-BSSE), ETH Zürich, Basel, Switzerland
- * E-mail:
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Chylek LA, Hu B, Blinov ML, Emonet T, Faeder JR, Goldstein B, Gutenkunst RN, Haugh JM, Lipniacki T, Posner RG, Yang J, Hlavacek WS. Guidelines for visualizing and annotating rule-based models. MOLECULAR BIOSYSTEMS 2011; 7:2779-95. [PMID: 21647530 PMCID: PMC3168731 DOI: 10.1039/c1mb05077j] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.
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Affiliation(s)
- Lily A Chylek
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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