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  • Review Article
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Mathematical and computational models of immune-receptor signalling

Nature Reviews Immunology volume 4, pages 445–456 (2004)Cite this article

Key Points

  • The subunits of the immune receptors that participate in signalling have at least one tyrosine-based activation motif in their cytoplasmic domains. Signalling is initiated by the phosphorylation of canonical tyrosine residues that are located in these domains. The phosphorylated forms of the cytoplasmic domains, and other scaffolding proteins, nucleate the association of kinases, phosphatases and adaptors, but the binding is reversible and the structures that form are temporary.

  • We review simple and detailed mathematical models of immune-receptor signalling and what we have learned from them.

  • The serial triggering of T-cell receptors has been suggested to explain how a small number of peptide–MHC complexes displayed on antigen-presenting cells can trigger the downregulation of the cell-surface expression of a large number of T-cell receptors.

  • From the binding properties and concentrations of the interacting ligands and receptors, it is straightforward to decide whether serial engagement occurs. However, a model of cell signalling must associate the lifetime of the bound ligand–receptor complex with a cellular response. McKeithan's simple kinetic proofreading model captures an important feature of the signalling cascade — that there is a temporal delay between binding and signalling.

  • Serial engagement requires rapid dissociation. Kinetic proofreading requires receptors to remain bound to ligands for long enough for the appropriate signalling complexes to form. For T-cell activation, competition between serial engagement and kinetic proofreading leads to the prediction that maximal signal generation occurs for an intermediate value of the lifetime of the ligand–receptor bond.

  • Detailed models comprise a limited set of proteins that participate in cell signalling and the interactions that are assumed to occur between them. Unlike simple models, these models can make predictions about the states of the individual components, while providing insights into how the components function together as a system. Although few such models have been developed for immune-receptor signalling, the present examples indicate that these models will become an important part of ongoing efforts to understanding cell signalling at the molecular level.

  • One impediment to creating and understanding detailed models is the problem of combinatorial complexity: because components can be modified and combine in many ways, the number of possible complexes that can form during a signalling cascade is exceedingly large. As a result, signalling cascades are large temporal biochemical networks and not simple chemical pathways.

Abstract

The process of signalling through receptors of the immune system involves highly connected networks of interacting components. Understanding the often counter-intuitive behaviour of these networks requires the development of mathematical and computational models. Here, we focus on the application of these models to understand signalling through immune receptors that are involved in antigen recognition. Simple models, which ignore the details of the signalling machinery, have provided considerable insight into how ligand–receptor binding properties affect signalling outcomes. Detailed models, which include specific molecular components and interactions beyond the ligand and receptor, are difficult to develop but have already provided new mechanistic understanding and uncovered relationships that are difficult to detect by experimental observation alone. They offer hope that models might eventually predict the full spectrum of signalling behaviour.

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Figure 1: Initiation of immune-receptor signalling.
Figure 2: Escape from kinetic proofreading.
Figure 3: Production of activated messengers and fully modified receptors in a single T cell, as a function of time after ligand stimulation.
Figure 4: Detailed model of early events in FcεRI signalling.
Figure 5: Effect on signalling events of varying the ligand–receptor off-rate in two detailed models.

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Acknowledgements

We thank the anonymous reviewers for constructive comments. This work was supported by grants from the National Institutes of Health and the US Department of Energy.

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Authors and Affiliations

  1. Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Byron Goldstein, James R. Faeder & William S. Hlavacek

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  1. Byron Goldstein
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DATABASES

Entrez Gene

CD2AP

CD3ζ

CD69

FOS

CSK

FYN

LCK

LYN

monocyte chemotactic protein 1

SYK

ZAP70

FURTHER INFORMATION

Systems Biology Markup Language

Kinetikit

Glossary

MULTICHAIN IMMUNE-RECOGNITION RECEPTOR

(MIRR). The prototypical members of the MIRR family are the B-cell receptor, the T-cell receptor and the high-affinity IgE receptor (FcεRI). Each of these cell-surface receptors is multimeric and involved in antigen recognition.

SRC HOMOLOGY 2 DOMAINS

(SH2 domains). Protein domains that bind phosphorylated tyrosine residues and are present in many signalling proteins, including the kinases of the SRC and SYK (spleen tyrosine kinase) families.

RATE CONSTANTS

Parameters with a constant value in a mathematical expression for the rate of a chemical reaction. The rate of the elementary chemical reaction A→B is given by k[A], where k is the rate constant and [A] is the concentration of species A.

PARTIAL DIFFERENTIAL EQUATIONS

(PDEs). Differential equations that involve more than one independent variable. Often the independent variables of interest are time and position in space.

ORDINARY DIFFERENTIAL EQUATIONS

(ODEs). Differential equations that involve only one independent variable, such as d[A]/dt = −k[A], where the independent variable is time (t), and the concentration of the species [A] is a dependent variable that depends on t. k is the rate constant. A system of ODEs involves multiple dependent variables, all of which are functions of the same independent variable.

LIPID RAFTS

Lipid rafts are microdomains of the cell membrane that are enriched in sphingolipids. Several membrane-associated signalling molecules, such as LYN, are concentrated in these rafts.

IMMUNOLOGICAL SYNAPSE

A stable region of contact between a T cell and an antigen-presenting cell that forms through cell–cell interaction of adhesion molecules. The mature immunological synapse contains two distinct, stable membrane domains: a central cluster of TCRs, known as the central supramolecular activation cluster (cSMAC) and a surrounding ring of adhesion molecules known as the peripheral supramolecular activation cluster (pSMAC).

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Goldstein, B., Faeder, J. & Hlavacek, W. Mathematical and computational models of immune-receptor signalling. Nat Rev Immunol 4, 445–456 (2004). https://doi.org/10.1038/nri1374

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