Modelling in immunology

Speakers and provisional programme

• 9:30-10:30

  Andrew George (Imperial College London)

  Extraordinary specificity and sensitivity - the story of the T cell

  In most sensing systems there is a trade off between specificity and sensitivity. However, the T cell is remarkable in being able to respond to antigen with both exquisite sensitivity (responding to as few as 1-10 peptide MHC complexes) and also extreme sensitivity (with single amino acid substitutions altering the response). For this to occur it is necessary for there to be mechanisms that operate at the level of the T cell receptor, that integrate the signals at the level of the cell and finally to interact at the level of the population of responding cells. We have shown that enzymatic feedback pathways can contribute to specificity at the level of the receptor. However, these are not enough, and stochastic dissociation means that cross talk between receptors and some integration of signals at the level of the cell is important. In addition, the induction of anergic signals by weak ligands prevents a ``Russian roulette'' activation of T cells by suboptimal ligands. Thus consideration of the system at three levels is necessary if we are to understand how T cell responses manage to combine sensitivity and specificity.
• 10:30-11:30

  Ed Evans (Oxford)

  Quantitative analysis of the ensemble behaviour of T-cell surface receptors

  Most proteins on the lymphocyte cell surface have now been identified. The new challenge is to understand the nature of their interactions and hence their function. The complex array of responses each of these cells can make on encountering other cells and the huge number of different molecules involved means that studies of single receptors in isolation are unlikely to give a clear understanding of their roles. We have begun to model the behavior of small sets of T-cell surface molecules using rigorously determined biophysical parameters and expression levels to understand the sources of complexity in T-cell responses. Initial work simulating the synaptic accumulation of costimulatory or inhibitory complexes formed between CD28 or CTLA-4 and B7-1 or B7-2 showed the importance of these parameters and of competition effects on functional outcomes. Further studies of the interactions of the coreceptor CD4 shows how proper modeling of its biophysical properties limits the possibilities for its function. Finally, preliminary work on the random interactions possible between molecules in the T cell membrane or between these molecules and those in the cytoplasm suggest refinements to the kinetic proof-reading model showing that the capacity for differential signaling is intrinsic to the architecture of the T-cell receptor triggering apparatus itself. Overall, our initial forays into the modeling of complex systems based on firm biophysical data have highlighted the importance of cross-reactivity, competition and hierarchies of affinities between leukocyte surface molecules.
• 11:30-12:00 coffee
• 12:00-1:00

  Shev MacNamara (Oxford)

  Stochastic modeling of T cell homeostasis for two competing clonotypes via the master equation

  Stochastic models for competing clonotypes of T cells by multivariate, continuous- time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-Paris and van den Berg (2008). A stochastic modeling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability-density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.
• 1:00-2:00 lunch
• 2:00-3:00

  Thomas Höfer (Heidelberg)

  Mathematical models for proliferation and differentiation decisions of T cells

  The last decade has seen an enormous advance of our knowledge on the molecules of the immune system and their interactions. By comparison, we still know rather little about the dynamics of the regulatory networks that are formed by the molecular players. We have developed an iterative approach of experimentation and mathematical modelling to dissect the regulatory networks that govern the proliferation and differentiation decisions of T cells. The models address different levels of molecular organization, including the activation of a gene in its chromatin context, the kinetics of gene-regulatory networks and spatio-temporal patterns in intercellular signalling. Both qualitative analyses of dynamic behavior and quantitative techniques for parameter estimation and model selection are being employed. In this talk, I will show how such mechanistically-based kinetic analyses have helped to uncover the origin of stochastic regulation of cytokine genes, find novel regulatory interactions in gene networks, and identify emergent phenomena that underlie the decision of a cell to proliferate upon antigenic stimulation.
• 3:00-4:00

  Andrew Sewell (Cardiff)

  Better T-cell immunity: you can improve any antigen and you can improve any T-cell receptor

• 4:00-4:30

  Andrew Phillips

  A dynamical systems model of relative MHC class I antigen presentation

  MHC class I molecules direct cytotoxic T lymphocytes to destroy virus-infected or cancerous cells, thereby preventing disease progression. MHC class I functions as a molecular detector by binding to peptides arising from intracellular protein turnover and by presenting these peptides at the cell surface. Peptides are selected for presentation on the basis of their ability to form a stable complex with MHC class I, by a process known as peptide editing. A better understanding of the molecular mechanisms underpinning the editing and relative presentation of peptides is important for our understanding of immunodominance, the predominance of some T lymphocyte specificities over others, which can determine the efficacy of an immune response, the danger of immune evasion, and the success of vaccination strategies. To aid our understanding of peptide editing we have created a dynamical systems model that can be used to predict the relative presentation of peptides for different MHC class I alleles. The model proposes a principle of peptide filtering to quantify relative presentation as a function of peptide supply and stability of the MHC class I-peptide complex. It also takes into account the effects of the chaperone molecule tapasin, which has been shown to influence the relative presentation of peptides to different extents for different MHC class I alleles. The model is in agreement with recent experimental observations of peptide editing both over time and at steady state, and forms the basis of a powerful predictive tool. The model is used to predict the relative presentation of Human Immunodeficiency Virus peptides by MHC class I.
• 4:30-5:00 Round table discussion: Joined-up Immunology