Journal of Statistical Physics

, Volume 128, Issue 1–2, pp 393–411 | Cite as

Cytotoxic Killing and Immune Evasion by Repair

  • Cliburn Chan
  • Andrew J. T. George
  • Jaroslav StarkEmail author


The interaction between the immune system and pathogens is a complex one, with pathogens constantly developing new ways of evading destruction by the immune system. The immune system's task is made even harder when the pathogen in question is an intra-cellular one (such as a virus or certain bacteria) and it is necessary to kill the infected host cell in order to eliminate the pathogen. This causes damage to the host, and such killing therefore needs to be carefully controlled, particularly in tissues with poor regenerative potential, or those involved in the immune response itself. Host cells therefore possess repair mechanisms which can counteract killing by immune cells. These in turn can be subverted by pathogens which up-regulate the resistance of infected cells to killing. In this paper, we explore the hypothesis that this repair process plays an important role in determining the efficacy of evasion and escape from immune control. We model a situation where cytotoxic T lymphocytes (CTL) and natural killer (NK) cells kill pathogen-infected and tumour cells by directed secretion of preformed granules containing perforin and granzymes. Resistance to such killing can be conferred by the expression of serine protease inhibitors (serpins). These are utilized by several virally infected and tumour cells, as well as playing a role in the protection of host bystander, immune and immuneprivileged cells. We build a simple stochastic model of cytotoxic killing, where serpins can neutralize granzymes stoichiometrically by forming an irreversible complex, and the survival of the cell is determined by the balance between serpin depletion and replenishment, which in its simplest form is equivalent to the well known shot noise process. We use existing analytical results for this process, and additional simulations to analyse the effects of repair on cytotoxic killing. We then extend the model to the case of a replicating target cell population, which gives a branching process coupled to shot noise. We show how the process of repair can have a major impact on the dynamics of pathogen evasion and escape of tumour cells from immune surveillance


Cytotoxic killing granzyme serpin repair immune evasion shot noise mean first passage time 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Cliburn Chan
    • 1
    • 2
  • Andrew J. T. George
    • 1
  • Jaroslav Stark
    • 3
    Email author
  1. 1.Department of Immunology, Division of MedicineFaculty of Medicine Imperial College LondonLondonUK
  2. 2.Department of Biostatistics and BioinformaticsDuke University Laboratory of Computational Immunology, Center for Bioinformatics and Computational BiologyDurhamUSA
  3. 3.Department of MathematicsImperial College LondonLondonUK

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