Stochastic niche structure and diversity maintenance in the T cell repertoire

Stirk, Emily R.; Molina-Parı́s, Carmen; Berg, Hugo van den

doi:10.1016/j.jtbi.2008.07.017

Cited by 43 publications

(66 citation statements)

References 55 publications

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“…Instrumental to this mechanism is the relationship between clonal lifetime and antigenic overlap with other clones. We previously investigated this relationship for moderate antigenic overlap, treating clonal size as a stochastic univariate birth and death process (Stirk et al, 2008). We here extend the analysis to the case of non-negligible antigenic overlap.…”

Section: Introductionmentioning

confidence: 93%

“…Thus, all clonotypes other than i are treated as part of the average background of competition (Stirk et al, 2008). We here consider the case of a pair of T cell clonotypes, i and j, such that Fig.…”

Section: Stochastic Model For a Pair Of Competing Clonotypesmentioning

confidence: 99%

“…where the approximation represents the mean-field character of the background clones (the argument is essentially the same as that given in Stirk et al, 2008). According to this approximation, Λ 1 depends only on the number of cells of clonotype 1 and clonotype 2 and the average clonal size n but not explicitly on the number of T cells belonging to other clonotypes.…”

Section: Derivation Of the Birth And Death Ratesmentioning

confidence: 99%

“…Without loss of generality, we may assume thatt 1 ≤t 2 . For t <t 2 only one of the clonotypes is extant in the repertoire, in which case the univariate model introduced in Stirk et al (2008) may be applied. We model the number of T cells of clonotypes 1 and 2 as a continuous-time bivariate Markov process {(X (t), Y(t)) : t ≥t 2 } on the state space S = {(n 1 , n 2 ) : n 1 , n 2 = 0, 1, 2, .…”

Section: Competition Processmentioning

confidence: 99%

“…The diagram on the left shows the repertoire analysed in Stirk et al (2008). The situation on the right is considered in this paper, where |Q i ∩ Q k | |Q i | and |Q j ∩ Q k | |Q k | for all k = i, j.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

Stirk

Lythe

Berg

et al. 2010

Journal of Theoretical Biology

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Recognition of antigens by the adaptive immune system relies on a highly diverse T cell receptor repertoire. The mechanism that maintains this diversity is based on competition for survival stimuli; these stimuli depend upon weak recognition of self-antigens by the T cell antigen receptor. We study the dynamics of diversity maintenance as a stochastic competition process between a pair of T cell clonotypes that are similar in terms of the self-antigens they recognise. We formulate a bivariate continuous-time Markov process for the numbers of T cells belonging to the two clonotypes. We prove that the ultimate fate of both clonotypes is extinction and provide a bound on mean extinction times. We focus on the case where the two clonotypes exhibit negligible competition with other T cell clonotypes in the repertoire, since this case provides an upper bound on the mean extinction times. As the two clonotypes become more similar in terms of the self-antigens they recognise, one clonotype quickly becomes extinct in a process resembling classical competitive exclusion. We study the limiting probability distribution for the bivariate process, conditioned on non-extinction of both clonotypes. Finally, we derive deterministic equations for the number of cells belonging to each clonotype as well as a linear Fokker-Planck equation for the fluctuations about the deterministic stable steady state.

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Section: Introductionmentioning

confidence: 93%

Section: Stochastic Model For a Pair Of Competing Clonotypesmentioning

confidence: 99%

Section: Derivation Of the Birth And Death Ratesmentioning

confidence: 99%

Section: Competition Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

Stirk

Lythe

Berg

et al. 2010

Journal of Theoretical Biology

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Mathematical Models and Immune Cell Biology

Molina-Parı́s¹,

Lythe²

2011

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We discuss continuum (lattice-free) and inherently stochastic models of immune cellular interactions, using the simplest hypothesis, that cells follow Brownian paths. The timescale for a cell to explore a volume such as a lymph node is L 2 =D, where L is the radius of the region and D the diffusivity of a cell. The average time a cell spends in a volume with an exit is proportional to L 3 =aD, where a is the radius of the exit. The mean time before a cell encounters a zone of attraction with radius b around, for example, an antigen presenting cell, is proportional to L 3 =bD.

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Stochastic Modelling of T Cell Homeostasis for Two Competing Clonotypes Via the Master Equation

MacNamara¹,

Burrage

2011

Mathematical Models and Immune Cell Biology

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Stochastic niche structure and diversity maintenance in the T cell repertoire

Cited by 43 publications

References 55 publications

Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

Mathematical Models and Immune Cell Biology

Stochastic Modelling of T Cell Homeostasis for Two Competing Clonotypes Via the Master Equation

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