Germinal center dynamics during acute and chronic infection

Samantha Erwin; Stanca M. Ciupe

doi:10.3934/mbe.2017037

Article Contents

2017, Volume 14, Issue 3: 655-671. Doi: 10.3934/mbe.2017037

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Germinal center dynamics during acute and chronic infection

Samantha Erwin and
Stanca M. Ciupe^,

460 McBryde Hall, Virginia Tech, Blacksburg, VA 24061, USA

* Corresponding author: Stanca M. Ciupe
* Corresponding author: Stanca M. Ciupe

Received: February 15, 2016

Accepted: October 11, 2016

Published: September 2017

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Abstract

The ability of the immune system to clear pathogens is limited during chronic virus infections where potent long-lived plasma and memory B-cells are produced only after germinal center B-cells undergo many rounds of somatic hypermutations. In this paper, we investigate the mechanisms of germinal center B-cell formation by developing mathematical models for the dynamics of B-cell somatic hypermutations. We use the models to determine how B-cell selection and competition for T follicular helper cells and antigen influences the size and composition of germinal centers in acute and chronic infections. We predict that the T follicular helper cells are a limiting resource in driving large numbers of somatic hypermutations and present possible mechanisms that can revert this limitation in the presence of non-mutating and mutating antigen.

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Mathematics Subject Classification: 92, 34.

Citation:

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Figure 1. Dynamics of model (2) applied to an acute infection

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Figure 2. Sensitivity Analysis

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Figure 3. Comparison of model (1)'s dynamics when $n$, $\alpha$ and $\sigma$ are varied

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Figure 4. B clone distribution in acute and chronic infections

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Figure 5. Comparison of model (3)'s dynamics when $f$ is varied

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Figure 6. Virus strains and B clone dynamics for slow mutating virus

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Figure 7. Models (3)-(4)'s dynamics

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Table 1. Variables and fixed parameter values.

Name	Value	Units	Description	Citation
$s_N$	$10^4$	cells per ml per day	Naive CD4 T-cell recruitment rate	[38]
$d_N$	$0.01$	per day	Naive CD4 T-cell death rate	[38]
$\alpha_N$	$1.8\times 10^{-11}$	ml per day per cell	Pre-Tfh cell production rate
$d_H$	$0.01$	per day	Pre-Tfh cell death rate	[38]
$d_G$	$0.01$	per day	Tfh cell death rate	[38]
$d$	$0.8$	per day	B-cell death rate	[11]
$\kappa$	$1.2$	per day	Plasma cells production rate
$\gamma$	$2$	per cell per day	Pre-Tfh cell differentiation rate	[36]
$\mu$	$2$	per cell per day	Antigen removal rate
$\eta$	$10^{-5}$	per cell per day	Tfh competition rate
$N(0)$	$10^6$	cells per ml	Initial amount of CD4 T cells	[38]
$H(0)$	0	cells per ml	Initial amount of Pre-Tfh cells
$G(0)$	0	cells per ml	Initial amount of Tfh cells
$B_0(0)$	3	cells	Initial amount of B-cells	[13,11]
$B_i(0)$	0	cells	Initial amount of B-cell clones
$P(0)$	0	cells	Initial amount of plasma cells
$V(0)$	$2\times 10^8$	per ml	Initial amount of non-mutating antigen	[9]

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Table 2. Parameter estimates and confidence intervals

Name	Units	Value	Description	Confidence Intervals
$\alpha$		27.469	B-cell offspring production rate	[14.015 40.924]
$\sigma$	ml per cell per day	$1.1 \times 10^{-5}$	Affinity maturation rate	[4.8 $\times 10^{-6}$ 1.7 $\times 10^{-5}$]

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