Autoimmunity as an immune defense against degenerative processes: a primary mathematical model illustrating the bright side of autoimmunity
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model contains partial differentials and as such can not currently be solved by existing CellML tools..
Model Structure
ABSTRACT: Self-tolerance, or the ability of the immune system to refrain from destroying the organism's own tissues, is a prerequisite for proper immune system operation. How such self-tolerance is achieved is still a subject of debate. The belief that autoimmunity poses a continuous threat to the organism was challenged by data demonstrating that autoimmunity has a protective function after traumatic injury to the central nervous system. This finding led us to suggest the 'comprehensive immunity' approach by which autoimmunity is viewed as a special case of immunity, namely as a defense mechanism that operates by fighting against the threat of potential destructive activity originated or mediated within the organism, similarly to the immune defense that operates against the threat from exogenous pathogens. We present a primary mathematical spatio-temporal model that supports this concept. The numerical solutions of this model illustrate the beneficial operation of a well-controlled immune response specific to self-antigens residing in the site of lesion. The model also explains how the response to self might be tolerated on a day-to-day basis. In addition, we demonstrate that the same autoimmune response, operating at different levels of regulation, can lead to either an autoimmune disease or a degenerative disorder. This preliminary qualitative model supports our contention that the way autoimmunity is perceived should be revised.
The original paper reference is cited below:
Autoimmunity as an immune defense against degenerative processes: a primary mathematical model illustrating the bright side of autoimmunity, Uri Nevo, Ido Golding, Avidan U. Neumann, Michal Schwartz, and Solange Akselrod, 2004, Journal of Theoretical Biology, 227, 583-592. PubMed ID: 15038992
cell diagram
Schematic diagram of the mathematical model. Healthy cells (H) can be lost via two routes, 1) self-perpetuating death (H-N-D), or 2) immune-mediated loss (H-P-D).
$\frac{d h}{d \mathrm{time}}=-(\mathrm{Tn}+\mathrm{Tp})$
$\frac{d n}{d \mathrm{time}}=\mathrm{Tn}-\mathrm{lamda\_n}n$
$\frac{d p}{d \mathrm{time}}=\mathrm{Tp}-\mathrm{lamda\_p}p$
$\frac{\partial^{1}\mathrm{s1}}{\partial \mathrm{time}}=\mathrm{K1}n-\mathrm{lamda\_1}\mathrm{s1}+\mathrm{D1}\mathrm{s1}$
$\frac{d \mathrm{s2}}{d \mathrm{time}}=\mathrm{K2}n-\mathrm{lamda\_2}\mathrm{s2}+\mathrm{D2}\mathrm{s2}$
$\mathrm{Tn}=\begin{cases}\mathrm{eta\_n}h(\mathrm{s1}-\mathrm{s1\_min}) & \text{if $\mathrm{s1\_min}< \mathrm{s1}$}\\ 0.0 & \text{otherwise}\end{cases}$
$\mathrm{Tp}=\mathrm{eta\_p}hE\mathrm{s2}$
$\frac{d E}{d \mathrm{time}}=\mathrm{fw}(\mathrm{s2\_}-\mathrm{s2\_min})-\mathrm{lamda\_E}E$
$\mathrm{fw}=\frac{1.0}{1.0+e^{\frac{-(x-c)}{w}}}$
$\mathrm{s2\_}=\mathrm{s2}$
immunology
autoimmunity
This is the CellML description of Nevo et al.'s 2004 mathematical model of autoimmunity.
immune stimulation
E
The University of Auckland
The Bioengineering Institute
immune-mediated tissue loss
p
transition to the negative loss pathway
Tn
Catherine
Lloyd
May
Uri
Nevo
transition to the positive loss pathway
Tp
self-perpetuating tissue loss
n
healthy tissue
h
15038992
damage inducing signal
s1
alerting signal
s2
c.lloyd@auckland.ac.nz
Ido
Golding
keyword
2004-10-25
Autoimmunity as an immune defense against degenerative processes: a
primary mathematical model illustrating the bright side of
autoimmunity
227
583
592
Journal of Theoretical Biology
Michal
Schwartz
2004-04-21
Catherine Lloyd
The University of Auckland, Bioengineering Institute
Nevo et al.'s 2004 mathematical model of autoimmunity.
Avidan
Neumann
U
Solange
Akselrod