Regulatory T Cells
Brynja Kohler
bkohler@math.utah.edu
IMA New Directions Short Course
Cellular Physiology
Friday, June 27, 2003
• The Immune System
• Multiple Sclerosis
• Regulatory Mechanisms
• Mathematical Model
Identify and Destroy anything doing damage to tissues in the body.
• Innate: evolutionary time
complement, macrophages, neutrophils, NKcells
• Adaptive: ontogenic time
lymphocytes (B cells and T cells), antibodies
Diverse and Specific through specialized transmembrane protein receptors.
Multiple Sclerosis
epidemiological data
diagnosis
MS hypothesis: A trigger early in life in genetically susceptible individuals...
Powrie and Maloy, Science, March 2003.
Question: Can we see switch behavior in this system?
AA + AR = 1
dAA
= IAR + k1TE AR − k2TR AA
dt
dT
= −kE AAT − kR AR T + σ − δT
dt
2
pTE
dTE
2 − δT
= kE AAT +
− µTE
E
dt
K + TE
dTR
= kR AR T − δTR
dt
Steady State Analysis
• With I = 0,
kR σ
σ , T =
AA = 0, TE = 0, AR = 1, T = δ+k
is a stable steady state
R
δ(δ+kR )
2
provided that k2kR > k1kE
• Other steady states satisfy
k2kR σAA
I
→ TE =
−
k1δ(kE AA + kR (1 − AA) + δ) k1
“AA nullcline”
σ
T =
kE AA + kR (1 − AA) + δ
→
2
pTE
1
σAA
2 + δT
=
−
+ µTE
E
kE AA + kR (1 − AA) + δ
kE
K + TE
TR =
kR σ(1 − AA)
δ(kE AA + kR (1 − AA) + δ)
!
“TE nullcline”
The AA - TE plane:
I=0
I=2
I=3
Indeed Powrie and Maloy’s description can exhibit “switch” behavior. So what?
• Biological Interpretations
– Suggests experiments to find I ∗
→ Freud’s adjuvant.
– System can exhibit hysteresis.
– Parameter constraints in the stability condition.
– Sensitivity to p and K → there may be additional mechanisms at work to
make the switch robust.
• Relation to MS
– Suggests the “latitude” data may be due to lack of TR .
– Requires more to obtain a relapsing remitting disease course.
Thanks to ...
• James P Keener
• Robert Fujinami
• Fred Adler
• Frank Lynch
• Math Physiology Group at University of Utah