Download T memory cells in a model of cell memory

Immune System
• Skin
• Complement
• Immune cells
– Macrophages
– T cells
– B cells
Cytokines
Intro-cellular events
Complement System
• 25 Proteins that complement t
he activity of antibodies in de
stroying bacteria
– Phagocytosis
– Puncturing cell membrane
– Proteases cleave proteins
• Rids body of antigen-antibod
y complexes
• Circulate in blood in in-active
form
– Creates complement cascade
Phagocytes
• Macrophages
– Antigen Presentation
– All over
• Dendritic cells
– Tenticles used to prese
nt antigen
– Located in Spleen
• Neutrophils
– Contain granules that h
ave potent chemicals
T cells
• Mature in Thymus
• Regulatory
– Helper T cells
– Present antigen to B cel
ls
– CD4
• Cytotoxic
– CD8
• Both secrete necessar
y cytokines
• Orchestrate elaborate
response
• Memory T cells
MHC Complexes
Two types
Bound or Free
Type 1
Most cells
Type 2
APC
B cells
• Programmed to make
one antibody
• Needs APC/Cytokines
• Creates Plasma cell
– Factories for antibody
• Done by Geometry
Where do they come from
Cytokines
Cytokine network
Disease of Immune System
• Allergy
• Auto Immune Diseases
– Rheumatoid Arthritis
– Lupus
• Diabetes
• Leukemia
• HIV
Memory T cells
Angela Mclean
Memory T Cells
• They are antigen-specific T
cells that persist long-term a
fter an infection
• If there is a second encounte
r with an infection, the memo
ry T cells are reactivated and
can reproduce to provide a f
aster and stronger immune re
sponse
The Model and Goals
• Uses 5 populations: resting Th cells (W), activated
Th cells (X) memory T cells (M), interleukin 2 (IL-2)
(I), and antigen (A).
• Using the model, the population dynamics are illus
trated both in vitro and in vivo. In previous models,
in vivo and in vitro had the same results, but in exp
eriments it was shown that the two were quite differ
ent. This model aims to correct this error.
• The model is created to have no numerical estimat
es of parameters, so the model’s behavior has all p
ossible types of population behavior.
Antigen
A
Antigen driven
activation
Immigration from the
bone marrow
Antigen driven
activation
W
Native
X
Activated
Background
activation
Interleukin-2
driven
proliferation
IL-2
M
Memory
Equation 1
Assume that naïve Th cells migrate from thymus
at a constant rate and naïve cells are activate
d at a rate proportional to the amount of activ
ated Th cells.
•
•
•
•
•
W = Naïve Th cells
Λ = constant rate of migration
1/μ = half life of the naïve cells
A = Specific antigen
α = rate of activation of naïve cells
dW/dt = Λ – αAW – μW
Equation 2
Assume that:
• Proliferation of an activated cell creates two memo
ry cells
– Occurs at a constant rate with high concentration of activ
ated cells
• The half-life of all Th cells are equal
• Memory cells can be reactivated by either reintrodu
ction of the antigen or from background influences
, such as a sequestered antigen
• Memory cells are activated at a faster rate than naï
ve cells
Equation 2
• X = Activated helper T cells
• M = Memory cells
• δ = Difference in the rate of activation of mem
ory cells and the rate of activation of naïve cel
ls
• ε = background activation rate (accounts for r
andom chances that a cell was activated for a
different reason)
Rate of activation
dX/dt = αAW - ρIX/1+ξX + (δαA+ε)M - μX
Equation 2
dX/dt = αAW - ρIX/1+ξX + (δαA+ε)M - μX
• The rate of change of the activated Th cells is
equal to the rate of activation of the naïve cell
multiplied by the probability of an antigen and
cell binding minus the proliferation rate of the
activated Th cells changing to memory cells p
lus the rate of memory cells reactivating minu
s the death rate of activated cells.
Equation 3
dM/dt =
2ρIX/
1+ξX
- (δαA+ε)M - μM
• The rate of change of memory cells is e
qual to double the rate of proliferation o
f activated cells (because 2 memory cel
ls are produced) minus the rate of reacti
vation of memory cells minus the death
rate of memory cells.
Equation 4
Assume that:
• IL-2 is produced
and absorbed by
only activated Th
cells
• The half-life of IL
-2 is constant
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Equation 4
I = amount of IL-2
1/ψ = half-life of IL-2
dI/dt = φX - βIX - ψI
• The rate of change of the amount of I
L-2 is equal to the amount of IL-2 m
ade by activated cells minus the amo
unt absorbed by activated Th cells mi
nus the death rate of IL-2.
Equation 5
Assume that:
• Activated cells
have a constan
t growth rate w
hen they are no
t in the presenc
e of specific im
munity
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Equation 5
r = growth rate of antigen
dA/dt = rA - γAX
• The rate of change of the specific antigen i
s equal to the growth rate of the antigen in
the absence of specific immunity minus th
e rate of interaction of activated cells and t
he antigen that causes removal of the anti
gen.
Finding a Steady State
• In order to find when the change of the differ
ent populations would be steady, the derivativ
es are set equal to zero.
• After doing this, it is found that the rates are
constant only when A (the amount of antigen)
equals zero and when X (the amount of activa
ted Th cells) equals a constant.
• A quadratic equation is derived to find what t
his constant is. Because it is quadratic, we kn
ow two roots will be found or X will be equal t
o zero.
Finding a Steady State cont
• For a replicating antigen, the only X that can be stabl
e is the positive root of the equation.
• For a non-replicating antigen, X can be the positive r
oot or X can be zero.
• The only time that memory cells will be formed is if X
is positive, so we are only interested in the replicating
antigen.
• The root will not be a real number unless the backgro
und activation rate (ε) is greater than the death rate o
f the Th cells. This is represented by the fact that wh
en e (e = ε/μ) is less than one, there are no real solut
ions to the equation.
In Vivo Simulation
• This models the changes in the amounts of m
emory, naïve, and activated cells in the prese
nce of antigen in vivo (in the body)
• All parameters are the same for each trial, the
only difference is the growth rate of the antig
en
• At time 0 there was a small amount of replicat
ing antigen was added to the system
• At time 10 there was a large challenging dose
of antigen introduced
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
In Vivo Simulation contd.
• With an intermediate growth rate the T cell
s are able to clear out the antigen relatively
quickly, and can clear out the infection aga
in much more quickly
• With a fast growth rate, the T cells can’t cl
ear it out completely, and there always is a
small amount of the antigen present even
after reintroduction of the antigen
In Vivo Simulation contd.
• With a slow growth rate a persistent infection is also
established, and the T cells do not clear out the infe
ction because they are only slightly stimulated by th
e slow-growing antigens. The T cells take a long tim
e to proliferate but when a larger dose of the antige
n is reintroduced it is able to completely clear it.
• At the reintroduction, where the amount was equal t
o the initial amounts in the first two trials, the memo
ry and activated cells are pushed past their threshol
d, clearing the antigen and returning to a stable stat
e.
In Vitro Simulation
• This model is much different because of three
major factors:
– There is no chance of random activation
– No extra naïve cells come from the bone marrow
– The antigen cannot grow
• The model no longer displays immune memor
y and a single exposure to antigen leads to a
short-lived activation and proliferation.
• All cells convert from naïve to memory
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
In Vitro Simulation contd.
• This shows that the amount of activated ce
lls increases because it is in the presence
of an antigen, but decreases with IL-2 exp
osure because the activated cells become
memory cells.
• When exogenous IL-2 is added to the syst
em the amount of activated cells decrease
s at a faster rate.
• The cells convert from being mostly naïve t
o mostly memory
Conclusions
• In vitro cultures of Th
cells must be re-expo
sed to antigens if they
want to maintain prolif
eration.
• In vivo this achieved th
rough background stim
ulation (random chanc
e of reactivation)
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Our Conclusions
• This new model has achieved its goal, the distinction
between in vivo and in vitro situations. There may be
some problems with it, but is so far the best represen
tation of the population dynamics of T helper cells an
d antigens in the human body and in a culture.
• Possible problems:
– In this model, rates including death and growth rates were as
sumed to be constant. If the rates were varying, even slightly,
there may be a great difference in results.
– In has not been shown that memory cells can hold their mem
ory for as long as the model shows.
– There are many things going on in the body that are unpredic
table and impossible to model perfectly.
Basic modelEquation for the
dynamics of activated Th
cells
Result of modeling T-cell
• A reduced version of the model with
just two variables is considered so
that isoclines can be inspected.
Result of modeling T-cell
-model2
aX
qA
dA  e  1
X

[
] X
1  A (1  bX )(1  vX ) dA  e  1
.
.
A  A(c  X )
(e  1)bvX  [(e  1)(b  v)  a(e  1)] X  (e  1)  0
2
Result of modeling T-cell
-in vivo simulation• First, a small amount of replicating antigen
is introduced at time zero, when all cells
are present are naïve cells.
• When there is not response of immune
system, antigen grow initially.
• Antigen drives naïve cells to become
activated and activated cell is divided into
two memory cells.
Result of modeling T-cell
-in vivo simulation• Antigen causes a rise in the number
of activated and memory cells.
• The size of the activated and memory
population maintained in the absence
of the replicating antigen depends
only on interactions among immune
system.
Result of modeling T-cell
-in vitro simulation• All is same as earier model in 1990.
• There is no cross-reactive stimulation
or antigens.
• There is no influx of naive cells.
Conclusion
• T-helper cells need to be re-exposed
to antigens every few weeks.
• Immune memory, persistent infection,
slow growing persistent infection.
aX 2
X  A
X
2
1  bX
.
.
A  A(c  X )
Conclusion
• Memory cell have some special
properties but not long-lived.
• Their ability maintain immune system.
• This model displays memory without
invoking long time.