simulating the immune system martin weigert department of molecular biology steven kleinstein, erich...
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IA 2000 Why simulate the immune system? Understand the big (system-level) picture Compared to lab experiments simulations are cheap, easy and quick! Make difficult or impossible measurements Help focus experiments Test “wild” theories in the privacy of your officeTRANSCRIPT
Simulating the Immune SystemSimulating the Immune System
Martin WeigertMartin WeigertDepartment of Molecular Biology
Steven KleinsteinSteven Kleinstein, Erich Schmidt, Tim Hilton, J.P. Singh, Erich Schmidt, Tim Hilton, J.P. SinghDepartment of Computer Science
Philip E. SeidenPhilip E. SeidenIBM Research and Department of Molecular Biology
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Program in Integrated Computer and Application SciencesPICASsoPICASso
C S
PPPL
Astro
Geo
BIO
Engg.
GFDL
Genomics
Finance
Foster interdisciplinary research & train a new breed of researcher
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Why simulate the immune system?
Understand the big (system-level) pictureCompared to lab experiments simulations
are cheap, easy and quick!Make difficult or impossible measurementsHelp focus experimentsTest “wild” theories in the privacy of your
office
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How to simulate the immune system?Ordinary (or Partial) Differential Equations
Generalized Cellular Automata
Statistical model, etc...
iiriifim
i CSCkSCkBfdt
dC 1
Ab2 Ab3 AbnAb1
Ag2 Ag3 AgmAg1
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(Takahashi et al. J. Exp. Med., 187:885 1998)
Example: Modeling Affinity Maturation
BB
Ag B
B
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Germinal Center:Germinal Center:The site of affinity maturation
Immunity 1996 4: 241–250
Germinal Center
http://www.chemistry.ucsc.edu/
Mouse Spleen
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Developing a mathematical model
Apoptosis Unbind Bind Flow
) 1(i i r iif i m
iC X k S C k B f
dtdC
Many parameters are based on experimental measurements
Light-ZoneB cell
Affinity
AgXiCi
B cell - AntigenComplex
Bi
Dark-ZoneB cell
flowbind
unbind
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Oprea-Perelson Model Equations
CBmC
BBmi
iiLCbB
iMiRRi
iRiRioffi
ioffiion
i
iioffiionim
i
iBimiRRiCbiiiCbidi
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ii
td
LLfdt
dL
LLfBpdt
dL
MdRmpdt
dM
RdRmXkdt
dR
XkSCkdtXd
CXkSCkBfdt
dC
BdBfRmpBpBiiBiiBiipBtkdt
dB
BtkMBBp
dtdB
XeStS S
3 Flow
3 FloweProliferat
Exit
ExitUnbind
UnbindBind
UnbindBind2 Flow
2 FlowExiteProliferat
11
1 Flow
0,
1 Flow
0
2
1
)1(
),1(),1(),(2)(
)(1
)(
Oprea, M., and A. Perelson. 1997. J. Immunol. 158:5155.
A complex model that includes many details
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Simulated Germinal Center Dynamics
0200400600800
100012001400160018002000
0 5 10 15 20 25Day
Num
ber o
f B c
ells
3210 (Germline)-1-2
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Extending the state-of-the-art...
Shortcomings ofcurrent models
Typical Response Qualitative validation Average-case dynamics Mechanism of selection
is implicit
Contributions ofour work
Specific Response Quantitative validation Average & Distribution Mechanism of selection
is explicit
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Validating model with data from the oxazolone response
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Days post-immunization
Frac
tion
of c
ells
that
are
hig
h-af
finity
Experiment
Simulation
(Berek, Berger and Apel, 1991)
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Dynamics of Individual Germinal Centers
In addition, response tends to be all-or-none
(Ziegner, Steinhauser and Berek, 1994)
SingleFounder
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Pitfalls of Differential EquationsImplicitly model average-case dynamics
and have no notion of individual cells
Develop discrete/stochastic implementation of the model
Follows individual cellsPredicts distribution of behaviors
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Run simulation 500 times to simulate a spleen’s worth of germinal centers
Making a discrete/stochastic simulation
Fixed-increment time advance frameworkAssume Poisson processesUse 1-e-t to calculate event probabilityRandom numbers determine occurrence
Use CS-MPI cluster to run this embarrassingly parallel program
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Conclusions of Simulation StudyThe standard model cannot explain dynamics
within individual germinal centers
Propose extension to standard model
Various assumptions necessary for agreement Suggest Experiments
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Visualization Using the Display Wall
How does clonal tree ‘shape’ reflect the underlying dynamics of the germinal center
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Using Clonal Trees to Measure Selection Pressure
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1
Fraction of cells carrying key mutation
Ste
m L
engt
h
(Hilton, Singh and Kleinstein, 2000)
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IMMSIMA cellular-automata based model of the
complete immune response
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For more information check outwww.cs.princeton.edu/immsim