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

dB

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