toward quantitative simulation of germinal center dynamics steven kleinstein...

Toward Quantitative Simulation Toward Quantitative Simulation of Germinal Center Dynamicsof Germinal Center Dynamics

Steven Kleinsteinstevenk@cs.princeton.eduDept. of Computer Science

Princeton University

J.P. SinghJ.P. Singhjps@cs.princeton.edu

Dept. of Computer SciencePrinceton University

With continual guidance from:

Martin WeigertDept. of Molecular Biology

Princeton University

Philip E. SeidenPhilip E. SeidenIBM Research Center,IBM Research Center,

Dept. of Molecular Biology

Affinity Maturation

(Takahashi et al. J. Exp. Med., 187:885 1998)

B cells with affinity-increasing mutations are selected for binding to antigen

``

The Germinal Center Physical site of B cell hypermutation and selection

http://www.chemistry.ucsc.edu/

Spleen

Germinal CenterImmunity 1996 4: 241–250

Experimental studies have elucidated the basic molecular mechanisms

underlying the germinal center reaction.(e.g., hypermutation, FDC binding, Apoptosis)

However, it is still not well understood how these mechanisms fit together.

How does the germinal center work?

Shortcomings of Current Models

Common Models

Prototypical Response Qualitative validation Average-case dynamics Mechanism of selection

is implicit

Our Goal

Specific Response Quantitative validation Average & Distribution Mechanism of selection

is explicit

Talk Outline

Background

Germinal center model during prototypical immune response

How to simulate the specific response to oxazolone

Experimental validation: average dynamics & individual dynamics

Summary & Conclusions

The Oprea-Perelson Model

(Liu et al. Immunity 1996 4: 241)

Includes mechanism underlying affinity maturation

Oprea, M., and A. Perelson. 1997. J. Immunol. 158:5155.

Affinity-DependentSelection

Proliferate & Diversify

Dark-Zone Light-Zone

Memory

Death

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

XkSCkdt

Xd

CXkSCkBfdt

dC

BdBfRmpBpBiiBiiBiipBtkdt

dB

BtkM

BBp

dt

dB

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

)(

CBmC

BBmi

iiLCbB

iMiRRi

iRiRioffi

ioffiion

i

iioffiionim

i

iBimiRRiCbiiiCbidi

dB

ii

td

LLfdt

dL

LLfBpdt

dL

MdRmpdt

dM

RdRmXkdt

dR

XkSCkdt

Xd

CXkSCkBfdt

dC

BdBfRmpBpBiiBiiBiipBtkdt

dB

BtkM

BBp

dt

dB

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

Simulated Germinal Center Dynamics

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25Day

Num

ber

of B

cel

ls

3210 (Germline)-1-2

Does model apply to specific system?

Compare dynamics with data from oxazolone response

GeneralGeneral

ParametersParameters

Response SpecificResponse Specific

Germline AffinityEffect of mutation

Half-lifeMigration Rates

Physical Capacity

Key Mutations are highly selected in germinal centerKey Mutations are highly selected in germinal center

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 16

Days post-immunization

Fra

ctio

n o

f ce

lls th

at a

re h

igh

-a

ffin

ity

Experiment

Simulation

Experimental Validation Step #1

(Berek, Berger and Apel, 1991)

The average dynamics of germinal centersThe average dynamics of germinal centers

Experimental Validation Step #2The dynamics within individual germinal centersThe dynamics within individual germinal centers

(Ziegner, Steinhauser and Berek, 1994)

SingleFounder

(all-or-none)

SingleFounder

(all-or-none)

A New Implementation is Needed

Differential equations implicitly model average-case dynamics and have no notion of individual cells

Differential equations implicitly model average-case dynamics and have no notion of individual cells

Create new discrete/stochastic simulation of the Oprea-Perelson model

Create new discrete/stochastic simulation of the Oprea-Perelson model

Follows individual cells

Predicts distribution of behaviors

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction of B cells that are high-affinity at day 14

Fra

ctio

n o

f ge

rmin

al c

en

ters

Model Differs From ExperimentModel predicts 7 founding cells per germinal

center

Model predicts 7 founding cells per germinal center

Limiting the Number of Founders

Affinity-DependentSelection

Proliferate & Diversify

Decreased Generation(e.g., lower mutation rate)

Decreased Selection(e.g. lower probability of recycling)

Memory

Death

Many hypothesis can be tested by changing parameter valuesMany hypothesis can be tested by changing parameter values

Affinity Maturation Founders

1

2

3

4

5

6

7

8

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02

Mutation Rate (base-pair-1 division-1)

Ave

rag

e N

um

be

r o

f Fo

un

de

rs

0

0.1

0.2

0.3

0.4

R2

Ave

rage

Num

ber

of F

ound

ers

R2

Parameter changes alone cannot bring simulation into strict agreement with data on average and individual

dynamics simultaneously

Two possibilities...Data not correctly interpreted

Changes to model are necessary

Two possibilities...Data not correctly interpreted

Changes to model are necessary

79%

21%

Dominant Lineage

Other Lineages

Key-Mutant PopulationDay 14 Post-Immunization

Is Problem Data Interpretation?The Case for Multiple Founders

Can be tested by collecting more data, or stronger statistical tests

Can Extending the Model Help?

Affinity-DependentSelection

Proliferate & Diversify

Memory

Death

Allow selected cells an advantage, independent of affinity

Motivation: processes which reduce number of founders restrict the growth rate of the actual founder

Motivation: processes which reduce number of founders restrict the growth rate of the actual founder

Extended Models Produce Agreement

Single founder predictedSingle founder predicted

Extensions can be tested by experiment

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

Days post-immunization

F(d)

00.020.040.060.08

0.10.120.140.160.18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Fraction of B cells that are high-affinity at day 14

Fra

ctio

n of

ger

min

al c

ente

rs

Applied Oprea-Perelson to Oxazolone• Allows prediction of specific experiments

Quantitative Validation• Predicts average GC dynamics• Fails to predict individual GC behavior

Analysis Two Possibilities• Experimental data is not correctly interpreted

– Too limited, need to collect more

– Develop stronger statistical tests

• Extensions to OP model are necessary

Summary & Conclusions