toward quantitative simulation of germinal center dynamics steven kleinstein...
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Toward Quantitative Simulation Toward Quantitative Simulation of Germinal Center Dynamicsof Germinal Center Dynamics
Steven [email protected]. of Computer Science
Princeton University
J.P. SinghJ.P. [email protected]
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
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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
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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