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Towards More Realistic Affinity Maturation Modeling. Erich R. Schmidt, Steven H. Kleinstein Department of Computer Science, Princeton University July 19, 2001. Recent germinal center models: simple responses (haptens – Ox, NP) single affinity-increasing mutation simple B cell model

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Towards more realistic affinity maturation modeling

Towards More Realistic Affinity Maturation Modeling

Erich R. Schmidt, Steven H. Kleinstein

Department of Computer Science, Princeton University

July 19, 2001


Germinal center models

Recent germinal center models:

simple responses (haptens – Ox, NP)

single affinity-increasing mutation

simple B cell model

no inter-cellular signals

no internal dynamics

Address limitations:

more complex receptor affinity space

multiple affinity-increasing mutations

more realistic model of B cell

inter-cellular signals

signal memory

Germinal center models


Simulation

affinitylandscape

internaldynamics

populationdynamics

Specific:

Ox, NP

Discrete/stochastic simulation

More complex, realistic

Simulation

B cell receptor affinity

B cell

Germinal center


Affinity landscapes nk landscape model

K=0

K=medium

K=high

Ox,NP

NK : easy to model different antigen, check stats vs. experimental data

Affinity landscapes:NK landscape model

  • N: sequence length  receptor space size

  • K: internal interactions  landscape ruggedness


Nk parameter values
NK parameter values

  • proposed by Kauffman/Weinberger:

    • correctly predicts:

      • number of steps to local optima

      • fraction of higher-affinity neighbors

      • “conserved” sites in local optima


Individual mutations vs population dynamics
Individual mutations vs. population dynamics

  • Kauffman/Weinberger:

    • single cell walk

    • mutations: uphill

    • no time

    • no other events

  • Our simulation:

    • entire population dynamics

    • mutations: random

    • time-dependent

    • division, death


Simulation1

Specific:

phOx, NP

Discrete/stochastic simulation

Simulation

B cell receptor affinity

B cell

Germinal center

More complex, realistic


B cell model decision making network

functionalnodes

output nodes(rates)

fitnessfunction(division)

mutation

death

division

B cell model – decision making network

input node(receptoraffinity)


Germinal center model
Germinal center model

  • single seed

  • all cells share same parameters

  • dynamic, stochastic, discrete

  • simulate for 14 days

  • different steps: change network parameters

  • search: best network for affinity maturation


Expectations

NK

Ox,NP

Expectations

  • Previous work: Ox, NP

    • single affinity-increasing mutation

    • fitness function = threshold

  • NK landscape

    • rugged, multiple peaks

    • expected smaller slope


Results
Results

  • threshold

  • select for small percentage of affinity-increasing mutations

  • high-affinity seed


Results1
Results

  • low affinity seed

    • smaller slope

    • very hard to walk up: smaller slope doesn’t help overall affinity maturation


Conclusions
Conclusions

  • dynamic model on NK landscape

    • generates affinity maturation

  • not reaching local optima

    • best division rate is a threshold function

    • affinity of seeding cell important factor

  • total mutation count consistent with bio data

    • Kauffman: all mutations up

    • our simulation: random mutations (up+down)


Future work

B cell receptor affinity

B cell

Germinal center

Morerealistic

Specific:

phOx, NP

Discrete/stochastic simulation

More complex, realistic

Future work

  • more complex decision network

  • optimization problem: mutate network, not only parameters


Acknowledgements
Acknowledgements

  • Steven Kleinstein, Jaswinder Pal Singh

  • Martin Weigert

  • Stuart A. Kauffman, Edward D. Weinberger, Bennett Levitan (Santa Fe)



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