Towards more realistic affinity maturation modeling
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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

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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

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


affinitylandscape

internaldynamics

populationdynamics

Specific:

Ox, NP

Discrete/stochastic simulation

More complex, realistic

Simulation

B cell receptor affinity

B cell

Germinal center


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

  • 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

  • Kauffman/Weinberger:

    • single cell walk

    • mutations: uphill

    • no time

    • no other events

  • Our simulation:

    • entire population dynamics

    • mutations: random

    • time-dependent

    • division, death


Specific:

phOx, NP

Discrete/stochastic simulation

Simulation

B cell receptor affinity

B cell

Germinal center

More complex, realistic


functionalnodes

output nodes(rates)

fitnessfunction(division)

mutation

death

division

B cell model – decision making network

input node(receptoraffinity)


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


NK

Ox,NP

Expectations

  • Previous work: Ox, NP

    • single affinity-increasing mutation

    • fitness function = threshold

  • NK landscape

    • rugged, multiple peaks

    • expected smaller slope


Results

  • threshold

  • select for small percentage of affinity-increasing mutations

  • high-affinity seed


Results

  • low affinity seed

    • smaller slope

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


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)


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

  • Steven Kleinstein, Jaswinder Pal Singh

  • Martin Weigert

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


The End


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