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

Simulation B cell receptor affinity B cell Germinal center More complex, realistic Specific: Ox, NP Discrete/ stochastic simulation affinity landscape internal dynamics population dynamics

Affinity landscapes: NK landscape model N: sequence length  receptor space size K: internal interactions  landscape ruggedness NK : easy to model different antigen, check stats vs. experimental data K=0K=mediumK=highOx,NP

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

Simulation B cell receptor affinity B cell Germinal center More complex, realistic Specific: phOx, NP Discrete/ stochastic simulation

B cell model – decision making network input node (receptor affinity) mutationdeathdivision output nodes (rates) functional nodes fitness function (division)

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 Previous work: Ox, NP single affinity-increasing mutation fitness function = threshold NK landscape rugged, multiple peaks expected smaller slope Ox,NPNK

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)

Future work more complex decision network optimization problem: mutate network, not only parameters B cell receptor affinity B cell Germinal center More complex, realistic Specific: phOx, NP Discrete/ stochastic simulation More realistic

Acknowledgements Steven Kleinstein, Jaswinder Pal Singh Martin Weigert Stuart A. Kauffman, Edward D. Weinberger, Bennett Levitan (Santa Fe)

The End