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Related Experiment Videos

Somatic hypermutation in B cells: an optimal control treatment

T B Kepler1, A S Perelson

  • 1Santa Fe Institute, NM 87501.

Journal of Theoretical Biology
|September 7, 1993
PubMed
Summary

The vertebrate immune system optimizes antibody affinity through somatic hypermutation. Mathematical modeling reveals that brief, high mutation rate bursts maximize antibody affinity, explaining germinal center reactions.

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Area of Science:

  • Immunology
  • Computational Biology
  • Biophysics

Background:

  • Vertebrate immune systems generate high-affinity antibodies via somatic hypermutation in germinal centers.
  • B cells undergo random mutations and selection for antigen binding, increasing antibody affinity significantly within weeks.

Purpose of the Study:

  • To understand the effectiveness of antibody affinity maturation by framing it as an optimization problem.
  • To mathematically model and identify optimal mutation rates over time to maximize total antibody affinity.

Main Methods:

  • Developed a single-compartment model for the germinal center reaction.
  • Applied an optimization algorithm based on the Pontryagin maximum principle to determine optimal mutation schedules.

Main Results:

  • The optimal mutation schedule involves intermittent bursts of high mutation rates, separated by periods of mutation-free growth.
  • This theoretical schedule provides a framework for understanding the observed anatomy and kinetics of germinal center reactions.

Conclusions:

  • The study proposes a novel mathematical framework for understanding antibody affinity maturation.
  • The findings suggest that a dynamic, non-uniform mutation rate strategy is optimal for maximizing antibody affinity.

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