Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood.
The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.
Biomathematics Graduate Program, Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.
M D
MD
Radmacher
T B
TB
Kepler
D000818:Animals; D000917:Antibody Formation / Q000235:genetics / Q000276:immunology; D001402:B-Lymphocytes / Q000276:immunology; D003198:Computer Simulation; D005799:Genes, Dominant; D018858:Germinal Center / Q000276:immunology*; D016013:Likelihood Functions; D008957:Models, Genetic; D009010:Monte Carlo Method; D009154:Mutation / Q000235:genetics* / Q000276:immunology; D009596:Nitrophenols / Q000276:immunology; D010648:Phenylacetates; D012641:Selection, Genetic; D013269:Stochastic Processes; D014714:Vertebrates / Q000235:genetics* / Q000276:immunology
D009596:Nitrophenols; D010648:Phenylacetates; C026242:4-hydroxy-5-nitrophenyl acetic acid