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.
Radmacher
M D
MD
Biomathematics Graduate Program, Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.
Kepler
T B
TB
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