Mutation parameters from DNA sequence data using graph theoretic measures on lineage trees

Abstract

We have developed a bioinformatic method based on a maximum likelihood analysis of phylogenetic lineage trees to estimate the parameters of a B cell clonal expansion model, which includes somatic hypermutation with the possibility of lethal mutations. Lineage trees are created from clonally related B cell receptor DNA sequences. Important links between tree shapes and underlying model parameters are identified using mutual information. Parameters are estimated using a likelihood function based on the joint distribution of several tree shapes, without requiring a priori knowledge of the number of generations in the clone (which is not available for rapidly dividing populations in vivo). A systematic validation on synthetic trees produced by a mutating birth-death process simulation shows that our estimates are precise and robust to several underlying assumptions. These methods are applied to experimental data from autoimmune mice to demonstrate the existence of hypermutating B cells in an unexpected location in the spleen.

Recirculation of germinal center B cells: a multilevel selection strategy for antibody maturation

“…Certainly, the increasing amount of data available by novel experimental techniques like in vivo imaging will lead to new insights. Yet another way to infer dynamics is using specific models to interpret observed B‐cell receptor sequences (33, 35, 66). Beyond particular models, general theoretical approaches like optimization theory can help formulate guidelines directing both mathematical modeling and experimental research.…”

The evolution of mathematical immunology

“…These models are closely tied to experimental results and are similar to the concept of mathematical models in theoretical physics (62–65). Two examples from our own work are the simulation of BCR light (L) chain rearrangement (66–68), and the analysis of genetic lineage of B cells (69–71). Following experiments performed in the Weigert laboratory (66, 72–74), showing the selection of a special λ chain (λ‐x) and B cells with two different L chains in lupus‐prone mice, we developed a stochastic simulation of the mouse L chain rearrangement process, based on the possibility that multiple alleles are simultaneously rearranged (67).…”

“…Such trees contain a large amount of information about the underlying process. We have developed methods to break up the full tree topology into a set of ‘tree measures’ and to use these measures to estimate the mutation rate and the lethal mutation frequency (69, 71). The results were validated on synthetic trees generated from a simulated GC reaction ().…”

“…to estimate the mutation rate and the lethal mutation frequency (69,71). The results were validated on synthetic trees generated from a simulated GC reaction ( Fig.…”

Getting Started in Computational Immunology

“…Unlike the case for phylogenetic trees, the relatively small number of mutations and sequences means there are often few ambiguities in creating these trees. Monte Carlo simulation approaches have been used to link the topological properties of B cell lineage trees to underlying biological processes such as somatic hypermutation [21] and selection [22]. Inferences based on lineage tree properties are challenging since many different biological processes can produce similar changes in tree shape, and direct tests for selection based on these properties have yet to be developed for the immune response.…”