Practical Variance Reduction via Regression for Simulating Diffusions

The well-known variance reduction methods—the method of importance sampling and the method of control variates—can be exploited if an approximation of the required solution is known. Here we employ conditional probabilistic representations of solutions together with the regression method to obtain sufficiently inexpensive (although rather rough) estimates of the solution and its derivatives by using the single auxiliary set of approximate trajectories starting from the initial position. These estimates can effectively be used for significant reduction of variance and further accurate evaluation of the required solution. The developed approach is supported by numerical experiments

Age-related accumulation of mutations reveals mechanisms of spontaneous mutation at tandem repeat DNA loci in mice

Expanded simple tandem repeat (ESTR) loci belong to the class of highly unstable loci in the mouse genome. The mechanisms underlying the very high spontaneous instability at these loci still remain poorly understood. Using single-molecule polymerase chain reaction, here we have compared the pattern of mutation accumulation in tissues with different proliferation capacities in male mice of age 12, 26, 48, and 96 weeks. In the nonproliferating brain, we did not observe any measurable age-related accumulation of ESTR mutations. In contrast, a highly elevated frequency of ESTR mutation was detected in the sperm samples taken from old mice; similar changes were also observed in the bone marrow tissue. The spectra of ESTR mutations accumulated in all tissues of young and old mice did not significantly differ. Taken together, these data clearly imply that spontaneous ESTR mutations occur almost exclusively in replication-proficient cells. To gain further insights into the mechanisms of ESTR mutation, we developed a stochastic model of age-related mutation accumulation. The observed spectra of ESTR mutants accumulated in the brain and sperm were fairly accurately approximated assuming the values of ESTR mutation rate, ranging from 0.01 to 0.04 per cell division. As these estimates dramatically exceed those for protein-coding genes and microsatellite loci, our data therefore suggest that ESTRs represent one of the most unstable loci in the mammalian genome. The results of our study also imply that ESTR loci can be regarded as a class of expanded microsatellites, with the mechanism of spontaneous mutation most probably attributed to replication slippage

Phase variable genes of Campylobacter jejuni exhibit high mutation rates and specific mutational patterns but mutability is not the major determinant of population structure during host colonisation

Phase variation of surface structures occurs in diverse bacterial species due to stochastic, high frequency, reversible mutations. Multiple genes of Campylobacter jejuni are subject to phase variable gene expression due to mutations in polyC/G tracts. A modal length of nine repeats was detected for polyC/G tracts within C. jejuni genomes. Switching rates for these tracts were measured using chromosomally-located reporter constructs and high rates were observed for cj1139 (G8) and cj0031 (G9). Alteration of the cj1139 tract from G8 to G11 increased mutability 10-fold and changed the mutational pattern from predominantly insertions to mainly deletions. Using a multiplex PCR, major changes were detected in ‘on/off’ status for some phase variable genes during passage of C. jejuni in chickens. Utilization of observed switching rates in a stochastic, theoretical model of phase variation demonstrated links between mutability and genetic diversity but could not replicate observed population diversity. We propose that modal repeat numbers have evolved in C. jejuni genomes due to molecular drivers associated with the mutational patterns of these polyC/G repeats, rather than by selection for particular switching rates, and that factors other than mutational drift are responsible for generating genetic diversity during host colonization by this bacterial pathogen