Intrinsic noise alters the frequency spectrum of mesoscopic oscillatory chemical reaction systems

Mesoscopic oscillatory reaction systems, for example in cell biology, can exhibit stochastic oscillations in the form of cyclic random walks even if the corresponding macroscopic system does not oscillate. We study how the intrinsic noise from molecular discreteness influences the frequency spectrum of mesoscopic oscillators using as a model system a cascade of coupled Brusselators away from the Hopf bifurcation. The results show that the spectrum of an oscillator depends on the level of noise. In particular, the peak frequency of the oscillator is reduced by increasing noise, and the bandwidth increased. Along a cascade of coupled oscillators, the peak frequency is further reduced with every stage and also the bandwidth is reduced. These effects can help understand the role of noise in chemical oscillators and provide fingerprints for more reliable parameter identification and volume measurement from experimental spectra

Germline selection shapes human mitochondrial DNA diversity.

Approximately 2.4% of the human mitochondrial DNA (mtDNA) genome exhibits common homoplasmic genetic variation. We analyzed 12,975 whole-genome sequences to show that 45.1% of individuals from 1526 mother-offspring pairs harbor a mixed population of mtDNA (heteroplasmy), but the propensity for maternal transmission differs across the mitochondrial genome. Over one generation, we observed selection both for and against variants in specific genomic regions; known variants were more likely to be transmitted than previously unknown variants. However, new heteroplasmies were more likely to match the nuclear genetic ancestry as opposed to the ancestry of the mitochondrial genome on which the mutations occurred, validating our findings in 40,325 individuals. Thus, human mtDNA at the population level is shaped by selective forces within the female germ line under nuclear genetic control, which ensures consistency between the two independent genetic lineages.NIHR, Wellcome Trust, MRC, Genomics Englan

Quantitative bounds of convergence for geometrically ergodic Markov chain in the Wasserstein distance with application to the Metropolis Adjusted Langevin Algorithm

International audienceIn this paper, we establish explicit convergence rates for Markov chains in Wasserstein distance. Compared to the more classical total variation bounds, the proposed rate of convergence leads to useful insights for the analysis of MCMC algorithms, and suggests ways to construct sampler with good mixing rate even if the dimension of the underlying sampling space is large. We illustrate these results by analyzing the Exponential Integrator version of the Metropolis Adjusted Langevin Algorithm. We illustrate our findings using a Bayesian linear inverse problem