Vestergaard, Christian Lyngby

Optimal estimering af diusionskoecienter fra tidsseriemalinger afenkeltpartikeltrajektorier med malestjEnkeltpartikelteknikker gr det muligt kvantitativt at flge enkelte molekylersdiusion. Tidsserier malt med disse teknikker er overvejende korte ogindeholder meget malestj. Standardmetoden for estimation af diusionskoecienter fra enkeltpartikeltrajektorier er baseret pa mindste kvadraters ttil eksperimentelt malte mean squared displacements. Denne metode er hjstineektiv, da den ignorerer de hje korrelationer mellem disse. Vi udlederden eksakte maksimum likelihood estimator for diusionskoecienten, sammenmed et eksakt benchmark for den maksimale prcision nogen middelretestimator kan opna, Cramer-Rao grnsen. Vi foreslar en simpel analytisk ogmiddelret covariansbaseret estimator, baseret pa autocovariansfunktionen, ogudleder et eksakt analystisk udtryk for dens momentgenererende funktion. Vinder at maksimum likelihood estimatorens prcision er hjere end Cramer-Rao grnsen, pa bekostning af en lille skvhed, mens den covariansbaseredeestimator, som er fdt middelret, er optimal for alle eksperimentelt relevanteparametervrdier. Vi udvider metoderne til partikler, som diunderer pa etuktuerende substrat, sasom DNA, og viser at hvis der ikke tages hjde foruktuationerne, inducerer de en skvhed i de estimerede diusionskoecienter.Vi anvender metoderne til prcis estimering af diusionskoecienter forhOgg1 proteiner, som diunderer pa strukket uktuerende DNA, udfra data,som tidligere er blevet analyseret med en suboptimal metode. Vores analyseviser at proteinerne har forskellige eektive diusionskoecienter og at deresdiusionskoecienter er korrelerede med deres residenstider pa DNA'et. Disseresultater peger pa en multitilstandsmodel for hOgg1's diusion pa DNA.Optimal Estimation of Diusion Coecients from Noisy Time-Lapse-Measurements of Single-Particle Trajectories Single-particle tracking techniques allow quantitative measurements of diusionat the single-molecule level. Recorded time-series are mostly short andcontain considerable measurement noise. The standard method for estimatingdiusion coecients from single-particle trajectories is based on leastsquarestting to the experimentally measured mean square displacements.This method is highly inecient, since it ignores the high correlations inherentin these. We derive the exact maximum likelihood estimator for the diusioncoecient, valid for short time-series, along with an exact benchmark for themaximum precision attainable with any unbiased estimator, the Cramer-Raobound. We propose a simple analytical and unbiased covariance-based estimatorbased on the autocovariance function and derive an exact analyticalexpression of its moment generating function. We nd that the maximumlikelihood estimator exceeds the precision set by the Cramer-Rao bound, butat the cost of a small bias, while the covariance-based estimator, which is bornunbiased, is almost optimal for all experimentally relevant parameter values.We extend the methods to particles diusing on a uctuating substrate, e.g., exible or semi exible polymers such as DNA, and show that uctuations induce an important bias in the estimates of diusion coecients if they are notaccounted for. We apply the methods to obtain precise estimates of diusioncoecients of hOgg1 repair proteins diusing on stretched uctuating DNAfrom data previously analyzed using a suboptimal method. Our analysis showsthat the proteins have dierent eective diusion coecients and that theirdiusion coecients are correlated with their residence time on DNA. Theseresults imply a multi-state model for hOgg1's diusion on DNA

Online Research Database In Technology

Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories

http://orbit.dtu.dk/ws/files/9905551/prod21341680163995.Thesis.pdf

Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories

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