A nested sampling algorithm for quantifying protein copy number in super-resolution microscopy

KOŠUTA, TINA (author), Perman, Mihael (mentor), Manzo, Carlo (comentor)

This master thesis addresses the issue of protein cluster quantification in superresolution microscopy. Methods in super-resolution microscopy, typically referred to as single molecule localization microscopy, have greatly improved the optical resolution by sequentially exciting only the part of fluorescent molecules and image their signals through time. The signal is processed and stored as a localization in space. The improved resolution has further demonstrated molecular clustering as a relevant biological feature for cellular function. However, each cluster can be composed of several molecules and each of them is subjected to stochasticity of molecule labeling and complex photophysics of the fluorescent probes. This leads to a broad distribution of number of localizations for each cluster size, which impacts exact quantification of cluster stoichiometry. The aim of this master thesis was to investigate the performance of nested sampling compared to the previously developed method in Zanacchi et al. (2017). In the said article, the authors developed a method based on numerical approximation which estimated the total protein count as the mixture model of several oligomeric states. The proportions of each oligomeric state were estimated based on the number of localizations in each cluster. In this master thesis, we implemented the nested sampling based on the mixture model described above and compared both approaches on simulated and real data. The goal of both approaches was firstly to estimate the number of different oligomeric states in the model and secondly their corresponding proportions. The methods were evaluated in a simulation study and on the data generated from STORM imaging. The simulation study showed better performance of nested sampling especially in smaller samples, while in larger samples the methods performed similarly. In the STORM image analysis, where all the samples were large (n > 1000), all fitted distributions were almost identical.

• Language: English
• Keywords: super-resolution microscopy, protein quantification, STORM, nestedsampling, Bayesian statistic, evidence
• Work type: Master's thesis/paper
• Organization: FE - Faculty of Electrical Engineering
• Year: 2021
• PID: 20.500.12556/RUL-128877
• COBISS.SI-ID: 71716355
• Publication date in RUL: 10.08.2021

Secondary language

• Language: Slovenian
• Title: Gnezden algoritem vzorčenja za določanje števila molekul proteina v super-resolucijski mikroskopiji

Abstract

Magistrsko delo obravnava težavo kvantifikacije proteinov v super-resolucijski mikroskopiji. Metode super-resolucijske mikroskopije so bistveno izboljšale ločljivost na način, da naenkrat vzbudijo le del fluorescenčnih molekul in jih slikajo. Ta proces je izveden večkrat zaporedoma, končna slika pa je sestavljena iz vseh zaporednih slik. Vsak signal je obdelan in shranjen kot lokacija molekule v prostoru. Kljub izboljšanju ločljivosti je meja difrakcije teh metod med 20 in 50 nm, zaradi česar so molekule, ki so si bližje od te razdalje, na končni rekonstruirani sliki vidne kot gruča. Gručenje proteinov je biološka lastnost, ki nas zanima. Ker je posamezna gruča na končni sliki lahko sestavljena iz ene ali več ločenih molekul in vsaka od molekul lahko odda več signalov, kvantifikacija s preprostim štetjem posameznih gruč ni mogoča in problem ni lahko rešljiv. Namen magistrskega dela je bil raziskati uspešnost “nested sampling” metode v primerjavi s predhodno razvito metodo v Zanacchi et al. (2017). V omenjenem članku so avtorji razvili metodo, ki je skupno število proteinov ocenila kot mešani model več oligomernih stanj. Delež vsakega oligomernega stanja je bil ocenjen na podlagi števila lokalizacij v vsaki gruči. Rezultati v Zanacchi et al. (2017) so bili pridobljeni z numerično optimizacjo. V tej magistrski nalogi smo izvedli “neseted sampling” na podlagi zgoraj opisanega mešanega modela in primerjali oba pristopa na simuliranih in realnih podatkih. Cilj obeh pristopov je bil najprej oceniti število različnih oligomernih stanj in nato oceniti še njihov delež v mešanem modelu. Metode so bile ovrednotene s simulacijsko študijo in na podatkih, pridobljenih s STORM slikanjem. Simulacijska študija je pokazala boljše delovanje “neseted sampling”, zlasti pri manjših vzorcih, medtem ko pri večjih vzorcih večjih razlik med metodami ni bilo. V analizi STORM podatkov, kjer so bili vsi vzorci veliki (n > 1000), so si bile ocenjene porazdelitve iz obeh metod zelo podobne.

• Keywords: super-resolucijska mikroskopija, kvantifikacija ˇstevila proteinov, STORM, nested sampling, Bayesova statistika, robno verjetje