The University of Southampton
University of Southampton Institutional Repository

Limits of accuracy for parameter estimation and localization in single-molecule microscopy via sequential Monte Carlo methods

Limits of accuracy for parameter estimation and localization in single-molecule microscopy via sequential Monte Carlo methods
Limits of accuracy for parameter estimation and localization in single-molecule microscopy via sequential Monte Carlo methods
Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.
single-molecule microscop, sequential Monte Carlo, SMC, Fisher information matrix,, uorescence microscopy, particle smoothing, Stochastic differential equation, SDE, particle filtering
139-171
d'Avigneau, A. Marie
5559c606-4cfc-4b88-8556-9b9e99bd72e8
Singh, Sumeetpal S.
4d4481ff-3b73-444d-8569-30d0294de4fd
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
d'Avigneau, A. Marie
5559c606-4cfc-4b88-8556-9b9e99bd72e8
Singh, Sumeetpal S.
4d4481ff-3b73-444d-8569-30d0294de4fd
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

d'Avigneau, A. Marie, Singh, Sumeetpal S. and Ober, Raimund J. (2022) Limits of accuracy for parameter estimation and localization in single-molecule microscopy via sequential Monte Carlo methods. SIAM Journal on Imaging Sciences, 15 (1), 139-171. (doi:10.1137/21M1422823).

Record type: Article

Abstract

Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.

Text
21m1422823 - Version of Record
Available under License Creative Commons Attribution.
Download (1MB)

More information

Accepted/In Press date: 15 September 2021
Published date: 27 January 2022
Keywords: single-molecule microscop, sequential Monte Carlo, SMC, Fisher information matrix,, uorescence microscopy, particle smoothing, Stochastic differential equation, SDE, particle filtering

Identifiers

Local EPrints ID: 455856
URI: http://eprints.soton.ac.uk/id/eprint/455856
PURE UUID: 67c397a9-6150-4a13-8367-a569eed8c9b7
ORCID for A. Marie d'Avigneau: ORCID iD orcid.org/0000-0001-8229-6850
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 06 Apr 2022 17:06
Last modified: 07 Apr 2022 02:02

Export record

Altmetrics

Contributors

Author: A. Marie d'Avigneau ORCID iD
Author: Sumeetpal S. Singh
Author: Raimund J. Ober ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×