Statistical Methodology in Single-Molecule Experiments

Du, Chao; Kou, S. C.

doi:10.1214/19-sts752

Cited by 12 publications

(8 citation statements)

References 145 publications

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“…This is of course not the only approach to differentiating these models. Techniques to either directly or indirectly observe the cluster’s state (size and binding status) from single particle data (Du and Kou, 2020; Falcao and Coombs, 2020; Kowalek et al, 2019; Mellnik et al, 2016; Menssen and Mani, 2019; Robin et al, 2014) would be a more direct way to test this. Experimental perturbations to cortical flow (Mittasch et al, 2018) may also be useful in distinguishing models.…”

Section: Methodsmentioning

confidence: 99%

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

Zmurchok

Holmes

2021

Preprint

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The clustering of membrane-bound proteins facilitates their transport by cortical actin flow in early Caenorhabditis elegans embryo cell polarity. PAR-3 clustering is critical for this process, yet the biophysical processes that couple protein clusters to cortical flow remain unknown. We develop a discrete, stochastic agent-based model of protein clustering and test four hypothetical models for how clusters may interact with the flow. Results show that the canonical way to assess transport characteristics from single particle tracking data used thus far in this area, the Péclet number, is insufficient to distinguish these hypotheses and that all models can account for transport characteristics quantified by this measure. However, using this model, we demonstrate that these different cluster-cortex interactions may be distinguished using a different metric, namely, the scalar projection of cluster displacement on to the flow displacement vector. Our results thus provide a testable way to use existing single particle tracking data to test how endogenous protein clusters may interact with the cortical flow to localize during polarity establishment. To facilitate this investigation, we also develop both improved simulation and semi-analytic methodologies to quantify motion summary statistics (e.g., Péclet number and scalar projection) for these stochastic models as a function of biophysical parameters.

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Section: Methodsmentioning

confidence: 99%

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

Zmurchok

Holmes

2021

Preprint

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“…Stochastic mode: In the stochastic mode, chemical complexity of dyes is exploited, forcing them to emit light at separate times which makes them resolvable in time. As an example, we mention Single Marker Switching (SMS) nanoscopy in its various variants [8,55,33,26,20], see also [59] for a survey from a statistical perspective and [17] for a survey on single-molecule techniques.…”

Section: From Microscopy To Nanoscopymentioning

confidence: 99%

“…Once the value of t has been fixed, the asymptotic statistical resolution (19) allows to compare our results to the classical resolution limits of Abbe (1) and Rayleigh (4). Recall that the FWHM of the Airy pattern is 0.51λ/ NA, and hence both criteria can be read as c (17). For ease of comparison, here we have set n = t in the homogeneous Gaussian model.…”

Section: Physical Implicationsmentioning

confidence: 99%

“…for t = 10 the Abbe criterion allows for a type I error of roughly 6.81%, whereas the Rayleigh criterion allows only 1.33%. We expect higher number of photons necessary in actual experiments, since we have completely disregarded the background noise by choosing the psf (17). Here we have assumed a Gaussian psf (17), so the formula ( 19) can be simply inverted to calculate α.…”

Section: Physical Implicationsmentioning

confidence: 99%

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What is resolution? A statistical minimax testing perspective on super-resolution microscopy

Kulaitis¹,

Munk²,

Werner³

2020

Preprint

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As a general rule of thumb the resolution of a light microscope (i.e. the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)-the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well known Abbe and Rayleigh criteria, dating back to the end of 19th century. However, during the last two decades conventional light microscopy has undergone a shift from microscopic scales to nanoscales. This increase in resolution comes with the need to incorporate the random nature of observations (light photons) and challenges the classical view of discernability, as we argue in this paper. Instead, we suggest a statistical description of resolution obtained from such random data. Our notion of discernability is based on statistical testing whether one or two objects with the same total intensity are present. For Poisson measurements we get linear dependence of the (minimax) detection boundary on the FWHM, whereas for a homogeneous Gaussian model the dependence of resolution is nonlinear. Hence, at small physical scales modeling by homogeneous gaussians is inadequate, although often implicitly assumed in many reconstruction algorithms. In contrast, the Poisson model and its variance stabilized Gaussian approximation seem to provide a statistically sound description of resolution at the nanoscale. Our theory is also applicable to other imaging setups, such as telescopes.

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“…As an example of stochastic mode photoswitching, we mention Single Marker Switching (SMS) nanoscopy in its various variants (Betzig et al, 2006;Rust et al, 2006;Hess et al, 2006;Heilemann et al, 2008;Egner et al, 2007), see also (Staudt et al, 2020) for a survey from a statistical perspective and (Du and Kou, 2020) for a survey on single-molecule techniques. Here one excites only a few dyes per pulse by using only a small illumination intensity.…”

Section: From Microscopy To Nanoscopymentioning

confidence: 99%

A Statistical Model of Microscope Resolution

Kulaitis¹

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I am grateful to the members of the committee for agreeing to evaluate my thesis, in particular, to Prof. Tatyana Krivobokova for taking up the duty of Korreferentin.I find myself lucky to have colleagues at the IMS. I think that the institute is a friendly, supportive and an inspiring place to work.A big thanks goes to my office mates: Florian Pein, Marco Seiler and Miguel del Álamo Ruiz for helping me with various (non)mathematical issues. Especially when I started and when I was sick. I would like to thank Natalia Khizanishvili and Heiner Keilholz for the same.My sincere gratitude goes to the RTG 2088 for organizing nice workshops, lecture series and conference funding. I would also like to thank the DFG, which partially supported my PhD through CRC 755.I would also like to acknowledge many great teachers outside of Göttingen: Virginija

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Statistical Methodology in Single-Molecule Experiments

Cited by 12 publications

References 145 publications

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

What is resolution? A statistical minimax testing perspective on super-resolution microscopy

A Statistical Model of Microscope Resolution

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