Image processing tools for the validation of CryoEM maps

Sorzano, Carlos Óscar S.; Vilas, José Luis; Ramírez-Aportela, Erney; Krieger, James; Hoyo, Daniel del; Herreros, David; Fernández-Giménez, E.; Marchán, Daniel; Macías, José Ramón; Sanchez-Lopez, Irene; Caño, Laura del; Fonseca-Reyna, Yunior César; Conesa, Pablo; Garcia-Mena, Alberto; Burguet–Castell, J.; Garcia-Condado, Jorge; Mendez-Garcia, Jeison; Martínez, Marta; Muñoz-Barrutia, Arrate; Marabini, Roberto; Vargas, Javier; Carazo, José Marı́a

doi:10.1039/d2fd00059h

Cited by 2 publications

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“…φ} coincides with that of R(1) in (B 42),. and similarly the conditional distribution of R1 on the event{|N 1 [k]| = n, ϕ N 1 [k] = ϕ X [k] + φ + π} coincides with that of R(2) in (B.43).…”

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confidence: 79%

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Einstein from Noise: Statistical Analysis

Balanov,

Huleihel,

Bendory

2024

Preprint

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Abstract“Einstein from noise” (EfN) is a prominent example of the model bias phenomenon: systematic errors in the statistical model that lead to erroneous but consistent estimates. In the EfN experiment, one falsely believes that a set of observations contains noisy, shifted copies of a template signal (e.g., an Einstein image), whereas in reality, it contains only pure noise observations. To estimate the signal, the observations are first aligned with the template using cross-correlation, and then averaged. Although the observations contain nothing but noise, it was recognized early on that this process produces a signal that resembles the template signal! This pitfall was at the heart of a central scientific controversy about validation techniques in structural biology.This paper provides a comprehensive statistical analysis of the EfN phenomenon above. We show that the Fourier phases of the EfN estimator (namely, the average of the aligned noise observations) converge to the Fourier phases of the template signal, explaining the observed structural similarity. Additionally, we prove that the convergence rate is inversely proportional to the number of noise observations and, in the high-dimensional regime, to the Fourier magnitudes of the template signal. Moreover, in the high-dimensional regime, the Fourier magnitudes converge to a scaled version of the template signal’s Fourier magnitudes. This work not only deepens the theoretical understanding of the EfN phenomenon but also highlights potential pitfalls in template matching techniques and emphasizes the need for careful interpretation of noisy observations across disciplines in engineering, statistics, physics, and biology.

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confidence: 79%

“…This precautionary approach aims to mitigate the risk of erroneous fittings, which could ultimately lead to inaccuracies in 3D density map reconstruction. Model bias is still a fundamental problem in cryo-EM, as highlighted by an ongoing debate concerning validation tools, see for example, [43,36,19,11,12,20,21,42].…”

Section: Cryo-em and Empirical Demonstrationmentioning

confidence: 99%