End-to-End Differentiable Blind Tip Reconstruction for Noisy Atomic Force Microscopy Images

Abstract

Observing the structural dynamics of biomolecules is vital to deepening our understanding of biomolecular functions. High-speed (HS) atomic force microscopy (AFM) is a powerful method to measure biomolecular behavior at near physiological conditions. In the AFM, measured image profiles on a molecular surface are distorted by the tip shape through the interactions between the tip and molecule. Once the tip shape is known, AFM images can be approximately deconvolved to reconstruct the surface geometry of the sample molecule. Thus, knowing the correct tip shape is an important issue in the AFM image analysis. The blind tip reconstruction (BTR) method developed by Villarrubia1 is an algorithm that estimates tip shape only from AFM images using mathematical morphology operators. While the BTR works perfectly for noise-free AFM images, the algorithm is susceptible to noise, or it is difficult to determine a threshold parameter against noise. To overcome this issue, we here propose an alternative BTR method, called end-to-end differentiable BTR, based on a modern machine learning approach. In the method, we introduce a loss function and a regularization term to prevent overfitting to noise, and the tip shape is optimized with automatic differentiation and backpropagations developed in deep learning frameworks. Using noisy pseudo-AFM images of myosin V motor domain as test cases, we show that our end-to-end differentiable BTR is robust against noise in AFM images. The method can also detect a double-tip shape and deconvolve doubled molecular images. Finally, application to real HS-AFM data of myosin V walking on an actin filament shows that the method can reconstruct the accurate surface geometry of actomyosin consistent with the structural model. Our method serves as a general post-processing for reconstructing hidden molecular surfaces from any AFM images. Codes are available at https://github.com/matsunagalab/differentiable_BTR.

DNA Origami Fiducial for Accurate 3D Atomic Force Microscopy Imaging

“…Inconveniently, these types of calibration samples must be measured either before or after the actual measurement of interest. In addition, since these types of calibration samples are typically very hard, the shape of the tip is prone to change due to wear when the sample is scanned, which will deteriorate or invalidate the resulting tip reconstruction. , In addition, measuring separate calibration samples cannot correct for changes in tip shape during measurement.…”

“…Yet, if the sample contains features whose aspect ratio is comparable to that of the tip, distortions due to the finite size of the tip become significant. To correct for the distortions introduced by the tip one can, in principle, estimate the tip geometry and use it to correct the image and estimate the true specimen shape. − Unfortunately, the exact shape of most commercial AFM tips is not precisely known. Moreover, the tip shape is variable, even within the same batch of tips, and can also change during the measurement due to wear or contamination of the tip while imaging.…”

A DNA origami fiducial for accurate 3D AFM imaging

“…Inconveniently, these types of calibration samples must be measured either before or after the actual measurement of interest. In addition, since these types of calibration samples are typically very hard, the shape of the tip is prone to change due to wear when the sample is scanned, which will deteriorate or invalidate the resulting tip reconstruction 20, 21 . In addition, measuring separate calibration samples cannot correct for the effects of changes in tip shape during measurement.…”