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 Villarrubia (J Res Natl Inst Stand Technol 102:425, 1997) 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. 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 including 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.

Particle Smoother to Assimilate Asynchronous Movie Data of High-Speed AFM with MD Simulations

“…To overcome this problem, Matsunaga et al recently proposed an improved BTR method, called the end-to-end differentiable BTR method. 23 The improved method was shown to be much more robust for noisy AFM images.…”

“…In fact, the BTR works well for noise-free AFM images, but the algorithm is rather sensitive to measurement noise. To overcome this problem, Matsunaga et al recently proposed an improved BTR method, called the end-to-end differentiable BTR method . The improved method was shown to be much more robust for noisy AFM images.…”

“…First, it can only detect a two-dimensional molecular surface via interactions with the cantilever probe tip, but cannot directly observe three-dimensional structures. Furthermore, AFM images of a soft biomolecule are blurred due to fluctuations during the measurement period , and due to the finite size of the probe tip. , To overcome these limitations, complementary computational methods are useful to predict the probe tip shape by de novo approaches , and to provide higher resolution three-dimensional structures that fit to the measured AFM images. Nowadays, for a given AFM image, we can build a molecular structure that fits the AFM image using the rigid-body fitting and flexible fitting methods. − …”

Spatiotemporal resolution in high-speed atomic force microscopy for studying biological macromolecules in action

“…This approach reduced image distortion and noise caused by data asynchronicity [ 147 ] and demonstrated that the detailed behaviors of biological molecules including their interiors can be analyzed far beyond the limits defined by the spatiotemporal resolution of HS-AFM [ 148–150 ]. Moreover, a method based on a modern machine learning approach was recently developed to remove the tip convolution effect as well as the multi-tip effect [ 151 ]. These computational methods could play an important role in extracting additional useful information from HS-AFM data.…”

DNA Origami Fiducial for Accurate 3D Atomic Force Microscopy Imaging

“…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. 18,20 In addition, measuring separate calibration samples cannot correct for changes in tip shape during measurement.…”