Case Report: Bayesian Statistical Inference of Experimental Parameters via Biomolecular Simulations: Atomic Force Microscopy

The atomic force microscopy (AFM) is a powerful tool for imaging structures of molecules bound on surfaces. To gain high-resolution structural information, one often superimposes structure models on the measured images. Motivated by high flexibility of biomolecules, we previously developed a flexible-fitting molecular dynamics (MD) method that allows protein structural changes upon superimposing. Since the AFM image largely depends on the AFM probe tip geometry, the fitting process requires accurate estimation of the parameters related to the tip geometry. Here, we performed a Bayesian statistical inference to estimate a tip radius of the AFM probe from a given AFM image via flexible-fitting molecular dynamics (MD) simulations. We first sampled conformations of the nucleosome that fit well the reference AFM image by the flexible-fitting with various tip radii. We then estimated an optimal tip parameter by maximizing the conditional probability density of the AFM image produced from the fitted structure.

Software (GUI/APP) for Developing AI-Based Models Capable of Predicting Load-Displacement Curve and AFM Image during Nanoindentation

During nanoindentation tests, the load-displacement curve is used for estimating mechanical properties, while an indent image obtained through atomic force microscopy (AFM) is used for studying deformation of a material. We present a computational platform for developing artificial intelligence-based models for predicting indentation depth (load-displacement curve) and AFM image as a function of test parameters like maximum applied load, loading rate, and holding time. A user can directly use machine generated data in text (.txt) and hierarchical data format (HDF, hdf) format for developing the AI-based models for indentation depth and AFM image, respectively. The software was tested on three different coatings/materials for indentation depth: heat-treated (HT) sample of cold sprayed aluminum-based bulk metallic glass (Al-BMG) coating, carbon nanotube reinforced aluminum composite (Al-5CNT) coating, and spark-plasma-sintered hydroxyapatite (SPS HA) sample. For AFM imaging, a heat-treated (HT) sample of cold sprayed aluminum-based bulk metallic glass (Al-BMG) coating was considered. Correlation or R-values are close to 1 for all the models developed in this work. Predicted load-displacement curve and AFM image are in good agreement with the experimental findings. Our approach will be helpful in virtual simulation of load-displacement curves and AFM indent images for a large number of new test parameters, thus significantly reducing the number of indents needed for characterizing/analyzing a material.

A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing

A novel method based on Bayesian compressed sensing is proposed to remove impulse noise from atomic force microscopy (AFM) images. The image denoising problem is transformed into a compressed sensing imaging problem of the AFM. First, two different ways, including interval approach and self-comparison approach, are applied to identify the noisy pixels. An undersampled AFM image is generated by removing the noisy pixels from the image. Second, a series of measurement matrices, all of which are identity matrices with some rows removed, are constructed by recording the position of the noise-free pixels. Third, the Bayesian compressed sensing reconstruction algorithm is applied to recover the image. Different from traditional compressed sensing reconstruction methods in AFM, each row of the AFM image is reconstructed separately in the proposed method, which will not reduce the quality of the reconstructed image. The denoising experiments are conducted to demonstrate that the proposed method can remove the impulse noise from AFM images while preserving the details of the image. Compared with other methods, the proposed method is robust and its performance is not influenced by the noise density in a certain range.

Flexible Fitting of Biomolecular Structures to Atomic Force Microscopy Images via Biased Molecular Simulations

Atomic force microscopy (AFM) is a prominent imaging technology that observes large-scale structural dynamics of biomolecules near the physiological condition, but the AFM data are limited to the surface shape of specimens. Rigid-body fitting methods were developed to obtain molecular structures that fit to an AFM image, without accounting for conformational changes. Here we developed a method to fit flexibly a three-dimensional biomolecular structure into an AFM image. First, we describe a method to produce a pseudo-AFM image from a given three-dimensional structure in a differentiable form. Then, using a correlation function between the experimental AFM image and the computational pseudo-AFM image, we developed a flexible fitting molecular dynamics (MD) simulation method, by which we obtain protein structures that well fit to the given AFM image. We first test it with a twin-experiment; for a synthetic AFM image produced from a protein structure different from its native conformation, the flexible fitting MD simulations sampled those that fit well the AFM image. Then, parameter dependence in the protocol is discussed. Finally, we applied the method to a real experimental AFM image for a flagellar protein FlhA, demonstrating its applicability. We also test the rigid-body fitting of a fixed structure to the AFM image. Our method will be a general tool for structure modeling based on AFM images and is publicly available through CafeMol software.