Resolving the data asynchronicity in high-speed atomic force microscopy measurement via the Kalman Smoother

Shintaroh Kubo,Suguru Kato,Noriyuki Kodera,Shoji Takada,Kazuyuki Nakamura

doi:10.1038/s41598-020-75463-1

Abstract

High-speed atomic force microscopy (HS-AFM) is a scanning probe microscopy that can capture structural dynamics of biomolecules in real time at single molecule level near physiological condition. Albeit much improvement, while scanning one frame of HS-AFM movies, biomolecules often change their conformations largely. Thus, the obtained frame images can be hampered by the time-difference, the asynchronicity, in the data acquisition. Here, to resolve this data asynchronicity in the HS-AFM movie, we developed Kalman filter and smoother methods, some of the sequential Bayesian filtering approaches. The Kalman filter/smoother methods use alternative steps of a short time-propagation by a linear dynamical system and a correction by the likelihood of AFM data acquired pixel by pixel. We first tested the method using a toy model of a diffusing cone, showing that the Kalman smoother method outperforms to reproduce the ground-truth movie. We then applied the Kalman smoother to a synthetic movie for conformational change dynamics of a motor protein, i.e., dynein, confirming the superiority of the Kalman smoother. Finally, we applied the Kalman smoother to two real HS-AFM movies, FlhAC and centralspindlin, reducing distortion and noise in the AFM movies. The method is general and can be applied to any HS-AFM movies.

Highlights

High-speed atomic force microscopy (HS-AFM) is a scanning probe microscopy that can capture structural dynamics of biomolecules in real time at single molecule level near physiological condition
We examine them for a toy model of a diffusing cone: we first generate a HS-AFM-like movie from a trajectory of the toy model, and apply the Kalman filter/smoother methods to this synthetic movie to test if they work, so-called a twin experiment
We show that the Kalman smoother method outperforms the raw AFM movie as well as the Kalman filter method

Summary

Introduction

High-speed atomic force microscopy (HS-AFM) is a scanning probe microscopy that can capture structural dynamics of biomolecules in real time at single molecule level near physiological condition. To quantify the similarity to the ground-truth movie, we calculated the average correlation coefficient (c.c.) over frame images for the raw AFM movie, the Kalman filter movie, and the Kalman smoother movie with different values of the parameter q (Fig. 4A, data sorted by the value of c.c.) (Note that the final time t = is discarded because the Kalman smoother does not produce the image at the final time point).

Results

Conclusion