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

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, FlhA and centralspindlin, reducing distortion and noise in the AFM movies. The method is general and can be applied to any HS-AFM movies.