Particle Filter Method to Integrate High-Speed Atomic Force Microscopy Measurements with Biomolecular Simulations

Abstract

The high-speed atomic force microscopy (HS-AFM) can observe structural dynamics of biomolecules at single-molecule level in real time near physiological condition, but its spatiotemporal resolution is limited. Complementarily, molecular dynamics (MD) simulations have higher spatiotemporal resolutions albeit with some artifact. Here, in order to integrate the HS-AFM data and coarse-grained (CG)-MD simulations, we develop a particle filter method, one of the sequential Bayesian data assimilation approaches. We tested the method in a twin experiment.We first made a reference HS-AFM movie from a CG-MD trajectory of a test molecule, a nucleosome, which serves as an "experimental measurement". Then, we performed the particle filter simulation with 512 particles that captured large-scale nucleosome structural dynamics compatible with the AFM movie. Comparing the particle filter simulations with 8 -8192 particles, we found that the use of more particles consistently results in larger likelihood for the whole AFM movie. By comparing the likelihoods from different ionic concentrations and from different timescales, we found that the "true" concentration and timescale can be inferred as the largest likelihood of the whole AFM movie, but not that of each AFM image. The particle filter method provides a general approach to integrate the HS-AFM data with MD simulations..

Hidden Markov Modeling of Molecular Orientations and Structures from High-Speed Atomic Force Microscopy Time-Series Images

“…In this approach, the parameters used to generate the pseudo-AFM image with the highest similarity are considered as the best estimate. The similarity measures include pixel-RMSD [22], cross correlation [18][20], cosine similarity [19], and structural similarity index measure (SSIM) [17]. For example, pixel-RMSD is defined as follows, essentially the same as peak signal-to-noise ratio (PSNR): where and are the heights at pixel i of the experimental AFM and the pseudo-AFM images, respectively.…”

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

“…We used the energy function AICG2+ for proteins (Li et al, 2014), 3SPN.2C for DNA (Freeman et al, 2014). Protein-DNA interactions are modeled by the excluded volume term and the electrostatic interaction (Fuchigami et al, 2020). See the reference (Fuchigami et al, 2020) for more details.…”

“…Protein-DNA interactions are modeled by the excluded volume term and the electrostatic interaction (Fuchigami et al, 2020). See the reference (Fuchigami et al, 2020) for more details. All the simulations were performed by CafeMol (Kenzaki et al, 2011).…”

“…We chose a nucleosome as the test molecule ( Figure 1A). The nucleosome consists of a histone octamer and a duplex DNA of 223 base pairs, and the initial structure was modeled using crystal structure (PDB ID: 3LZ0), as described in our previous work (Niina et al, 2017;Fuchigami et al, 2020).…”

Constrained Abridged Gaussian Sum Extended Kalman Filter: Constrained Nonlinear Systems with Non-Gaussian Noises and Uncertainties

“…Over the decades, great efforts have been made to develop Kalman filter-based approaches that can improve the estimation for real-world applications featuring constrained states and non-Gaussian noises/uncertainties. Extended Kalman filter (EKF), − unscented Kalman filter (UKF), − and the sampling-based group of filters referred to as particle filters (PFs) − have been widely used to deal with the nonlinearity of the systems. Both UKF and PFs require additional computational costs when compared to EKF.…”