While nucleosomes are highly stable structures as fundamental units of chromatin, they also slide along the DNA, either spontaneously or by active remodelers. Here, we investigate the microscopic mechanisms of nucleosome sliding by multiscale molecular simulations, characterizing how the screw-like motion of DNA proceeds via the formation and propagation of twist defects. Firstly, coarse-grained molecular simulations reveal that the sliding dynamics is highly dependent on DNA sequence. Depending on the sequence and the nucleosome super-helical location, we find two distinct types of twist defects: a locally under-twisted DNA region, previously observed in crystal structures, and a locally over-twisted DNA, an unprecedented feature. The stability of the over-twist defect was confirmed via all-atom simulations. Analysis of our trajectories via Markov state modeling highlights how the sequence-dependence of the sliding dynamics is due to the different twist defect energy costs, and in particular how nucleosome regions where defects cannot easily form introduce the kinetic bottlenecks slowing down repositioning. Twist defects can also mediate sliding of nucleosomes made with strong positioning sequences, albeit at a much lower diffusion coefficient, due to a high-energy intermediate state. Finally, we discuss how chromatin remodelers may exploit these spontaneous fluctuations to induce unidirectional sliding of nucleosomes.

While nucleosome positioning on eukaryotic genome play important roles for genetic regulation, molecular mechanisms of nucleosome positioning and sliding along DNA are not well understood. Here we investigated thermally-activated spontaneous nucleosome sliding mechanisms developing and applying a coarse-grained molecular simulation method that incorporates both long-range electrostatic and short-range hydrogen-bond interactions between histone octamer and DNA. The simulations revealed two distinct sliding modes depending on the nucleosomal DNA sequence. A uniform DNA sequence showed frequent sliding with one base pair step in a rotation-coupled manner, akin to screw-like motions. On the contrary, a strong positioning sequence, the so-called 601 sequence, exhibits rare, abrupt transitions of five and ten base pair steps without rotation. Moreover, we evaluated the importance of hydrogen bond interactions on the sliding mode, finding that strong and weak bonds favor respectively the rotation-coupled and -uncoupled sliding movements.

High-speed (HS) 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 (3D) biomolecular structure into an AFM image. First, we describe a method to produce a pseudo-AFM image from a given 3D 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; using an AFM image produced from a protein structure different from its native conformation as a reference, we performed the flexible fitting MD simulations to sample conformations that fit well the reference AFM image, and the method was confirmed to work well. Then, parameter dependence in the protocol was discussed. Finally, we applied the method to a real experimental HS-AFM image for a flagellar protein FlhA, demonstrating its applicability. We also test the rigid-body fitting of a molecular structure to an AFM image. Our method will be a general tool for dynamic structure modeling based on HS-AFM images and is publicly available through the CafeMol software.

the f o motor in f o f 1 Atp synthase rotates its rotor driven by the proton motive force. While earlier studies elucidated basic mechanisms therein, recent advances in high-resolution cryo-electron microscopy enabled to investigate proton-transfer coupled F o rotary dynamics at structural details. Here, taking a hybrid Monte Carlo/molecular dynamics simulation method, we studied reversible dynamics of a yeast mitochondrial f o. We obtained the 36°-stepwise rotations of F o per one proton transfer in the ATP synthesis mode and the proton pumping in the ATP hydrolysis mode. In both modes, the most prominent path alternatively sampled states with two and three deprotonated glutamates in c-ring, by which the c-ring rotates one step. The free energy transduction efficiency in the model f o motor reached ~ 90% in optimal conditions. Moreover, mutations in key glutamate and a highly conserved arginine increased proton leakage and markedly decreased the coupling, in harmony with previous experiments. This study provides a simple framework of simulations for chemical-reaction coupled molecular dynamics calling for further studies in ATP synthase and others. F O F 1 ATP synthase is a ubiquitous protein complex that plays the central role in the energy generation of living cells 1,2. The enzyme complex is located at the inner membrane of mitochondria, the thylakoid membrane of chloroplast, and the bacterial membrane, working for most of ATP production in cells. Dysfunction in the ATP synthase causes severe diseases such as neuropathy, maternally inherited leigh syndrome, ataxia and retinitis pigmentosa syndrome 3-5. F O F 1 ATP synthase is composed of two regions, F O embedded in the membrane and F 1 protruded to the matrix solution (Fig. 1A); each of the regions works as a reversible rotary motor 2,6. Driven by the proton motive force, the proton flux through the F O motor from the inter membrane space (IMS) to the matrix generates a torque in the rotor. The torque is transmitted to the central rotor in F 1 where the rotary motion is used to synthesis ATP 7,8. Conversely, in vitro, and in vivo for bacteria, the F 1 motor can hydrolyze ATP to generate a torque in the inverse direction and drives F O to pump up protons. The motor function of F O arises from a complex of c-ring and a-subunit (Fig. 1B). The c-ring is made up of 8-15 c-subunits depending on the species 6,9-14. Here, we focus on yeast mitochondrial F O having 10 c-subunits in the c-ring, which we call c 10-ring 10,15. The c-subunit has a key glutamate (cE59, throughout, the residue number is for yeast F O F 1) nearly at the middle point in the membrane, which serves as the carrier of protons: A protonation in the cE59 allows c 10-ring to hold a proton, whereas it is deprotonated upon a proton release. It is experimentally confirmed that the bacterial ATP synthase activity drastically decreases when the corresponding key residue is mutated into the amino acids that cannot carry a proton 16,17. The a-subunit is considered to be a mediator between the aqueous envi...

While nucleosome positioning on eukaryotic genome play important roles for genetic regulation, molecular mechanisms of nucleosome positioning and sliding along DNA are not well understood. Here we investigated thermally-activated spontaneous nucleosome sliding mechanisms developing and applying a coarse-grained molecular simulation method that incorporates both long-range electrostatic and short-range hydrogen-bond interactions between histone octamer and DNA. The simulations revealed two distinct sliding modes depending on the nucleosomal DNA sequence. A uniform DNA sequence showed frequent sliding with one base pair step in a rotation-coupled manner, akin to screw-like motions. On the contrary, a strong positioning sequence, the so-called 601 sequence, exhibits rare, abrupt transitions of five and ten base pair steps without rotation. Moreover, we evaluated the importance of hydrogen bond interactions on the sliding mode, finding that strong and weak bonds favor respectively the rotation-coupled and -uncoupled sliding movements. Author summaryNucleosomes are fundamental units of chromatin folding consisting of double-stranded DNA wrapped ~1.7 times around a histone octamer. By densely populating the eukaryotic genome, nucleosomes enable efficient genome compaction inside the cellular nucleus. However, the portion of DNA occupied by a nucleosome can hardly be accessed by other DNA-binding proteins, obstructing fundamental cellular processes such as DNA replication and transcription. DNA compaction and access by other proteins can simultaneously be achieved via the dynamical repositioning of nucleosomes, which can slide along the DNA sequence. In this study, we developed and used coarse-grained molecular dynamics simulations to reveal the molecular details of nucleosome sliding. We find that the sliding mode is highly dependent on the underlying DNA sequence. Specifically, a sequence with a strong nucleosome positioning signal slides via large jumps by five and ten base pairs, preserving the optimal DNA bending profile. On the other hand, uniform sequences without the positioning signal slide via a screw-like motion of DNA, one base pair at the time. These results show that sequence has a large effect not only on the formation of nucleosomes, but also on the kinetics of repositioning.

Atomic force microscopy (AFM) can visualize functional biomolecules near the physiological condition, but the observed data are limited to the surface height of specimens. Since the AFM images highly depend on the probe tip shape, for successful inference of molecular structures from the measurement, the knowledge of the probe shape is required, but is often missing. Here, we developed a method of the rigid-body fitting to AFM images, which simultaneously finds the shape of the probe tip and the placement of the molecular structure via an exhaustive search. First, we examined four similarity scores via twin-experiments for four test proteins, finding that the cosine similarity score generally worked best, whereas the pixel-RMSD and the correlation coefficient were also useful. We then applied the method to two experimental high-speed-AFM images inferring the probe shape and the molecular placement. The results suggest that the appropriate similarity score can differ between target systems. For an actin filament image, the cosine similarity apparently worked best. For an image of the flagellar protein FlhAC, we found the correlation coefficient gave better results. This difference may partly be attributed to the flexibility in the target molecule, ignored in the rigid-body fitting. The inferred tip shape and placement results can be further refined by other methods, such as the flexible fitting molecular dynamics simulations. The developed software is publicly available.

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..

The FO motor in FOF1 ATP synthase rotates its rotor driven by the proton motive force. While earlier studies elucidated basic mechanisms therein, recent advances in high-resolution cryo-electron microscopy enabled to investigate proton-transfer coupled FO rotary dynamics at structural details. Here, developing a hybrid Monte Carlo/molecular dynamics simulation method, we studied reversible dynamics of a yeast mitochondrial FO. We obtained the 36°-stepwise rotations of FO per one proton transfer in the ATP synthesis mode and the proton pumping in the ATP hydrolysis mode. In both modes, the most prominent path alternatively sampled states with two and three deprotonated glutamates in c-ring, by which the c-ring rotates one step. The free energy transduction efficiency in the model FO motor reaches ~ 90% in optimal conditions. Moreover, mutations in key glutamate and a highly conserved arginine increased proton leakage and markedly decreased the coupling, in harmony with previous experiments.