FO-F1 coupling and symmetry mismatch in ATP synthase resolved in every FO rotation step.

FOF1 ATP synthase, a ubiquitous enzyme that synthesizes most ATP in living cells, is composed of two rotary motors: a membrane-embedded proton-driven FO motor and a catalytic F1 motor. These motors share both central and peripheral stalks. Although both FO and F1 have pseudo-symmetric structures, their symmetries do not match. How symmetry mismatch is solved remains elusive because of the missing intermediate structures of the rotational steps. Here, for the case of Bacillus PS3 ATP synthases with three- and 10-fold symmetries in F1 and FO, respectively, we uncovered the mechanical couplings between FO and F1 at every 36° rotation step via molecular dynamics simulations and comparative studies of cryoelectron microscopy (cryo-EM) structures from three species. We found that the mismatch could be solved using several elements: 1) the F1 head partially rotates relative to the FO a subunit via elastic distortion of the b subunits, 2) the rotor is twisted, and 3) comparisons of cryo-EM structures further suggest that the c ring rotary angles can deviate from the symmetric ones. In addition, the F1 motor may have non-canonical structures, relieving stronger frustration. Thus, we provide new insights for solving the symmetry mismatch problem.

The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation.

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

Cooperation among c-subunits of FoF1-ATP synthase in rotation-coupled proton translocation.

In FoF1-ATP synthase, proton translocation through Fo drives rotation of the c-subunit oligomeric ring relative to the a-subunit. Recent studies suggest that in each step of the rotation, key glutamic acid residues in different c-subunits contribute to proton release to and proton uptake from the a-subunit. However, no studies have demonstrated cooperativity among c-subunits toward FoF1-ATP synthase activity. Here, we addressed this using Bacillus PS3 ATP synthase harboring a c-ring with various combinations of wild-type and cE56D, enabled by genetically fused single-chain c-ring. ATP synthesis and proton pump activities were decreased by a single cE56D mutation and further decreased by double cE56D mutations. Moreover, activity further decreased as the two mutation sites were separated, indicating cooperation among c-subunits. Similar results were obtained for proton transfer-coupled molecular simulations. The simulations revealed that prolonged proton uptake in mutated c-subunits is shared between two c-subunits, explaining the cooperation observed in biochemical assays.

Cells need to be able to store and transfer energy to fuel their various activities. To do this, they produce a small molecule called ATP to carry the energy, which is then released when the ATP is broken down. An enzyme found in plants, animals and bacteria, called F_oF₁ ATP synthase, can both create and use ATP. When it does this, protons, or positive hydrogen ions, are transported across cellular boundaries called membranes. The region of the enzyme that is responsible for pumping the protons contains different parts known as the c-ring and the a-subunit. The movement of protons drives the c-ring to rotate relative to the a-subunit, which leads to producing ATP. Previous research using simulations and the protein structures found there are two or three neighbouring amino acids in the c-ring that face the a-subunit, suggesting that these amino acids act together to drive the rotation. To test this hypothesis, Mitome et al. mutated these amino acids to examine the effect on the enzyme's ability to produce ATP. A single mutation reduced the production of ATP, which decreased even further with mutations in two of the amino acids. The extent of this decrease depended on the distance between the two mutations in the c-ring. Simulations of these changes also found similar results. This indicates there is coordination between different parts of the c-ring to increase the rate of ATP production. This study offers new insights into the molecular processes controlling ATP synthesis and confirms previous theoretical research. This will interest specialists in bioenergetics because it addresses a fundamental biological question with broad impact.

Rigid-body fitting to atomic force microscopy images for inferring probe shape and biomolecular structure.

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.

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.

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

High-speed atomic force microscopy (HS-AFM) can be used to observe the structural dynamics of biomolecules at the single-molecule level in real time under near-physiological conditions; however, its spatiotemporal resolution is limited. Complementarily, molecular dynamics (MD) simulations have higher spatiotemporal resolutions, albeit with some artifacts. Here, to integrate HS-AFM data and coarse-grained molecular dynamics (CG-MD) simulations, we develop a particle filter method that implements a sequential Bayesian data assimilation approach. We test the method in a twin experiment. First, we generate a reference HS-AFM movie from the CG-MD trajectory of a test molecule, a nucleosome; this serves as the "experimental measurement". Then, we perform a particle filter simulation with 512 particles, which captures the large-scale nucleosome structural dynamics compatible with the AFM movie. Comparing particle filter simulations with 8-8192 particles, we find that using greater numbers of particles consistently increases the likelihood of the whole AFM movie. By comparing the likelihoods for different ionic concentrations and time scale mappings, we find that the "true" concentration and time scale mapping 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 for integrating HS-AFM data with MD simulations.

Molecular dynamics simulation of proton-transfer coupled rotations in ATP synthase FO motor.

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, taking 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 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.

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

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.

DNA sliding in nucleosomes via twist defect propagation revealed by molecular simulations.

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.

Sequence-dependent nucleosome sliding in rotation-coupled and uncoupled modes revealed by molecular simulations.

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.